an abbreviation for two stage least squares, an instrumental variables estimation technique.

Source: econterms

A kind of simultaneous equations estimation. Made up of 2SLS followed by SUR. First proposed by Zellner and Theil, Econometrica, 1962, pp 54-78.

Source: econterms

Latin for "even stronger". Can be used to compare two theorems or proofs. Could be interpreted to mean "in the same way."

Source: econterms

abbreviation for Arrow-Debreu equilibrium.

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American Agricultural Economics Association. See their web site at http://www.aaea.org.

Source: econterms

Used in the context of stock returns; means the return to a portfolio in excess of the return to a market portfolio. Contrast excess returns which means something else. Note that abnormal returns can be negative.
Example: Suppose average market return to a stock was 10% for some calendar year, meaning stocks overall were 10% higher at the end of the year than at the beginning, and suppose that stock S had risen 12% in that period. Then stock S's abnormal return was 2%.

Source: econterms

An attribute of a utility function. See Arrow-Pratt measure.

Source: econterms

A limit to the rate or quantity of scientific or technological information that a firm can absorb. If such limits exist they provide one explanation for firms to develop internal R&D capacities. R&D departments can not only conduct development along lines they are already familiar with, but they have formal training and external professional connections that make it possible for them to evaluate and incorporate externally generated technical knowledge into the firm better than others in the firm can. In other words a partial explanation for R&D investments by firms is to work around the absorptive capacity constraint.

This term comes from Cohen and Levinthal (1990).

Source: econterms

a phrase that generally means "leaving out". A model abstracts from some elements of the real world in its demonstration of some specific force.

Source: econterms

That it is the growth of output that induces continuing net investment. That is, net investment is a function of the change in output not its level.

Source: econterms

Occurs in the context of hypothesis testing. Let T be a test statistic. Possible values of T can be divided into two regions, the acceptance region and the rejection region. If the value of T comes out to be in the acceptance region, the null hypothesis being tested is not rejected. If T falls in the rejection region, the null hypothesis is rejected.

The terms 'acceptance region' and 'rejection region' may also refer to the subsets of the sample space that would produce statistics T in the acceptance region or rejection region as defined above.

Source: econterms

Advisory Council on Intergovernmental Relations, in the U.S.

Source: econterms

In the context of combating unemployment: policies designed to improve the access of the unemployed to the labor market and jobs, job-related skills, and the functioning of the labor market. Contrast passive measures.

Source: econterms

The stochastic process {X_t} and information sets {Y_t} are adapted if {X_t} is a martingale difference sequence with respect to {Y_t}.

Source: econterms

American Economics Association

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An abbreviation for the American Economic Review.

Source: econterms

From Milgrom and Weber (Econometrica, 1982, page 1096): Bidders' valuations of a good being auctioned are affiliated if, roughly: "a high value of one bidder's estimate makes high values of the others' estimates more likely."

There may well be good reasons not to use the word correlated in place of affiliated. This editor is advised that there is some mathematical difference.

Source: econterms

adjective, describing a function with a constant slope. Distinguished from linear which sometimes is meant to imply that the function has no constant term; that it is zero when the independent variables are zero. An affine function may have a nonzero value when the independent variables are zero.
Examples: y = 2x is linear in x, whereas y = 2x + 7 is an affine function of x.
And y = 2x + z² is affine in x but not in z.

Source: econterms

A pricing schedule where there is a fixed cost or benefit to the consumer for buying more than zero, and a constant per-unit cost per unit beyond that. Formally, the mapping from quantity purchased to total price is an affine function of quantity.
Using, mostly, Tirole's notation, let q be the quantity in units purchased, T(q) be the total price paid, p be a constant price per unit, and k be the fixed cost, an example of an affine price schedule is T(q)=k+pq.
For alternative ways of pricing see linear pricing schedule and nonlinear pricing.

Source: econterms

Armed Forces Qualifications(?) Test -- a test given to new recruits in the U.S. armed forces. Results from this test are used in regressions of labor market outcomes on possible causes of those outcomes, to control for other causes.

Source: econterms

An abbreviation for Adjusted Gross Income, a line item which appears on the U.S. taxpayer's tax return and is sometimes used as a measure of income which is consistent across taxpayers. AGI does not include any accounting for deductions from income that reduce the tax due, e.g. for family size.

Source: econterms

"Agricultural Economics is an applied social science that deals with how producers, consumers, and societies use scarce resources in the production, processing, marketing, and consumption of food and fiber products." (from Penson, Capps, and Rosson (1996), as cited by Hallam 1998).

Source: econterms

abbreviation for Akaike's Information Criterion

Source: econterms

An abbreviation for the American Journal of Sociology.

Source: econterms

A criterion for selecting among nested econometric models. The AIC is a number associated with each model:
AIC=ln (s_m²) + 2m/T
where m is the number of parameters in the model, and s_m² is (in an AR(m) example) the estimated residual variance: s_m² = (sum of squared residuals for model m)/T. That is, the average squared residual for model m.
The criterion may be minimized over choices of m to form a tradeoff between the fit of the model (which lowers the sum of squared residuals) and the model's complexity, which is measured by m. Thus an AR(m) model versus an AR(m+1) can be compared by this criterion for a given batch of data.
An equivalent formulation is this one: AIC=T ln(RSS) + 2K where K is the number of regressors, T the number of obserations, and RSS the residual sum of squares; minimize over K to pick K.

Source: econterms

A Marxist term. Alienation is the subjugation of people by the artificial creations of people 'which have assumed the guise of independent things.' Because products are thought of as commodities with money prices, the social process of trade and exchange becomes driven by forces operating independently of human will like natural laws.

Source: econterms

With probability one. In particular, the statement that a series {W_n} limits to W as n goes to infinity, means that Pr{W_n->W}=1.

Source: econterms

"The hypothesis that the restriction or set of restrictions to be tested does NOT hold." Often denoted H₁. Synonym for 'maintained hypothesis.'

Source: econterms

A member of a certain subfield of political science.

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American Stock Exchange, which is in New York City

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A statistical data analysis program, discussed at http://www.smallwaters.com/amos.

Source: econterms

Often means 'algebraic', as opposed to 'numeric'. E.g., in the context of taking a derivative, which could sometimes be calculated numerically on a computer, but is usually done analytically by finding an algebraic expression for the derivative.

Source: econterms

Denoted []₊ with a lag operator polynomial in the brackets. Has the effect of removing the terms with an L to a negative power; that is, future values in the expression. Their expected value is assumed to be zero by whoever applies the operator.

Source: econterms

If annuity payments over time are (0,P,P,...P) for n periods, and the constant interest rate r>0, then the net present value to the recipient of the annuity can be calculated this way: NPV(A) = (1-(1+r)^-n)P/r

Source: econterms

Stands for analysis-of-variance, a statistical model meant to analyze data. Generally the variables in an ANOVA analysis are categorical, not continuous. The term main effect is used in the ANOVA context. The main effect of x seems to mean the result of an F test to see if the different categories of x have any detectable effect on the dependent variable on average. ANOVA is used often in sociology, but rarely in economics as far as this editor can tell. The terms ANCOVA and ANOCOVA mean analysis-of-covariance. When I understand ANCOVA and main effect better, I'll make separate entries for them. From Kennedy, 3rd edition, pp226-227: 'Analysis of variance is a statistical technique designed to determine whether or not a particular classification of the data is meaningful. The total variation of the dependent variable (the sum of squared differences between each observation and the overall mean) can be expressed as the sum of the variation between classes (the sum of the squared differences between the mean of each class and the overall mean, each times the number of observations in that class) and the variation within each class (the sum of the squared difference between each observation and its class mean). This decomposition is used to structure an F test to test the hypothesis that the between-class variation is large relative to the within-class variation, which implies that the classification is meaningful, i.e., that there is a significant variation in the dependent variable between classes. If dummy variables are used the capture these classifications and a regression is run, the dummy variable coefficients turn out to be the class means, the between-class variation is the regression's 'explained' variation, the within-class variation is the regression's 'unexplained' variation, and the analysis of variance F test is equivalent to testing whether or not the dummy variable coefficients are significantly different from one another. The main advantage of the dummy variable regression is that it provides estimates of he magnitudes of class variation influences on the dependent variables (as well as testing whether or not the classification is meaningful). 'Analysis of covariance is an extension of analysis of variance to handle cases in which there are some uncontrolled variables that could not be standardized between classes. These cases can be analyzed by using dummy variables to capture the classifications and regressing the dependent variable on these dummies and the uncontrollable variables. The analysis of covariance F tests are equivalent to testing whether the coefficient of the dummies are significantly different from one another. These tests can be interpreted in terms of changes in the residual sums of squares caused by adding the dummy variables. Johnston (1972, pp 192-207) has a good discussion. In light of the above, it can be concluded that anyone comfortable with regression analysis and dummy variables can eschew analysis of variance and covariance techniques.' [Except that one needs to understand the academic work out there, not just write one's own. -ed.]

Source: econterms

Arbitrage Pricing Theory; from Stephen Ross, 1976-78. Quoting Sargent, "Ross posited a particular statistical process for asset returns, then derived the restrictions on the process that are implied by the hypothesis that there exist no arbitrage possibilities."

The APT includes multiple risk factors, unlike the CAPM.

Source: econterms

Stands for "autoregressive." Describes a stochastic process (denote here, e_t) that can be described by a weighted sum of its previous values and a white noise error. An AR(1) process is a first-order one, meaning that only the immediately previous value has a direct effect on the current value:
e_t = re_t-1 + u_t
where r is a constant that has absolute value less than one, and u_t is drawn from a distribution with mean zero and finite variance, often a normal distribution.
An AR(2) would have the form:
e_t = r₁e_t-1 + r₂e_t-2 + u_t
and so on. In theory a process might be represented by an AR(infinity).

Source: econterms

A first-order autoregressive process. See AR for details.

Source: econterms

Stands for Autoregressive Conditional Heteroskedasticity. It's a technique used in finance to model asset price volatility over time. It is observed in much time series data on asset prices that there are periods when variance is high and periods where variance is low. The ARCH econometric model for this (introduced by Engle (1982)) is that the variance of the series itself is an AR (autoregressive) time series, often a linear one.
Formally, per Bollerslev et al 1992 and Engle (1982): An ARCH model is a discrete time stochastic process {e_t} of the form: e_t = z_ts_t
where the z_t's are iid over time, E(z_t)=0, var(z_t)=1, and s_t is positive and time-varying. Usually s_t is further modeled to be an autoregressive process.

According to Andersen and Bollerslev 1995/6/7, "ARCH models are usually estimated by maximum likelihood techniques." They almost always give a leptokurtic distrbution of asset returns even if one assumes that each period's returns are normal, because the variance is not the same each period. Even ARCH models, however, do not usually generate enough kurtosis in equity returns to match U.S. stock data.

Source: econterms

Describes a stochastic process or a model of one. Stands for "autoregressive integrated moving-average". An ARIMA process is made up of sums of autoregressive and moving-average components, and may not be stationary.

Source: econterms

Describes a stochastic process or a model of one. Stands for "autoregressive moving-average". An ARMA process is a stationary one made up of sums of autoregressive and moving-average components.

Source: econterms

Measurable risk, that is, measurable variation in possible outcomes, on the basis of knowledge or believed assumptions in advance. Contrast Knightian uncertainty.

Source: econterms

Means, in practice, competitive equilibrium of the kind shown in Debreu's Theory of Value.
The Arrow-Debreu reference may be to a particular paper: "Existence of an Equilibrium for a Competitive Economy", Econometrica. Vol 22 July 1954, pp 265-290. I haven't checked that out.

Source: econterms

An attribute of a utility function.

Denote a utility function by u(c). The Arrow-Pratt measure of absolute risk aversion is defined by:
R_A=-u''(c)/u'(c)
This is a measure of the curvature of the utility function. This measure is invariant to affine transformation of the utility function, which is a useful attributed because such transformation do not affect the preferences expressed by u().

If R_A() is decreasing in c, then u() displays decreasing absolute risk aversion. If R_A() is increasing in c, then u() displays increasing absolute risk aversion. If R_A() is constant with respect to changes in c, then u() displays constant absolute risk aversion.

Source: econterms

An abbreviation for the journal Administrative Science Quarterly which tends to be closer to sociology than to economics.

Source: econterms

An abbreviation for the journal American Sociological Review.

Source: econterms

A way of mapping from abstract states of the world into the prices of financial assets like stocks and bonds. The prices are always conceived of as endogenous; that is, the states of the world cause them, not the other way around, in an asset pricing model.
Several general types are discussed in the research literature. The CAPM is one, distinguished from three that Fama (1991) identifies: (a) the Sharpe-Lintner-Black class of models, (b) the multifactor models like the APT of Ross (1976), and (c) the consumption based models such as Lucas (1978).
An asset pricing model might or might not include the possibility of fads or bubbles.

Source: econterms

maps the state of the economy at time t into the price of a capital asset at time t.

Source: econterms

An adjective meaning 'of a probability distribution as some variable or parameter of it (usually, the size of the sample from another distribution) goes to infinity.'
In particular, see asymptotic distribution.

Source: econterms

A limiting distribution of an estimator is usually normal. (details!)

This is usually proven with a mean value expansion of the score at the estimated parameter value? (details)

Source: econterms

Definition of the asymptotic variance of an estimator may vary from author to author or situation to situation. One standard definition is given in Greene, p 109, equation (4-39) and is described there as "sufficient for nearly all applications." It's

asy var(t_hat) = (1/n) * lim_n->infinity E[ {t_hat - lim_n->infinity E[t_hat] }² ]

Source: econterms

Estimators are asymptotically equivalent if they have the same asymptotic distribution.

Source: econterms

"There are at least three possible definitions of asymptotic unbiasedness:
1. The mean of the limiting distribution of n^.5(t_hat - t) is zero.
2. lim_n->infinity E[t_hat] = t.
3. plim t_hat = t."
Usually an estimator will have all three of these or none of them. Cases exist however in which left hand sides of those three are different. "There is no general agreement among authors as to the precise meaning of asymptotic unbiasedness, perhaps because the term is misleading at the outset; asymptotic refers to an approximation, while unbiasedness is an exact result. Nonetheless the majority view seems to be that (2) is the proper definition of asymptotic unbiasedness. Note, though, that this definition relies upon quantities that are generally unknown and that may not exist." -- Greene, p 107

Source: econterms

a kind of steady state in a dynamical system. There are three types of attractor: stable steady states, cyclical attractors, and chaotic attractors.

Source: econterms

A test for a unit root in a time series sample. An augmented Dickey-Fuller test is a version of the Dickey-Fuller test for a larger and more complicated set of time series models.

(Ed.: what follows is only my best understanding.) The augmented Dickey-Fuller (ADF) statistic, used in the test, is a negative number. The more negative it is, the stronger the rejection of the hypothesis that there is a unit root at some level of confidence. In one example, with three lags, a value of -3.17 constituted rejection at the p-value of .10.

Source: econterms

A school of thought which "takes as its central concern the problem of human coordination, through which order emerges not from a dictator, but from the decisions and judgments of numerous individuals in a world of highly disperced and sometimes only tacit knowledge." -- Cass R. Sunstein, "The Road from Serfdom" The New Republic Oct 20, 1997, p 42.

Well-known authors along this line include Carl Menger, Ludwig von Mises, and Friedrich von Hayek. See Deborah L. Walker's essay for a clear account.

Source: econterms

The state of an individual who does not trade with anyone.

Source: econterms

the jth autocorrelation of a covariance-stationary process is defined as its jth autocovariance divided by its variance.

In a sample, the kth autocorrelation is the OLS estimate that results from the regression of the data on the kth lags of the data.

Below is Gauss code to calculate autocorrelations from a sample.

  /* This functions calculates autocorrelation estimates for lag k */  
proc autocor(series, k);   
   local rowz,y,x,rho;    
   rowz = rows(series);    
   y = series[k+1:rowz];    
   x = series[1:rowz-k];    
   rho = inv(x'x)*x'y;            /* compute autocorrelation by OLS */    
   retp(rho);  
endp;  

Source: econterms

The jth autocovariance of a stochastic process y_t is the covariance between its time t value and the value at time t-j. It is denoted gamma below, and E[] means expectation, or mean:
gamma_jt = E[(y_t - Ey)(y_t-j-Ey)]
In that equation the process is assumed to be covariance stationary. If there is a trend, then the second Ey should be the expected value of at the time t-j.

Source: econterms

Defined for a vector random process, denoted y_t here. The ij'th element of the autocovariance matrix is cov(y_it, y_j,t-k).

Source: econterms

See AR.

Source: econterms

abbreviation or symbol for the operation of taking the asymptotic variance of an expression, thus: avar().

Source: econterms

b(n,q) is notation for a binomial distribution with parameters n and q, where n is the number of draws and q is the probability that each is a one; the value of X~b(n,q) is a count of the number of ones drawn.

Source: econterms

B¹ denotes the Borel sigma-algebra of the real line. It will contain every open interval by definition, which implies that it contains every closed interval and every countable union of open, half-open, and closed intervals. What won't it contain? In practice, only obscure sets. Here's an example: Define the equivalence class ~ on the real line such that x~y (read: x is in the same equivalence class as y) if x-y is a rational number. Now consider the set of all numbers in [0,1] such that none of them are in the same equivalence class. How many members of that set are there? Well, it's not a countable number. This set is not in B¹.

Source: econterms

A country's balance of payments is the quantity of its own currency flowing out of of the country (for purchases, for example, but also for gifts and intrafirm transfers) minus the amount flowing in.

[Ed: this next part is partly speculation; feel free to correct it.] For some purposes this term refers to a stock value and for others a flow value. It is well defined over a period in the sense that it has changed from time A to time B.

Source: econterms

A macro model exhibits balanced growth if consumption, investment, and capital grow at at a constant rate while hours of work per time period stays constant.

Source: econterms

Any complete normed vector space is a Banach space.

Source: econterms

In kernel estimation, a scalar argument to the kernel function that determines what range of the nearby data points will be heavily weighted in making an estimate. The choice of bandwidth represents a tradeoff between bias (which is intrinsic to a kernel estimator, and which increases with bandwidth), and variance of the estimates from the data (which decreases with bandwidth).
Cross-validation is one way to choose the bandwidth as a function of the data.
Has a variety of similar definitions in spectral analysis. Generally, a bandwidth is some way of defining the range of frequencies that will be included by the estimation process. In some estimations it is an argument to the estimation process.

Source: econterms

In periods of free banking, such as most states in the U.S. from 1839-1863, banks could issue their own money, called bank notes. A bank note was a risky, perpetual debt claim on a bank which paid no interest, and could be redeemed on demand at the original bank, usually in gold. There was a risk that the bank would not be able or willing to redeem it.

Source: econterms

An economy that does not have a medium of exchange, or money, and where trade occurs instead by exchanging useful goods for useful goods.

Source: econterms

The practice of firms setting prices as if their transportation costs to all locations were the same, even if all the vendors are distant from one another and have substantially different costs of transportation to each location. One might interpret this as a form of monitored collusion between the vendor firms.

Source: econterms

the region of states, in a dynamical system, around a particular stable steady state, that lead to trajectories going to the stable steady state. (E.g. the region inside the event horizon around a black hole.)

Source: econterms

One-hundredth of a percentage point. Used in the context of interest rates.

Source: econterms

A known set of fixed quantites of known goods, needed for defining a price index.

Source: econterms

"In Bayesian analysis all quantities, including the parameters, are random variables. Thus, a model is said to be identified in probability if the posterior distribution for [the parameter to be estimated] is proper."

Source: econterms

Any value or flow value equation. For a discrete problem it can generally be of the form:
v(k) = max over k' of { u(k,k') + b*v(k') }
where:
u() is the one-period return function (e.g., a utility function) and
v() is the value function and
k is the current state and
k' is the state to be chosen and
b is a scalar real parameter, the discount rate, generally slightly less than one.

Source: econterms

A bidding war in which the bidders end up at a zero-profit price. See Bertrand game.

Source: econterms

The two firms producing in a market modeled as a Bertrand game.

Source: econterms

Model of a bidding war between firms each of which can offer to sell a certain good (say, widgets), but no other firms can. Each firm may choose a price to sell widgets at, and must then supply as many as are demanded. Consumers are assumed to buy the cheaper one, or to purchase half from each if the prices are the same. Best for the firms (both collectively and individually) is to cooperate, charge monopoly price, and split the profits. Each firm could seize the whole market by lowering price slightly, however, and the noncooperative Nash equilibrium outcome of a Bertrand game is that both charge a zero-profit price.

Source: econterms

The graph of the inverse relation of unemployment to job vacancies.

Source: econterms

A numerical optimization method from Berndt, Hall, Hall, and Hausman (1974). Used in Gauss, for example. The following discussion of BHHH was posted to the newsgroup sci.econ.research by Paul L. Schumann, Ph.D., Professor of Management at Minnesota State University, Mankato (formerly Mankato State University). It is included here without any explicit permission whatsoever.

  BHHH usually refers to the procedure explained in Berndt, E., Hall, B.,  
Hall, R., & Hausman, J. (1974), 'Estimation and Inference in Nonlinear  
Structural Models,' Annals of Economic and Social Measurement, 3/4: 653-665.    

BHHH provides a method of estimating the asymptotic covariance matrix of a  
Maximum Likelihood Estimator. In particular, the covariance matrix for a MLE  
depends on the second derivatives of the log-likelihood function. However,  
the second derivatives tend to be complicated nonlinear functions. BHHH  
estimates the asymptotic covariance matrix using first derivatives instead  
of analytic second derivatives. Thus, BHHH is usually easier to compute than  
other methods.    

In addition to the original BHHH article referenced above, BHHH is also  
discussed in Greene, W.H., Econometric Analysis, 3rd Edition, Prentice-Hall,  
1997. Greene's econometric software program, LIMDEP, uses BHHH for some of  
the estimation routines.    

Someone (perhaps BHHH themselves?) wrote a Fortran subroutine in the 1970's  
to do BHHH. I do not have a copy of this subroutine at the present time. You  
may want to check out Green's econometric software, LIMDEP, to see if it  
will do what you require, rather than writing your own program to use an  
existing BHHH subroutine. The Web address for LIMDEP is:    
  http://www.limdep.com/index.htm    

Cheers,  
Paul.    
--
   Paul L. Schumann, Ph.D., Professor of Management 
   Minnesota State University, Mankato (formerly Mankato State University) 
   Mankato, MN  56002    
   mailto:paul.schumann@mankato.msus.edu    
   http://krypton.mankato.msus.edu/~schumann/www/welcome.html  

Source: econterms

British Household Panel Survey. A British government database going back to 1990. Web page: http://www.iser.essex.ac.uk/bhps/index.php

Source: econterms

the difference between the parameter and the expected value of the estimator of the parameter.

Source: econterms

In an auction analysis, a bidding function (often denoted b()) is a function whose value is the bid that a particular player should make. Often it is a function of the player's value, v, of the good being auctioned. Thus the common notation b(v).

Source: econterms

From the late Middle Ages. A contract entitling an exporter to receive immediate payment in the local currency for goods that would be shipped elsewhere. Time would elapse between payment in one currency and repayment in another, so the interest rate would also be brought into the transaction.

Source: econterms

A mixture of silver and copper, from which small coins were made in medieval Europe. Larger coins were made of silver or gold.

Source: econterms

A commodity money regime in which there is concurrent circulation of coins made from each of two metals and a fixed exchange rate between them. Historically the metals have almost always been gold and silver. Bimetallism was tried many times with varying success but since about 1873 the practice has been generally abandoned.

Source: econterms

Bell Journal of Economics, the previous name of the RAND Journal of Economics or RJE.

Source: econterms

An equation for option securities prices on the basis of an assumed stochastic process for stock prices.

The Black-Scholes algorithm can produce an estimate the value of a call on a stock, using as input:
-- an estimate of the risk-free interest rate now and in the near future
-- current price of the stock
-- exercise price of the option (strike price)
-- expiration date of the option
-- an estimate of the volatility of the stock's price
Click here for a derivation of Black-Scholes equation. From the Black-Scholes equation one can derive the price of an option.

Source: econterms

Abbrevation for the U.S. government's Bureau of Labor Statistics, in the Labor Department.

Source: econterms

Suppose a certain treatment of a patient has no effect. If one runs a test of statistical significance on enough randomly selected subsets of the patient base, one would find some subsets in which statistically significant differences were apparently distinguished by the treatment. The Bonferroni criterion is a redefinition of the statistical signficance criterion for the testing of many subgroups: e.g. if there are five subgroups and one of them shows an effect of the treatment at the .01 significance level, the overall finding is significant at the .05 level. This is discussed in more detail (and probably more correctly) in Bland and Altman (1995) in the statistics notes of the British Medical Journal. Either of these links should go there:
Llink 1.
Link 2; search for Bonferroni.

Source: econterms

The activity of applying estimators to each of many subsamples of a data sample, in the hope that the distribution of the estimator applied to these subsamples is similar to the distribution of the estimator when applied to the distribution that generated the sample.

It is a method that gives a sense of the sampling variability of an estimator. "After the set of coefficients b0 is computed, M randomly drawn samples of T observations are drawn from the original data set with replacement. T may be less than or equal to n, the sample size. With each such sample the ... estimator is recomputed." -- Greene, p 658-9.
The properties of this distribution of estimates of b0 can then be characterized, e.g. its variance. If the estimates are highly variable, the investigator knows not to think of the estimate of b0 as precise.

Bootstrapping could also be used to estimate by simulation, or empirically, the variance of an estimation procedure for which no algebraic expression for the variance exists.

Source: econterms

Any element of a Borel sigma-algebra.

Source: econterms

The Borel sigma-algebra of a set S is the smallest sigma-algebra of S that contains all of the open balls in S. Any element of a Borel sigma-algebra is a Borel set.

Example: The set B¹ is the Borel sigma-algebra of the real line, and thus contains every open interval.

Example: Consider a filled circle in the unit square. It can be constructed by a countable number of non-overlapping open rectangles (since a series of such rectangles can be defined that would cover every point in the circle but no point outside of it. Therefore it is in the smallest sigma-algebra of open subsets of the unit square.

Source: econterms

Models of bounded rationality are defined in a recent book by Ariel Rubinstein as those in which some aspect of the process of choice is explicitly modeled.

Source: econterms

The Box-Cox transformation, below, can be applied to a regressor, a combination of regressors, and/or to the dependent variable in a regression. The objective of doing so is usually to make the residuals of the regression more homoskedastic and closer to a normal distribution:

{	y(l) = ((y^l) - 1) / l for l not equal to zero y(l)=log(y) l=0

Box and Cox (1964) developed the transformation.

Estimation of any Box-Cox parameters is by maximum likelihood.

Box and Cox (1964) offered an example in which the data had the form of survival times but the underlying biological structure was of hazard rates, and the transformation identified this.

Source: econterms

A "methodology for identifying, estimating, and forecasting" ARMA models. (Enders, 1996, p 23). The reference in the name is to Box and Jenkins, 1976.

Source: econterms

Defined on a time series sample for each natural number k by the sum of the squares of the first k sample autocorrelations. The k^th sample autocorrelation is denoted r:
BP(k)=S_s=1^k [r_s²]
Used to tell if a time series is nonstationary.
Below is Gauss code with a procedure that calculates the Box-Pierce statistic for a set of residuals.

  
/* A series of residuals eps_hat[] is generated from a regression, e.g.: */    

eps_hat = y - X*betaols;    

/* Then the Box-Pierce statistic for each k can be calculated this way: */    

print 'Box-Pierce statistic for k=1 is' BP(eps_hat,1);  
print 'Box-Pierce statistic for k=2 is' BP(eps_hat,2);  
print 'Box-Pierce statistic for k=3 is' BP(eps_hat,3);    

proc BP(series, k);    
   local beep, rho;    
   beep = 0;    
   do until k < 1;      
     rho = autocor(series, k);      
     beep = beep + rho * rho;      
     k = k - 1;    
   endo;    
   beep = beep * rows(series);     /* BP = T* (the sum) */    
   retp(beep);  
endp;    

/* This functions calculates autocorrelation estimates for lag k */  
proc autocor(series, k);    
   local rowz,y,x,rho;    
   rowz = rows(series);    
   y = series[k+1:rowz];    
   x = series[1:rowz-k];    rho = inv(x'x)*x'y;            /* compute autocorrelation by OLS */    
   retp(rho);  
endp;  

Source: econterms

An abbreviation for the Brookings Papers on Economic Activity.

Source: econterms

An algorithm for choosing the step lengths when numerically calculating maximum likelihood estimates.

Source: econterms

The international monetary framework of fixed exchange rates after World War II. Drawn up by the U.S. and Britain in 1944. Keynes was one of the architects.
The system ended on August 15, 1971, when President Richard Nixon ended trading of gold at the fixed price of $35/ounce. At that point for the first time in history, formal links between the major world currencies and real commodities were severed.

Source: econterms

A diagnostic test of a regression. It is a statistic for testing whether dependent variable y is heteroskedastic as a function of regressors X. If it is, that suggests use of GLS or SUR estimation in place of OLS. The test statistic is always nonnegative. Large values of test statistic reject the hypothesis that y is homoskedastic in X. The meaning of 'large' varies with the number of variables in X.

Quoting almost directly from the Stata manual: The Breusch and Pagan (1980) chi-squared statistic -- a Lagrange multiplier statistic -- is given by

l = T * [S_m=1^m=M [S_n=1^n=m-1 [r_mn² ]]

where r_mn² is the estimated correlation between the residuals of the M equations and T is the number of observations. It has a chi-squared distribution with M(M-1)/2 degrees of freedom.

Source: econterms

A substantial movement in market price away from a price determined by fundamental value. In practice, "bubble" always refers to a situation where the market price is higher than the conjectured fundamentally supported price. The idea of a fundamental value requires some model or outside knowledge of what the security (or other good) is worth.

Bubbles are often described as speculative and it is conjectured that bubbles could be risky ventures for speculators who earn a fair rate of return on them. [ed: I believe these are "rational" bubbles.]
There exist statistical models of a bubbles. For example, stochastic collapsing bubbles are cited to Blanchard and Watson (1982) -- in this form, "the bubble continues with a certain conditional probability and collapses otherwise."

Source: econterms

A budget is a description of a financial plan. It is a list of estimates of revenues to and expenditures by an agent for a stated period of time. Normally a budget describes a period in the future not the past.

Source: econterms

A consumer's budget line characterizes on a graph the maximum amounts of goods that the consumer can afford. In a two good case, we can think of quantities of good X on the horizontal axis and quantities of good Y on the vertical axis. The term is often used when there are many goods, and without reference to any actual graph.

Source: econterms

The set of bundles of goods an agent can afford. This set is a function of the prices of goods and the agents endownment.

Assuming the agent cannot have a negative quantity of any good, the budget set can be characterized this way. Let e be a vector representing the quantities of the agent's endowment of each possible good, and p be a vector of prices for those goods. Let B(p,e) be the budget set. Let x be an element of R₊^L; that is, the space of nonnegative reals of dimension L, the number of possible goods. Then:
B(p,e) = {x: px <= pe}

Source: econterms

A form of organization in which officeholders have defined positions and (usually) titles. Formal rules specify the duties of the officeholders. Personalistic distinctions are usually discouraged by the rules.

Source: econterms

Has density function (pdf):
f(x) = ckx^c-1(1+x^c)^k+1 for constants c>0, k>0, and for x>0.
Has distribution function (cdf): F(x) = 1 - (1+x^c)^-k.

Source: econterms

business

Source: econterms

Three to five years. Called the business cycle frequency by Burns and Mitchell (1946), and this became standard language.

Source: econterms

Bayesian VAR (Vector Autoregression)

Source: econterms

Cumulative Average Growth Rate

Source: econterms

A model of political voting behavior in which a citizen chooses to vote if the costs of doing so are outweighed by the strength of the citizen's preference for one candidate weighted by the anticipated probability that the citizen's vote will be decisive in the election.

Source: econterms

NOT SURE WHICH OF THESE (IF EITHER) IS RIGHT:
1. The estimation of some parameters of a model, under the assumption that the model is correct, as a middle step in the study of other parameters. Use of this word suggests that the investigator wishes to give those other parameters of the model a 'fair chance' to describe the data, not to get stuck in a side discussion about whether the calibrated parameters are ideally modeled or estimated.

2. Taking parameters that have been estimated for a similar model into one's own model, solving one's own model numerically, and simulating. Attributed to Edward Prescott.

Source: econterms

A call option conveys the right to buy a specified quantity of an underlying security.

Source: econterms

Something owned which provides ongoing services. In the national accounts, or to firms, capital is made up of durable investment goods, normally summed in units of money. Broadly: land plus physical structures plus equipment. The idea is used in models and in the national accounts.

See also human capital and social capital.

Source: econterms

In national accounts, this is the amount by which gross investment exceeds net investment. It is the same as replacement investment.
-- Oulton (2002, p. 13)

Source: econterms

Increase in capital intensity, normally in a macro context where it is measured by something analogous to the capital stock available per labor hour spent. In a micro context, it could mean the amount of capital available for a worker to use, but this use is rare.

Capital deepening is a macroeconomic concept, of a faster-growing magnitude of capital in production than in labor. Industrialization involved capital deepening - that is, more and more expensive equipment with a lesser corresponding rise in wage expenses.

Capital deepening of a certain input (e.g. a certain kind of capital input, a recent key example being computer equipment) can be measured in the following way. Estimate the growth of the services provided by this input, per unit of labor input, in year T and in year T+1. The growth rate of that ratio is one common measure of the rate of capital deepening. Oulton, p. 31

Source: econterms

Amount of capital per unit of labor input.

Source: econterms

A measure of a bank's capital strength used by U.S. regulatory agencies.

Source: econterms

The capital structure of a firm is broadly made up of its amounts of equity and debt.

Source: econterms

One of the ways in which an effectiveness variable could be included in a production function in a Solow model. If effectiveness A is multiplied by capital K but not by labor L, then we say the effectiveness variable is capital-augmenting.
For example, in the model of output Y where Y=(AK)^aL^1-a the effectiveness variable A is capital-augmenting but in the model Y=AK^aL^1-a it is not.
Another example would be a capital utilization variable as measured say by electricity usage. (E.g., as in Eichenbaum). ----------------- An example: in the context of a railroad, automatic railroad signaling, track-switching, and car-coupling devices are capital-augmenting. From Moses Abramovitz and Paul A. David, 1996. 'Convergence and Deferred Catch-up: productivity leadership and the waning of American exceptionalism.' In Mosaic of Economic Growth, edited by Ralph Landau, Timothy Taylor, and Gavin Wright.

Source: econterms

The system of payment for each customer served, rather than by service performed. Both are used in various ways in U.S. medical care.

Source: econterms

Capital Asset Pricing Model

Source: econterms

stands for Cumulative Average Return.

A portfolio's abnormal return (AR) at each time is AR_t=Sum from i=1 to N of each ar_it/N. Here ar_it is the abnormal return at time t of security i.

Over a window from t=1 to T, the CAR is the sum of all the ARs.

Source: econterms

A class of utility functions. Also called exponential utility. Has the form, for some positive constant a:
u(c)=-(1/a)e^-ac
"Under this specification the elasticity of marginal utility is equal to -ac, and the instantaneous elasticity of substitution is equal to 1/ac."
The coefficient of absolute risk aversion is a; thus the abbreviation CARA for Constant Absolute Risk Aversion. "Constant absolute risk aversion is usually thought of as a less plausible description of risk aversion than constant relative risk aversion" (that's the CRRA, which see), but it can be more analytically convenient.

Source: econterms

cumulative average adjusted returns

Source: econterms

A modeling idea. In a basic Arrow-Debreu general equilibrium there is no need for money because exchanges are automatic, through a Walrasian auctioneer. To study monetary phenomena, a class of models was made in which money was required to make purchases of other goods. In such a model the budget constraint is written so that the agent must have enough cash on hand to make any consumption purchase. Using this mechanism money can have a positive price in equilibrium and monetary effects can be seen in such models. Contrast money-in-the-utility function for an alternative modeling approach.

Source: econterms

''Catch-up' refers to the long-run process by which productivity laggards close the proportional gaps that separate them from the productivity leader .... 'Convergence,' in our usage, refers to a reduction of a measure of dispersion in the relative productivity levels of the array of countries under examination.' Like Barro and Sala-i-Martin (92)'s 'sigma-convergence', a narrowing of the dispersion of country productivity levels over time.

Source: econterms

Has thicker tails than a normal distribution.
density function (pdf): f(x) = 1/[pi*(1+x²)]. distribution function (cdf): F(x) = .5 + (tan^-1x)/pi.

Source: econterms

A sequence satisfies the Cauchy criterion iff for each positive real epsilon there exists a natural number N such that the distance between any two elements of the sequence past the Nth element is less than epsilon. 'Distance' must be defined in context by the user of the term.

One sometimes hears the construction: 'The sequence is Cauchy' if the sequence satisfies the definition.

Source: econterms

Stands for Consumption-based Capital Asset Pricing Model.
A theory of asset prices. Formulated in Lucas, 1978, and Breeden, 1979.

Source: econterms

Stands for Corporate Data Exchange, an organization which has data on the shareholdings of large U.S. companies.

Source: econterms

cumulative distribution function. This function describes a statistical distribution. It has the value, at each possible outcome, of the probability of receiving that outcome or a lower one. A cdf is usually denoted in capital letters. Consider for example some F(x), with x a real number is the probability of receiving a draw less than or equal to x. A particular form of F(x) will describe the normal distribution, or any other unidimensional distribution.

Source: econterms

Stands for Concavity of distribution function condition.

Source: econterms

A dependent variable in a model is censored if observations of it cannot be seen when it takes on vales in some range. That is, the independent variables are observed for such observations but the dependent variable is not.

A natural example is that if we have data on consumers and prices paid for cars, if a consumer's willingness-to-pay for a car is negative, we will see observations with consumer information but no car price, no matter how low car prices go in the data. Price observations are then censored at zero.

Contrast truncated dependent variables.

Source: econterms

A government bank; a bank for banks.

Source: econterms

Imagine that a stochastic objective function is a function only of output and output-squared. Then the solution to the optimization problem of choosing output will have the special characteristic that only the conditional means of the future forcing variables appear in the first order conditions. (By conditional means is meant the set of means for each state of the world.) Then the solution has the "certainty equivalence" property. "That is, the problem can be separated into two stages: first, get minimum mean squared error forecasts of the exogenous [variables], which are the conditional expectations...; second, at time t, solve the nonstochastic optimization problem," using the mean in place of the random variable. "This separation of forecasting from optimization.... is computationally very convenient and explains why quadratic objective functions are assumed in much applied work. For general [functions] the certainty equivalence principle does not hold, so that the forecasting and opt problems do not 'separate.'"

Source: econterms

The amount of payoff (e.g. money or utility) that an agent would have to receive to be indifferent between that payoff and a given gamble is called that gamble's 'certainty equivalent'. For a risk averse agent (as most are assumed to be) the certainty equivalent is less than the expected value of the gamble because the agent prefers to reduce uncertainty.

Source: econterms

CES stands for constant elasticity of substitution. This is a function describing production, usually at a macroeconomic level, with two inputs which are usually capital and labor. As defined by Arrow, Chenery, Minhas, and Solow, 1961 (p. 230), it is written this way:

V = (bK^-r + aL^-r) ^-(1/r)

where V = value-added, (though y for output is more common),
K is a measure of capital input,
L is a measure of labor input,
and the Greek letters are constants. Normally a>0 and b>0 and r>-1. For more details see the source article.

In this function the elasticity of substitution between capital and labor is constant for any value of K and L. It is (1+r)^-1.

Source: econterms

Example, adapted from Caselli and Ventura:
For capital k, labor input n, and constant b<?? (?less that what?)
f(k,n) = (k^b + n^b)^1/b
Here the elasticity of substitution between capital and labor is less than one, i.e. 1/(1-b)<1.

Source: econterms

Stands for Constant Elasticity of Substitution, a kind of utility function. A synonym for CRRA or isoelastic utility function. Often written this way, presuming a constant g not equal to one:
u(c)=c^1-g/(1-g)
This limits to u(c)=ln(c) as g goes to one.
The elasticity of substitution between consumption at any two points in time is constant, equal to 1/g. "The elasticity of marginal utility is equal to" -g. g can also be said to be the coefficient of relative risk aversion, defined as -u"(c)c/u'(c), which is why this function is also called the CRRA (constant relative risk aversion) utility function.

Source: econterms

means "assuming all else is held constant". The author is attempting to distinguish an effect of one kind of change from any others.

Source: econterms

Abbreviation for the U.S. government's Consumer Expenditure Survey

Source: econterms

The U.S. government's Commodities and Futures Trading Commission.

Source: econterms

An occasional abbreviation for 'computable general equilibrium' models.

Source: econterms

Describes an index number that is frequently reweighted. An example is an inflation index made up of prices weighted by frequency with which they are paid, and frequent recomputation of weights makes it a chained inded.

Source: econterms

A description of a dynamic system that is very sensitive to initial conditions and may evolve in wildly different ways from slightly different initial conditions.

Source: econterms

polynomial whose roots are eigenvalues

Source: econterms

Denoted here PSI(t) or PSI_X(t). Is defined for any random variable X with a pdf f(x). PSI(t) is defined to be E[e^itX], which is the integral from minus infinity to infinity of e^itXf(x). This is also the cgf, or cumulant generating function. "Every distribution has a unique characteristic function; and to each characteristic function there corresponds a unique distribution of probability." -- Hogg and Craig, p 64

Source: econterms

Synonym for eigenvalue.

Source: econterms

or "state theory of money" -- 19th century monetary theory, based more on the idea that legal restrictions or customs can or should maintain the value of money, not intrinsic content of valuable metal.

Source: econterms

A continuous distribution, with natural number parameter r. Is the distribution of sums of squares of r standard normal variables. Mean is r, variance is 2r, pdf and cdf is difficult to express in html, and moment-generating function (mgf) is (1-2t)^-r/2.

From older definition in this same database: If n random values z₁, z₂, ..., z_n are drawn from a standard normal distribution, squared, and summed, the resulting statistic is said to have a chi-squared distribution with n degrees of freedom: z₁² + z₂² + ... + z_n²) ~ X²_(n) This is a one-parameter family of distributions, and the parameter, n, is conventionally labeled the degrees of freedom of the distribution. -- quoted and paraphrased from Johnston See also noncentral chi-squared distribution

Source: econterms

Refers to an perspective on economics of the University of Chicago circa 1970. Variously interpreted to imply:
1) A preference for models in which information is perfect, and an associated search for empirical evidence that choices, not institutional limitations, are what result in outcomes for people. (E.g., that committing crime is a career choice; that smoking represents an informed tradeoff between health risk and immediate gratification.)
2) That antitrust law is rarely necessary, because potential competition will limit monopolist abuses.

Source: econterms

The lowest price at which the quantity demanded is zero.

Source: econterms

Given a symmetric positive definite square matrix X, the Cholesky decomposition of X is the factorization X=U'U, where U is the square root matrix of X, and satisfies:
(1) U'U = X
(2) U is upper triangular (that is, it has all zeros below the diagonal) Once U has been computed, one can calculate the inverse of X more easily, because X^-1 = U^-1(U')^-1, and the inverses of U and U' are easier to compute.

Source: econterms

Same as Cholesky decomposition.

Source: econterms

A particular test for structural change; an econometric test to determine whether the coefficients in a regression model are the same in separate subsamples. In reference to a paper of G.C. Chow (1960), "the standard F test for the equality of two sets of coefficients in linear regression models" is called a Chow test. See derivation and explanation in Davidson and MacKinnon, p. 375-376. More info in Greene, 2nd edition, p 211-2.

Homoskedasticity of errors is assumed although this can be dubious since we are open to the possibility that the parameter vector (b) has changed.
RSSR = the sum of squared residuals from a linear regression in which b₁ and b₂ are assumed to be the same
SSR₁ = the sum of squared residuals from a linear regression of sample 1
SSR₂ = the sum of squared residuals from a linear regression of sample 2
b has dimension k, and there are n observations in total
Then the F statistic is:
((RSSR-SSR₁-SSR₂)/k ) / ((SSR₁+SSR₂)/(n-2k).
That test statistic is the Chow test.

Source: econterms

flows of value within a production organization. Includes stocks of raw material, work in process, finished goods inventories, and cash on hand needed to pay workers and suppliers before products are sold.

Source: econterms

An abbreviation for the Canadian Journal of Economics.

Source: econterms

Stands for the "Censored Least Absolute Deviations" estimator. If errors are symmetric (with median of zero), this estimator is unbiased and consistent though not efficient. The errors need not be homoskedastic or normally distributed to have those attributes.

CLAD may have been defined for the first time in Powell, 1984.

Source: econterms

According to Lucas (1998), a classical theory would have no explicit reference to preferences. Contrast neoclassical.

Source: econterms

A 1914 U.S. law on the subject of antitrust and price discrimination.
Section two prohibits price discrimination.
Section three prohibits sales based on an exclusive dealing contract requirement that may have the effect of lessening competition.
Section seven prohibits mergers where "the effect of such acquisition may be substantially to lessen competition, or tend to create a monopoly" in any line of commerce.

Source: econterms

A verb. A market clears if the vector of prices for goods is such that the excess demand at those prices is zero. That is, the quantity demanded of every good at those prices is met.

Source: econterms

the study of economic history; the 'metrics' at the end was put to emphasize (possibly humorously) the frequent use of regression estimation.

'The cliometric contribution was the application of a systematic body of theory -- neoclassical theory -- to history and the application of sophisticated, quantitative techniques to the specification and testing of historical models.' -- North (1990/1993) p 131.

Source: econterms

Data whose observations are not iid but rather come in clusters that are correlated together -- e.g. a data set of individuals some of whom are siblings of others, and are therefore similar demographically.

Source: econterms

Informally: that in presence of complete competitive markets and the absence of transactions costs, an efficient set of inputs to production and outputs from production will be chosen by agents regardless of how property rights over the inputs were assigned to the agents. A detailed discussion is in the Encyclopedia of Law and Economics, online.

Source: econterms

A standard production function which is applied to describe much output two inputs into a production process make. It is used commonly in both macro and micro examples.

For capital K, labor input L, and constants a, b, and c, the Cobb-Douglas production function is
f(k,n) = bk^an^c

If a+c=1 this production function has constant returns to scale. (Equivalently, in mathematical language, it would then be linearly homogenous.) This is a standard case and one often writes (1-a) in place of c.

Log-linearization simplifies the function, meaning just that taking logs of both sides of a Cobb-Douglass function gives one better separation of the components.

In the Cobb-Douglass function the elasticity of substitution between capital and labor is 1 for all values of capital and labor.

Source: econterms

A theoretical model of an adjustment process that on a price/quantity or supply/demand graph spirals toward equilibrium.

Example, from Ehrenberg and Smith: Suppose the equilibrium labor market wage for engineers is stable over a ten-year period, but at the beginning of that period the wage is above equilibrium for some reason. Operating on the assumption, let's say, that engineering wages will remain that high, too many students then go into engineering. The wage falls suddenly from oversupply when that population graduates. Too few students then choose engineering. Then there is a shortage following their graduation. Adjustment to equilibrium could be slow.

"Critical to cobweb models is the assumption that workers form myopic expectations about the future behavior of wages." "Also critical to cobweb models is that the demand curve be flatter than the supply curve; if it is not, the cobweb 'explodes' when demand shifts and an equilibrium wage is never reached."

Source: econterms

An algorithm for estimating a time series linear regression in the presence of autocorrelated errors. The implicit citation is to Cochrane-Orcutt (1949).

The procedure is nicely explained in the SHAZAM manual section online at the SHAZAM web site. Their procedure includes an improvement to include the first observation attributed to the Prais-Winsten transformation. A summary of their excellent description is below. This version of the algorithm can handle only first-order autocorrelation but the Cochrane-Orcutt method could handle more.

Suppose we wish to regress y[t] on X[t] in the presence of autocorrelated errors. Run an OLS regression of y on X and construct a series of residuals e[t]. Regress e[t] on e[t-1] to estimate the autocorrelation coefficient, denoted p here. Then construct series y^* and X^* by: y^*₁ = sqrt(1-p²)y₁,
X^*₁ = sqrt(1-p²)X₁,

and
y^*_t = y_t - py_t-1,
X^*_t = X_t - pX_t-1

One estimates b in y=bX+u by applying this procedure iteratively -- renaming y^* to y and X^* to X at each step, until estimates of p have converged satisfactorily.

Using the final estimate of p, one can construct an estimate of the covariance matrix of the errors, and apply GLS to get an efficient estimate of b.

Transformed residuals, the covariance matrix of the estimate of b, R², and so forth can be calculated; see source.

Source: econterms

Same as R-squared.

Source: econterms

An attribute of a distribution: its standard deviation divided by its mean.

Example: In a series of wage distributions over time, the standard deviation may rise over time with inflation, but the coefficient of variation may not, and thus the fundamental inequality may not.

Source: econterms

A sub-population going through some specified stage in a process. The term is often applied to describe a population of persons going through some life stage, like a first year in a new school.

Source: econterms

"An (n x 1) vector time series y_t is said to be cointegrated if each of the series taken individually is ... nonstationary with a unit root, while some linear combination of the series a'y is stationary ... for some nonzero (n x 1) vector a."
Hamilton uses the phrasing that y_t is cointegrated with a', and offers a couple of examples. One was that although consumption and income time series have unit roots, consumption tends to be a roughly constant proportion of income over the long term, so (ln income) minus (ln consumption) looks stationary.

Source: econterms

commoditized short-term corporate debt.

Source: econterms

A set is compact if it is closed and bounded.

The concept comes up most often in economics in the context of a theory in which a function must be maximized. Continuous functions that are well defined on a compact domain have a maximum and minimum; this is the Weierstrauss Theorem. Noncontinuous functions, or functions on a noncompact domain, may not.

Source: econterms

To illustrate the concept of comparative advantage requires at least two goods and at least two places where each good could be produced with scarce resources in each place. The example drawn here is from Ehrenberg and Smith (1997), page 136. Suppose the two goods are food and clothing, and that 'the price of food within the United States is 0.50 units of clothing and the price of clothing is 2 units of food. [Suppose also that] the price of food in China is 1.67 units of clothing and the price of clothing is 0.60 units of food.' Then we can say that 'the United States has a comparative advantage in producing food and China has a comparative advantage in producing clothing. It follows that in a trading relationship the U.S. should allocate at least some of its scarce resources to producing food and China should allocate at least some of its scarce resources to producing clothing, because this is the most efficient allocation of the scarce resources and allows the price of food and clothing to be as low as possible.

Famous economist David Ricardo illustrated this in the 1800s using wool in Britain and wine from Portugal as examples. The comparative advantage concept seems to be one of the really challenging, novel, and useful abstractions in economics.

Source: econterms

The price a consumer would need to be paid, or the price the consumer would need to pay, to be just as well off after (a) a change in prices of products the consumer might buy, and (b) time to adapt to that change. It is assumed the consumer does not benefit or lose from producing the product.

Source: econterms

(economics theory definition) A model's markets are complete if agents can buy insurance contracts to protect them against any future time and state of the world.

(statistics definition) In a context where a distribution is known except for parameter q, a minimal sufficient statistic is complete if there is only one unbiased estimator of q using that statistic.

Source: econterms

One in which the complete set of possible gambles on future states-of-the-world can be constructed with existing assets.
This is a theoretical ideal against which reality can be found more or less wanting. It is a common assumption in finance or macro models, where the set of states-of-the-world is formally defined.

Source: econterms

a data set used in finance

Source: econterms

A property of a distribution function-utility function pair. (At least, it MAY require specification of the utility function; this editor can't tell well.) It is assumed to hold in some principal-agent models so as to make certain conclusions possible.

Source: econterms

A way of measuring the concentration of market share held by particular suppliers in a market. "It is the percentage of total market sales accounted for by a given number of leading firms." Thus a four-firm concentration ratio is the total market share of the four firms with the largest market shares. (Sometimes this particular statistic is called the CR4.)

Source: econterms

A measure of how close a matrix is to being singular. Relevant in estimation if the matrix of regressors is nearly singular the data are nearly collinear and (a) it will be hard to make an accurate or precise inverse, (b) a linear regression will have large standard errors.

The condition number is computed from the characteristic roots or eigenvalues of the matrix. If the largest characteristic root is denoted L and the smallest characteristic root is S (both being presumed to be positive here, that is, the matrix being diagnosed is presumed to be positive definite), then the condition number is:

gamma = (L/S)^.5

Values larger than 20, according to Greene (93), are observed if and only if the matrix is 'nearly singular'. Greene cites Belsley et al (1980) for this term and the number 20.

Source: econterms

has a special use in finance when used without other modifiers; often means 'conditional on time and previous asset returns'. In that context, one might read 'returns are conditionally normally distributed.'

Source: econterms

a collection of functions that give the optimal demands for each of several inputs as a function of the output expected, and the prices of inputs. Often the prices are taken as given, and incorporated into the functions, and so they are only functions of the output.

Usual forms:

x₁(w₁, w₂, y) is a conditional factor demand for input 1, given input prices w₁ and w₂, and output quantity y

Source: econterms

Shorthand often used in finance to mean, roughly, "variance at time t given that many events up through time t-1 are known."

For example, it has been useful in studying aggregate stock prices, which go through periods of high volatility and periods of low volatility, to model them econometrically as having the variance at time t as coming from an AR process. This is the ARCH idea. In such a statistical model, the conditional variance is generally different from the unconditional variance. That is, the unconditional variance is the variance of the whole process, whereas the 'conditional variance' can be better estimated since in this phrasing it is assumed that we can estimate the immediately previous values of variance.

Source: econterms

A matrix may not have the right dimension or shape to fit into some particular operaton with another matrix. Take matrix addition -- the matrices are supposed to have the same dimensions to be summed. If they don't, we can say that they are not conformable for addition. The most common application of the term comes in the context of multiplication. Multiplying an M x N matrix A by an R x S matrix B directly can only be done if N=R. Otherwise the matrices are not conformable for this purpose. If instead M=R, then the intended operation may be to take the transpose of A and multiply it by B. This operation would properly be denoted A'B, where the prime denotes the transpose of A.

Source: econterms

A firm operating in several industries.

Source: econterms

An estimator for a parameter is consistent iff the estimator converges in probability to the true value of the parameter; that is, the plim of the estimator, as the sample size goes to infinity, is the parameter itself. Another phrasing: an estimator is consistent if it has asymptotic power of one.

"Consistency", without a modifier, is synonymous with weak consistency.

From Davidson and Mackinnon, p. 79: If for any possible value of the parameter q in a region of a parameter space the power of a test goes to one as sample size n goes to infinity, that test is said to be consistent against alternatives in that region of the parameter space. That is, if as the sample size increases we can in the limit reject every false hypothesis about the parameter, the test is consistent.

How does one prove that an estimator is consistent? Here are two ways.
(1) Prove directly that if the model is correct, the estimator has power one in the limit to reject any alternative but the true parameter.
(2) Sufficient conditions for proving that an estimator is consistent are (i) that the estimator is asymptotically unbiased and (ii) that its variance collapses to zero as the sample size goes to infinity. This method of proof is usually easier than (1) and is commonly used.

Source: econterms

An attribute of a production function. A production function exhibits constant returns to scale if changing all inputs by a positive proportional factor has the effect of increasing outputs by that factor. This may be true only over some range, in which case one might say that the production function has constant returns over that range.

Source: econterms

Conducted by the U.S. government. See its Web site.

Source: econterms

"A security's consumption beta is the slope in the regression of its return on per capita consumption."

Source: econterms

The set of affordable consumption bundles. One way to define a consumption set is by a set of prices, one for each possible good, and a budget. Or a consumption set could be defined in a model by some other set of restrictions on the set of possible consumption bundles.
E.g. if consumer i can consume nonnegative quantities of all goods, it is standard to define x_i as i's consumption set, a member of R₊^L where L is the number of goods. Normally if the agent is endowed with a set of goods, the endowment is in the consumption set.

Source: econterms

The use of questionnaires about valuation to estimate the willingness of respondents to pay for public projects or programs.

Often the question is framed, "Would you accept a tax of x to pay for the program?" Any such survey must be carefully done, and even so there is dispute about the value of the basic method, as is discussed in the issue of the JEP with the Portney (1994) article.

Source: econterms

Same as Pareto set, with the implication that it is drawn in an Edgeworth box.

Source: econterms

Given a metric space S with distance measure d(), and T:S->S mapping S into itself, T is a contraction mapping if for some b ('b') in the range (0,1), d(Tx,Ty) is less than or equal to b*d(x,y) for all x and y in S.

One often abbreviates the phrase 'contraction mapping' by saying simply that T is a contraction.

The function resulting from the applications of a contraction could slope the opposite way of the original function as long as it is less steeply sloped.

A standard way to prove that an operator T is a contraction is to prove that it satisfies Blackwell's conditions.

Source: econterms

A government policy of reducing spending and raising taxes.
In the language of some first courses in macroneconomics, it shifts the IS curve (investment/saving curve) to the left.

Source: econterms

A government policy of raising interest rates charged by the central bank.
In the language of some first courses in macroeconomics, it shifts the LM curve (liquidity/money curve) to the left.

Source: econterms

As used in the following way: "The effect of X on Y disappears when we control for Z", the phrase means to regress Y on both X and Z, together, and to interpret the direct effect of X as the only effect. Here the effect of Z on X has been "controlled for". It is implied that X is not causing changes in Z.

Source: econterms

A variable in a model controlled by an agent in order to optimize something.

Source: econterms

Multiple meanings: (1) a mathematical property of a sequence or series that approaches a value;
In macro: ''Catch-up' refers to the long-run process by which productivity laggards close the proportional gaps that separate them from the productivity leader .... 'Convergence,' in our usage, refers to a reduction of a measure of dispersion in the relative productivity levels of the array of countries under examination.' Like Barro and Sala-i-Martin (92)'s 'sigma-convergence', a narrowing of the dispersion of country productivity levels over time.

Source: econterms

A kind of convergence of random variables. If x_t converges in quadratic mean it converges in probability but it does not necessarily converge almost surely.

The following is a best guess, not known to be correct.
Let e_t be a stochastic process and F_t be an information set at time t uncorrelated with e_t:

E[e_t|F_t-m] converges in quadratic mean to zero as m goes to infinity IFF:
E[E[e_t|F_t-m]²] converges to zero as m goes to infinity.

Source: econterms

The convolution of two functions U(x) and V(x) is the function:
U*V(x) = (integral from 0 to x of) U(t)V(x-t) dt

Source: econterms

A metric for deciding whether a particular point alone affects regression estimates much. After a regression is run one can consider for each data point how far it is from the means of the independent variables and the dependent variable. If it is far from the means of the independent variables it may be very influential and one can consider whether the regression results are similar without it.

[Need to add the equation defining the Cook's d here.]

Source: econterms

A game structure in which the players have the option of planning as a group in advance of choosing their actions. Contrast noncooperative game.

Source: econterms

Defined in terms of an original allocations of goods among agents with specified utility functions. The core is the set of possible reallocations such that no subset of agents could break off from the others and all do better just by trading among themselves.
Equivalently: The intersection of individually rational allocations with the Pareto efficient allocations. Individually rational, here, means the allocations such that no agent is worse off than with his endowment in the original allocation.

Source: econterms

A choice made by an agent that is at a constraint, and not at the tangency of two classical curves on a graph, one characterizing what the agent could obtain and the other characterizing the imaginable choices that would attain the highest reachable value of the agents' objective.

A classic example is the intersection between a consumer's budget line (characterizing the maximum amounts of good X and good Y that the consumer can afford) and the highest feasible indifference curve. If the agent's best available choice is at a constraint -- e.g. among affordable bundles of good X and good Y the agent prefers quantity zero of good X -- that choice is often not at a tangency of the indifference curve and the budget line, but at a "corner"

Contrast interior solution.

Source: econterms

Two random variables are positively correlated if high values of one are likely to be associated with high values of the other. They are negatively correlated if high values of one are likely to be associated with low values of the other.

Formally, a correlation coefficient is defined between the two random variables (x and y, here). Let s_x and x_y denote the standard devations of x and y. Let s_xy denote the covariance of x and y. The correlation coefficent between x and y, denoted sometimes r_xy, is defined by:

r_xy = s_xy / s_xs_y

Correlation coefficients are between -1 and 1, inclusive, by definition. They are greater than zero for positive correlation and less than zero for negative correlations.

Source: econterms

A graph of total costs of production as a function of total quantity produced.

Source: econterms

is a function of input prices and output quantity. Its value is the cost of making that output given those input prices. A common form: c(w₁, w₂, y) is the cost of making output quantity y using inputs that cost w₁ and w₂ per unit.

Source: econterms

An approach to public decisionmaking. Quotes below from Sugden and Williams, 1978 p. 236, with some reordering: 'Cost-benefit analysis is a 'scientific' technique, or a way of organizing thought, which is used to compare alternative social states or courses of action.' 'Cost-benefit analysis shows how choices should be made so as to pursue some given objective as efficiently as possible.' 'It has two essential characteristics, consistency and explicitness. Consistency is the principle that decisions between alternatives should be consistent with objectives....Cost-benefit analysis is explicit in that it seeks to show that particular decisions are the logical implications of particular, stated, objectives.' 'The analyst's skill is his ability to use this technique. He is hired to use this skill on behalf of his client, the decision-maker..... [The analyst] has the right to refuse offers of employment that would require him to use his skills in ways that he believes to be wrong. But to accept the role of analyst is to agree to work with the client's objectives.' p. 241: Two functions of cost-benefit analysis: It 'assists the decision-maker to pursue objectives that are, by virtue of the community's assent to the decision-making process, social objectives. And by making explicit what these objectives are, it makes the decision-maker more accountable to the community.' 'This view of cost-benefit analysis, unlike the narrower value-free interpretation of the decision-making approach, provides a justification for cost-benefit analysis that is independent of the preferences of the analyst's immediate client. An important consequence of this is that the role of the analyst is not completely subservient to that of the decision-maker. Because the analyst has some responsibility of principles over and above those held by the decision-maker, he may have to ask questions that the decision-maker would prefer not to answer, and which expose to debate conflicts of judgement and of interest that might otherwise comfortably have been concealed.'

Source: econterms

A cost-of-living price index measures the changing cost of a constant standard of living. The index is a scalar measure for each time period. Usually it is a positive number which rises over time to indicate that there was inflation. Two incomes can be compared across time by seeing whether the incomes changed as much as the index did.

Source: econterms

A costate variable is, in practice, a Lagrangian multiplier, or Hamiltonian multiplier.

Source: econterms

the third of the properties of a measure.

Source: econterms

A bond can be resold into two parts that can be thought of as components: (1) a principal component that is the right to receive the principal at the end date, and (2) the right to receive the coupon payments. The components are called strips. The right to receive coupon payments is the coupon strip.

Source: econterms

A pair of firms who split a market, modeled as in the Cournot game.

Source: econterms

A game between two firms. Both produce a certain good, say, widgets. No other firms do. The price they receive is a decreasing function of the total quantity of widgets that the firms produce. That function is known to both firms. Each chooses a quantity to produce without knowing how much the other will produce.

Source: econterms

A generalization of the Cournot game to describe industry structure. Each of N firms will choose a quantity of output. Price is a commonly-known decreasing functions of total output. All firms know N and take the output of the others as given. Each firm has a cost function c_i(q_i). Usually the cost functions are treated as common knowledge. Often the cost functions are assumed to be the same for all firms.

The prediction of the model is that the firms will choose Nash equilibrium output levels.

Formally, from notes given by Michael Whinston to the Economics D50-1 class at Northwestern U. on Sept 23, 1997:
Denote x_i as a quantity that firm i considers,
X as the total quantity (the sum of the x_i's),
x_i* and X* as the Nash equilibrium levels of those quantities,
X_-i as the total quantity chosen by all firms other than firm i,
and p(X) as the function mapping total quantity to price in the market.

Each firm i solves:
max_xi p(x_i+X_-i)-c_i(x_i)

The first order conditions are, for i from 1 to N:

p'(x_i*+X_-i)+p(X*)-c_i'(x_i*)=0

Assuming x_i* is greater than 0 for all i, then the Nash equilibrium output levels are characterized by the N equations:

p'(X*)x_i* + p(X*) = c_i'(x_i*) for each i.

Source: econterms

A stochastic process is covariance stationary if neither its mean nor its autocovariances depend on the index t.

Source: econterms

A 1950s, probably British, panel on econometrics which focussed attention on the problem of simultaneous equations. In some tellings of the history this had an impact on the field -- other problems such as errors-in-variables (measurement errors in the independent variables), were set aside or given lower priority elsewhere too because of the prestige and influence of the Cowles Commission.

Source: econterms

The Consumer Price Index, which is a measure of the cost of goods purchased by average U.S. household. It is calculated by the U.S. government's Bureau of Labor Statistics.


As a pure measure of inflation, the CPI has some flaws:
1) new product bias (new products are not counted for a while after the appear)
2) discount store bias (consumers who care won't pay full price)
3) substitution bias (variations in price can cause consumers to respond by substituting on the spot, but the basic measure holds their consumption of various goods constant)
4) quality bias (product improvements are under-counted)
5) formula bias (overweighting of sale items in sample rotation)

Source: econterms

The Current Population Survey (of the U.S.) is compiled by the U.S. Bureau of the Census, which is in the Dept of Commerce. The CPS is the source of official government statistics on employment and unemployment in the U.S. Each month 56,500-59,500 households are interviewed about their average weekly earnings and average hours worked. The households are selected by area to represent the states and the nation. "Each household is interviewed once a month for four consecutive months in one year and again for the corresponding time period a year later" to make month-to-month and year-to-year comparisons possible. The March CPS is special. For one thing the respondents are asked about insurance then.

Source: econterms

Whenever the Fisher information I(b) is a well-defined matrix or number, the variance of an unbiased estimator B for b is at least as large as [I(B)]^-1.

Source: econterms

Synonym for loss function. Used in reference to econometrics.

Source: econterms

synonym for rejection region

Source: econterms

A test for a model or survey's internal consistency. Called a 'scale reliability coefficient' sometimes. The remainder of this definition is partial and unconfirmed.

Cronbach's alpha assesses the reliability of a rating summarizing a group of test or survey answers which measure some underlying factor (e.g., some attribute of the test-taker). A score is computed from each test item and the overall rating, called a 'scale' is defined by the sum of these scores over all the test items. Then reliability a is defined to be the square of the correlation between the measured scale and the underlying factor the scale was supposed to measure. (Which implies that one has another measure in test cases of that underlying factor, or that it's imputed from the test results.) (In Stata's examples it remains unclear what the scale is, and how it's measured; apparently alpha can be generated without having a measure of the underlying factor.)

Source: econterms

Parallel data on many units, such as individuals, households, firms, or governments. Contrast panel data or time series data.

Source: econterms

A way of choosing the window width for a kernel estimation. The method is to select, from a set of possible window widths, one that minimizes the sum of errors made in predicting each data point by using kernel regression on the others.

Formally, let J be the number of data points, j an index to each one, from one to J, y_j the dependent variable for each j, X_j the independent variables for that j, Y_j the dependent variable for that j, and {h_i} for i=1 to n the set of candidate window widths. The h_i's might be a set of equally spaced values on a grid. The algorithm for choosing one of the h_i's is:

For each candidate window width h_i
{
..For each j from 1 to J
..{
....Drop the data point (X_j, Y_j) from the sample temporarily
....Run a kernel regression to estimate Y_j using the remaining X's and Y's
....Keep track of the square of the error made in that prediction
..}
..Sum the squares of the errors for every j to get a score for candidate window width h_i
..Record that in a list as the score for h_i
}
Select as the outcome h of this algorithm the h_i with the lowest score

The grid approach is necessary because the problem is not concave. Otherwise one might try a simpler maximization e.g., with the first order conditions.
Note however that a complete execution of the cross-validation method can be very slow because it requires as many kernel regressions as there are data points. E.g. in this author's experience, the cross-validation computation for one window width on 500 data points on a Pentium-90 in Gauss took about five seconds, 1000 data points took circa seventeen seconds, but for 15000 data points it took an hour. (Then it takes another hour to check another window width; so even the very simplest choice, between two window widths, takes two hours.)

Source: econterms

Stands for Constant Relative Risk Aversion, a property of some utility functions, also said to have isoelastic form. CRRA is a synonym for CES.

Example 1: for any real a<1, u(c)=c^a/a is a CRRA utility function. It is a vNM utility function.

Source: econterms

Stands for Constant Returns to Scale.

Source: econterms

Center for Research in Security Prices, a standard database of finance information at the University of Chicago. Has daily returns on NYSE, AMEX, and NASDAQ stocks.

Started in early 1970s by Eugene Fama among others. The data there was so much more convenient than alternatives that it drove the study of security prices for decades afterward. It did not have volume data which meant that volume/volatility tests were rarely done.

Source: econterms

A particular nonparametric estimator of a function. Given a data set {X_i, Y_i} it estimates values of Y for X's other than those in the sample. The process is to construct a function that balances the twin needs of (1) proximity to the actual sample points, (2) smoothness. So a 'roughness penalty' is defined. See Hardle's equation 3.4.1 near p. 56 for exact equation. The cubic spline seems to be the most common kind of spline smoother.

Source: econterms

The difference between a country's savings and its investment. "[If] positive, it measures the portion of a country's saving invested abroad; if negative, the portion of domestic investment financed by foreigners' savings."

Defined by the sum of the value of imports of goods and services plus net returns on investments abroad, minus the value of exports of goods and services, where all these elements are measured in the domestic currency.

Source: econterms

decreasing absolute risk aversion

Source: econterms

data

Source: econterms

Data analysis software, discussed at http://www.datadesk.com.

Source: econterms

Either (1) a function that maps from the current state to the agent's decision or choice or (2) a mapping from the expressed preferences of each of a group of agents to a group decision. The first is more relevant to decision theory and dynamic optimization; the second is relevant to game theory.

The phrase allocation rule is sometimes used to mean the same thing as decision rule. The term strategy-proof has been defined in both contexts.

Source: econterms

Synonym for FWL theorem or Frisch-Waugh-Lovell theorem.

Source: econterms

Characterizing a reasoning process of logical reasoning from stated propositions. Contrast inductive.

Source: econterms

A capital market may be said to be deep if it has great depth (which see).

May less formally be used to describe a market with large total market capitalization.

Source: econterms

As used with respect to options: The rate of change of a financial derivative's price with respect to changes in the price of the underlying asset. Formally this is a partial derivative.

A derivative is perfectly delta-hedged if it is in a portfolio with a delta of zero. Financial firms make some effort to construct delta-hedged portfolios.

Source: econterms

Gives the distribution of a function of random variables for which one has a distribution. In particular, for the function g(b,l), where b and l are estimators for true values b₀ and l₀:
g(b,l) ~ N(g(b₀,l₀), g'(b,l)var(b,l)g'(b,l)')

Source: econterms

A relation between each possible price and the quantity demanded at that price.

[Aspects of the population doing the demanding are often left implicit. An actual supply is not necessary to conceive of demand because demand involves hypothetical quantities.]

Source: econterms

For a given good, the demand curve is a relation between each possible price of the good and the quantity that would be bought at market sale at that price.

Drawn in introductory classes with this arrangement of the axes, although price is thought of as the independent variable:

Price   |  \
        |    \
        |      \
        |        \ Demand
        |________________________
                        Quantity

Source: econterms

The money stored in the form of checking accounts at banks.

Source: econterms

In a model, the set of the most-preferred bundles of goods an agent can afford. This set is a function of the preference relation for this agent, the prices of goods, and the agent's endowment.

Assuming the agent cannot have a negative quantity of any good, the demand set can be characterized this way:
Define L as the number of goods the agent might receive an allocation of. An allocation to the agent is an element of the space R₊^l; that is, the space of nonnegative real vectors of dimension L.
Define >^p as a weak preference relation over goods; that is, x>^px' states that the allocation vector x is weakly preferred to x' .
Let e be a vector representing the quantities of the agent's endowment of each possible good, and p be a vector of prices for those goods. Let D(>^p,p,e) denote the demand set. Then:
D(>^p,p,e) = {x: px <= pe and x >^p x' for all affordable bundles x'}.

Source: econterms

Literally "rule by the people". This is a dictionary definition and is not considered sharp enough for academic use. Schumpeter (1942) contrasts these two definitions below and regards only the second one as useful and plausible enough to work with: "The eighteenth-century philosophy of democracy may be couched in the following definition: the democratic method is that institutional arrangement for arriving at political decisions which realizes the common good by making the people itself decide issues through the election of individuals who are to assemble in order to carry out its will." (p 250) This "classical" definition has the problem that the will of the people is not clearly defined here (e.g. consider voting paradoxes) or known (perhaps even to the people at the time), and this can lead to ambiguity about whether a given political system is democratic. The following definition is preferred for its clarity but has a modern feel that is at some distance from the original dictionary definition. Political representation is assumed to be necessary here. "[T]he democratic method is that institutional arrangement for arriving at political decisions in which individuals acquire the power to decide by means of a competitive struggle for the people's vote." (p 269) More clearly: the democratic method is one in which people campaign competitively for the people's votes to achieve the power to make public decisions. This definition is the sharpest.

Source: econterms

The study of the size, growth, and age and geographical distribution of human populations, and births, deaths, marriages, and migrations.

Source: econterms

A synonym for pdf.

Source: econterms

The decline in price of an asset over time attributable to deterioration, obsolescence, and impending retirement. Applies particularly to physical assets like equipment and structures.

Source: econterms

An attribute of a market.

In securities markets, depth is measured by "the size of an order flow innovation required to change prices a given amount." (Kyle, 1985, p 1316).

Source: econterms

securities whose value is derived from the some other time-varying quantity. Usually that other quantity is the price of some other asset such as bonds, stocks, currencies, or commodities. It could also be an index, or the temperature. Derivatives were created to support an insurance market against fluctuations.

Source: econterms

The process or occurrence of an asset's declining productivity as it ages. This is a component of depreciation.

Source: econterms

An operator defined on square matrices or the value of that operator. For a matrix B the determinant is denoted |B|. Its value is a unique scalar. Calculation of the value of the determinant is discussed in linear algebra books.

Source: econterms

Not random. A deterministic function or variable often means one that is not random, in the context of other variables available.

That is, those other variables determine the variable in question unerringly, by a function that would give the same value every time those other variables were given to it as arguments, unlike a random one which with some probability would give different answers.

Source: econterms

The study of industrialization.
development

Source: econterms

A Dickey-Fuller test is an econometric test for whether a certain kind of time series data has an autoregressive unit root. In particular in the time series econometric model y[t] = by[t-1] + e[t], where t is an integer greater than zero indexing time, and b=1, let b^OLS denote the OLS estimate of b from a particular sample. Let T be the sample size.

Then the test statistic T*(b^OLS -1) has a known, documented distribution. Its value in a particular sample can be compared to that distribution to determine a probability that the original sample came from a unit root autoregressive process; that is, one in which b=1.

Source: econterms

A formal game with two players: Allocator A and Recipient R. They have received a windfall of, say, $1. The allocator, moving first, proposes a split so that A would receive x and R would receive 1-x. The recipient then accepts, no matter what A proposed. In a subgame perfect equilibrium, A would offer R nothing. In experiments with human subjects, however, in which A and R do not know one another, A offers relatively large shares to R (often 50-50). See also Ultimatum Game.

Source: econterms

In Bayesian statistics the investigator has to specify a prior distribution for a parameter, before the experiment or regression that is to update that distribution. A diffuse prior is a distribution of the parameter with equal probability for each possible value, coming as close as possible to representing the notion that the analyst hasn't a clue about the value of the parameter being estimated.

Source: econterms

In a multi-period model, agents may have different utility functions for consumption (or other experiences) in different time periods. Usually in such models they value future experiences, but to a lesser degree than present ones. For simplicity the factor by which they discount next period's utility may be a constant between zero and one, and if so it is called a discount factor. One might interpret the discount factor not as a reduction in the appreciation of future events but as a subjective probability that the agent will die before the next period, and so discounts the future experiences not because they aren't valued, but because they may not occur.

A present-oriented agents discounts the future heavily and so has a LOW discount factor. Contrast discount rate and future-oriented.
In a discrete time model where agents discount the future by a factor of b, one usually lets b=1/(1+r) where r is the discount rate.

Source: econterms

At least two meanings:

(1) The interest rate at which an agent discounts future events in preferences in a multi-period model. Often denoted r. A present-oriented agent discounts the future heavily and so has a HIGH discount rate. Contrast 'discount factor'. See also 'future-oriented'.
In a discrete time model where agents discount the future by a factor of b, one finds r=(1-b)/b, following from b=1/(1+r).

(2) The Discount Rate is the name of the rate at which U.S. banks can borrow from the U.S. Federal Reserve.

Source: econterms

An econometric model: Pr(y_i=1) = F(X_i'b) = X_i'b

Source: econterms

An econometric model in which the actors are presumed to have made a choice from a discrete set. Their decision is modeled as endogenous. Often the choice is denoted y_i.

Source: econterms

Econometrics models in which the dependent variables assumes discrete values.

Source: econterms

Like economies of scale but with the implication that they are negative, so larger scale would increase cost per unit.

Source: econterms

prevention of banks from flowing money from savers to borrowers as an effect of regulations; e..g the U.S. home mortgage market is partly blocked from banks and left to savings and loan institutions.

Source: econterms

Refers to economics, which because it is so often about tradeoffs, is widely thought to be depressing to study.

Source: econterms

A synonym for cdf.

Source: econterms

A continuous-time index number. "The Divisia index is a weighted sum of growth rates, where the weights are the components' shares in total value." -- Hulten (1973, p. 1017)

See also http://www.geocities.com/jeab_cu/paper2/paper2.htm.

Source: econterms

Abbreviaton for the U.S. national Department of Justice, which does among other things investigations into violations of antitrust law. See also FTC.

Source: econterms

This seems to be the principle that the growth rate of an aggregate is the weighted average of the growth rates of its components, where each component is weighted by the share of the aggregate it makes up. The idea comes up in the context of national accounts and national statistics.

Source: econterms

After a technological innovcation and a subsequent era of ferment in an industry, a basic architecture of product or process that becomes the accepted market standard. From Abernathy& Utterback 1978, cited by A&T 1991. Dominant designs may not be better than alternatives nor innovative. They have the benchmark features to which subsequent designs are compared. Examples include the IBM 360 computer series and Ford's Model T automobile, and the IBM PC.

Source: econterms

Synonymous with Functional Central Limit Theorem (FCLT).

Source: econterms

phrasing from Jevons (1893). "[T]he first difficulty in barter is to find two persons whose disposable possessions mutually suit each other's wants. There may be many people wanting, and many possessing those things wanted; but to allow of an act of barter there must be a double coincidence, which will rarely happen." That is, paraphrasing Ostroy and Starr, 1990, p 26, the double coincidence is the situation where the supplier of good A wants good B and the supplier of good B wants good A.
The point is that the institution of money gives us a more flexible approach to trade than barter, which has the double coincidence of wants problem.

Source: econterms

In an econometric model, a variable that marks or encodes a particular attribute. A dummy variable has the value zero or one for each observation, e.g. 1 for male and 0 for female. Same as indicator variables or binary variables.

Source: econterms

An informal name for the practice of selling a product in a foreign country for less than either (a) the price in the domestic country, or (b) the cost of making the product. It is illegal in some countries to dump certain products into them, because they want to protect their own industries from such competition.

Source: econterms

An algorithm for detecting autocorrelation in the errors of a time series regression. The implicit citation is to Durbin (1970). The h statistic is asymptotically distributed normally if the hypothesis that there is no autocorrelation.

Source: econterms

A test for first-order serial correlation in the residuals of a time series regression. A value of 2.0 for the statistic indicates that there is no serial correlation. For tables to interpret the statistic see Greene pgs 738-743, and context discussing them is on pages 424-425.
This result is biased toward the finding that there is no serial correlation if lagged values of the regressors are in the regression. Formally, the statistic is:
d=(sum from t=2 to t=T of: (e_t-e_t-1)²/(sum from t=1 to t=T of: e_t²)
where the series of e_t are the residuals from a regression.

Source: econterms

synonym for dyadic transformation.

Source: econterms

For whole numbers t and initial value x₀ in [0,1], consider the mapping:

x_t+1 = (2x_t) mod 1

"This law of motion is a standard example of chaotic dynamics. It is commonly known as the dyadic transformation. It is mixing (and hence also ergodic)."
-- Domowitz and Muus, 1992, p 2849

All the x_t's will be in [0,1]. Their distribution will depend on the initial value x₀. If x₀ is rational, the mapping will eventually become periodic (for large enough values of t). If x₀ is irrational, the mapping is never periodic.

Source: econterms

means 'changing over time'.

Source: econterms

A possible attribute of a player's strategy in a dynamic decision-making environment (such as a game).
When the best plan that a player can make for some future period will not be optimal when that future period arrives, the plan is dynamically inconsistent.
In one stylized example, addicted smokers face this problem -- each day, their best plan is to smoke today, and to quit (and suffer) tomorrow in order to get health benefits subesquently. But the next day, that is once again the best plan, so they do not quit then either. (In a model this can come about if the planner values the present much more than the near future, -- that is, has a low short-run discount factor -- but has a higher discount factor between two future periods.)
Monetary policy is sometimes said to suffer from a dynamic inconsistency problem. Government policymakers are best off to promise that there will be no inflation tomorrow. But once agents and firms in the economy have fixed nominal contracts, the government would get seigniorage revenues from raising the level of inflation.

Source: econterms

The impulse responses in a distributed lag model.

Source: econterms

dynamic optimization

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maximization problems to which the solution is a function; equivalently, optimization problems in infinite-dimensional spaces.

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The study of dynamic optimization problems through the analysis of functional equations like value equations.

This phrase is normally used, analogously to linear programming to describe the study of discrete problems; e.g. those for which a decision must be made at times t for t=1,2,3,...

Source: econterms

The branch of mathematics describing processes in motion. Some are predictable and others are not. Two reasons a process might be unpredictable are that it might be random, and it might be chaotic.

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Stands for "earnings before interest and taxes" which is used as a measure of earnings performance of firms that is not clouded by changes in debt or equity types, or tax rules.

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An electronic bibliography of economics literature organized by the American Economics Association, derived partly from the Journal of Economic Literature. EconLit is made available through libraries and universities. See http://www.econlit.org for more information.

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An economic model formulated so that its parameters can be estimated if one makes the assumption that the model is correct.

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A journal whose web site is at http://www.econometricsociety.org/es/journal.html .

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econometrics

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in labor markets: the presence of different pay for workers of the same ability but who are in different groups, e.g. black, white; male, female.

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In a model, a specification of preferences, technology, and the stochastic processes underlying the forcing variables.

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Paraphrasing directly from Mokyr, 1990: Economic growth has four basic causes:
1) Investment, meaning increases in the capital stock (Solovian growth)
2) Increases in trade (Smithian growth)
3) Size or scale effects, e.g. by overcoming fixed costs, or achieving specialization
4) Increases in knowledge, most of which is called technological progress (Schumpeterian growth).

Further elaboration is in Mokyr's book.

Source: econterms

Piore (1996) writes of two definitions of economics, a narrow one organized around optimization and a broad one organized around scarcity, and suggests that the subjects included by the larger one but not in the smaller one are the subjects of economic sociology discussed in the Handbook (1994).

More specifically, the broad definition of economics is "the study of how people employ scarce resources and distribute them over time and among competing demands" paraphrasing Paul Samuelson (1961). The narrower definition is from Gary Becker (1976): "The combined assumptions of maximizing behavior, market equilibrium, and stable preferences, used relentlessly and unflinchingly . . . [B]ehavior [of] participants who maximize their utility from a stable set of preferences and accumulate an optimal amount of information and other inputs in a variety of markets."

A bit more specifically -- optimization and formal equilibrium are not natural subjects or methods of economic sociology, but the general subjects of economics are. Economic sociology is more likely than economics to use groups or organizations rather than individuals as units of analysis. The practical definition seems to be evolving over time.

Source: econterms

Usually one says there are economies of scale in production of cost per unit made declines with the number of units produced. It is a descriptive, quantitative term. One measure of the economies of scale is the cost per unit made. There can be analosous economies of scale in marketing or distribution of a product or service too. The term may apply only to certain ranges of output quantity.

Source: econterms

European Currency Unit

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A frequent and dangerous mistake for those not familiar with this language is to think that discussion of 'time series' are about data values in a sample. Actually, they are about probability distributions. It has taken this author years to get used to that, which may just be normal.

An example of the error is to think that a discussion about E[X_t] is testable or measurable. Usually it's not. It's assumed in the discussion. A sample has a computable mean, but whether a time series has a trend, or a unit root, or heteroskedasticity are statements about a conjectured process, not statements about data.

Source: econterms

Usually a function mapping quantities of measured inputs to a school and student characteristics to some measure of school output, like the test scores of students from the school.

For empirical purposes one might assume this function is linear and generate the linear regression:

Y = X'b + S'c + e

where Y is a measure of school outputs like a vector of student test scores, X is a set of measures of student attributes (collectively or individually), S is vector of measures of schools those students attend, b and c are coefficients, and e is a disturbance term.

Source: econterms

An abbreviation for the journal Explorations in Economic History.

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An abbreviation for European Economic Review.

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In the context of a Solow model, if labor time is denoted L and labor's effectiveness, or knowledge, is A, then by effective labor we mean AL. In general means 'efficiency units' of labor or 'productive effort' as opposed to time spent.

Source: econterms

Has several meanings. Sometimes used in a theoretical context as a synonym for Pareto efficiency. Below is the econometric/statistical definition. Efficiency is a criterion by which to compare unbiased estimators. For scalar parameters, one estimator is said to be more efficient than another if the first has smaller variance. For multivariate estimators, one estimator is said to be more efficient than another if the covariance matrix of the second minus the covariance matrix of the first is a positive semidefinite matrix. Sometimes properties of the most efficient estimator can be computed; see efficiency bound.

Computation of efficiency is defined on the basis of assumed distributions of errors ('disturbance terms'). It is not calculated directly on the basis of sample information unless the sample information come from a simulation where the actual error distribution was known.

Source: econterms

The minimum possible variance for an estimator given the statistical model in which it applies. An estimator which achieves this variance is called efficient.

Source: econterms

Usually interpretable as "output per worker per hour."
More generally: An abstract measure of the amount produced for a constant production technology by a worker in some time period. Often the context is theoretical and the time period and production technology do not have to be specified.
But efficiency units can be conceived of (and theorized about) as a function of each worker's characteristics, of the vintage of equipment, of the date in history, of the production technology, and so forth.

Source: econterms

The hypothesis that workers' productivity depends positively on their wages. (For reasons this might be the case see the entry on efficiency wages.)
This could explain why employers in some industries pay workers more than employers in other industries do, even if the workers have apparently comparable qualifications and jobs. A contrasting explanation is that of hedonic models in which these differentials are explained by quality differences in the jobs.

Source: econterms

A higher than market-clearing wage set by employers to, for example:
-- discourage shirking by raising the cost of being fired
-- encourage worker loyalty
-- raise group output norms
-- improve the applicant pool
-- raise morale

Labor productivity in efficiency wage models is positively related to wage.

By contrast, consider models in which the wage is equal to labor productivity in equilibrium, or models in which wages are set to reduce the likelihood of unionization (union threat models). In these, productivity is not a function of the wage.

Source: econterms

A description of either:
-- an allocation that is Pareto efficient
or
-- an estimator that has the minimum possible variance given the statistical model; see efficiency bound.

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"A market in which prices always 'fully reflect' available information is called 'efficient.'" -- Fama, p. 383

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Exponential GARCH. The EGARCH(p,q) model is attributed to Nelson, (1991).

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An eigenvalue or characteristic root of a square matrix A is a scalar L that satisfies the equation:

det [ A - LI ] = 0

where "det" is the operator that takes a determinant of its argument, and I is the identity matrix with the same dimensions as A.

Source: econterms

Same as spectral decomposition.

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For each eigenvalue L of a square matrix A there is an associated right eigenvector, denoted b that has the dimension of the number of rows of A. The right eigenvector satisfies: Ab = Lb

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An occasional abbreviation for the British academic journal Economic Journal.

Source: econterms

A measure of responsiveness. The responsiveness of behavior measured by variable Z to a change in environment variable Y is the change in Z observed in response to a change in Y. Specifically, this approximation is common:

elasticity = (percentage change in Z) / (percentage change in Y)

The smaller the percentage change in Y is practical, the better the measure is and the closer it is to the intended theoretically perfect measure.

Elasticities are often negative, but are sometimes reported in absolute value (perhaps for brevity) in which case the author is depending on the reader knowing, or quickly applying, some theory. Usually the theory is the theory of supply and demand.

Among the elasticities that show up in the economics literature are:
elasticity of quantity demanded of some product in response to a change in price of that product-- I think this is 'elasticity of demand' or 'price elasticity of demand'. These are ordinarily negative, and when author reports a positive figure it is usually just an absolute value. A reader has to decide whether the true value is negative; hopefully this is obvious.
elasticity of supply, which is analogous
elasticity of quantity demanded in response to a change in the potential consumer's income -- called 'income elasticity of demand'. These are normally positive.

Inventing another kind of elasticity is plausible. Doing so implies a partial theory of behavior -- e.g. that Y creates a reason for the agent to change behavior Z.

Source: econterms

An occasional abbreviation for the journal Econometrica.

Source: econterms

The tendency of some contingent valuation survey responses to be similar across different survey questions in conflict with theories about what is valued in the utility function.

An example from Diamond and Hausman (1994): A survey might come up with a willingness-to-pay amount that was the same for either (a) one lake or (b) five lakes which include the one that was asked about individually. If lakes have some utility value to the respondent, one would have expected that five lakes would be worth more than one. Possibly the difference arises because the respondent was not expressing a specific preference for the first lake, and/or was not taking a budget constraint into account. Diamond and Hausman argue that for this reason among others contingent valuation surveys cannot arrive at good estimates for values of public goods.

Source: econterms

An attribute of the way technological progress affects productivity. In Solow (1956), any improvement in technology instantaneously affects the productivity of all factors of production. In Solow (1960) however productivity improvements were a property of only of new capital investment. In the second case we say the technologies are embodied in the new equipment, but in the first case they are disembodied.

Source: econterms

European Monetary System -- founded in 1979, its purpose was to reduce currency fluctuations, and evolved toward offering a common currency.

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European Monetary Union.

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A variable is endogenous in a model if it is at least partly function of other parameters and variables in a model. Contrast exogenous.

Source: econterms

An endogenous growth macro model is one in which the long-run growth rate of output per worker is determined by variables within the model, not an exogenous rate of technological progress as in a neoclassical growth model like those following from Ramsey (1928), Solow (1956), Swan (1956), Cass (1965), Koopmans (1965). Influential early endogenous growth models are Romer (1986), Lucas (1988), and Rebelo (1991). See the sources for this entry for more information. Hulten (2000) says 'What is new in endogenous growth theory is the assumption that the marginal product of (generalized) capital is constant, rather than diminishing as in classical theories.' Generalized capital includes the result of investments in research and development (R&D).

Source: econterms

In a general equilibrium model, an individual's endowment is a vector made up of quantities of every possible good that the individual starts out with.

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energy consumption relative to total output (GDP or GNP).

Source: econterms

On a graph with good 1 on the horizontal axis and good 2 on the vertical axis, envision a convex indifference curve, and a diagonal budget constraint that meets it at one point. Now move the budget constraint in and out and mark the points where the tangencies with indifference curves are. The locus of such points is the Engel curve -- it's the mapping from wealth into the space of the two goods. That is, the Engel curve is (x(w), y(w)) where w is wealth and x() and y() are the amounts of each of the goods purchased at those levels of wealth.

Hardle (1990) p 18 defines the Engel curve as the graph of average expenditure (e.g. on food) as a function of income. And on p 118, defines food expenditure as a function of total expenditure.

The name refers to 19th century Prussian statistician Ernst Engel, according to Fogel (1979).

Source: econterms

Changes in commodity demands by people because their incomes are rising. A generalization of Engel's law.

Source: econterms

The observation that "the proportion of a family's budget devoted to food declines as the family's income increases."

See also Engel effects.

Source: econterms

A possible description of the actions of managers of firms. Managers can make investments that are more valuable under themselves than under alternative managers. Those investments might not maximize shareholder value. So shareholders have a moral hazard in contracting with managers.

Or, in the phrasing of Weisbach (1988): "Managerial entrenchment occurs when managers gain so much power that they are able to use the firm to further their own interests rather than the interests of shareholders."

The abstract to Shleifer and Vishny, 1989, p 123, is nicely explicit: "By making manager-specific investments, managers can reduce the probability of being replaced, extract higher wages and larger perquisities from shareholders, and obtain more latitude in determining corporate strategy."

Source: econterms

European Options Exchange

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The Epanechnikov kernel is this function: (3/4)(1-u²) for -1<u<1 and zero for u outside that range. Here u=(x-x_i)/h, where h is the window width and x_i are the values of the independent variable in the data, and x is the value of the scalar independent variable for which one seeks an estimate.
For kernel estimation.

Source: econterms

"Of, relating to; or involving knowledge or the act of knowing." An economic theory might take aspects of human understanding or belief as fundamental to economic processes or outcomes.

Source: econterms

"1. The division of philosophy that investigates the nature and origin of knowledge. 2. A theory of the nature of knowledge."

Source: econterms

(Usually written with a true epsilon character.)

In a noncooperative game, for any small positive number epsilon, an epsilon-equilibrium is a profile of totally mixed strategies such that each player gives more probability weight than epsilon only to strategies that are best responses to the profile of strategies the others are playing.

For a more formal definition see sources. This is a rough paraphrase.

Source: econterms

In a noncooperative game, a profile of strategies is an epsilon-proper equilibrium if "every player is giving his better responses much more probability weight than his worse responses (by a factor 1/epsilon), whether or not those 'better' responses are 'best'."
-- Myerson (1978), p 78.

For a more formal definition see sources. This is a rough paraphrase.

Source: econterms

Some balance that can occur in a model, which can represent a prediction if the model has a real-world analogue. The standard case is the price-quantity balance found in a supply and demand model. If the term is not otherwise qualified it often refers to the supply and demand balance. But there also exist Nash equilibria in games, search equilibria in search models, and so forth.

Source: econterms

Real returns to investors from the purchases of U.S. government bonds have been estimated at one percent per year, while real returns from stock ("equity") in U.S. companies have been estimated at seven percent per year (Kocherlakota, 1996). General utility-based theories of asset prices have difficulty explaining (or fitting, empirically) why the first rate is so low and the second rate so high, not only in the U.S. but in other countries too. The phrase equity premium puzzle comes from the framing of this problem (why is the difference so great?) and the attention focused on it by Mehra and Prescott (1985); sometimes the phrase risk free rate puzzle is used to describe the closely related question: why is the bonds rate so low? The problem can be inverted to ask: why do investors not reject the low-returning bonds in order to buy stocks, which would then raise the price of stocks and lower their subsequent returns?

The above is drawn from the excellent review by Kocherlakota (1996) which surveys the substantial literature on this subject. Abbreviating further from it: the theories against which the evidence constitute a "puzzle" (or paradox, which see) tend to have these aspects in common: (1) standard preferences described by standard utility functions, (2) contractually complete asset markets (against possible time- and state-of-the-world contingencies), and (3) costless asset trading (in terms of taxes, trading fees, and presumably information).

Overwhelmingly the discussion in the economics literature has focused on expansions to the formal theory and on refinements and expansions of data sources, rather than survey evidence. A survey of U.S. households would answer (has answered?) the question of why they invest so little in stocks.

[Editorial comment follows.] It is likely (but this is conjecture) that large fractions of the population do not seriously consider investing in stocks, and are thus not rejecting stocks because their returns are low, but rather because they do not know how and think there are some barriers to learning how; and/or they perceive the risks of stocks to be higher than they have historically been; and/or they believe their savings are insufficient to invest. These explanations suggest that as stock trading becomes easier (e.g. over the Web, with heavy marketing and easy interfaces) the theories will fit better because more of the population will buy stocks. Indeed, this has been observed over the last few years. Another class of likely explanations is that people are highly impatient to spend their income (which would conflict with standard constant-discount-rate utility functions, but agree with the evidence; see hyperbolic discounting). Seen this way, the puzzle is not why the evidence looks the way it does, but the hard theoretical problem of getting these factors into the asset pricing models.

Source: econterms

Informally: a stochastic process is ergodic if no sample helps meaningfully to predict values that are very far away in time from that sample. Another way to say that is that the time path of the stochastic process is not sensitive to initial conditions.

Two events A and B (e.g. possible sets of states of the process) are ergodic iff, taking the limit as h goes to infinity:
lim (1/h)SUM_{from i=1}^{to i=h} |Pr(A intersection with L^-iB)-Pr(A)Pr(B)| = 0
Here L is the lag operator. This definition is like that of 'mixing on average'. A stochastic process is ergodic, I believe, if all possible events in it are ergodic by this definition.

If a random process is mixing, it is ergodic.

Priestly, p 340: A process is ergodic iff 'time averages' over a single realization of the process converge in mean square to the corresponding 'ensemble averages' over many realizations.

Example 1: Let x_t (for integer t=0 to infinity) is known to be drawn iid from a standard normal distribution. Then knowing the value of x₁ doesn't help predict the value of x₂, because they are independently drawn. This time series process is ergodic.

Example 2: Suppose the process is x_t=k+sin(t)+e_t where k is unknown and e_t is a white noise error. Then any sample of x_t for a known t gives information about k and that is enough information to make predictions at remote times in the future that are just as good as predictions at nearby times. This process is not ergodic.

Source: econterms

means persistent properties

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In the context of a stochastic processes {x_t}, set E is an ergodic set if:
(i) it is a subset of the state space S of possible values of x_t,
(ii) if x_t is in E, then Pr(x_t+1 is in E}=1, and
(iii) no proper subset of E has the property in (ii).

Source: econterms

The Employee Retirement Income Security Act of 1974, a major U.S. law which guaranteed certain categories of employees a pension after some period at their employer; there had been more ambiguity before about what rules an employer could put on which employees could get a pension. Also ERISA changed the perceived rules about whether pensions could be invested in venture capital.

Source: econterms

A dynamic model in which "the movement of the variables in any periods is related to the previous period's gap from long-run equilibrium."

Source: econterms

A time series process {x_t} is essentially stationary iff E[x_t²] is uniformly bounded. (from Wooldridge)

This definition may not be standard or widely used.

I believe this means that even if the variance wanders around and is different for different t, there is a finite bound to those variances. The variance of the distribution of x_t is never infinite for any t and indeed never exceeds that finite bound. Thus an ARCH-type process might be essentially stationary even though its variance is not constant for all t.

Note that there are strictly stationary processes that have infinite second moments; such processes are not essentially stationary.

Source: econterms

estimation

Source: econterms

A function of data that produces an estimate for an unknown parameter of the distribution that produced the data.
The way estimators are often discussed, they can be thought of as chosen before the data are seen. This can be hard to understand for the person new to the term. Properties of estimators (such as unbiasedness in finite samples, asymptotic unbiasedness, efficiency, and consistency) are discussed without considering any particular sample, by making assumptions about the distribution of the data, and considering the estimator in the context of the distributions.

Source: econterms

A first order condition that is across a time or state boundary. (Across a state boundary means a tradeoff between uncertain events.) That is, a first order condition that is a relation between a variable that has different values in different periods or different states. E.g. k_t = b(1+r)k_t+1 is an Euler equation, but 2n_t² - 3k_t = 0 is not.

Source: econterms

May refer to either the natural logarithm base e, approximately 2.71828, or to the Euler-Mascheroni (sp) constant, which is approximately .57721566.

Source: econterms

"Originally, it was a dollar-denominated deposit created either in a European bank or in the European subsidiary of an American bank, usually located in London." Here's why: (1) Americans overseas might want their deposits in dollars; (2) the dollar being the most common international currency, borrowers and lenders internationally may want to make their accounts in it; (3) the Eurodollar market was "exempt from reserve requirements and other regulatory costs imposed on domestic American banks. Superior terms in the Eurodollar market attracted American borrowers and depositors who would have otherwise patronized domestic institutions." An example of such regulation was the US Regulation Q which limited interest banks could pay.

Source: econterms

a name for the 'disease' of rigid, slow-moving labor markets in Europe in contrast to fast-moving markets, e.g. in North America.

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A function f() is even iff f(x)=f(-x).

Source: econterms

Empirical study of prices of an asset just before and after some event, like an announcement, merger, or dividend. Can be used to discuss whether the market priced the information efficiently, whether there was private information, etc.

This method was developed by Fama, Fisher, Jensen, and Roll (1969) according to Weisbach, 1988, p 455

Source: econterms

Describes game models in which players choose their strategies through a trial-and-error process in which they learn over time that some strategies work better than others.

Source: econterms

Latin for "beforehand". In models where there is uncertainty that is resolved during the course of events, the ex antes values (e.g. of expected gain) are those that are calculated in advance of the resolution of uncertainty.

Source: econterms

Firms pay dividends to those who are shareholders on a certain date. The next day is called the ex dividend date. People who own no shares until the ex dividend date do not receive the dividend. The price of the stocks is often adjusted downward before the start of trading on the ex dividend date because to compensate for this.

Source: econterms

Latin for "after the fact". In models where there is uncertainty that is resolved during the course of events, the ex post values (e.g. of expected gain) are those that are calculated after the uncertainty has been resolved.

Source: econterms

Sample kurtosis minus 3, which means when 'excess kurtosis' is positive, there is greater kurtosis than in the normal distribution.

Source: econterms

Asset returns in excess of the risk-free rate. Used especially in the context of the CAPM. Excess returns are negative in those periods in which returns are less than the risk-free rate. Contrast abnormal returns.

Source: econterms

In a simultaneous equation system -- that some of the exogenous variables are not in some of the equations; often this idea is expressed by saying the coefficient next to that exogenous variable is zero. This way of putting it may make this restriction (hypothesis) testable, and may make a simultaneous equation system identified.

Source: econterms

A requirement in a contract that the buyer will only buy goods of a certain type from the stated seller.

Source: econterms

data set from Standard and Poors on compensation to American corporate executives, including stock and options ownership.

Source: econterms

The value that individuals may attach to the mere knowledge of the existence of something, as opposed to having direct use of that thing. Synonymous with nonuse value.

For example, knowledge of the existence of rare and diverse species and unique natural environments may have value to environmentalists who do not actually see them.

Source: econterms

A variable is exogenous to a model if it is not determined by other parameters and variables in the model, but is set externally and any changes to it come from external forces. Contrast endogenous.

Source: econterms

There are several, overlapping definitions: 1) The mean of a probability distribution. If the probability distribution function is F(x) then the mean would be calculated by integrating dF(x) over the domain of the probability distribution function. The expectation operator, E[], is a linear operator per Hogg and Craig, 1995, page 55.
2) In a model, the agents may have to anticipate the value of variables whose realizations may occur in the future. The values they anticipate are often called their expectations. The agents may generalize only from past realizations in a way that we can call "adaptive expectations" or they may have other information from which they hypothesize a distribution from which the realization will be drawn. From such a distribution they can calculate the mean value, and variance, and so forth. This process is one of "rational expectations." --- Note: the notation E_x[] means the expectation of the expression taken over the random variable X. The result of the expression could still be a random variable if there are other random variables in the expression.

Source: econterms

That the utility of an agent facing uncertainty is calculated by considering utility in each possible state and constructing a weighted average, where the weights are the agent's estimate of the probability of each state. Arrow, 1963 attributes to Daniel Bernoulli (1738) the earliest known written statement of this hypothesis.

Source: econterms

The expected value of a random variable is the mean of its distribution.
In its technical use this word does not have exactly the same meaning as in ordinary English. For example, people buying a lottery ticket that has a 1/10,000 chance of paying $10,000 can expect to get zero since that is overwhelmingly the likely outcome. They can be certain they won't get $1. But the expected value of their winnings is $1.
Having said this, it is a standard implementation of 'rational expectations' to assume that agents behave in response to the expected values of the distributions they face.

Source: econterms

e(p,u) -- the minimum income necessary for a consumer to achieve utility level u given a vector of prices for goods p. (The consumer is presumed to get utility from the goods.)

Source: econterms

In the context of studies of employees, length of time employed anywhere. Sometimes narrowed to include only length of time employed in relevant jobs. Contrast tenure.

Source: econterms

A particular function form for a continuous distribution with parameter k, a scalar real greater than zero. Has pdf f(x)=ke^-kx.
The mean is E[x]=1/k, and variance var(x)=1/k². Moment-generating function is (1-kt)^-1.

Source: econterms

A distribution is a member of the exponential family of distributions if its log-likelihood function can be written in the form below.

ln L(q | X) = a(X) + b(q) + c₁(X)s₁(q) + c₂(X)s₂(q) + . . . + c_K(X)s_K(q) where a(), b(), and c_j() and s_j() for each j=1 to K are functions; q is the vector of all parameters; X is the matrix of observable data; and L() is the likelihood function as defined by the maximum likelihood procedure.

The members of the exponential family vary from each other in a(), b(), and the c_j()s and s_j()s. Most common named distributions are members of the exponential family.

Quoting from Greene, 1997, page 149: "If the log-likelihood function is of this form, then the functions c_j() are called sufficient statistics [and] the method of moments estimators(s) will be functions of them," Those estimators will be the maximum likelihood estimators which are asymptotically efficient here.

Source: econterms

A particular functional form for the utility function. Some versions of it are used often in finance.

Here is the simplest version. Define U() as the utility function and w as wealth. a is a positive scalar parameter.
U(w) = -e^-aw

is the exponential utility function.

Now consider events over time. An agent might have a utility function mapping possible streams of consumption into utility values. Here is one way this is often parameterized:
Define (b) as a constant discount rate known to the agent. It's a scalar that is between zero and one, and usually thought of as near one.
Define t as a time subscript that starts at zero and increases over the integers, either to some fixed T or to infinity.
Define c(t) as the amount the agent gets to consume at each t, and {c(t)} as the series of consumptions for all relevant t. c(t) is random here. its value is not known but its distribution is assumed known to the agent.
Let E[] be the expectations operator that takes means of distributions.

Using this notation a common dynamic version of exponential utility is:
u({c_t} = the sum over all t of (b)^tE[-e^-ac(t)]

Whether this utility function describes observed investment decisions is discussable and testable. It is not often discussed, however. If clear information on that becomes known to this author, it will be added here.
Most uses of the exponential utility function in finance are driven by these aspects: (a) its analytic tractability; e.g. that it can be differentiated with respect to choice variables that affect future wealth w or consumption c(t); (b) for some applications it aggregates usefully, meaning that if every agent has this exact utility function and they can buy securities then a representative agent can be defined which also has this analytically convenient form and for whom the securities prices would be the same. It's convenient for computing securities prices in some abstract economies to use that representative agent. There are 'no wealth effects' -- that is, the amount of risky securities that the agent wants to hold is not a function of his own wealth, as long as he can borrow infinitely (which is often assumed for tractability in these models.)

Source: econterms

Or, extendend real numbers, or extended real line. The set of reals plus the elements (infinity) and (minus infinity). Addition and multiplication can generally be extended to this set; see Royden, p. 36

Source: econterms

Refers to the range to which a resource is utilized or applied. Example: the number of hours worked by an employee. Contrast intensive margin.

Source: econterms

An effect of a purchase or use decision by one set of parties on others who did not have a choice and whose interests were not taken into account.
Classic example of a negative externality: pollution, generated by some productive enterprise, and affecting others who had no choice and were probably not taken nto account.
Example of a positive externality: Purchase a car of a certain model increases demand and thus availability for mechanics who know that kind of car, which improves the situation for others owning that model.

Source: econterms

The F distribution is defined in terms of two independent chi-squared variables. Let u and v be independently distributed chi-squared variables with u₁ and v₁ degrees of freedom, respectively.
Then the statistic: F=(u/u₁)/(v/v₁) has an F distribution with (u₁,v₁) degrees of freedom. As can be computed from the definition of the t distribution, the square of a t statistic may be written: t²=(z²/1)/(v/v₁), where z², being the square of a standard normal variable, has a chi-squared distribution. Thus the square of a t variable with v1 degrees of freedom is an F variable with (1,v₁) degrees of freedom, that is: t²=F(1,v₁).

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Normally a test for the joint hypothesis that a number of coefficients are zero. Large values (greater than two?) generally reject the hypothesis, depending on the level of significance required.

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Indicates which services come with a price. Stands for 'free on board.' Describes a price which includes goods plus the services of loading those goods onto some vehicle or vessel at a named location, sometimes put in parentheses after the f.o.b.

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"A security's factor loadings are the slopes in a multiple regression of its return on the factors."

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An effect observed in models of international trade -- that the prices of inputs to ("factors of") production in different countries, like wages, are driven towards equality in the absence of barriers to trade. This happens among other reasons because price incentives cause countries to choose to specialize in the production of goods whose factors of production are abundant there, which raises the prices of the factors towards equality with the prices in countries where those factors are not abundant. Shocks to factor availability in a country would cause only a temporary departure from factor price equality.

The basic theorem of this kind is attributed to Samuelson (1948) by Hanson and Slaughter (1999) who also cite Blackorby, Schworm, and Venables (1993). The context of the theorem is a Heckscher-Ohlin model.

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factories may have been more efficient by reducing transactions costs, as argued by Oliver Williamson (1980).

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The conjecture that market prices for securities take long swings away from their fundamental values and tend to return to them.
In a time series of data this suggests that "the market price differs from the fundamental price by a highly serially correlated fad.". This formulation attributed to Shiller(1981, 1994), Summers (1986) and Poterba and Summers (1988) by Bollerslev and Hodrick (1992) p. 13.

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Contrasted with free trader, a holder of the the point of view that one's country's government must prevent foreign companies from having artificial advantages over domestic ones.

The term dates at least as far back as 1886 Britain, where tariffs were recommended by one point of view expressed in a Royal Commission report 'not to countervail any natural and legitimate advantage which foreign manufacturers may possess, but simply to prevent our own industries being placed at an artificial disadvantage by the interference of either home or foreign legislation....' (Carr and Taplin, p 122)

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A panel study of stocks to estimate CAPM or APT parameters

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two or more persons related by blood, marriage, or adoption, and residing together.

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Financial Accounting Standards Board, which sets accounting rules for the US. (public? private?)

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describes a distribution with excess kurtosis.

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Let {X_n} for n=1,2,3,... be a sequence of nonnegative real random variables.
Then lim inf_n->infinity E[X_n] ≥ E[lim inf_n->infinity X_n].

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stands for 'functional central limit theorem', and is synonymous with Donsker's theorem.

Briefly: if {e_t} is a series of independent and mean zero random variables, partial sums (from 1 to T) of the e's converge to a standard Brownian motion process on [0,1] as T goes to infinity. See other sources for a proper formal statement.

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Foreign Direct Investment, a component of a country's national financial accounts. Foreign direct investment is investment of foreign assets into domestic structures, equipment, and organizations. It does not include foreign investment into the stock markets. Foreign direct investment is thought to be more useful to a country than investments in the equity of its companies because equity investments are potentially "hot money" which can leave at the first sign of trouble, whereas FDI is durable and generally useful whether things go well or badly.

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stands for Fixed Effects estimator. That is, a linear regression in which certain kinds of differences are subtracted out so that one can estimate the effects of another kind of difference.

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The interest rate at which U.S. banks lend to one another their excess reserves held on deposit at the U.S. Federal Reserve.

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Feasible GLS. That is, the generalized least squares estimation procedure (see GLS), but with an estimated covariance matrix, not an assumed one.

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is intrinsically useless; is used only as a medium of exchange.

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Most terms are in one of these categories. You can click on one to see a list of terms relevant to it.
fields

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A filter is a way of treating or adjusting data before it is analyzed. Examples are the Hodrick-Prescott filter or Kalman filter.

More exactly, a filter is an algorithm or mathematical operation that is applied to a time series sample to get another sample, often called the 'filtered' data. For example a filter might remove some high-frequency effects from the data; or detrend it; or remove seasonal frequencies but leave monthly frequencies in.

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Full Information Maximum Likelihood, an approach to the estimation of simultaneous equations.

As portrayed in Johnston's book: Define A as the matrix of coefficients in the multiple-equation model, u as the vector of residuals for each choice of A, and s as the covariance matrix E(uu'). FIML consists of maximizing ln(L(A, s)) with respect to the elements of A and s.

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The study of securities, borrowing, and ownership. finance

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Federal Information Processing Standards. These are encodings defined by the U.S. government and used to encode some data (like states and counties) in U.S. data sets. Listings can be found at the NIST FIPS site.

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Defined by Alchian and Demsetz (1972) this way: "The essence of the classical firm is identified here as a contractual structure with: 1) joint input production [see team production]; 2) several input owners [e.g. the workers]; 3) one party [the firm or its owners] who is common to all the contracts of the joint inputs; 4) who has rights to renegotiate any input's contract independently of contracts with other input owners; 5) who holds the residual claim; and 6) who has the right to sell his central contractual residual status. The central agent is call the firm's owner and the employer. No authoritarian control is involved; the arrangement is simply a contractual structure subject to continuous renegotiation with the central agent. The contractual structure arises as a means of enhancing efficient organization of team production." ---------- a firm is a hierarchical organization attempting to make profits.

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The statement that a Walrasian equilibrium is weakly Pareto optimal. Such a theorem is true in a large and important class of general equilibrium models (usually static ones). The standard case is if every agent has a positive quantity of every good, and every agent has a utility function that is convex, continuous, and strictly increasing, the then the First Welfare Theorem holds.

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Usually means stochastic dominance.

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An extreme Keynesian view, that money doesn't matter at all as aggregate demand policy. Assumes that investment demand does not respond to interest rate changes. Relevant only in depression conditions (Branson, p 386).

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This is a necessary condition for maximum likelihood estimation to be consistent. Maximizing the likelihood function L gives an estimate for parameter b that is Fisher-consistent if: E[d(ln L)/db]=0 at b=b₀, where b₀ is the true value of b.

Another interpretation or phrasing: "An estimation procedure is Fisher consistent if the parameters of interest solve the population analog of the estimation problem." (Wooldridge).

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That in a model where inflation is expected to be steady, the nominal interest rate changes one-for-one with the inflation rate; see Fisher equation. The empirical analogy is the Fisher hypothesis.

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nominal rate of interest = real rate of interest + inflation

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That the real rate of interest is constant. So the nominal rate moves with inflation.
The real rate of interest would be determined by the time preferences of the public and technological constraints determining the return on real investment.

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The 'geometric mean of the fixed-weighted Paasche and Laspeyres indexes.' Proposed as a price index by Irving Fisher in 1922. This is a superlative index number formula. -- Triplett, 1992.

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A price index, computed for a given period by taking the square root of the product of the the Paasche index value and the Laspeyres index value.

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The Fisher information is an attribute or property of a distribution with known form but uncertain parameter values. It is only well-defined for distributions satisfying certain assumptions. It is a (k x k) matrix, where k is the number of elements in a vector of parameters b. Thus, for parameter b of pdf f(x):
I(b)=E{ [f'(x)/f(x)]² | b}
That's from DeGroot. I think this is the same as in Greene p 96:
I(b)=E[{d/db(ln L(b))}²]
=-E[d²/db²(ln L(b))]
If the Fisher information is 'large' then the estimated distribution will change radically as new data (x) are incorporated into the estimate of the distribution by maximum likelihood. The Fisher information is the main ingredient in the Cramer-Rao lower bound, and in some maximum likelihood estimators.

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Hypotheses about the value of r, the correlation coefficient between variables x and y of the underlying population, can be tested using the Fisher transformation of a sample's correlation coefficient r. Let N be the sample's size. This transformation is defined by: z = 0.5 * ln ( (1+r)/(1-r) ) z is approximately normally distributed with mean r, and standard error 1/((N-3)^0.5). This is a common way of testing whether a correlation coefficient is significantly different from 0, and hence ascribing a p-value. ------ [Editor: We suspect that for x and y bivariate normal the distribution works exactly in all sample sizes, otherwise only asymptotically.] [See Kennedy, p 369. Bickel and Dobson, 'Mathematical Statistics: Basic Ideas and selected topics' page 221 also gives derivation, but makes no mention of any distribution requirements.]

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for optimal investment by a firm -- that it should invest in real assets until their marginal internal rate of return equals the appropriately risk-adjusted rate of return on securities

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A method of estimating parameters from a panel data set. The fixed effects estimator is obtained by OLS on the deviations from the means of each unit or time period. This approach is relevant when one expects that the averages of the dependent variable will be different for each cross-section unit, or each time period, but the variance of the errors will not. In such a case random effects estimation would give inconsistent estimates of b in the model: y = Xb + e
The fixed effects estimator is: (X'QX)^-1X'Qy
where Q is the matrix that "partials out" the averages from the groups that have different variances.
Example: Define L as I_N x 1_T, where x is the Kronecker cross product operator, T is the number of time periods, and N is the number of cross-section units (individuals, say). Now individual effects can be screened out by premultiplying the model's equation by Q and running OLS, or equivalently using the estimator equation above. Thus estimating b.

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A macro model in which there is a variable relationship between the growth rate of out put and the level of net investment. The relation between the change in output and the level of net investment is the accelerator principle.

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An occasional compressed form of f.o.b..

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The theorem is that a Nash equilibrium exists in repeated games in which sufficiently patient players to reach Pareto optimal payoffs in a Nash equilibrium. (Fudenberg and Tirole, p 150, describes the achievable payoffs as the individually rational ones, not the Pareto optimal ones.) The strategies that achieve this often have the pattern that they 'punish' the other player at length for any defection from the Pareto optimal choice. In equilibrium that encourages the other player not to defect for a short term gain.

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Informally: A derivative (slope) defined for mappings from one vector space to another.

The first e in Frechet should have an accent aigu.

Formally (this taken more or less directly from Tripathi, 1996):
Let T be a transformation defined on an open domain U in a normed space X and mapping to a range in a normed space Y.
(Does normed space mean normed vector space? Or might it not?)

Holding fixed an x in U and for each h in X, if a linear and continuous operator L (mapping from X to Y) exists such that:

lim_{||h|| falls to 0} (1/||h||) * (||T(x+h)-T(x)-L(h)||) = 0

Then the operator L, often denoted T'(x), is the Frechet derivative of T() and we can say T is Frechet differentiable at x. (Ed.: I believe any such L is unique.)

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Informally: A possible property of mappings from one space to another. For such a transformation, a Frechet derivative may exist at each point and if so we say the transformation is Frechet differentiable at that point.

Properly the first e in Frechet should have an accent aigu.

See the entry at Frechet derivative for a formal definition.

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Shorthand for U.S. Federal Home Loan Mortgage Corporation.

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cash flow to a firm in excess of that required to fund all projects that have positive net present values when discounted at the relevant cost of capital.
Free cash flow can be a source of principal-agent conflict between shareholders and managers, since shareholders would probably want it paid out in some form to them, and managers might want to control it, e.g. to use it for unprofitable projects, for perquisites, to make acquisitions, to create jobs for friends and allies, and so forth. A possible partial solution to the conflict for the shareholders is for the company to have heavy debts on which frequent, heavy payments are due. Those payments keep the managers focused on delivering consistent revenues and clear out the extra cash.

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An assumption posited in a search and matching model of a market. The assumption is that there is no institutional constraint on firms entering the market (e.g. to hire workers). There is no fixed number of firms. The number of firms is determined in equilibrium, by the costs of starting up.

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excess reserves minus borrowed reserves (Branson, p 353).

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Holder of the political point of view that the best policy is to allow free trade into one's own country.

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The frequency function is the probability of drawing each particular value from a discrete distribution: p(x) = Pr(X=x). Here X is the random variable and x is one of its possible values.

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Unemployment that comes from people moving between jobs, careers, and locations. Contrast structural unemployment.

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In a cash-in-advance model of a monetary system, the Friedman rule for monetary policy is to deflate so that it is not costly to those who have money to continue to hold it. Then the cash-in-advance constraint isn't binding on them.

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Abbreviaton for the U.S. national Federal Trade Commission, which rules in some circumstances on some antitrust regulations. See also FTC.

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A 1914 U.S. law creating a regulatory body for antitrust, price discrimination, and regulation. Section five says "Unfair methods of competition in or affecting commerce, and unfair or deceptive acts or practices in or affecting commerce, are hereby declared unlawful."

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a mapping from paths of functions to the reals (e.g. a value function defined by a mapping from possible paths of choices)

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an equation where the unknown is a function. Example: a value function is the solution to the equation that sets the value function equal to the present discounted value of the current period's utility and the discounted value function of next period's state.

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"Being of such a nature or kind that one unit or part may be exchanged or substituted for another unit or equal part to discharge an obligation."
Examples: money or grain. Not examples: works of art.

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A future-oriented agent discounts the future lightly and so has a LOW discount rate, or equivalently a HIGh discount factor. See also present-oriented, discount rate, and discount factor.

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Given a statistical model y = X₁b₁ + X₂b₂+ e
where
y is a vector of values of a dependent variable,
the X's are linearly independent matrices of predetermined variables, and
the e's are errors, we could premultiply the equation by M₁=I-X₁(X₁'X₁)^-1X' which projects vectors in the space spanned by X₁ to zero, and run OLS on the resulting equation M₁y = M₁X₂b₂+ M₁e
and (the theorem says) would get exactly the same estimate of b₂ that OLS on the first equation would have given.
This use of premultiplying is used in the derivation of many estimators: notably IV estimators and FE estimators.

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A game is a model with (1) players who make (2) strategy (or action) choices in a (3) predefined time order, and then (4) receive payoffs, which are usually conceived of in money or utility terms. Classic games are the Prisoner's Dilemma, Matching Pennies, the Battle of the Sexes, the dictator game, the ultimatum game, the Bertrand game, and the Cournot game.

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game theory

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As used with respect to options: The rate of change of the portfolio's delta with respect to the price of the underlying asset. Formally this is a partial derivative.

A portfolio is gamma-neutral if it has zero gamma.

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A distribution relevant to, for example, waiting times. Expression of its pdf requires reference to the gamma function which will be called GAMMA(a) here. (When HTML supports math a better display will be possible.) The gamma distribution's pdf has parameters a>0 and b>0, and GAMMA(a) is also greater than zero. The support is on x>0:
f(x)=[x^a-1e^-x/b]/[GAMMA(a)b^a]

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A function of a real a>0. It is the integral over y from zero to infinity of y^a-1e^-y dy. This integral is the gamma function of a, GAMMA(a). (When HTML supports math a better display will be possible.) The gamma distribution is a function that includes the gamma function.

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Generalized ARCH. First paper may have been Bollerslev, 1986, Journal of Econometrics

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abbreviation for the Generalized Axioms of Revealed Preference.

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A matrix programming language and programming environment. Made by Aptech.

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an adjective that describes a random variable, meaning it has a normal distribution.

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The Gaussian kernel is this function: (2PI)^-.5exp(-u²/2). Here u=(x-x_i)/h, where h is the window width and x_i are the values of the independent variable in the data, and x is the value of the independent variable for which one seeks an estimate. Unlike most kernel functions this one is unbounded on x; so every data point will be brought into every estimate in theory, although outside three standard deviations they make hardly any difference.
For kernel estimation.

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A white noise process with a normal distribution.

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Gross domestic product. For a region, the GDP is "the market value of all the goods and services producted by labor and property located in" the region, usually a country. It equals GNP minus the net inflow of labor and property incomes from broad. -- Survey of Current Business

A key example helps. A Japanese-owned automobile factory in the US counts in US GDP but in Japanese GNP.

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A measure of the cost of goods purchased by U.S. households, government, and industry. Differs conceptually from the CPI measure of inflation, but not by much in practice.

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An abbreviation for the journal Games and Economic Behavior.

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general equilibrium

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A model of the form y=g(b'x) where y is a vector of dependent variables, x is a column vector of independent variables, b' is a row vector of parameters (that is, b is not a function of x) and g() is a possibly random function called a link function.

Examples: linear regression (y=b'x+errs) and logistic regression y=1/(1+e^-x)+errs.

An example that is not in the class of generalized linear models is: y=x₁*x₂.

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See GMM.

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Synonym for Heckit.

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A continuous-time random walk with a drift and random jumps at every point in time (roughly speaking). Algebraically:
a(x,t)dt + b(x,t)c(dt)^.5
describes a generalized Wiener process, where:
a and b are deterministic functions
t is a continuous index for time
x is a set of exogenous variables that may change with time
dt is a differential in time
c is a random draw from a standard normal distribution at each instant

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in a dynamical system, the generator function maps the old state N_t into new state N_t+1 E.g. N_t+1 = F(N_t).
A steady state would be an N^* such that F(N^*) = N^*.

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Geometric mean is a kind of average of a set of numbers that is different from the arithmetic average. The geometric mean is well defined only for sets of positive real numbers. Geometric mean of A and B is the square root of (A*B). The geometric mean of A, B, and C is the cube root of (A*B*C). And so forth. Contrast this to the arithmetic means, which are .5*(A+B) and .333*(A+B+C).

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abbrevation for Generalized Extreme Value distribution. The difference between two draws of GEV type 1 variables has a logistic distribution, which is why a GEV distribution for errors gets assumed in certain binary econometric models.

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Refers to a paper by Greenwood, Hercowitz, and Huffman (1988) with utility functions across agents and across time by:
u(C_it, N_it) = C_it - N_it^b
where a>0 and b>1 are constants, and C_it and N_it stand for consumption and hours worked by each agent i at date t.
-- this utility function has Gorman form and so it aggregates
-- it has been successful at matching cross-section data relative to other functions that do.

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A way to generate empirical distributions of two variables from a model. Say the model defines probability distributions F(X|Y) and G(Y|X). Then start with a random set of possible X's, draw Y's from G(), then use those Y's to draw X's, and so on indefinitely. Keep track of the X's and Y's seen, and this will give samples enough to find the unconditional distributions of X and Y.

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A descriptive relationship between size and growth -- that the size of units and their growth percentage statistics are statistically independent. Sometimes Gibrat's law is thought to apply to large firms, and sometimes to cities (Gabaix, May 1999 American Economic Review, page 130).

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A number between zero and one that is a measure of inequality. An example is the concentration of suppliers in a market or industry.

The Gini coefficient is the ratio of the area under the Lorenz curve to the area under the diagonal on a graph of the Lorenz curve, which is 5000 if both axes have percentage units. The meaning of the Gini coefficient: if the suppliers in a market have near-equal market share, the Gini coefficient is near zero. If most of the suppliers have very low market share but there exist one or a few supplies providing most of the market share then the Gini coefficient is near one.,

In labor economics, inequality of the wage distribution can be discussed in terms of a Gini coefficient, where the wages of subgroups are fractions of the total wage bill.

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A 1933 United States national law separating investment banking and commercial banking firms. Also prohibited banks from owning corporate stock. It was designed to confront the problem that banks in the Great Depression collapsed because they held a lot of stock.

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Generalized Least Squares. A generalization of the OLS procedure to make an efficient linear regression estimate of a parameter from a sample in which the disturbances are heteroskedastic. That is, in
y = Xb + e (equation 1)
that the e's vary in magnitude with the X's.
The estimator of b is: (X'O^-1X)^-1X'O^-1y (equation 2)
where O, standing for omega, is the covariance matrix. (As you see in the estimator, the covariance matrix is assumed to be invertible.)
The procedure to derive this is to multiply through the first equation by the square root of the inverse of the covariance matrix (which assumed to be known; if it estimated, one calls this procedure FGLS, for feasible GLS.) Then take OLS of the resulting equation.

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Stands for Generalized Method of Moments, an econometric framework of Hansen, 1982. It is an approach to estimating parameters in an economic model from data. Used often to figure out what standard errors on parameter estimates should be.

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Gross national product. The GDP is "the market value of all the goods and services producted by labor and property belonging to the region, usually a country. It equals GDP plus the net inflow of labor and property incomes from broad. A Japanese-owned automobile factory in the US counts in US GDP but in Japanese GNP.

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f'(k^*)=(1+n) where k^* is optimal capital stock, f() is the aggregate production function, and n is population growth rate. f(k)-k is consumed by the population. 'Golden Rule' may refer to a Solow fairy tale.

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A good is a desired commodity.

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The accounting term to describe the premium that acquiring companies pay over the book value of the firm being acquired. Goodwill can include value for R&D and trademarks.

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Of a stock price. From M. R. Gordon (1962). This model is sometimes used as a baseline for comparison or for intuition.
Assume a constant rate of return r, and a constant dividend growth rate g. Define P_t to be the price of the stock in period t, and D_t to be its dividend in period t. Implication is that price of stock P_t = D_t/(r-g).

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A utility function or indirect utility function is in Gorman form if it is affine with respect to some argument. Which argument should be clear from context. E.g.:
U_i(x_i, z) = A(z)x_i + B_i(z)
Here the utility U_i for individual i is is affine in argument x_i. A critical implication is that the sum of Gorman form utility functions for individuals is a well-defined aggregate utility function under some conditions....

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A situation, usually discussed in a model not in the real world, in which the behavior of optimizing agents in a market with a government would not produce a Pareto optimal allocation. The point is not that a particular government had, or would have, failed at something, but that the problem abstractly put cannot be perfectly solved by the government. The most common source of government failures in models is private information among the agents.

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Informally, if one time series helps predict another, we can say it Granger causes the other. The original definition, for linear predictors, is in Granger, 1980. From Sargent: A stochastic process z_t is said NOT to Granger-cause a random process x_t if E(x_t+1 | x_t,x_t-1,...,z_t,z_t-1,...) = E(x_t+1 | x_t,x_t-1,...) *** NOTE in J Pehkonen, Applied Economics, 1991, 23, 1559-1568, p. 1560. *** Expert treatment of this subject and more formal, less ambiguous definitions are in Chamberlain, Econometrica, May 82

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Conditions on the regressors under which the OLS estimator will be consistent.

The Grenander conditions are weaker than the assumption on the regressor X that lim_n->infinity(X'X)/n is a fixed positive definite matrix, which is a common starting assumption.

See Greene, 2nd ed, 1993, p 295.

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Some version of "Bad money will drive out good." I think the context is that if there are two suppliers of the same money (e.g. if one of them is a counterfeiter) or of two monies with a fixed exchange rate between them (per Hayek, Denationalization of Money, 1976 p. 39), there will be a tendency for overproduction and that the actual money stock will be made up of the bad, or less valuable, one. (Another situation is if one supplier makes coins that are 90% gold and the other has the option of making coins with less gold, Bertrand competition for coins would drive the gold fraction down over time.)

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German Socio-Economic Panel. A German government database going back to at least 1984.

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Stands for Herfindahl-Hirschman index, which is a way of measuring the concentration of market share held by particular suppliers in a market. It is the sum of squares of the percentages of the market shares held by the firms in a market. If there is a monopoly -- one firm with all sales, the H index is 10000. If there is perfect competition, with an infinite number of firms with near-zero market share each, the H index is approximately zero. Other industry structures will have H indices between zero and 10000.
Tirole's version is bounded between zero and one because each of the market shares is between zero and one.

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That high wages and labor scarcity stimulated technological progress in the U.S. in the 1800s, and in particular brought about the American system of manufacturing based on interchangeable parts. (This description from Mokyr, 1990; idea from Habakkuk, 1962).

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Hahn (1965) question: when does there exist an equilibrium in a model in which money has positive value?

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See J statistic

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A synonym for labor-augmenting, in practice.

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Given a model and data in which fixed effects estimation would be appropriate, a Hausman test tests whether random effects estimation would be almost as good. In a fixed-effects kind of case, the Hausman test is a test of H₀: that random effects would be consistent and efficient, versus H₁: that random effects would be inconsistent. (Note that fixed effects would certainly be consistent.) The result of the test is a vector of dimension k (dim(b)) which will be distributed chi-square(k). So if the Hausman test statistic is large, one must use FE. If the statistic is small, one may get away with RE.

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escape rate; rate of transition out of current state

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Is a mapping from the real line to {0, 1}, denoted (at least sometimes) hv(x). hv(x) is zero for x<0, and is one for x>=0.

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An occasional name for generalized Tobit. This approach allows a different set of explanatory variables to predict the binary choice from those which predict the continuous choice. (The data environment is one in which the continuous choice is measured only when the binary choice is nonzero -- e.g., if we have data on people, whether they bought a car, and how expensive it was, we can estimate a statistical model of how expensive a car other people would buy, but only on the basis of the ones who did buy a car in the data sample.) A regular, non-generalized Tobit constrains the two sets of variables to be the same, and the signs of their effects to be the same in the two estimated equations. 'Heck' is for James Heckman.

-- Christopher Baum, Boston College economics department, 20 May 2000, in a broadcast to the statalist, the email list of people interested in the software Stata.

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A way of estimating treatment effects when the treated sample is self-selected and so the effects of the treatment are confounded with the population that chose it because they expected it would help -- the classic example is that college educations may be selected by those most likely to benefit.

Taking that example, we wish to advance past the following regression:
w_i = a + bX_i + dC_i + e_i
where i indexes people, w_i is the wage (or other outcome variable) for agent i, X_i are variables predicting i's wage, and C_i is 1 if i went to college and 0 if not. e_i is the remaining error after least squares estimation of a, b, and d.

Source: econterms

A model of the effects of international trade. "The Heckscher-Ohlin framework typically is presented as a two-country, two-good, two-factor model. The two countries are assumed to share identical, homothetic tastes for the two substitutable goods and identical, constant-returns-to-scale technologies with some factor substitutability. Perfect competition prevails in each market with zero transport costs and no artificial barriers to international trade in goods, although factors are internationally immobile. In this framework, each country will (incompletely) specialize in production and export the good using intensively in production the factor that the country has in relative abundance." That effect is called factor-price equalization across countries, and is used sometimes to explain how rising international trade would lead to greater income inequality in the most developed countries. (from Bergstrand, Cosimano, Houck, and Sheehan, 1994, p 3)
The reference in the name is to "Scandinavian economists Eli Heckscher and Bertil Ohlin early in [the twentieth century]" in work that is rarely cited directly. (from Bluestone, 1994, p 336).

Source: econterms

of or relating to utility. (Literally, pleasure-related.) A hedonic econometric model is one where the independent variables are related to quality; e.g. the quality of a product that one might buy or the quality of a job one might take.

A hedonic model of wages might correspond to the idea that there are compensating differentials -- that workers would get higher wages for jobs that were more unpleasant.

"A product that meets several needs, or has a variety of features ... generates a number of hedonic services. Each one of these services can be thought of as generating its own demand, along with a resulting hedonic price. Although each separate component is not observable, the aggregation of all the components results in the observed product demand and equilibrium price.... [Q]uality improvements will appear to an observer as an outward shift of the product demand curve, as consumers are willing to purchase more at the prevailing price." -- William J. White, "A Hedonic Index of Farm Tractor Prices: 1910-1955", Ohio State University working paper, October 1998, pp. 3-4.

Source: econterms

A list of fields contained here is below. There is some other advice at this help page: http://econterms.com/help.html

Most terms are in one of these categories. You can click on one to see a list of terms relevant to it.
fields

Source: econterms

See 'H index'.

Source: econterms

The Hermite polynomials are a series of polynomials defined for each natural number r, used for statistical approximations I believe. Click here for the equation and graphs of the first several.

Source: econterms

The matrix of second derivatives of a multivariate function. That is, the gradient of the gradient of a function. Properties of the Hessian matrix at an optimum of differentiable function are relevant in many places in economics: 1) In maximum likelihood estimation, the information matrix is (-1) times the Hessian.

Source: econterms

A stochastic process is heterogeneous if it is not identically distributed every period.

Source: econterms

An alternate spelling of heteroskedastic. McCulloch (1985) argues that the spelling with the k is preferred, on the basis of the pronunciation and etymology (Greek not French derivation) of the term.

Source: econterms

An adjective describing a data sample or data-generating process in which the errors are drawn from different distributions for different values of the independent variables.
Most commonly this takes the form of changes in variance with the magnitude of X. That is, in
y = Xb + e
that the e's vary in magnitude with the X's. (An example is that variance of income across individuals is systematically higher for higher income individuals.)
If the errors are drawn from different distributions, or if higher moments of the error distributions vary systematically, these are also forms of heteroskedasticity.

Source: econterms

For whether a cost-benefit analysis supports a public project. The criterion is that the gainers from the project could in principle compensate the losers. That is, that total gains from the project exceed the losses. The criterion does not go so far as the Pareto criterion, according to which the gainers would in fact have to compensate the losers.

Source: econterms

An attribute of an effectiveness variable in a production function. The attribute is that it does not affect labor differently from the way it affects capital.

The canonical example is the Solow model production function Y=AF(K,L). There Y is output, L labor, K capital, F a production variable, and A represents some kinds of effectiveness variable. In Y=F(AK,L) the effectiveness variable affects capital but not labor. In Y=F(K,AL) it affects labor but not capital. These two cases can be described as Hicks-biased. In Y=AF(K,L) it is Hicks-neutral.

Source: econterms

Given a production function AF(K,L) changes in A are Hicks-neutral, meaning that they do not affect the optimal choice of K or L. The subject comes up in practice only for aggregate production functions.

Uzawa, H. 'Neutral Inventions and the Stability of Growth Equilibrium,' The Review of Economic Studies 28:2 (Feb., 1961), 117-124 contains the first known published use of the adjective 'Harrod neutral' According to it, the criterion of Harrod-neutrality comes from

Harrod, Roy F., 'Review of Joan Robinson's Essays in the Theory of Employment,' Economic Journal, vol. 47 (1937), 326-330.

Uzawa also proves that AF(K,L) and F(K,AL) are the right functional forms to meet Hicks and Harrod-neutrality, and that only the Cobb-Douglas form accomplishes both.

Source: econterms

h(p,u) -- the amount of a good that demanded by a consumer given that it costs p per unit and that the consumer will have utility u from all goods. h(p,u) is the cost-minimizing amount.

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A panel data set on U.S. high school students.

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reserves plus currency

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A complete normed metric space with an inner product. So the Hilbert spaces are also Banach spaces. L² is an example of a Hilbert space. Any Rⁿ with n finite is another.

Source: econterms

The subject of economic history is anything in history that is subject to economic explanations. Application of formal theory or statistical analysis of data may be relevant, although it is possible to make a contribution without either, e.g. with a case study or a contextual reinterpretation. Historians tend to be focused on what happened, how, and why, not on the question of whether a model fits the evidence.
history

Source: econterms

Statistical software for Hierarchical Linear Modeling, from Scientific Software International.

Source: econterms

Algorithm for choosing smoothed values for a time series. The H-P filter chooses smooth values {s_t} for the series {x_t} of T elements (t=1 to T) that solve the following minimization problem: min { {(x_t-s_t)² ... etc. } Parameter l>0 is the penalty on variation, where variation is measured by the average squared second difference. A larger value of l makes the resulting {s_t} series smoother; less high-frequency noise. The commonly applied value of l is 1600. For the study of business cycles one uses not the smoothed series, but the jagged series of residuals from it. See Cooley, 1995, p 27-29. That H-P filtered data shows less fluctuation than first-differenced data, since the H-P filter pays less attention to high frequency movements. H-P filtered data also shows more serial correlation than first-differenced data. For l=1600: "if the series were stationary, then [this choice] would eliminate fluctuations at frequencies lower than about thirty-two quarters, or eight years."

Source: econterms

One of a certain class of contracting problems.

Imagine a situation where there is profit to be made if agents A and B work together, so they consider an agreement to do so after A buys the necessary equipment. The hold-up problem (in this context) is A might not be willing to take that agreement, even though the outcome would be Pareto efficient, because after A has made that investment, B would have the power might decide to demand a larger share of the profits than before, since A is now deeply invested in the project but B is not, so B has some bargaining power that wasn't there before the investment. B could demand all of the profits, in fact, since A's alternative is to lose the investment entirely.

Other hold-up problems are analogous to this one.

Source: econterms

An attribute of a function g:R^d->R. g can be said to be Holder continuous if there exist constants C and 0<=E<=1 such that for all u and v in R^d:
|g(u)-g(v)| <= C||u-v||^E

So if g is Holder continuous for C=1 then it is Lipschitz continuous? And if g is Holder continuous then it is continuous.

Source: econterms

An alternate spelling of homoskedastic. McCulloch (1985) argues that the spelling with the k is preferred, on the basis of the pronunciation and etymology (Greek not French derivation) of the term.

Source: econterms

An adjective describing a statistical model in which the errors are drawn from the same distribution for all values of the independent variables. Contrast heteroskedastic.
This is a strong assumption, and includes in particular the assumption in a linear regression, for example,
y = Xb + e
that the variance of the e's is the same for all X's.

(The observed variance will differ in almost any sample. But if one believes that the data-generating process does not in principle have greater variances for different values of the independent variable, one would describe the sample as homoskedastic anyway.)

Source: econterms

Let u(x) be a function homogeneous of degree one in x. Let g(y) be a function of one argument that is monotonically increasing in y. Then u(g()) is a homothetic function of y.

So a function is homothetic in y if it can be decomposed into an inner function that is monotonically increasing in y and an outer function that is homogeneous of degree one in its argument.

In consumer theory there are some useful analytic results that can come from studing homothetic utility functions of consumption.

Source: econterms

Health and Retirement Study, a longitudinal panel of older Americans studied by the Survey Research Center at the University of Michigan. Their Web site is at http://www.umich.edu/~hrswww.

Source: econterms

High School and Beyond, a panel data set on U.S. high school students.

Source: econterms

Same as Huber-White standard errors.

Source: econterms

Standard errors which have been adjusted for specified assumed-and-estimated correlations of error terms across observations.

The implicit citations are to Huber, 1967, White, 1980, and White, 1982.

Source: econterms

The attributes of a person that are productive in some economic context. Often refers to formal educational attainment, with the implication that education is investment whose returns are in the form of wage, salary, or other compensation. These are normally measured and conceived of as private returns to the individual but can also be social returns.

''Human capital' was invented by the economist Theodore Schultz in 1960 to refer to all those human capacities, developed by education, that can be used productively -- the capacity to deal in abstractions, to recognize and adhere to rules, to use language at a high level. Human capital, like other forms of capital, accumulates over generations; it is a thing that parents 'give' to their children through their upbringing, and that children then successfully deploy in school, allowing them to bequeath more human capital to their own children.' -- Traub (2000)

Source: econterms

A way of accounting in a model for the difference in the preferences an agent has over consumption now versus consumption in the future.

For a and g scalar real parameters greater than zero, under hyperbolic discounting events t periods in the future are discounted by the factor (1+at)^(-g/a).

That expression describes the "class of generalized hyperbolas". This formulation comes from a 1999 working paper of C. Harris and D. Laibson, which cites Ainslie (1992) and Loewenstein and Prelec (1992).

In dynamic models it is common to use the more convenient assumption that agents have a common discount rate applying for any t-period forecast, starting now or starting in the future. Hyperbolic discounting is less convenient but fits the psychological evidence better, and when contrasted to the constant-discount-rate assumption can get models to fit the noticeable fall in consumption that U.S. workers are observed to experience when they retire. In a constant-discount-rate model the worker would usually have forecast the fall in income and their consumption expenses would be smooth.

One reason hyperbolic preferences are less convenient in a model is not only that there are more parameters but that the agent's decisions are not time-consistent as they are with a constant discount rate. That is, when planning for time two (two periods ahead) the agent might prepare for what looks like the optimal consumption path as seen from time zero; but at time two his preferences would be different.

Contrast quasi-hyperbolic discounting.

Source: econterms

a hypothesized property of unemployment rates -- that there is a ratcheting effect, so a short-term rise in unemployment rates tends to persist.
Theories that would lead to hysteresis:
-- an insider/outsider model of decisionmaking about employment; insiders such as the unionized workers ratchet up wage rates beyond where it is profitable to hire the unemployed; outsiders who are unemployed don't get to be part of the negotiation process.
-- behavioral and human capital changes among the unemployed, such as forgetting the details of work or work behavior, or losing interest or skill in getting new jobs, could lead to declining chances of becoming employed.

Source: econterms

increasing absolute risk aversion

Source: econterms

IC stands for "incentive compatible".
When solving a principal-agent maximization problem for a contract that meets various criteria, the IC constraints are those that require agents to prefer to act in accordance with the solution. If the IC constraint were not imposed, the solution to the problem might be economically meaningless, insofar as it produced an outcome that met some criterion of optimality but which an agent would choose not to act in accord with.
See also IR constraint.

Source: econterms

Intertemporal CAPM. From Merton, 1973.

Source: econterms

A matrix M is idempotent if MM=M. (M times M equals M.)
Example: the identity matrix, denoted I.

Source: econterms

A parameter in a model is identified if and only if complete knowledge of the joint distribution of the observed variables gives enough information to calculate the parameter exactly.

If the model has been written in such a way that its parameters can be consistently estimated from the observables, then the parameters are identified. There exist cases (mostly obscure) where parameters are identified but consistent estimators are not possible. (See, e.g. Gabrielsen, 1978)
A model is identified if there is no observationally equivalent model. That is, potentially observable random variables in the model have different distributions for different values of the parameter.

Formally:
Let h^* be a vector of unknown functions and distributions in an econometric model.
Let H denote a set which h^* is known to belong. H is defined by the model's restrictions.
Let P(h) denote the joint distribution of observable variables of the model for various elements of h in H. The distribution for the actual data will be assumed to be P(h^*).
Now, vector h^* is identified within H if for all h in H such that h<>h^* it is true that P(h)<>P(h^*).
Note: Linear models are either globally identified or there are an infinite number of observably equivalent ones. But for models that are nonlinear in parameters, "we can only talk about local properties." Thus the idea of locally identified models, which can be distinguished in data from any other 'close by' model.

"An identification problem occurs when a specifed set of assumptions combined with unlimited observations drawn by a specified sampling process does not reveal a distribution of interest." -- Manski, Charles F. "Identification problems and decisions under ambiguity: empirical analysis of treatment response and normative analysis of treatment choice" Northwestern University Department of Economics and Institute for Policy Research, September 1998, p. 2

Source: econterms

An identity matrix is a square matrix of any dimension whose elements are ones on its northwest-to-southeast diagonal and zeroes everywhere else. Any square matrix multiplied by the identity matrix with those dimensions equals itself. One usually says 'the' identity matrix since in most contexts the dimension is unambiguous. It is standard to denote the identity matrix by I.

Source: econterms

Sometimes used to name the state of people who are not in school but also not working. Context is usually industrialized countries with established labor markets, and the idle are often poor.

Source: econterms

An abbreviation for the journal International Economic Review.

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abbreviation for "if and only if"

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Integrated GARCH, a kind of econometric model of a stochastic process in which there is a unit root in a GARCH environment.
The IGARCH(p,q) process was proposed in Engle and Bollerslev (1986).

Source: econterms

stands for Irrelevance of Independent Alternatives, an assumption in a model. In a discrete choice setting, the multinomial logit model is appropriate only if the introduction or removal of a choice has no effect on the proportion of probability assigned to each of the other choices.
This is a strong assumption; a standard example where IIA is not an appropriate assumption is if one compares a model of transportation choices between a car and a red bus, then introduces a blue bus. The blue bus is functionally like the red bus, so presumably its introduction draws ridership more heavily from the red bus than from the car.

Source: econterms

An abbreviation for "independently and identically distributed." One would say this about two or more random variables to describe their joint distribution. A common use is to describe ongoing disturbances to a stochastic process, indicating that they are not correlated to one another.

Source: econterms

An occasional abbreviation for the academic journal International Journal of Industrial Organization.

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Indirect Least Squares, an approach to the estimation of simultaneous equations models. Steps: 1) Rearrange the structural form equations into reduced form 2) Estimate the reduced form parameters 3) Solve for the structural form parameters in terms of the reduced form parameters, and substitute in the estimates of the reduced form parameters to get estimates for the structural ones.

Source: econterms

International Monetary Fund -- an international organization with liquidity services to maintain financial stability.

Source: econterms

A decision rule (a mapping from expressed preferences by each of a group of agents to a common decision) "is implementable (in Nash equilibrium) if there exists a game form whose Nash equilibrium outcome is the desired outcome for the true preferences."

Source: econterms

A non-contractual agreement that corresponds to a Nash equilibrium to the repeated bilateral trading game other than the sequence of Nash equilibria to the one-shot trading game. In the labor market -- an implicit contract is formally represented by a series of games in which the firm pays a salary and the employee works effectively because they expect to play the game again (continue the agreement) if it goes well, not because they have an explicit, enforceable contract. That is, "by implicit contracts is meant nonbinding commitments from employers to offer ... continuity of wages, employment, and working conditions, and from employees to forgo such temptations as shirking and quitting for better opportunities." -- Granovetter, Ch 9

Source: econterms

One of a class of theorems following Arrow (1951) showing that social welfare functions cannot have certain collections of desirable attributes in common.

Source: econterms

Consider a shock to a system. A graph of the response of the system over time after the shock is an impulse response function graph. One use is in models of monetary systems. One graphs for example the percentage deviations in output or consumption over time after a one-time one percent increase in the money stock.

Source: econterms

A function f() satisfies the Inada conditions if: f(0) = 0, f'(0) = infinity, and f'(infinity) = 0. f() is usually a production function in this context.

Source: econterms

A possible action by a player in a game may be said to be inadmissible if it is dominated by another feasible actions.
The term comes the view of a game as a math problem. An action is or is not admissible as a candidate solution to the problem of choosing a utility-maximizing strategy for the game player.

As used in Manski, Charles F. "Identification problems and decisions under ambiguity: empirical analysis of treatment response and normative analysis of treatment choice" Northwestern University Department of Economics and Institute for Policy Research, September 1998, p. 2

Source: econterms

When used without another referent, appears to mean 'of consumption'. That is for income I and consumption C:
income elasticity = (I/C)*(dC/dI)
In one paper estimates were shown of .2 to .6 for a random sample of industrialized country middle class people.
For more details see elasticity.

Source: econterms

A kind of insurance, in which payment is made (often in previously determined amounts) for injuries suffered, not for the costs of recovery. The payment is designed not to be a dependent on anything the patient can control. From the point of view of the insurer, this mechanism avoids the moral hazard problem of victim spending too much in recovery.

Source: econterms

Two random variables X and Y are statistically independent if and only if their joint density (pdf) is the product of their marginal densities, that is if f(x,y)=f_x(x)f_y(y).

If two random variables are independent they are also uncorrelated.

Source: econterms

In a regression, a variable that is one if a condition is true, and zero if it is false. Approximately synonymous with dummy variable, binary variable, or flag.

Source: econterms

Represented for example on a graph whose horizontal and vertical axes are quantities of goods an individual might consume, an indifference curve represents a contour along which utility for that individual is constant. The curve represents a set of possible consumption bundles between which the individual is indifferent. Normally, with desirable goods on both axes (say, income today and income tomorrow) the curve has a certain shape, further from the origin when both quantities are positive than when one is zero.

Source: econterms

Denoted v(p, m) where p is a vector of prices for goods, and m is a budget in the same units as the prices. This function takes the value of the maximum utility that can be achieved by spending the budget m on the consumption goods with prices p.

Source: econterms

An allocation is individually rational if no agent is worse off in that allocation than with his endowment.

Source: econterms

Characterizing a reasoning process of generalizing from facts, instances, or examples. Contrast deductive.

Source: econterms

A period commonly dated 1760-1830 in Britain (as in Mokyr, 1993, p 3 and Ashton, 1948). Characterized by: "a complex of technological advances: the substitution of machines for human skills and strength; the development of inanimate sources of power (fossil fuels and the steam engine); the invention, production, and use of new materials (iron for wood, vegetable for animal matter, mineral for vegetable matter); and the introduction and spread of a new mode of production, known by contemporaries as the factory system." -- Landes (1993b) p 137.

Source: econterms

A historical phase and experience. The overall change in circumstances accompanying a society's movement population and resources from farm production to manufacturing production and associated services.

Source: econterms

Stands for 'infimum'. A value is an infimum with respect to a set if all elements of the set are at least as large as that value. An infimum exists in context where a minimum does not, because (say) the set is open; e.g. the set (0,1) has no minimum but 0 is an infimum.

inf is a mathematical operator that maps from a set to a value that is syntactically like the members of that set, although the value may not actually be a member of the set.

Source: econterms

Reduction in value of a currency. Measured often by percentage increases in the general price level per year.

Source: econterms

information

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In maximum likelihood estimation, the variance of the score vector. It's a k x k matrix, where k is the dimension of the vector of parameters being estimated. The vector of parameters is denoted q here:
I(q) = var S(q) = E[(S(q)-ES(q))²] = E[S(q)²]
where the score is S(q) = dL(q)/d(q)

The information matrix can also be calculated by multiplying the Hessian of the log-likelihood function by (-1).

Source: econterms

Synonym for Fisher information (which see).

Source: econterms

"An informational cascade occurs when it is optimal for an individual, having observed the actions of those ahead of him, to follow [that is, imitate] the behavior of the preceding individual without regard to his own information." -- Bikhchandani, Hirshleifer, and Welch, 1992, p 992

Source: econterms

An American-style business school near Paris. Operates in English.

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Any debt that is used as money. Is a liability to the issuer. Total amount of inside money in an economy is zero. Contrast outside money.

Source: econterms

There are several definitions. Here's one: 'An institution is a social mechanism through which men work together for common or like ends. It is a necessary arrangement wherever regulated group behavior over a broad field of activity is found. It is opposed in sociological thought to 'face to face' grouping and to local community forms of life ...' (Ware, p. 6)

For more see new institutionalism.

Source: econterms

Either (1) an estimation technique, often abbreviated IV, or (2) the exogenous variables used in the estimation technique.
Suppose one has a model:
y = Xb + e
Here y is a T x 1 vector of dependent variables, X is a T x k matrix of independent variables, b is a k x 1 vector of parameters to estimate, and e is a k x 1 vector of errors. OLS can be imagined, but suppose in the environment being modelled that the matrix of independent variables X may be correlated to the e's. Then using a T x k matrix of independent variables Z, correlated to the X's but uncorrelated to the e's one can construct an IV estimator that will be consistent:
b_IV = (Z'X)^-1Z'y
The two stage least squares estimator is an important extension of this idea.

In that discussion above, the exogenous variables Z are called instrumental variables and the instruments (Z'Z)^-1(Z'X) are estimates of the part of X that is not correlated to the e's.

Source: econterms

When regressors are correlated to errors in a model, one may be able to replace the regressors by estimates for these regressors that are not correlated to the errors. This is the technique of instrumental variables, and the replacement regressors are called instruments.

The replacement regressors are constructed by running regressions of the original regressors on exogenous variables that are called the instrumental variables.

Source: econterms

Said in reference to a random process. A random process is said to be 'integrated of order d' (sometimes denoted I(d)) for some natural number d if the series would be stationary after being first-differenced d times.
Example: a random walk is I(1).
Example: "Most macroeconomic flows and stocks that relate to population size, such as output or employment, are I(1)." They are growing.
Example: "An I(2) series [might] be growing at an ever-increasing rate."

Source: econterms

Refers to the degree (intensity) to which a resource is utilized or applied. For example, the effort put in by a worker or the number of hours the worker works. Contrast extensive margin.

Source: econterms

"Among other things"

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From Latin, 'between lives'. Used to describe gifts beetween people, usually from one generation to the next, which are like bequests except that both parties are alive. Quantities and timing of such gifts are studied empirically in the same way that quantities and purposes of bequests are subjects of empirical study.

Source: econterms

Defined, apparently, in Holmstrom and Myerson (1983) with reference to Rothschild and Stiglitz (1976). In Imderst (2000) this term is used to characterize the set ('family') of Rothschild-Sticlitz contracts in a particular model setting.

Source: econterms

A choice made by an agent that can be characterized as an optimum located at a tangency of two curves on a graph.

A classic example is the tangency between a consumer's budget line (characterizing the maximum amounts of good X and good Y that the consumer can afford) and the highest possible indifference curve. The slope of that tangency is where:

(marginal utility of X)/(price of X) = (marginal utility of Y)/(price of Y)

Contrast corner solution.

Source: econterms

positive learning or knowledge externalities between programs or plants within a production organization.

Source: econterms

A function p(q) that maps from a quantity of output to a price in the market; one might model the demand a firm faces by positing an inverse demand function and imagining that the firm chooses a quantity of output.

Source: econterms

Usually denoted l(Z), and defined by l(Z)=phi(Z)/PHI(Z), where phi() is the standard normal pdf and PHI() is the standard normal cdf.

Source: econterms

In context of time series processes, represented for example by a lag polynomial, inverting means to solve for the e's (epsilons) in terms of the y's.
One inverts moving average (MA) processes to get AR representations.

Source: econterms

Any use of resources intended to increase future production output or income.

Source: econterms

stands for 'Industrial Organization', the field of industry structure, conduct, and performance. By structure we usually mean the size of the firms in the industry -- e.g. whether firms have monopoly power. IO

Source: econterms

Stands for "initial public offering", the event of a firm's first sale of stock shares.

Source: econterms

Integrated Public Use Microdata Series. These are collections of U.S. Census data, adapted for easy use by the University of Minnestota Social History Research Laboratory, at its Web site http://www.ipums.umn.edu.

Source: econterms

IR stands for "individually rational".
When solving a principal-agent maximization problem for a contract that meets various criteria, the IR constraints are those that require agents to prefer to sign the contract than not to. If the IR constraint were not imposed, the solution to the problem might be economically meaningless, insofar as it was a contract that met some criterion of optimality but which an agent would refuse to sign.
See also IC constraint.

Source: econterms

The United States national tax collection agency, called the Internal Revenue Service.

Source: econterms

means 'is a consistent estimator of'

Source: econterms

Given a production function, an isoquant is 'the locus of input combinations that yield the same output level.' (Chiang, p. 360) There is an isoquant set for each possible output level. Mathematically the isoquant is a level curve of the production function.

Examples and discussion is at Martin Osborne's web page: http://www.chass.utoronto.ca/~osborne/2x3/tutorial/ISOQUANT.HTM.

Source: econterms

A stochastic process: a generalized Wiener process with normally distributed jumps.

Source: econterms

abbrevation for Instrumental Variables, an estimation technique

Source: econterms

In a GMM context, when there are more moment conditions than parameters to be estimated, a chi-square test can be used to test the overidentifying restrictions. The test statistic can be called the J statistic.
In more detail: Say there are q moment conditions and p parameters to be estimated. Let the weighting matrix be the inverse of the asymptotic covariance matrix. Let T be the sample size. Then T times the minimized value of the objective function (TJ_T(b_T)) is asymptotically distributed with a chi-square distribution with (q-p) degrees of freedom.

Source: econterms

Has multiple, overlapping definitions numbered below: (1) kind of nonparametric estimator for a regression function. A jackknife estimator is a linear combination of kernel estimators with different window widths. Jackknife estimators have higher variance but less bias than kernel estimators. (Hardle, p. 145.) (2) creates a series of statistics, usually a parameter estimate, from a single data set by generating that statistic repeatedly on the data set leaving one data value out each time. This produces a mean estimate of the parameter and a standard deviation of the estimates of the parameter. (Nick Cox, in an email broadcast to Stata users on statalist, circa 7/5/2000.)

Source: econterms

An occasional abbreviation for the academic journal Journal of Econometrics.

Source: econterms

An abbreviation for the Journal of Economic History.

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Journal of Economic Literature. See also JEL classification codes.

Source: econterms

These define a classification system for books and journal articles relevant to the economic researcher. The list has three levels of precision: categories A-Z, subcategories like A0-A2 (these are used to classify books), and sub-subcategories like A10-A14 (which are used to classify journal articles). The second level is detailed here; for the complete set of possible JEL codes see any issue, e.g. in the Sept 1997 issue, pages 1609-1620. The list below comes from that same issue, pages 1437-1439. A more up-to-date list is online at http://www.aeaweb.org/journal/elclasjn.html

A. General Economics and Teaching (A0 General, A1 General Economics, A2 Teaching of Economics)
B. Methodology and History of Economic Thought (B0 General, B1 History of Economic Thought through 1925, B2 History of Economic Thought since 1925, B3 History of Thought: Individuals, B4 Economic Methodology)
C. Mathematical and Quantitative Methods (C0 General, C1 Econometric and Statistical Methods: General, C2 Econometric and Statistical Methods: Single Equation Models, C3 Econometric and Statistical Methods: Multiple Equation Models, C4 Econometric and Statistical Methods: Special Topics, C5 Econometric Modeling, C6 Mathematical Methods and Programming, C7 Game Theory and Bargaining Theory, C8 Data Collection and Data Estimation Methodology; Computer Programs, C9 Design of Experiments)
D. Microeconomics (D0 General, D1 Household Behavior and Family Economics, D2 Production and Organizations, D3 Distribution, D4 Market Structure and Pricing, D5 General Equilibrium and Disequilibrium, D6 Economic Welfare, D7 Analysis of Collective Decision-Making, D8 Information and Uncertainty, D9 Intertemporal Choice and Growth)
E. Macroeconomics and Monetary Economics (E0 General, E1 General Aggregative Models, E2 Consumption, Saving, Production, Employment, and Investment, E3 Prices, Business Fluctuations, and Cycles, E4 Money and Interest Rates, E5 Monetary Policy, Central Banking and the Supply of Money and Credit, E6 Macroeconomic Aspects of Public Finance, Macroeconomic Policy, and General Outlook)
F. International Economics (F0 General, F1 Trade, F2 International Factor Movements and International Business, F3 International Finance, F4 Macroeconomic Aspects of International Trade and Finance) G. Financial Economics (G0 General, G1 General Financial Markets, G2 Financial and Institutions and Services, G3 Corporate Finance and Governance) H. Public Economics (H0 General, H1 Structure and Scope of Government, H2 Taxation and Susidies, H3 Fiscal Policies and Behavior of Economic Agents

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An abbreviation for the Journal of Economics and Management Strategy.

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If X is a real-valued random variable with E(|X|) finite and the function g() is convex, then E[g(X)] >= g(E[X]).
One application: By Jensen's inequality, E[X²] >= (E[X])². Since the difference between these is the variance, we have just shown that any random variable for which E[X²] is finite has a variance and a mean.
This is the inequality one can refer to when showing that an investor with a concave utility function prefers a certain return to the same expected return with uncertainty.

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An abbreviation for the Journal of Economic Perspectives.

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An abbreviation for the Journal of Economic Theory.

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Journal of Finance

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Journal of Financial Economics

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Journal of Financial Intermediation, at http://www.bus.umich.edu/jfi/

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Journal of Human Resources

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An abbreviation for the Journal of Industrial Economics .

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An abbreviation for the Journal of Law and Economics.

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An abbreviation for the Journal of Law, Economics and Organization.

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Describes the situation of a person with a U.S. job who is not free to leave for another job because the first job has medical benefits associated with it that the person needs, and the second one would not, perhaps because 'pre-existing conditions' are often not covered under U.S. health insurance.

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The monthly US publication Job Openings for Economists.

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In the context of research economics these are academic periodicals, usually with peer-reviewed contents. An amazingly complete list of hyperlinks to journals is at the WebEc web site. Some are also in this glossary directly, below.
journals

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Journal of Policy Analysis and Management

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Abbreviation for the Journal of Political Economy

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Journal of Public Economics

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An abbreviation for the Journal of Regulatory Economics.

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A monetary policy rule of keeping the growth of money at a fixed rate of k percent a year. This phrase is often used as stated, without specifying the percentage.

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A kind of nonparametric estimator of a function. Given a data set {X_i, Y_i} it estimates values of Y for X's other than those in the sample. The process is to choose the k values of X_i nearest the X for which one seeks an estimate, and average their Y values. Here k is a parameter to the estimator. The average could be weighted, e.g. with the closest neighbor having the most impact on the estimate.

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The Kalman filter is an algorithm for sequentially updating a linear projection for a dynamic system that is in state-space representation.

Application of the Kalman filter transforms a system of the following two-equation kind into a more solvable form:
x_t+1=Ax_t+Cw_t+1 y_t=Gx_t+v_t in which:
A, C, and G are matrices known as functions of a parameter q about which inference is desired (this is the PROBLEM to be solved),
t is an whole number, usually indexing time,
x_t is a true state variable, hidden from the econometrician,
y_t is a measurement of x with scalings G and measurement errors v_t,
w_t are innovations to the hidden x_t process,
Ew_t+1w_t'=1 by normalization,
Ev_tv_t=R, an unknown matrix, estimation of which is necessary but ancillary to the problem of interest which is to get an estimate of q. The Kalman filter defines two matrices S_t and K_t such that the system described above can be transformed into the one below, in which estimation and inference about q and R is more straightforward, possibly even by OLS:
z_t+1=Az_t+Ka_t y_t=Gz_t+a_t where z_t is defined to be E_t-1x_t,
a_t is defined to be y_t-E_t-1y_t,
K is defined to be lim K_t as t goes to infinity.

The definition of those two matrices S_t and K_t is itself most of the definition of the Kalman filter:
K_t=AS_tG'(GS_tG'+R)^-1 S_t+1=(A-K_tG)S_t(A-K_tG)'+CC'+K_tRK_t'
K_t is called the Kalman gain.

It's not yet clear to me what specific examples there are of problems that the Kalman filter solves.

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One of the two equations that characterizes the application of the Kalman filter process defines an expression sometimes denoted K_t, which is called the Kalman gain.

That equation, using notation from Sargent's lectures, is:

K_t=AS_tG'(GS_tG'+R)^-1

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The framework of relationships in postwar Japan's big banks and big firms. Related companies organized around a big bank (like Mitsui, Mitsubishi, and Sumitomo) which own a lot of equity in one another and in the bank and do much business with one another. This system has the virtue of maintaining long term business relationships and stability in suppliers and customers. It has the disadvantage of reacting slowly to outside events since the players are partly protected from the external market. (p 412)

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Kernel estimation means the estimation of a regression function or probability density function. Such estimators are consistent and asymptotically normal if as the number of observations n goes to infinity, the bandwidth (window width) h goes to zero, and the product nh goes to infinity. In practice, means use of the Nadaraya-Watson estimator, which see.

Source: econterms

A weighting function used in nonparametric function estimation. It gives the weights of the nearby data points in making an estimate. In practice kernel functions are piecewise continuous, bounded, symmetric around zero, concave at zero, real valued, and for convenience often integrate to one. They can be probability density functions. Often they have a bounded domain like [-1,1].

Source: econterms

As prices fall, a given nominal amount of money will be a larger real amount. Consequently the interest rate would fall and investment demanded rise. This Keynes effect disappears in the liquidity trap. Contrast the Pigou effect. Another phrasing: that a change in interest rates affects expenditure spending more than it affects savings.

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Describes a regression where the regressors are not in the opinion of the writer thoroughly 'justified' by an argument or a theory. Often used pejoratively; other times describes an exploratory regression.

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Kullback-Leibler Information Criterion. An unpublished paper by Kitamura (1997) describes this as a distance between probability measures. It is defined in that paper thus. The KLIC between probability measures P and Q is:

I(P||Q) = [integral of] ln(dP/dQ) dP if P << Q
........ = infinity otherwise

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Unmeasurable risk. Contrast Knightian uncertainty.

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If a regression will be run to estimates different linear slopes for different ranges of the independent variables, it's a spline regression, and the endpoints of the ranges are called knots.

The spline regression is designed so that the resulting spline function, estimating the dependent variable, is continuous at the knots.

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If {w_t} is a sequence of iid draws from a distribution and Ew_t exists (call it mu) then the average of the w_t's goes 'almost surely' to mu as t goes to infinity.
Same as strong law of large numbers, I believe.

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This is an operator that takes two matrix arguments. It is denoted by a small circle with an x in it, but will be denoted here by 'o'. Let A be an M x N matrix, and B be an R x S matrix. Then AoB is an MR x NS matrix, formed from A by multiplying each element of a by the entire matrix B and putting it in the place of the element of A, e.g.:
a₁₁B a₁₂B ... a_1nB
. . . . . .
. . . . . .
a_M1B a_M2B ... a_MnB
Kronecker products have the following useful properties:
(AoB)(CoD)=ACoBD
(AoB)^-1 = A^-1oB^-1 (AoB)' = A'oB' (AoB)+(AoC)=Ao(B+C) AoC+BoC = (A+B)oC

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Let X be a set of regressors, y be a vector of dependent variables, and the model be: y=Xb+e where E[ee'] is the matrix OMEGA. The theorem is that if the column space of (OMEGA)X is the same as the column space of X; that is, that there is heteroskedasticity but not cross-correlation, then the GLS estimator of b is the same as the OLS estimator of b.

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An attribute of a distribution, describing 'peakedness'. Kurtosis is calculated as E[(x-mu)⁴]/s⁴ where mu is the mean and s is the standard deviation.

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A graph with measures of increased economic development (presumed to correlate with time) on the horizontal axis, and measures of income inequality on the vertical axis hypothesized by Kuznets (1955) to have an inverted-U-shape. That is, Kuznets made the proposition when an economy is primarily agricultural it has a low level of income inequality, that during early industrialization income inequality increases over time, then at some critical point it starts to decrease over time. Kuznets (1955) showed evidence for this.

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A journal, whose Web site is at http://www.kyklos-review.ch/kyklos/index.html.

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The set of Lebesgue-integrable real-valued functions on [0,1].

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A Hilbert space with inner product (x,y) = integral of x(t)y(t) dt.
Equivalently, L² is the space of real-valued random variables that have variances. This is an infinite dimensional space.

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is the set of continuous bounded functions with domain Rⁿ

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"[L]abor economics is primarily concerned with the behavior of employers and employees in response to the general incentives of wages, prices, profits, and nonpecuniary aspects of the employment relationship, such as working conditions."
labor

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Shorthand for worker (never employer) variables that are often considered endogeneous in a labor market regression. Such variables, which often appear on the right side of such regressions: wage rates, employment dummies or employment rates.

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Quantity of output per time spent or numbers employed. Could be measured in, for example, U.S. dollars per hour.

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"Both Ricardo and Marx say that the value of every commodity is (in perfect equilibrium and perfect competition) proportionaly to the quantity of labor contained in the commodity, provided this labor is in accordance with the existing standard of efficiency of production (the 'socially necessary quantity of labor'). Both measure this quantity in hours of work and use the same method in order to reduce different qualities of work to a single standard." And neither accounts well for monopoly or imperfect competition. (Schumpeter, p 23)

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One of the ways in which an effectiveness variable could be included in a production function in a Solow model. If effectiveness A is multiplied by labor L but not by capital K, then we say the effectiveness variable is labor-augmenting.

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Stands for 'Least absolute deviations' estimation.

LAD estimation can be used to estimate a smooth conditional median function; that is, an estimator for the median of the process given the data. Say the data are stationary {x_t, y_t}. The dependent variable is y and the independent variable is x.The criterion function to be minimized in LAD estimation for each observation t is:
q(x_t,y_t,q) = |y_t=m(x_t,q)|

where m() is a guess at the conditional median function.

Under conditions specified in Wooldridge, p 2657, the LAD estimator here is Fisher-consistent for parameters of the estimator of the median function.

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Denoted L. Operates on an expression by moving the subscripts on a time series back one period, so: Le_t = e_t-1 Why? Well, it can help manipulability of some expressions. For example it turns out one can could write an MA(2) process (which see) to look like this, in lag polynomials (which see): et = (1 + p₁L + p₂L²)u_t and then divide both sides by the lag polynomial, and get a legal, meaningful, correct expression.

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A polynomial expression in lag operators (which see). Example: (1 - p₁L + p₂L²) where L² = LL, or the lag operator L applied twice. These are useful for manipulating time series. For example, one can quickly show an AR(1) is equivalent to an MA(infinity) by dividing both sides by the lag polynomial (1-pL).

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An algebraic term that arises in the context of problems of mathematical optimization subject to constraints, which in economics contexts is sometimes called a shadow price.

A long example: Suppose x represents a quantity of something that an individual might consume, u(x) is the utility (satisfaction) gained by that individual from the consumption of quantity x. We could model the individual's choice of x by supposing that the consumer chooses x to maximize u(x):

x = arg max_x u(x)

Suppose however that the good is not free, so the choice of x must be constrained by the consumer's income. That leads to a constrained optimization problem ............ [Ed.: this entry is unfinished]

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stands for 'locally asymptotically normal', a characteristic of many ('a family of') distributions.

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Usually a synonym for 'asymptotic' rather than a reference to an actual sample magnitude.

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A price index following a particular algorithm.

It is calculated from a set ('basket') of fixed quantities of a finite list of goods. We are assumed to know the prices in two different periods. Let the price index be one in the first period, which is then the base period. Then the value of the index in the second period is equal to this ratio: the total price of the basket of goods in period two divided by the total price of exactly the same basket in period one.

As for any price index, if all prices rise the index rises, and if all prices fall the index falls.

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Often exemplified by E_tE_t+1(.) = E_t(.) That is, "one cannot use limited information [at time t] to predict the forecast error one would make if one had superior information [at t+1]." -- Campbell, Lo, and MacKinlay, p 23.

Source: econterms

Leveraged buy-out. The act of taking a public company private by buying it with revenues from bonds, and using the revenues of the company to pay off the bonds.

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The kind of learning that an agent in a model exhibits by adapting to past data by running least squares on it to estimate a hypothesized parameter and behaving as if that parameter were correct.

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In some models, individuals spend some time working and the rest is lumped into a category called leisure, the details of which are usually left out.

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Describes models like that of Akerlof's 1970 paper, in which the fact that a good is available suggests that it is of low quality. For example, why are used cars for sale? In many cases because they are "lemons," that is, they were problematic to their previous owners.

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Has the form q=min{x1,x2} where q is a quantity of output and x1 and x2 are quantities of inputs or functions of the quantities of inputs.

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An adjective describing a distribution with high kurtosis. 'High' means the fourth central moment is more than three times the second central moment; such a distribution has greater kurtosis than a normal distribution. This term is used in Bollerslev-Hodrick 1992 to characterize stock price returns.
Lepto- means 'slim' in Greek and refers to the central part of the distribution.

Source: econterms

A government benefit to the underemployed will presumably reduce their hours of work. The ratio of the actual increase in income to the benefit is the Lerman ratio, which is ordinarily between zero and one. Moffitt (1992) estimates it in regard to the U.S. AFDC program at about .625.

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A measure of the profitability of a firm that sells a good: (price - marginal cost) / price.

One estimate, from Domowitz, Hubbard, and Petersen (1988) is that the average Lerner index for manufacturing firms in their data was .37.

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Meaning differs by context. Often: the ratio of debts to total assets. Can also be the ratio of debts (or long-term debts in particular, excluding for example accounts payable) to equity.

Normally used to describe a firm's but could describe the accounts of some other organization, or an individual, or a collection of organizations.

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The all-powerful kind of state that Hobbes thought "was necessary to solve the problem of social order." -- Cass R. Sunstein, "The Road from Serfdom" The New Republic Oct 20, 1997, p 37.

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In maximum likelihood estimation, the likelihood function (often denoted L()) is the joint probability function of the sample, given the probability distributions that are assumed for the errors. That function is constructed by multiplying the pdf of each of the data points together:
L(q) = L(q; X) = f(X; q) = f(X₀;q)f(X₁;q)...f(X_N;q)

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A program for the econometric study of limited dependent variables. Limdep's web site is at 'http://www.limdep.com'.

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A dependent variable in a model is limited if it is discrete (can take on only a countable number of values) or if it is not always observed because it is truncated or censored.

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stands for Limited Information Maximum Likelihood, an estimation idea

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For {w_t} an iid sequence, Ew_t=mu, and var(w_t)=s²:
Let W=the average of the T w_t's. Then: T^1/2(W-mu)/s converges in distribution as T goes to infinity to a N(0,1) distribution

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linear algebra

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An econometric model is linear if it is expressed in an equation which the parameters enter linearly, whether or not the data require nonlinear transformations to get to that equation.

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Say the number of units, or quantity, paid for is denoted q, and the total paid is denoted T(q), following the notation of Tirole. A linear pricing schedule is one that can be characterized by T(q)=pq for some price-per-unit p.

For alternative pricing schedules see nonlinear pricing or affine pricing schedule.

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Econometric models in which the dependent variable is a probability between zero and one. These are easier to estimate than probit or logit models but usually have the problem that some predictions will not be in the range of zero to one.

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Defined in the context of the generalized linear model, which see.

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A function g:R->R satisfies a Lipschitz condition if
|g(t¹)-g(t²) <= C|t¹-t²|
for some constant C. For a fixed C we could say this is "the Lipschitz condition with constant C."

A function that satisfies the Lipschitz condition for a finite C is said to be Lipschitz continuous, which is a stronger condition than regular continuity; it means that the slope so steep as to be outside the range (-C, C).

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A function is Lipschitz continuous if it satisfies the Lipschitz condition for a finite constant C. Lipschitz continuity is a stronger condition than regular continuity. It means that the slope is never outside the range (-C, C).

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A liquid market is one in which it is not difficult or costly to buy or sell.

More formally, Kyle (1985), following Black (1971), describes a liquid market as "one which is almost infinitely tight, which is not infinitely deep, and which is resilient enough so that prices eventually tend to their underlying value."

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A property of a good: a good is liquid to the degree it is easily convertible, through trade, into other commodities. Liquidity is not a property of the commodity itself but something established in trading arrangements.

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Many households, e.g. young ones, cannot borrow to consume or invest as much as they would want, but are constrained to current income by imperfect capital markets.

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A Keynesian idea. When expected returns from investments in securities or real plant and equipment are low, investment falls, a recession begins, and cash holdings in banks rise. People and businesses then continue to hold cash because they expect spending and investment to be low. This is a self-fulfilling trap.

See also Keynes effect and Pigou effect.

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Same as portmanteau test.

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Linear models are either globally identified or there are an infinite number of observably equivalent ones. But for models that are nonlinear in parameters, "we can only talk about local properties." Thus the idea of locally identified models, which can be distinguished in data from any other 'close by' model. "A sufficient condition for local identification is that" a certain Jacobian matrix is of full column rank.

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An agent's preferences are locally nonsatiated if they are continuous and strictly increasing in all goods.

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In the context of economics, log always means 'natural log', that is log_e, where e is the natural constant that is approximately 2.718281828. So x=log y <=> e^x=y.

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A utility function. Some versions of this are used often in finance.
Here is the simplest version. Define U() as the utility function and w as wealth. a is a positive scalar parameter.
U(w) = ln^-w

is the log utility function.

Source: econterms

A function f(w) is said to be log-concave if its natural log, ln(f(w)) is a concave function; that is, assuming f is differentiable, f''(w)/f(w) - f'(w)² <= 0 Since log is a strictly concave function, any concave function is also log-concave. A random variable is said to be log-concave if its density function is log-concave. The uniform, normal, beta, exponential, and extreme value distributions have this property. If pdf f() is log-concave, then so is its cdf F() and 1-F(). The truncated version of a log-concave function is also log-concave. In practice the intuitive meaning of the assumption that a distribution is log-concave is that (a) it doesn't have multiple separate maxima (although it could be flat on top), and (b) the tails of the density function are not "too thick". An equivalent definition, for vector-valued random variables, is in Heckman and Honore, 1990, p 1127. Random vector X is log-concave iff its density f() satisfies the condition that f(ax₁+(1-a)x₂)≥[f(x₁)]^a[f(x₂)]^(1-a) for all x₁, and x₂ in the support of X and all a satisfying 0≤a≤1.

Source: econterms

A random variable is said to be log-convex if its density function is log-concave. Pareto distributions with finite means and variances have this property, and so do gamma densities with a coefficient of variation greater than one. [Ed.: I do not know the intuitive content of the definition.] A log-convex random vector is one whose density f() satisfies the condition that f(ax₁+(1-a)x₂) ≤ [f(x₁)]^a[f(x₂)]^(1-a) for all x₁, and x₂ in the support of X and all a satisfying 0≤a≤1.

Source: econterms

Has the cdf F(x) = 1/(1+e^-x)
This distribution is quicker to calculate than the normal distribution but is very similar. Another advantage over the normal distribution is that it has a closed form cdf. pdf is f(x) = e^x(1+e^x)^-2 = F(x)F(-x)

Source: econterms

A univariate binary model. That is, for dependent variable y_i that can be only one or zero, and a continuous indepdendent variable x_i, that:
Pr(y_i=1)=F(x_i'b)
Here b is a parameter to be estimated, and F is the logistic cdf. The probit model is the same but with a different cdf for F.

Source: econterms

Let X be a random variable with a standard normal distribution. Then the variable Y=e^X has a lognormal distribution.
Example: Yearly incomes in the United States are roughly log-normally distributed.

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a synonym for panel data

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used to discuss concentration of suppliers (firms) in a market. The horizontal axis is divided into as many pieces as there are suppliers. Often it is given a percentage scale going from 0 to 100. The firms are in order of decreasing size. On the vertical axis are the market sales in percentage terms from 0 to 100. The Lorenz curve is a graph of the sales of all the firms to the right of each point on the horizontal axis.

So (0,0) and (100,100) are the endpoints on the Lorenz curve and it is weakly convex, and piecewise linear, between. See also Gini coefficient.

Source: econterms

Or, 'criterion function.' A function that is minimized to achieve a desired outcome. Often econometricians minimize the sum of squared errors in making an estimate of a function or a slope; in this case the loss function is the sum of squared errors. One might also think of agents in a model as minimizing some loss function in their actions that are predicated on estimates of things such as future prices.

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No appearing points

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Longitudinal Research Database, at the U.S. Bureau of the Census. Used in the study of labor and productivity. The data is not publicly available without special certification from the Census. The LRD extends back to 1982.

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A criticism of econometric evaluations of U.S. government policy as they existed in 1973, made by Robert E. Lucas. "Keynesian models consisted of collections of decision rules for consumption, investment in capital, employment, and portfolio balance. In evaluating alternative policy rules for the government,.... those private decision rules were assumed to be fixed.... Lucas criticized such procedures [because optimal] decision rules of private agents are themselves functions of the laws of motion chosen by the government.... policy evaluation procedures should take into account the dependence of private decision rules on the government's ... policy rule." In Cochrane's language: "Lucas argued that policy evaluation must be performed with models specified at the level of preferences ... and technology [like discount factor beta and permanent consumption c^* and exogenous interest rate r], which presumably are policy invariant, rather than decision rules which are not." [I believe the canonical example is: what happens if government changes marginal tax rates? Is the response of tax revenues linear in the change, or is there a Laffer curve to the response? Thus stated, this is an empirical question.]

Source: econterms

Estimators that maximize a sample average. The 'm' means 'maximum-likelihood-like'. (from Newey-McFadden)

The term was introduced by Huber (1967). "The class of M-estimators included the maximum likelihood estimator, the quasi-maximum likelihood estimator, multivariate nonlinear least squares" and others. (from Wooldridge, p 2649)

I think all m-estimators have scores.

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A measure of total money supply. M1 includes only checkable demand deposits.

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A measure of total money supply. M2 includes everything in M1 and also savings and other time deposits.

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Stands for "moving average." Describes a stochastic process (here, e_t) that can be described by a weighted sum of a white noise error and the white noise error from previous periods. An MA(1) process is a first-order one, meaning that only the immediately previous value has a direct effect on the current value:
e_t = u_t + pu_t-1
where p is a constant (more often denoted q) that has absolute value less than one, and u_t is drawn from a distribution with mean zero and finite variance, often a normal distribution.
An MA(2) would have the form:
e_t = u_t + p₁u_t-1 + p₂u_t-2
and so on. In theory a process might be represented by an MA(infinity).

Source: econterms

A first-order moving average process. See MA for details.

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macro

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As contrasted to interaction effect.

In the regression

y_i = aX_i + bXZ_i + cZ_i + errors

The bXZ_i term measures the interaction effect. The main effect is cZ_i.

This term is usually used in an ANOVA context, where its meaning is presumably analogous but this editor has not verified that.

Source: econterms

Synonym for 'alternative hypothesis'. "The hypothesis that the restriction or set of restrictions to be tested does NOT hold." Often denoted H₁.

Source: econterms

An index number enabling a productivity comparison between economy A and economy B. Imagine that we have an aggregate production function Q_AA=f_A(K_A,L_A) that describes economy A and an aggregate production Q_BB=f_B(K_B,L_B) that describes economy B. K and L stand for capital and labor inputs. We substitute the inputs of B into the production function of A to compute Q_AB=f_A(K_B,L_B). We also compute Q_BA=f_B(K_A,L_A) with the inputs from country A.

The Malmquist index of A with respect to B is the geometric mean of Q_AA/Q_AB and Q_BA/Q_BB. It will be greater than one if A's aggregate production technology is better than B's.

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Fractional part of a real number.

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a rare abbreviation, for moving-average representation

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Also known as the Annual Demographic File. Conducted in March of each year by the Census Bureau in the U.S. Gets the information from the regular monthly CPS survey, plus additional data on work experience, income, noncash benefits, and migration.

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a synonym for 'P value'

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An organized exchange between buyers and sellers of a good or service.

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Total number of shares times the market price of each. May be said of a firm's shares, or of all the shares on an equity market.

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A situation, usually discussed in a model not in the real world, in which the behavior of optimizing agents in a market would not produce a Pareto optimal allocation. Sources of market failures:
-- monopoly. Monopoly or oligopoly producers have incentives to underproduce and to price above marginal cost, which then gives consumers incentives to buy less than the Pareto optimal allocation.
-- externalities

Source: econterms

Shares of public firms are traded, and in large enough blocks this means control over corporations is traded. That puts some pressure on managers to perform, otherwise their corporation can be taken over.

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Power held by a firm over price, and the power to subdue competitors.

Source: econterms

That established firms use advertising as a barrier to entry through product differentiation. Such a firm's use of advertising differentiates its brand from other brands to a degree that consumers see its brand is a slightly different product, not perfectly substituted by existing or potential competitors. This makes it hard for new competitors to gain consumer acceptance.

Source: econterms

Synonym for Sharpe ratio.

Source: econterms

A stochastic process is a Markov chain if:
(1) time is discrete, meaning that the time index t has a finite or countably infinite number of values;
(2) the set of possible values of the process at each time is finite or countably infinite; and
(3) it has the Markov property of memorylessness.

Source: econterms

A characteristic of some Nash equilibria. "A Markov perfect equilibrium (MPE) is a profile of Markov strategies that yields a Nash equilibrium in every proper subgame." A Markov strategy is one that does not depend at all on variables that are functions of the history of the game except those that affect payoffs.
A tiny change to payoffs can discontinuously change the set of Markov perfect equilibria, because a state variable with a tiny effect on payoffs can be part of a Markov perfect strategy, but if its effect drops to zero, it cannot be included in a strategy; that is, such a change makes many strategies disappear from the set of Markov perfect strategies.

Source: econterms

A stochastic process where all the values are drawn from a discrete set. In a first-order Markov process only the most recent draw affects the distribution of the next one; all such processes can be represented by a Markov transition density matrix. That is,
Pr{x_t+1 is in A | x_t, x_t-1,...} = Pr{x_t+1 is in A | x_t}
Example 1: x_t+1 = a + bx_t + e_t is a Markov process
For a=0, b=1 it is a martingale.


A Markov process can be periodic only if it is of higher than first order.

Source: econterms

A property that a set of stochastic processes may have. The system has the Markov property if the present state predicts future states as well as the whole history of past and present states does -- that is, the process is memoryless.

Source: econterms

In a game, a Markov strategy is one that does not depend at all on state variables that are functions of the history of the game except those that affect payoffs.
[Ed.: I believe random elements can be in a Markov strategy: e.g. a mixed strategy could be a Markov strategy.]

Source: econterms

A square matrix describing the probabilities of moving from one state to another in a dynamic system. In each ?row? are the probabilities of moving from the state represented by that row, to the other states. Thus the rows of a Markov transition matrix each add to one. Sometimes such a matrix is denoted something like Q(x' | x) which can be understood this way: that Q is a matrix, x is the existing state, x' is a possible future state, and for any x and x' in the model, the probability of going to x' given that the existing state is x, are in Q. (An example would be good here)

Source: econterms

Quoting almost strictly from Goldberger, 1994, p 31:

If Y is a nonnegative random variable, that is, if Pr(Y<0)=0, and k is any positive constant, then E(Y) ≥ kPr(Y ≥ k).

The proof is amazingly quick. See Goldberger page 31 or Hogg and Craig page 68.

Source: econterms

In macro, the ratio of price to marginal cost. Can be used as a measure of market power across firms, industries, or economies.

Source: econterms

x(p,m) -- the amount of a factor of production that is demanded by a producer given that it costs p per unit and the budget limit that can be spent on all factors is m. p and x can be vectors.

Source: econterms

Same as martingale difference sequence.

Source: econterms

** This definition is not usable as is ** A stochastic process {X_t} is a martingale (or, equivalently, martingale difference sequence) with respect to information {Y_t} if and only if:
(i) E|X_t| < infinity
(ii) E[X_n+1 | Y₀, Y₁, ... , Y_n] = X_n E(g_t+1) = g_t.

Martingale differences are uncorrelated but not necessarily independent.

Source: econterms

'A production system characterized by mechanization, high wages, low prices, and large-volume output.' (Hounshell, p.305) Usually refers to factory processes on metalwork, not to textiles or agriculture. The term came into use in the 1920s and referred to production approaches analogous to those of the Ford Motor Company in the US.

Source: econterms

		Player Two
		C	D
Player One	C	1,-1	-1,1
	D	-1,1	1,-1

A zero-sum game with two players. Each shows either heads or tails from a coin. If both are heads or both are tails then player One wins, otherwise Two wins. The payoff matrix is at right.

There is no Nash equilibrium to this game.

Source: econterms

A matrix programming language and programming environment. Used more by engineers but increasingly by economists. There's a very brief tutorial at Tutorial: Matlab.
The software is made by The Mathworks, Inc.

Source: econterms

A justice criterion proposed by the philosopher Rawls. A principle about the just design of social systems -- e.g., rights and duties. According to this principle the system should be designed to maximize the position of those who will be worst off in it.

"The basic structure is just throughout when the advantages of the more fortunate promote the well-being of the least fortunte, that is, when a decrease in their advantages would make the least fortunate even worse off than they are. The basic structure is perfectly just when the prospects ofthe least fortunate are as great as they can be." -- Rawls, 1973, p 328

Source: econterms

A nonparametric estimator of certain coefficients of a binary choice model. Avoids assumptions about the distribution of errors that would be made by a probit or logit model in the same circumstances.

In the econometric model: the dependent variable y_i is either zero or one; the regressors X_i are multiplied by a parameter vector b. y_i often represents which of two choices was selected by a respondent. b is estimated to maximize an objective function that is given by an expression: max_b sum_{i=1 to N} [(y_i-.5)sign(X_ib)]

where i indexes observations, of which there are N, and the function sign() has value one if its argument is greater than or equal to zero, and has value zero otherwise.

b chosen this way has the property that it maximizes the correct prediction of y_i given the information in X. Notice that although the maximum value of the maximand may be well defined, b is not usually uniquely estimated in a finite data set, because values of b near betahat would make the same predictions. Often, however, b is estimated within a narrow range.

Source: econterms

Stands for Management Buy-Out, the purchase of a company by its management. Sometimes means Management By Objectives, a goal-oriented personnel evaluation approach.

Source: econterms

A criterion for an estimator: the choice is the one that minimizes the sum of squared errors due to bias and due to variance.

Source: econterms

The mean squared error of an estimator b of true parameter vector B is:
MSE(b) = E[(b - B)²]
which is also
MSE(b) = var(b) + (bias(b))(bias(b)')

Source: econterms

If (S, A) is a measurable space, elements of A are A-measurable.

Source: econterms

(S, A) is a measurable space if S is a set and A is a sigma-algebra of S. Elements of A are said to be A-measurable.

Source: econterms

A noun, in the mathematical language of measure theory: a measure is a function from sets to the real line. Probability is a common kind of measure in economic models. Other measures are the counting measure, which is the number of elements in the set, the length measure, the area measure, and the volume measure. Length, area, and volume are defined along lines, planes, and spaces just as one would expect, and they have the natural meanings.
Formally: a measure is a mapping m from a sigma algebra A to the extended real line such that
(i) m(null) = 0
(ii) m(B) >= 0 for all B in A
(iii) m(any countable union of disjoint sets in A) = the sum of m(each of those sets)
The third property is called the countable additivity property. An example: imagine probability mass distributed evenly on a unit square. Probability is then defined on any area within the square. The measure (probability, here) is the size (area) of the subset.
The kinds of subsets on which measures such as probability are defined are called sigma-algebras (which see).

Source: econterms

measure theory

Source: econterms

The data used in an econometric problem may have been measured with some error, and if so this violates a basic condition of the abstract environment in which OLS is validly derived. This turns out not to be seriously problematic if the dependent variable is affected by an iid mean-zero measurement error, but if the regressors have been measured with a mean-zero iid error the estimates can be biased. There are standard approaches to this problem, notably the use of instrumental variables. Paraphrasing from Schennach, 2000, p 1: In a linear econometric specification, a measurement error on the regressors can be viewed as a particular type of endogeneity problem causing the disturbance to be correlated with the regressors, which is precisely the problem addressed by standard IV techniques.

Source: econterms

A certain class of principal-agent problems are called mechanism design problems. In these, a principal would like to condition her own actions on the private information of agents. The principal must offer incentives for the agents to reveal information.
Examples from the theoretical literature are auction design, monopolistic price discrimination, and optimal taxation. In an auction the seller would like to set a price just below the highest valuation of a potential buyer, but does not know that price, and an auction is a mechanism to at least partially reveal it. In a price discrimination, the seller would like to offer the product at different prices to groups with different valuations but may not be able to identify which group an agent is a member of in advance.

Source: econterms

A distinguishing characteristic of money is that it is taken as a medium of exchange, that is, in the language of Wicksell (1935) p. 17, that it is "habitually, and without hesitation, taken by anybody in exchange for any commodity."

Source: econterms

Given a space of possible events, the meet is the finest common coarsening of the information sets of all the players. The meet is the finest partition of the space of possible events such that all players have beliefs about the probabilities of the elements of the partition.

Source: econterms

An adjective describing a distribution with kurtosis of 3, like the normal distribution. See by contrast leptokurtic and platykurtic.

Source: econterms

Means best-practice production function -- depending on context, either the most efficient feasible practice, or most efficient actual practice of the existing entities converting inputs X into output y. Often in practice y is an agricultural output, and data from a sample of farms, and the meta-production function could be estimated by estimating production functions for the farms and choosing among the most efficient ones. In the (macro) context of the quote below, the entities are not farms but countries, producing GDP. 'The term 'meta-production function' is due to Hayami and Ruttan (1970, 1985). For an exposition of the meta-production function approach, see Lau and Yotopoulos (1989) and Boskin and Lau (1990).... The two most important maintained hypotheses [of this approach] are: (1) that the aggregate production functions of all countries are identical in terms of 'efficiency-equivalent' units of output and inputs; and (2) that technical progress in all countries can be represented in the commodity-augmentation form, with constant geometric augmentation factors....' The framework allows 'the researcher to consider and potentially to reject the maintained hypotheses of traditional growth accounting [such as] (1) constant returns to scale, (2) neutrality of technical progress; and (3) profit maximization.' (p66) An assumption related to the second maintained hypothesis above, which the theory depends on (p69) is that 'the measured outputs and inputs of the different countries may be converted into unobservable standardized, or 'efficiency-equivalent,' quantities of output and inputs by multiplicative country- and output- and input-specific time-varying augmentation factors....' (where 'time-varying' seems to conflict with the requirement, above, that the augmentation factors be 'constant'.) (p69) In this approach 'countries may differ in the quantities of their factor inputs and intensities and possibly in the qualities and efficiencies of their inputs and outputs, but they do not differ with regard to the technological opportunities .... [T]hey are assumed to have equal access to technologies.' From p66, 69, 73 of Lau (1996).

Source: econterms

An informal term for a proposition that can be proved in a class of economic model environments.

Source: econterms

A way of generating estimators: set the distribution moments equal to the sample moments, and solve the resulting equations for the parameters of the distribution.

Source: econterms

Abbreviation for Multi-factor productivty.

Source: econterms

stands for 'moment generating function', which see.

Source: econterms

Data analysis software, discussed at http://www.minitab.com.

Source: econterms

In the context of stochastic processes, events A and B (that is, subsets of possible outcomes of the process) "are mixing" if they are asymptotically independent in the following way.

Let L be a lag operator that moves all time subscripts back by one (e.g. replacing t by t-1). Iff A and B are mixing, then taking the limit as h goes to infinity:
lim Pr(A intersected with L^hB) = Pr(A)Pr(B).

The event L^h is the event B, but h periods ago; it's NOT some kind of stochastic ancestor of B.

If two events are independent, they are mixing.
If two events are mixing, they are ergodic.

I *believe* that a stochastic process is mixing iff all pairs of possible values it can take, taken as events, are mixing.

Source: econterms

maximum likelihood estimator

Source: econterms

Abbreviation for monotone likelihood ratio property of a statistical distribution.

Source: econterms

Generally means theoretical or structural models. Can also mean econometric models which in this glossary are listed separately. models

Source: econterms

Quoting from Landes: "Modernization comprises such developments as urbanization (the concentration of the population in cities that serve as nodes of industrial production, administration, and intellectual and artistic activity); a sharp reduction in both death rates and birth rates from traditional levels (the so-called demographic transition); the establishment of an effective, fairly centralized bureaucratic government; the creation of an educational system capable of training and socializing the children of the society to a level compatible with their capacities and best contemporary knowledge; and, of course, the acquisition of the ability and means to use an up-to-date technology."

Source: econterms

that the total value of the bonds and equities issued by a firm in a model is independent of the number of bonds outstanding or their interest rate.

The theorem was shown by Modigliani and Miller, 1958 in a particular context with no fixed costs, transactions costs, asymmetric information, and so forth. Analogous theorems are shown in various contexts. The assumptions made by such theorems offer a way of organizing what it would be that makes corporations choose to offer various levels of bonds. The choice of numbers and types of bonds and stocks a corporation offers is the choice of capital structure. Among the factors affecting the capital structure of a firm are taxes, bankruptcy costs, agency costs, signalling, bargaining position in litigation, and differences between firms and investors in access to capital markets.

Source: econterms

Denoted M(t) or M_X(t), and describes a probability distribution. A moment-generating function is defined for any random variable X with a pdf f(x). M(t) is defined to be E[e^tX], which is the integral from minus infinity to infinity of e^tXf(x). A use for these is that the t^th moment of X is M^(t)(0), that is the t^th derivative of M() at zero.

Source: econterms

The view that monetary policy is a prime source of the business cycle, and that the time path of the money stock is a good index of monetary policy. As presented by Milton Friedman and Anna Schwartz, monetarism emphasizes the relation between the level of the money stock and the level of output without a detailed theory of why changes in the money stock are not neutral in the short run. Later versions posed an explicit basis for noneutrality in the form of barriers to information flow about prices.

In policy terms monetarists, notably Friedman, advocated a monetary rule, that is, a steady growth in the money supply to match economic growth, without allowing central banks room for discretion. If the rule is credible, public expectations of inflation be low, and thus inflation itself, if high, would fall almost immediately.

Source: econterms

In extreme form: that only the quantity of money matters by way of aggregate demand policy. Relevant only in an overheated economy (Branson p 391).

Source: econterms

In a modern industrialized monetary economy, the monetary base is made up of (1) the currency held by individuals and firms and (2) bank reserves kept within a bank or on deposit at the central bank.

Source: econterms

"A monetary regime can be thought of as a set of rules governing the objectives and the actions of the monetary authority."

Examples: (1) "A gold standard is one example of a monetary regime -- the monetary authority is obligated to maintain instant convertibility between its liabilities and the gold. Th monetary authority may have considerable room to maneuver in that monetary regime, but it can do nothing that would cause it to violate its commitment."
(2) "The same remarks would apply to a monetary regime obligating the monetary authority to maintain a fixed exchange rate between its own and another currency." (3) "A monetary regime of a very different sort could be based on a Monetarist rule specifying the rate of growth of some monetary aggregate. The basic distinction is between regimes based on a convertibility or redemption principle and those based on a quantity principle."

Source: econterms

See the policy discussion in monetarism.

Source: econterms

A model economy that has a medium of exchange: money

Source: econterms

A good that acts as a medium of exchange in transactions. Classically it is said that money acts as a unit of account, a store of value, and a medium of exchange. Most authors find that the first two are nonessential properties that follow from the third. In fact, other goods are often better than money at being intertemporal stores of value, since most monies degrade in value over time through inflation or the overthrow of governments.

Theory: Ostroy and Starr, 1990, p. 25, define money in certain models "as a commodity of positive price and zero transaction cost that does not directly enter in production or consumption."

History: See this Web site on the History of Money.

Related terms: money

Source: econterms

'the belief that money [that is, a particular currency] represents a constant value'

Source: econterms

A modeling idea. In a basic Arrow-Debreu general equilibrium there is no need for money because exchanges are automatic, through a 'Walrasian auctioneer'. To study monetary phenomena, a class of models was made in which money was a good that brought direct utility to the agent holding it; e.g., a utility function took the form u(x,m) where x is a vector of other commodities, and m is a scalar quantity of real money held by the agent. Using this mechanism money can have a positive price in equilibrium and monetary effects can be seen in such models. Contrast 'cash-in-advance constraint' for an alternative approach.

Source: econterms

If a certain firm is the only one that can produce a certain good, it has a monopoly in the market for that good.

Source: econterms

The degree of power held by the seller to set the price for a good. In U.S. antitrust law monopoly power is not measured by market share. (Salon magazine, 1998/11/11)

Source: econterms

A state in which demand comes from one source. If there is only one customer for a certain good, that customer has a monopsony in the market for that good. Analogous to monopoly, but on the demand side not the supply side. A common theoretical implication is that the price of the good is pushed down near the cost of production. The price is not predicted to go to zero because if it went below where the suppliers are willing to produce, they won't produce. Market power is a continuum from perfectly competitive to monopsony and there's an extensive practice/industry/science of measuring the degree of market power.

Examples: For workers in an isolated company town, created by and dominated by one employer, that employer is a monopsonist for some kinds of employment. For some kinds of U.S. medical care, the government program Medicare is a monopsony.

Source: econterms

A property of a set of pdfs which is assumed in theoretical models to characterize risk and uncertainty because it makes more conclusions feasible and is often plausible.

Example: Let e ('effort') be an input variable into a stochastic production function, and y be the random variable that represent output. Let f(y | e) be the pdf of y for each e. Then the statement that f() has the monotone likelihood ratio property (MLRP) is the same as the statement that:
for e2>e1, f(y|e2)/f(y|e1) is increasing in y.
This says that output is positively related to effort, and something stronger, something like: of two outcomes or ranges of outcomes, the worse one will not become relatively more likely than the better one if effort were to rise. By relatively more likely is meant that the likelihood ratio, above, rises.

The set of pdfs for which the MLRP is assumed above is the set of f()'s indexed by values of e. Each holds that specified relationship to the others. In practice the MLRP assumption tends to rule out multimodal classes of distributions, and this is its main effect. (By multimodal we mean those with multiple-peaked pdfs.)

Normally e is scalar, taking on either discrete or continuous sets of values. An analogous definition, for a multidimensional (vector) e, is feasible. Whether it is used in existing models is not known to this author.

Source: econterms

An operator that preserves inequalities of its arguments. That is, if T is a monotone operator, then: (i) iff x>y, then Tx>Ty, and iff x<y, then Tx<Ty.

Same basic meaning as monotone transformation.

The most common monotone operator is the natural log function. For example in maximum likelihood estimation, one usually maximizes the log of the likelihood function, not the likelihood function itself, because this is more tractable and the log is a monotone operator so it doesn't change the answer.

Source: econterms

A transformation that preserves inequalities of its arguments. That is, if T is a monotone transformation, then: (i) iff x>y, then Tx>Ty, and iff x<y, then Tx<Ty.

Same basic meaning as monotone operator.

Source: econterms

These are data obtained by simulating a statistical model in which all parameters are numerically specified.

One might use Monte Carlo simulations to test how an estimation procedure would behave, for example under conditions when exact analytic descriptions of the performance of the estimation are not algebraically feasible, or when one wants to verify that one's analytic calculation for a confidence interval is correct.

Source: econterms

Same as pseudoinverse.

Source: econterms

Incidence of ill health. It is measured in various ways, often by the probability that a randomly selected individual in a population at some date and location would become seriously ill in some period of time. Contrast to mortality.

Source: econterms

Incidence of death in a population. It is measured in various ways, often by the probability that a randomly selected individual in a population at some date and location would die in some period of time. Contrast to morbidity.

Source: econterms

Same as SMSA.

Source: econterms

mean squared error (which see)

Source: econterms

Same as total factor productivity, a certain type of Solow residual.

MFP = d(ln f)/dt = d(ln Y)/dt - s_Ld(ln L)/dt - s_Kd(ln K)/dt where f is the global production function; Y is output; t is time; s_L is the share of input costs attributable to labor expenses; s_K is the share of input costs attributable to capital expenses; L is a dollar quantity of labor; K is a dollar quantity of capital.

Source: econterms

In the context of discrete choice models, multinomial means there are more than two possible values of the dependent variable, the choice, which is a scalar.

For specific constructions see multinomial logit and multinomial probit.

Source: econterms

Relatively easy to compute but has the problematic IIA property by construction. Multinomial probit with correlation between structural residuals does not suffer from the IIA problem but is computationally expensive. (Ed.: I don't know why the IIA problem gets sucked into this when the actual different between logit and probit is the functional form.) Multinomial logit is available in more software packages than is multinomial probit.

Source: econterms

Multinomial probit with correlation between structural residuals does not suffer from the IIA problem but is computationally expensive. Multinomial logit which solves a similar problem is relatively easy to compute but has the problematic IIA property by construction. (Ed.: I don't know why the IIA problem gets sucked into this when the actual different between logit and probit is the functional form.) Multinomial logit is available in more software packages than is multinomial probit.

Source: econterms

A discrete choice model in which the choice is made from a set with more than one dimension is said to be a multivariate discrete choice model.

Source: econterms

That nominal interest rates would rise less than one-for-one with inflation because in response to inflation the public would hold less in money balances and more in other assets, which would drive interest rates down.

Source: econterms

"The necessary changes having been made; substituting new terms."

Source: econterms

An abbrevation for 'multivariate normal' distribution.

Source: econterms

Used to estimate regression functions based on data {X_i, Y_i}. See the equation in the middle of Hardle's page 25. The equation produces an estimate for Y at any requested value of X (not only the ones in the data), using as input (1) the data set {X_i, Y_i}, and (2) a kernel function (which see) describing the weights to be put on values in the data set near X in estimating Y. The kernel function itself can be parameterized by the choice of its functional form and its 'bandwidth' which scales its width in the X-direction. (!@#$ must add the equation when math avail in html)

Source: econterms

North American Industry Classification System, a set of industry categories standardized between the U.S. and Canada. In the U.S. it is taking over from the SIC code system.

Source: econterms

Non-Accelerating Inflation Rate of Unemployment. That is, a steady state unemployment rate above which inflation would fall and below which inflation would rise. By some estimates the NAIRU is 6% in the U.S. NAIRU is approximately a synonym for the natural rate of unemployment.

Paraphrased from Eisner's article: The essential hypotheses of the theory that there is a stable NAIRU are that (1) an existing rate of inflation self-perpetuates by generating expectations of future inflation; (2) higher unemployment reduces inflation and lower unemployment raises inflation.

Source: econterms

Synonym for weak topology.

Source: econterms

National Association of Securities Dealers automatic quotation market. A mostly-electronic market of stocks in the United States. There is no 'pit' -- market makers in each stock offer buy and sell prices which are different.

Source: econterms

Sets of strategies for players in a noncooperative game such that no single one of them would be better off switching strategies unless others did.

Formally: Using the normal form definitions, let utility functions as functions of payoffs for the n players u₁() ... u_n() and sets of possible actions A=A₁ x ... x A_n, be common knowledge to all the players. Also define a_-i as the vector of actions of the other players besides player i. Then a Nash equilibrium is an array of actions a^* in A such that u_i(a^*) >= u_i(a_-i^* | a_i) for all i and all a_i in A_i.
In a two-player game that can be expressed in a payoff matrix, one can generally find Nash equilibria if there are any by, first, crossing out strictly dominated strategies for each player. After crossing out any strategy, consider again all the strategies for the other player. When done crossing out strategies, consider which of the remaining cells fail to meet the criteria above, and cross them out too. At the end of the process, each player must be indifferent among his remaining choices, GIVEN the action of the others.

In most noncooperatives games of interest, each player has to calculate what the strategies of the others will be before his own Nash equilibrium strategy can become clear. Introspection may also be needed to envision his own payoffs. This approach tends to presume that the payoffs are known, or knowable, and that the players are rational. An alternative line of thought with its own detailed theory, is that the players can arrive at Nash equilibria by repeated experimentation, searching for an optimal strategy. Theories of learning and evolutionary game theory are related.

A Nash equilibrium represents a prediction if there is a real world analog to the game.

Source: econterms

The maximand of the Nash Bargaining Solution: (s₁-d₁)(s₂-d₂)
where d₁ and d₂ are the threat points, and s₁ and s₂ are the shares of the good to be divided.

Source: econterms

The strategy of a player in a Nash equilibrium.

Source: econterms

A measure of macroeconomic categories of production and purchase in a nation. The production categories are usually defined to be output in currency units by various industry categories, plus imports. (Output is usually approximately the same as industry revenue.) The purchase categories are usually government, investment, consumption, and exports, or subsets of these. The amount produced is supposed to be approximately equal to the amount purchased. Measures are in practice made by national governments.

a different definition, by Peter Wardley:

national accounts: a measure of all the income received by economic actors within an economy. It can be measured as expenditure (on investment and consumption), income (wages, salaries, profits and rent) or as the value of output (expenditure of all goods and services). Inevitably these three different methods of estimating national accounts will produce different results but these discrepancies are usually relatively small.

Source: econterms

If economists could experiment they could test some theories more quickly and thoroughly than is now possible. Sometimes an isolated change occurs in one aspect of the economic environment and economists can study the effects of that change as if it were an experiment; that is, by assuming that every other exogenous input was held constant.
An interesting example is that of the U.S. ban on the television and radio broadcast of cigarette advertising which took effect on Jan 2, 1971. The ban seems to have had substantial effects on industry profitability, the rate of new entrants, the rate of consumers switching brands and types of cigarettes, and so forth. The ban can be used as a natural experiment to test theories of the effects of advertising.

Source: econterms

population increase due to more births and less mortality

Source: econterms

"The natural rate of unemployment is the level which would be ground out by the Walrasian system of general equilibrium equations, provided that there is [e]mbedded in them the actual structural characteristics of the labor and commodity markets, including market imperfections, stochastic variability in demands and supplies, the cost of gathering information about job vacancies and labor availiabilities, the costs of mobility, and so on." -- Milton Friedman, "The Role of Monetary Policy" AER March 1968 1-21 This is a long-run rate. Transitory shocks could move unemployment away from the natural rate. Real wages would increase with productivity as long as unemployment were kept at the natural rate.

Source: econterms

The U.S. National Bureau of Economic Research. At 1050 Massachusetts Avenue, Cambridge, MA 02138, USA. Focuses on macroeconomics. Data source by ftp: ftp nber.harvard.edu. NBER web site

Source: econterms

Nash Bargaining Solution

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Nash Equilibrium

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National Educational Longitudinal Survey, a U.S. survey administered to 24,599 eighth grade students from 1052 schools in 1988, with follow-up surveys to the same students every two years afterward. Many similar questions were asked of the parents of the students as well to obtain more accurate information.

Source: econterms

A macro model in which the long-run growth rate of output per worker is determined by an exogenous rate of technological progress, like those following from Ramsey (1928), Solow (1956), Swan (1956), Cass (1965), and Koopmans (1965).

Source: econterms

Often means Walrasian general equilibrium model.

Describes a model in which firms maximize profits and markets are perfectly competive.

Source: econterms

According to Lucas (1998), neoclassical theory has explicit reference to preferences. Contrast classical.

Source: econterms