Glossary of research economics

/* 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;

Contexts: econometrics; time series

autocovariance: 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 g below, and E[] means expectation, or mean:
g_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 E(y_t-j).

Contexts: econometrics; time series

autocovariance matrix: 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).

Contexts: econometrics; time series

autoregressive process: See AR.

Contexts: econometrics; statistics; time series

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

Contexts: econometrics

average treatment effect: In a treatment model where some observations receive the treatment (for example, a training program) and some do not, the average treatment effect is the difference between the conditional expectation of the dependent variable with the treatment effect and the conditional expectation of the dependent variable without the treatment effect. This is the average benefit from the treatment.

Often this term is abbreviated ATE.

Source: source: John Pencavel, lecture notes for Econ 247, Stanford University, circa 2000-2005.
Contexts: estimation; labor

b: 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.

Contexts: statistics

B1: 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.

Contexts: math; measure theory; real analysis

balance of payments: 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: 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: Cooley, 1995, p 16
Contexts: macro; modelling

Banach space: Any complete normed vector space is a Banach space.

Contexts: real analysis

bandwidth: 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: Hardle, 1990, especially p 148
Contexts: econometrics; statistics

bank note: 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.

Contexts: money; history

barter economy: 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: McCallum, 1983
Contexts: money; models

base point pricing: 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.

Contexts: IO

basin of attraction: 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: James Montgomery, social networks paper
Contexts: macro; models

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

Contexts: finance; business

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

Contexts: macro; price indexes

Bayesian analysis: "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: Hsiao, The New Palgrave: Econometrics, p 98
Contexts: econometrics; statistics

Bellman equation: 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.

Contexts: dynamic optimization; macro; models

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

Contexts: game theory; IO

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

Contexts: IO

Bertrand game: 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.

Contexts: game theory; IO

Beveridge curve: The graph of the inverse relation of unemployment to job vacancies.

Contexts: labor; macro

BHHH: 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: Gauss Applications: Maximum Likelihood; Berndt, Hall, Hall, and Hausman (1974)
With thanks to: 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

Contexts: numerical methods; estimation

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

Contexts: data; labor

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

Contexts: econometrics; estimation

bidding function: 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).

Contexts: micro theory; IO

bill of exchange: 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: Glasner, p. 23
Contexts: history; money

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

Source: Thomas J Sargent and Francois R Velde, 1997, "The Evolution of Small Change", unpublished paper, p. 6

bimetallism: 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: Velde, Francois R., and Warren E. Weber. 1998. "A Model of Bimetallism." Working paper, Federal Reserve Bank of Chicago, Federal Reserve Bank of Minneapolis, and University of Minnesota. page 2.
Contexts: money

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

Contexts: journals

Black-Scholes equation: 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.

Click here for a simplified derivation which assumes risk-neutrality.

Contexts: finance; business

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

Contexts: data

Bonferroni criterion: 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: British Medical Journal, statistics notes by Bland and Altman.
Contexts: statistics; epidemiology

bootstrapping: 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: Greene, 1993, p 658-9
Contexts: econometrics; estimation; statistics

Borel set: Any element of a Borel sigma-algebra.

Contexts: math; measure theory; real analysis

Borel sigma-algebra: 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.

Contexts: math; measure theory; real analysis

bounded rationality: 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: Rubinstein, Ariel. 1998. Modeling Bounded Rationality.
Contexts: game theory; micro theory

Box-Cox transformation: 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: Box and Cox, 1964; Stata 7 manual entry for boxcox; Davidson and Mackinnon, 1993, pp 481-488.
Contexts: econometrics; statistics

Box-Jenkins: 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: Enders, 1996, p 23
Contexts: time series; econometrics

Box-Pierce statistic: 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;

Contexts: finance, time series

BPEA: An abbreviation for the Brookings Papers on Economic Activity.

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

Source: Gauss Applications: Maximum Likelihood
; Brent, 1972
Contexts: numerical methods; estimation

Bretton Woods system: 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 meetings occurred at Bretton Wood, New Hampshire, in the U.S., in July 1944. The International Bank for Reconstruction and Development, now called the World Bank, was planned at the meetings. So was the International Monetary Fund or IMF.
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: Glasner, p 157-160;
The International Forum on Globalization. Alternatives to Economic Globalization. 2002. p.18
Contexts: money; history

Breusch-Pagan statistic: 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: Breusch, T. and A. Pagan. 1980. "The LM test and its applications to model specification in econometrics." Review of Economic Studies. 47: 239-254.

StataCorp. 1999. Stata statistical software release 6.0 manual, vol 4., page 14.

Contexts: estimation; econometrics

bubble: 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: Bollerslev and Hodrick (1992), p 15;

For more discussion of the definition and a history of examples, see:
Garber, Peter M. 2000. Famous First Bubbles. MIT Press.
especially its introduction. And academic articles by Garber too.
Contexts: finance

budget: 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.

budget line: 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.

Contexts: micro theory; phrases

budget set: 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}

Contexts: general equilibrium; models

bureaucracy: 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.

Burr distribution: 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: Maddala, 1983/96, p 10-11; Burr, 1942
Contexts: econometrics

business:
Relevant terms: basis point, Black-Scholes equation, call option, conglomerate, coupon strip, EBITDA, ex dividend date, NASDAQ, NYSE, option, principal strip, pro forma, put option, reinsurance.

Contexts: fields

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

Source: Cooley, 1995, p 28
Contexts: macro

BVAR: Bayesian VAR (Vector Autoregression)

Contexts: time series; econometrics; estimation

CAGR: Cumulative Average Growth Rate

calculus of voting: 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: Downs, 1957; Riker and Ordeshook, 1968
Contexts: political science

calibration: 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.

Contexts: econometrics; estimation

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

Contexts: finance; business

capital: 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.

Contexts: macro; IO

capital consumption: 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: Oulton, Nicholas. 2002. "Productivity versus welfare: or GDP versus Weitzman's NDP." Bank of England. On the web.
Contexts: macro; measurement; government

capital deepening: 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 has been measured by a rising ratio of some kind of capital in production, or services provided by capital to production, to total output. Capital may include land, structures, equipment, or the relevant capital may be a more narrowly defined input (e.g. a computer equipment).

Source: Oulton, Nicholas. 2002. "Productivity versus welfare: or GDP versus Weitzman's NDP." Bank of England. page 31. On the Web.

Margo, Atack, and others on US national growth 1850-1880. ~2003 NBER paper.
Contexts: macro

capital intensity: Amount of capital per unit of labor input.

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

Contexts: money; banking

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

Contexts: finance

capital-augmenting: 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: Romer, 1996, p 7
Contexts: macro

capitation: 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: Weisbrod's class circa 5/21/97
Contexts: public

CAPM: Capital Asset Pricing Model

Contexts: finance; models

CAR: 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.

Contexts: finance

CARA utility: 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: Blanchard and Fischer, p. 44
Contexts: models

CARs: cumulative average adjusted returns

Contexts: finance

cash-in-advance constraint: 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: Ostroy and Starr, 1990, pp 6-7
Contexts: money; models

catch-up: "'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: 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.
Contexts: international; macro

Cauchy distribution: 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: Maddala, p. 9 
Contexts: econometrics; statistics 
 

Cauchy sequence:<a name=

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<br><br>
Source: Maddala, p. 9<br>
Contexts: econometrics; statistics<br>
<br>

<strong>Cauchy sequence:</strong><a name=

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

><br>

<br><br>
Source: Takeshi Amemiya,

The New Palgrave: Econometrics, and Davidson and MacKinnon, 1993, p 515
Contexts: econometrics; statistics

logit model: 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: Takeshi Amemiya, "Discrete Choice Models," The New Palgrave: Econometrics
Contexts: econometrics; estimation

lognormal distribution: 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.

If random variable X is distributed N(m, v), then the random variable Y=e^X has a lognormal distribution with mean e^m+.5v and variance e^2m+v(e^v-1). A proof is shown by John Norstad; see sources for that.

Source: A series of proofs relevant to this distribution is at Norstad's finance proofs.
Contexts: statistics; econometrics

longitudinal data: a synonym for panel data

Contexts: data

Lorenz curve: 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: Greer, 1992, p. 173
Contexts: IO

loss function: 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.

Contexts: econometrics; models; estimation

lower hemicontinuous: No appearing points

Contexts: real analysis; models

LRD: 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.

Contexts: data sets

Lucas critique: 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: Sargent, 1979, Ch 14, p. 398; Cochrane, Econ 330 notes
Contexts: macro; public finance

m-estimators: 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.

Source: Newey-McFadden, Handbook of Econometrics, Ch 36, p 2115; Wooldridge, 1995, p 2649
Contexts: econometrics; estimation

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

Contexts: money; macro; data

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

Contexts: money

MA: 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).

Contexts: econometrics; statistics; time series

MA(1): A first-order moving average process. See MA for details.

Contexts: econometrics

macro:
Relevant terms: accelerator principle, active measures, asset-pricing function, attractor, balance of payments, balanced growth, basin of attraction, basket, Bellman equation, Beveridge curve, business cycle frequency, capital, capital consumption, capital deepening, capital-augmenting, catch-up, CCAPM, central bank, certainty equivalence principle, CES production function, CES utility, contraction mapping, contractionary fiscal policy, contractionary monetary policy, cost-of-living index, CPI, current account balance, decision rule, demand deposits, depreciation, disintermediation, Divisia index, Domar aggregation, dynamic inconsistency, dynamic multipliers, dynamic optimizations, dynamic programming, economic growth, effective labor, efficiency units, elasticity, embodied, endogenous growth model, Engel effects, equity premium puzzle, ergodic set, Euler equation, Eurosclerosis, expectation, FDI, fiat money, fiscalist view, Fisher effect, Fisher equation, Fisher hypothesis, Fisher Ideal Index, flexible-accelerator model, free entry condition, frictional unemployment, functional equation, GDP, GDP deflator, generator function, GGH preferences, GMM, GNP, Golden Rule capital rate, Harrod-neutral, Hicks-neutral, Hicks-neutral technical change, Hodrick-Prescott filter, hyperbolic discounting, hysteresis, IMF, impulse response function, Inada conditions, inflation, investment, k percent rule, Kalman filter, Kalman gain, Keynes effect, Kuznets curve, labor productivity, labor-augmenting, lag operator, Laspeyres index, Law of iterated expectations, least squares learning, liquidity constraint, liquidity trap, Lucas critique, M1, markup, metaproduction function, monetarism, monetarist view, monetary base, monetary rule, multi-factor productivity, NAIRU, natural rate of unemployment, neoclassical growth model, neutrality, New Classical view, new growth theory, NNP, nondivisibility of labor, numeraire, passive measures (to combat unemployment), Phillips curve, physical depreciation, Pigou effect, price index, pricing kernel, productivity, productivity paradox, property income, putty-putty, Q ratio, quasi-hyperbolic discounting, Ramsey equilibrium, Ramsey outcome, rational expectations, RBC, real business cycle theory, recession, reservation wage property, Ricardian proposition, risk free rate puzzle, RMPY, saddle point, Schumpeterian growth, sink, Smithian growth, Solovian growth, Solow growth model, Solow residual, source, stabilization policy, stable steady state, state price vector, state-space approach to linearization, stochastic difference equation, Stolper-Samuelson theorem, structural unemployment, substitution bias, superneutrality, technical change, technology shocks, tertiary sector, TFP, time consistency, time deposits, Tobin's marginal q, total factor productivity, trajectory, transient, transversality condition, unemployment, value function, VARs, vintage model, Walrasian model, welfare capitalism, Wold's theorem.

Contexts: fields

main effect: 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: Phrasing example drawn from
Hamermesh, Daniel S. "The Art of Labormetrics." NBER Working paper 6927. February 1999. http://www.nber.org/papers/w6927
Contexts: statistics; econometrics

maintained hypothesis: An ambiguous term. Probably it is wise to avoid it.

Most common meaning: synonym for alternative hypothesis. "The model in which the restrictions do not hold is usually called the alternative hypothesis, or sometimes the maintained hypothesis, and may be denoted H₁." (Davidson and MacKinnon, 1993, p. 78). However Greene, 1993/7, third edition, defines it to mean precisely the opposite. From p. 155: "The formal procedure involves a statement of the hypothesis, usually in terms of a 'null' or maintained hypothesis and an 'alternative,' conventionally denoted H₀ and H₁, respectively."

Source: Davidson and MacKinnon, 1993, p 78-79.

Greene, 1993, 3rd edition, p 155.
Contexts: econometrics; estimation

Malmquist index: 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.

Source: Hulten, 2000, pp 26-27.
Contexts: index numbers

MANOVA: This is a generalization of the ANOVA statistical model. It allows multiple dependent variables. Output is reported as one or more multivariate test statistics which are asymptotically equivalent but differ in their small sample properties. These tests include Wilks's lambda, Pillai's trace, Lawley-Hotelling trace, and Roy's largest root. If the test statistics are significantly different from zero, the hypothesis that there is no difference between the multidimensional mean vectors of the categories is rejected.

Source: Stata manuals
Contexts: statistics; sociology

mantissa: Fractional part of a real number.

MAR: a rare abbreviation, for moving-average representation

Contexts: econometrics

March CPS: 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.

Source: Blanchflower and Oswald, Ch 4, p. 171
Contexts: data

marginal significance level: a synonym for 'P value'

Source: Davidson and MacKinnon, 1993, p 78-79
Contexts: econometrics; estimation

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

Contexts: models

market capitalization: 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.

Contexts: finance

market failure: 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: Layard and Glaister, 1972, p 15
Contexts: general equilibrium; public

market for corporate control: 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.

Source: Jensen and Ruback, 1983
Contexts: corporate finance

market power: Power held by a firm over price, and the power to subdue competitors.

Contexts: IO

market power theory of advertising: 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.

Contexts: IO

market price of risk: Synonym for Sharpe ratio.

Contexts: finance

Markov chain: 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: Hoel, Port, and Stone, 1987, pg v and pg 1
Contexts: time series

Markov perfect: 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: Fudenberg and Tirole, 1991/1993, p 501-2; originally defined in Maskin, E., and J. Tirole (1988), "A Theory of Dynamic Oligopoly: I & II," Econometrica 56:3, 549-600.
Contexts: game theory

Markov process: 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.

Contexts: models; statistics

Markov property: 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: Hoel, Port, and Stone, 1987, pg v and pg 1
Contexts: time series

Markov strategy: 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: Tirole, 1988/1993, p 343; Fudenberg and Tirole, 1991/1993, p 502
Contexts: game theory; IO

Markov transition matrix: 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)

Contexts: models

Markov's inequality: 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: goldberger, hogg and craig
Contexts: statistics

markup: In macro, the ratio of price to marginal cost. Can be used as a measure of market power across firms, industries, or economies.

Contexts: macro; models

Marshallian demand function: 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: Varian, 1992
Contexts: production theory; micro

martingale: Same as martingale difference sequence.

Contexts: statistics; econometrics

martingale difference sequence: ** 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.

Contexts: statistics; econometrics

mass production: "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: Hounshell, David. 1984. From the American System to Mass Production, 1800-1932. Johns Hopkins University Press. p. 305.
Contexts: history

Matching Pennies: 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.

		Player Two
		C	D
Player One	C	1,-1	-1,1
Player One	D	-1,1	1,-1

><br>

<br><br>
Contexts: statistics; econometrics<br>
<br>

<strong>normal form:</strong><a name=

A way of writing out a game. Synonymous with strategic form.
Formally:
let n be the number of players,
let A_i be the set of possible actions (or strategies) of player i,
and let u_i:A₁ x A₂ x ... x A_n -> R represents the payoff function (or utility function) for player i. That is once all players have chosen that set of actions, the payoff for player i is the value of that function.
Then the normal form of the game is characterized by G = (A₁, A₂, ... A_n, u₁, ... , u_n)

Contexts: game theory

normality: When used to describe a random variable, means that it has a normal distribution.

notation: Unusual notation, hard to put in glossary for definition, is listed here:

2^A has a particular meaning. For a finite set A, the expression 2^A means "the set of all subsets of A.". If as is standard we denote the number of elements in set A by |A|, the number of elements in 2^A is 2^|A|.

Contexts: set theory; mathematics; probability

NPV: Net Present Value. Same as PDV (present discounted value).

Contexts: finance

NSF: The U.S. National Science Foundation, which funds much economic research.

Contexts: organizations

null hypothesis: The set of restrictions on parameters that is formally being tested. "The hypothesis that the restriction or set of restrictions to be tested does in fact hold." (Davidson and MacKinnon, 1993, p. 78) It is standard to use the notation H₀ for the null hypothesis. The alternative hypothesis, that the restrictions do not hold is denoted H₁.

Often H₁ is the conjecture of interest to the investigator. (Hogg and Craig, p. 281) The problem gets framed this way so that the data and statistical methods can potentially reject H₀. The term is from formal statistical language describing the test to which the restrictions are being subjected. The real hypothesis of interest to the investigator may not be either H₀ nor H₁. Even if it is H₁, the statistical rejection of H₀ may not be strong and specific evidence.

Source: Davidson and MacKinnon, 1993, p 78-79
Contexts: econometrics; estimation

numeraire: The money unit of measure within an abstract macroeconomic model in which there is no actual money or currency. A standard use is to define one unit of some kind of goods output as the money unit of measure for wages.

Source: An example is in Arrow, Chenery, Minhas, and Solow, 1961
Contexts: macro; models

NYSE: New York Stock Exchange, the largest physical exchange in the U.S. Is in New York City.

Contexts: finance; business

obsolescence: An object's attribute of losing value because the outside world has changed. This is a source of price depreciation.

ocular regression: A term, generally intended to be amusing, for the practice of looking at the data to estimate by eye how data variables are related. Contrast formal statistical regressions like OLS.

Contexts: phrases; econometrics

ODE: Abbreviation for "ordinary differential equation".

Contexts: math

OECD: Organization of Economic Cooperation and Development; includes about 25 industrialized democracies.

OES: The Occupational Employment Statistics survey of the United States, conducted by its Bureau of Labor Statistics. It surveys approximately 400,000 establishments each year, excluding those in agriculture, forestry, fishing, and the national government.

Source: Jeffrey A. Groen working paper, 2003.
BLS web site.
Contexts: U.S.; data

offer curve: Consider an agent in a general equilibrium (e.g., an Edgeworth box). Assume that agent has a fixed known budget and known preferences which predict what set (or possible sets) of quantities that agent will demand at various relative prices. The offer curve is the union of those sets, for all relative prices, and can be drawn in an Edgeworth box.

Source: Varian, 1992, p 316
Contexts: micro theory; general equilibrium; models

OLG: Abbreviation for overlapping generations model, in which agents live a finite length of time long enough to live one period at least with the next generations of agents.

Contexts: models

oligopsony: The situation in which a few, possibly collusive, buyers are the only ones who buy a certain good.
Has the same relation to monopsony that oligopoly has to monopoly.

Contexts: IO; labor

OLS: Ordinary Least Squares, the standard linear regression procedure. One estimates a parameter from data and applying the linear model
y = Xb + e
where y is the dependent variable or vector, X is a matrix of independent variables, b is a vector of parameters to be estimated, and e is a vector of errors with mean zero that make the equations equal.
The estimator of b is: (X'X)^-1X'y
A common derivation of this estimator from the model equation (1) is:
y = Xb + e
Multiply through by X'. X'y = X'Xb + X'e
Now take expectations. Since the e's are assumed to be uncorrelated to the X's the last term is zero, so that term drops. So now:
E[X'Xb] = E[X'y] Now multiply through by (X'X)^-1 E[(X'X)^-1X'Xb] = E[(X'X)^-1X'y] E[b] = E[(X'X)^-1X'y] Since the X's and y's are data the estimate of b can be calculated.

Contexts: econometrics

omitted variable bias: There is a standard expression for the bias that appears in an estimate of a parameter if the regression run does not have the appropriate form and data for other parameters.

Define: y as a vector of N dependent variable observations, X₁ as an (N by K₁) matrix of regressors, X₂ as an (N by K₂ matrix of additional regressors), and e as an (N by 1) vector of disturbance terms with sample mean zero.
Suppose the true regression is:
y = X₁b₁ + X₂b₂ + e
for fixed values of b₁ and b₂. (If "true regression" seems ambiguous, imagine for the rest of the description that the values of X₁, X₂, b₁, and b₂ were chosen in advance by the econometrician and e will be chosen by a random number generator with expectation zero, and y is determined by these choices; in this framework we can be certain what the true regression is and can study the behavior of possible estimators.)

Suppose given the data above one ran the OLS regression

y = X₁c₁ +errors

Would E[c₁]=b₁ despite the absence of X₂b₂? It will turn out in the following derivation that in most cases the answer is no and the difference between the two values is called the omitted variable bias.

The OLS estimator for c₁ will be:

c₁^OLS = (X₁'X₁)^-1X₁'y
= (X₁'X₁)^-1X₁'(X₁b₁ + X₂b₂ + e)
= (X₁'X₁)^-1X₁'X₁b₁ + (X₁'X₁)^-1X₁'X₂b₂ + (X₁'X₁)^-1X₁'e
= b₁ + (X₁'X₁)^-1X₁'X₂b₂ + (X₁'X₁)^-1X₁'e

So since E[X₁'e] = 0, taking expectations of both sides gives:

E[c₁] = b₁ + (X₁'X₁)^-1X₁'X₂b₂

In general c₁^OLS will be a biased estimator of b₁. The omitted variables bias is (X₁'X₁)^-1X₁'X₂b₂. An exception occurs if X₁'X₂=0. Then the estimator is unbiased.

There is more to be learned from the omitted variables bias expression. Leaving off the final b₂, the expression (X₁'X₁)^-1X₁'X₂b₂ is the OLS estimator from a regression of X₂ on X₁.

Source: Greene, 1993, p 245-246
Contexts: econometrics

Op(1): statistical abbreviation for "converges in distribution" or, equivalently, "the average is bounded in probability."
That is X_t/n is bounded in probability.

Contexts: statistics; econometrics

open: An economy is said to be open if it has trade with other economies. (Implicitly these are usually assumed to be countries.)
One measure of a country's openness is the fraction of its GDP devoted to imports and exports.

option: A contract that gives the holder the right, but not the duty, to make a specified transaction for a specified time.

The most common option contracts give the holder the right buy a specific number of shares of the underlying security (equity or index) at a fixed price (called the exercise price or strike price) for a given period of time. Other option contracts allow the holder to sell.

This is its most common practical business meaning, and the use in theoretical economics is analogous -- e.g. that owning a plant gives a firm the option to manufacture in it at any time or to sell it at any time.

Contexts: finance; business

order condition: In a econometric system of simultaneous equations, each equation may satisfy the order condition, or not do so. If it does not, its parameters are not all identified.

The order condition is often easy to verify. Often the econometrician verifies that the order condition is satisfied and assumes with this justification that the equation is identified, although formally a stronger requirement, the rank condition, must be satisfied. For each equation there must be enough instrumental variables available for the equation to have as many instruments as there are parameters.

The system can satisfy a form of the order condition: that there be as many exogenous variables in the reduced form of the system as there are parameters.

Contexts: econometrics

order of a kernel: The order of a kernel function is defined as the first nonzero moment.

Source: Hardle and Linton paper, June 1993, "Applied Nonparametric Methods"
Contexts: econometrics; nonparametrics

order of a sequence: Two relevant concepts are denoted O() and o().

Let c_n be a random sequence. Quoting from Greene, p 110: "c_n is of order 1/n, denoted O(1/n), if plim nc_n is a nonzero constant."
And
"c_n is of order less than 1/n, denoted o(1/n), if plim nc_n equals 0."

Source: Greene, 1993, p 110
Contexts: econometrics

order statistic: The first order statistic of a random sample is the smallest element of the sample. The second order statistic is the second smallest. And the n^th order statistic in a sample of size n is the largest element. The pdf of the order statistics can be derived from the pdf from which the random sample was drawn.

Source: Hogg and Craig, 1995, pp. 193-200.
Contexts: statistics

organizational capital: "whatever makes a collection of people and assets more productive together than apart. Firm-specific human capital (Becker 1962), management capital (Prescott and Visscher 1980), physical capital (Ramey and Schapiro 1996), and a cooperative disposition in the firm's workforce (Eeckhout 2000 and Rb and Zemsky 1997) are examples of organizational capital." -- from Boyan Jovanovic and Peter L. Rousseau, Sept 20 2000, "Technology and the Stock Market: 1885-1998" NYU and Vanderbilt University, working paper

Source: Boyan Jovanovic and Peter L. Rousseau, Sept 20 2000, "Technology and the Stock Market: 1885-1998" NYU and Vanderbilt University, working paper
Contexts: organizations

organizational routines: Almost all of this is condensed from the literature review in Becker (2004). Organizational routines are recurrent sequences of behavior, or related cognitive patterns such as rules and recipes, in organizations. These are context-specific ways of coordinating multiple actors. Generally they achieve, or enable, a systematic response to events or input by the organization. Routines therefore store operational or tacit knowledge.

Organizational routines tend:
- to have path-dependent, local histories
- to satisfice, that is, reach a kind of level of aspriation, and not to be tested for optimality
- to be triggered, perhaps by performance below that level of aspiration, which may be implicit
- to exert control in the context of uncertainty, and by being standardized across events, to enable measurement of processes within the organization
- to reduce surprises, error handling, and emergency handling of inputs
- to create or tolerate some internal delays by definition
- to economize on cognitive resources like the information processing and decision capacity of agents within the organization, by defining structures of response
- to guide inexperienced members of the organization
- to provide stability and predictability, but also to evolve with time Organizational routines may serve as heuristics or guidelines, not rules.

Becker (2004) treats Nelson and Winter (1982), as a central source work in this area, and cites a variety of empirical and theoretical academic literature on organizational routines.

Organizational routines are so common it's not clear whether one example clarifies the subject but I inferred that this was a good example. Suppose an organization maintains software, and converts complaints and bug reports about this software into records in a database (classically, a "bugbase") which will be addressed in a substantively appropriate way by specialists. This mode of behavior is an organizational routine that satisfies the above description. The substance and addressee of each bug report record will vary; the substance includes the uncertain input from outside, plus various tacit information like the appropriate addressee.

Source: Becker, Markus C. "Organizational routines: a review of the literature." Industrial and Corporate Change. Vol 13, no. 4 (August 2004), pp. 643-677.

Nelson, R.R., and S.G. Winter. 1982. An Evolutionary Theory of Economic Change. Belknap Press/Harvard University Press: Cambridge, MA.
Contexts: management; sociology; organizations

organizations:
Relevant terms: absorptive capacity, ACIR, AMEX, competency trap, EMS, EOE, FIPS, institution, NBER, NSF, organizational capital, organizational routines, SOFFEX, TRIPs, WIPO, World Bank.

Contexts: fields

output elasticity: "The output elasticity of an input is roughly the percentage increase in output for a 1 percent [increase] in that input, holding other factors constant. If [an] input has a 'normal' rate of return, then [its] output elasticity should equal its share of total inputs." -- Hitt and Brynjolfsson (2002), p. 85.

The output elasticity idea presumes that somebody is monitoring a production function and adjusting production to maximize something, perhaps output, revenue, or profit. It also presumes the input and output are continuous so that small changes in inputs and outputs are well-defined (e.g., we are not talking about a slight increase over one hand-crafted violin per year; the abstraction of output elasticity of inputs applies poorly in a case like that). For more on elasticity and concepts analogous to output elasticity, see elasticity.

Source: Hitt, Lorin M., and Erik Brynjolfsson. 2002. "Information Technology, Organizational Transformation, and Business Performance." Chapter 2 of Productivity, Inequality, and the Digital Economy, edited by Nathalie Greenan, Yannick L'Horty, and Jacques Mairesse. The MIT Press.
Contexts: micro; estimation; industrial organization

outside money: monetary base. Is held in net positive amounts in an economy. Is not a liability of anyone's. E.g., gold or cash. Contrast inside money.

Contexts: money; models

overshooting: Describes "a situation where the initial reaction of a variable to a shock is greater than its long-run response."

Source: Romer, 1996, p 7

own: This word is used in a very particular way in the discussion of time series data. In the context of a discussion of a particular time series it refers to previous values of that time series. E.g. 'own temporal dependence' as in Bollerslev-Hodrick 92 p 8 refers to the question of whether values of the time series in question were detectably a function of previous values of that same time series.

Contexts: time series

Ox: An object-oriented matrix language sometimes used for econometrics. Details are at http://hicks.nuff.ox.ac.uk/Users/Doornik/doc/ox/ .

Contexts: econometrics; time series

p value: A p-value is associated with a test statistic. It is "the probability, if the test statistic really were distributed as it would be under the null hypothesis, of observing a test statistic [as extreme as, or more extreme than] the one actually observed."
The smaller the P value, the more strongly the test rejects the hypothesis being tested (the null hypothesis).

A p-value of .05 or less rejects the null hypothesis "at the 5% level" that is, the statistical assumptions used imply that only 5% of the time would the supposed statistical process produce a finding this extreme if the null hypothesis were true.

5% and 10% are common significance levels to which p-values are compared and in academic seminars, a p-value of .05 is treated as strong evidence that the result is a signal, not just noise.

Source: Davidson and MacKinnon, 1993, p 78-79 ; and with relieved thanks to Ed DeMattia and Steven Hetzler for pointing out that this definition was mistaken before fall 2005.
With thanks to: Ed De Mattia;
Contexts: econometrics; estimation

Paasche index: A kind of index number. The official method for US price deflators computes them as a Paasche index. The algorithm is just like the Laspeyres index but the base quantities are chosen from the second, later period.

See also http://www.geocities.com/jeab_cu/paper2/paper2.htm. From Aizcorbe (2004), p.9: If one assumes there is a representative consumer then the Paashe index can be, and has been, interpreted as a lower bound for the representative consumer's cost of living increase. That is, it shows the change in income needed to make the representative consumer indifferent between purchasing current quantities at the base and current time periods.

Source: http://www.geocities.com/jeab_cu/paper2/paper2.htm;

Gordon, 1990, p. 5

Aizcorbe, Ana. "Price Indexes for Intermittent Purchases and an Application to Price Deflators for High Technology Goods" working paper, Bureau of Economic Analysis, U.S. Department of Commerce.
Contexts: index numbers

panel data: Data from a (usually small) number of observations over time on a (usually large) number of cross-sectional units like individuals, households, firms, or governments.

Contexts: econometrics; estimation

par: Can by a synonym for 'face value' as in the expression "valuing a bond at par".

Contexts: finance

paradox: This word is used in a particular way within the literature of economics -- not to describe a situation in which facts are apparently in conflict, but to describe situations in which apparent facts are in conflict with models or theories to which some class of people holds allegiance. This use of the word implies strong belief in the measured facts, and in the theory, and the resolution to economic paradoxes tend to be of the form that the data do not fit the model, the data are mismeasured or, (the most common case) the model or theory does not fit the environment measured.

In some ways the term paradox is awkward in economics since the data are so poorly measured, the models so brutally simplified, and the mapping between environment and evidence so stochastic. So this editor avoids the term where possible, but often it is a compact and vigorous way of telling the reader the context of the subsequent discussion.

A list of these that an economist may be expected to recognize includes: Allais paradox, Ellsberg paradox, Condorcet voting paradox, Scitovsky paradox, and productivity paradox.

Contexts: phrases

parametric: adjective. A function is 'parametric' in a given context if its functional form is known to the economist.
Example 1: One might say that the utility function in a given model is increasing and concave in consumption. But it only becomes parametric once one says that u(c)=ln(c) or u(c)=c^1-A/1-A. At this point only parameters such as A remain to be specified or estimated.
Example 2: In an econometric model one often imposes assumptions such as that the the relationship being estimated is linear, thence to do a linear regression. These are parametric assumptions. One might also make some estimates of the 'regression function' (the relationship) without such parametric assumptions. This field is called nonparametric estimation.

Contexts: econometrics; estimation; models

Pareto chart: The message below was posted to a Stata listserv and is reproduced here without any permission whatsoever.

Date: Thu, 28 Jan 1999 08:59:57 -0500
From: "Steichen, Thomas" 
Subject: RE: statalist: Re: Pareto diagrams

[snip]

Pareto charts are bar charts in which the bars are arranged in descending
order, with the largest to the left. Each bar represents a problem.  The chart
displays the relative contribution of each sub-problem to the total problem.

Why:  This technique is based on the Pareto principle, which states that a
few of the problems often account for most of the effect.  The Pareto
chart makes clear which "vital few" problems should be addressed first.

How:  List all elements of interest.  Measure the elements, using the same
unit of measurement for each element.  Order the elements according to
their measure, not their classification.  Create a cumulative distribution
for the number of items and elements measured and make a bar and line
graph.  Work on the most important elements first.

Reference:  Wadsworth, Stephens and Godfrey. Modern Methods for Quality
Control and Improvement, New York: John Wiley, 1986 and Kaoru Ishikawa,
Guide To Quality Control, Asian Productivity Organization, 1982, Quality
Resources, 1990.

(Note: above info "borrowed" from a web page)

Source: Stata listserv
With thanks to: Statalist and Thomas Steichen , as of 4/15/1999
Contexts: econometrics

Pareto distribution: Has cdf H(x) = 1 - x^(-a) where x>=0, a>0. This distribution is unbounded above. (A slightly different version, with two parameters, is shown in Hogg and Craig on p. 207.)
>

 
Contexts: econometrics; statistics 
 

Pareto optimal:<a name=

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Contexts: econometrics; statistics<br>
<br>

<strong>Pareto optimal:</strong><a name=

In an endowment economy, an allocation of goods to agents is Pareto Optimal if no other allocation of the same goods would be preferred by every agent. Pareto optimal is sometimes abbreviated as PO.

Optimal is the descriptive adjective, whereas optimum is a noun. A Pareto optimal allocation is one that is a Pareto optimum. There may be only one such optimum.

Contexts: models

Pareto set: The set of Pareto-efficient points, usually in a general equilibrium setting.

Source: Varian, 1992, p 324
Contexts: micro theory; general equilibrium; models

partially linear model: Refers to a particular econometric model which is between a linear regression model and a completely nonparametric model:
y=b'X+f(Z)+e
where X and Z are known matrices of independent variables, y is a known vector of the dependent variable, f() is not known but often some assumptions are made about it, and b is a parameter vector. Assumptions are often made on e such as that e~N(0,s²I) and that E(e|X,Z)=0.
The project at hand is to estimate b and/or to estimate f() in a non-parametric way, e.g. with a kernel estimator.

Source: possibly first discussed in Robinson, P., 1988, "Root-n-consistent semiparametric regression", Econometrica vol 56, pp 931-954.
Contexts: econometrics; estimation

partition: "[A] partition of a finite set (capital omega) is a collection of disjoint subsets of (capital omega) whose union is (capital omega)." -- Fudenberg and Tirole p 55

Source: Fudenberg and Tirole, 1991/1993, p 55
Contexts: information theory; econometrics; micro theory

passive measures (to combat unemployment): unemployment and related social benefits and early retirement benefits. (contrast active)

Source: John P. Martin, D16 readings book
Contexts: labor; macro

path dependence: Following David (97): describes allocative stochastic processes. Refers to the way the history of the process relates to the limiting distribution of the process. "Processes that are non-ergodic, and thus unable to shake free of their history, are said to yield path dependent outcomes." (p. 13) "A path-dependent stochastic process is one whose asymptotic distribution evolves as a consequence" of the history of the process. (p. 14) The term is relevant to the outcome of economic processes through history. For example, the QWERTY keyboard standard would not be the standard if it had not been chosen early; thus the keyboard standard evolved through a path-dependent process.

Source: David, 1997, p 13-14
Contexts: history; stochastic processes

path dependency: The view that technological change in a society depends quantitatively and/or qualitatively on its own past. "A variety of mechanisms for the autocorrelation can be proposed. One of them, due to David (1975) is that technological change tends to be 'local,' that is, learning occurs primarily around techniques in use, and thus more advanced economies will learn more about advanced techniques and stay at the cutting edge of progress." (Mokyr, 1990, p 163) A noted example of technological path dependence is the QWERTY keyboard, which would not be in use today except that it happened to be chosen a hundred years ago. A special interest in the research literature was taken in the question of whether technological path dependence has been observed to lead to noticeably Pareto-inferior outcomes later. Liebowitz and Margolis in a series of papers (e.g. in the JEP) have made the case that it has not -- that is that the QWERTY keyboard is not especially inferior to alternatives in productivity, and that the VHS videotapes were not especially inferior to Beta videotapes at the time consumers chose between them.

Source: Mokyr, 1990, p 163
Contexts: stochastic processes; history

payoff matrix: In a game with two players, the payoffs to each player can be shown in a matrix. The one at right is from the classic Prisoners Dilemma game:

		Player Two
		C	D
Player One	C	3,3	0,4
Player One	D	4,0	1,1

Here, player one's strategy choices (shown, conventionally, on the left) are C and D, and player two's, shown on the top, are also C and D. The payoffs of each possible choice of strategy pairs is in each cell of the matrix. The first number is the payoff to player one, and the second is the payoff to player two.

Contexts: game theory; models

PBE: abbreviation for perfect Bayesian equilibrium.

Contexts: game theory

pdf: probability distribution function. This function describes a statistical distribution. It has the value, at each possible outcome, of the probability of receiving that outcome. A pdf is usually denoted in lower case letters. Consider for example some f(x), with x a real number is the probability of receiving a draw of x. A particular form of f(x) will describe the normal distribution, or any other unidimensional distribution.

Contexts: econometrics; statistics

PDV: Present Discounted Value

Contexts: finance

pecuniary externality: An effect of production or transactions on outside parties through prices but not real allocations.

perfect Bayesian equilibrium: A perfect Bayesian equilibrium is a game-theoretic concept. It is very like a Nash equilibrium but in which each player's beliefs are also defined and are integrated into the definition.

A perfect Bayesian equilibrium (PBE) is defined to exist in a game in which payoffs and players are stated and are common knowledge within the game. It can be described by this set of things taken together:

- a profile of strategies and
- a profile of belief functions

To be a PBE they also satisfy these rules:
- the strategies satisfy sequential rationality rule and
- the beliefs are updated over time according to Bayes rule whenever possible.

[Ed.: Normally one also assumes that the players know with certainty that they are in a PBE. Without this assumption it may not be possible to locate any PBE of the game, but with this assumption this equilibrium is less likely to describe the real world.]

-- F&T 1993? pp 321-333

it also describes separating and pooling equilibria as subsets of PBE
There is a thm in Kreps that all seq eqms are also subgame perfect.

Contexts: game theory

perfect equilibrium: In a noncooperative game, a profile of strategies is a perfect equilibrium if it is a limit of epsilon-equilibria as epsilon goes to zero.

There can be more than one perfect equilibrium in a game.

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

Source: Pearce, 1984, p 1037
Contexts: game theory

PERT: Program Evaluation and Review Technique (is this used?)

Source: Hogg and Craig, 163-4

phase portrait: graph of a dynamical system, depicting the system's trajectories (with arrows) and stable steady states (with dots) and unstable steady states (with circles) in a state space. The axes are of state variables.

Contexts: models

Phillips curve: A relation between inflation and unemployment. Follows from William Phillips' 1958 "The relation between unemployment and the rate of change of money wage rates in the United Kingdom, 1861-1957" in _Economica_. In the subsequent discussion the relation was thought to be a negative one -- high unemployment would correlate with low inflation. That stylized fact lost empirical support with the stagflation of the U.S. in the 1970s, in which high inflation and high unemployment occurred together. More recent evidence suggests that over the long term, across countries, there is a POSITIVE correlation between inflation and unemployment. Discussion continues on which of these is more 'causal to' the other and less 'caused by' the other. In recent use, "[T]he 'Phillips curve' has become a generic term for any relationship between the rate of change of a nominal price or wage and the level of a real indicator of the intensity of demand in the economy, such as the unemployment rate." -- Gordon, Robert G., "Foundations of the Goldilocks Economy" for Brookings Panel on Economic Activity, Sept 4, 1998.

Contexts: macro

Phillips-Perron test: A test of a unit root hypothesis on a data series.

(Ed.: what follows is my best, but imperfect, understanding.) The Phillips-Perron 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 a value of -4.49 constituted rejection at the p-value of .10.

Source: cites of Phillips, Peter C.B. and Pierre Perron. "Testing for a Unit Root in Time Series Regression." Biometrika June 1988, 75, pp 335-346.
With thanks to: Don Watson (as of 1999/03/31: drw@matilda.vm.edu.au)
Contexts: econometrics; time series

phrases:
Relevant terms: a fortiori, a priori, abstracting from, analytic, budget line, ceteris paribus, Chicago School, classical, climacteric, control for, corner solution, creative destruction, deterministic, dismal science, endogenous, equity premium puzzle, exogenous, inter alia, interior solution, is consistent for, mutatis mutandis, neoclassical model, neolassical, nests, New Economy, ocular regression, paradox, priori, proof, quango, rational, rational ignorance, rationalize, risk free rate puzzle, significance, solution concept, stylized facts, the standard model, transition economics, under the null, unity.

Contexts: fields

physical depreciation: Decline in ability of assets to produce output. For example, computers, light bulbs, and cars have low physical depreciation; they work until they expire. Could be said to be made up of deterioration and exhaustion.

Contexts: macro; capital measurement

piecewise linear: A set of line segments each of which represents a linear relationship between two variables over some subset of their domains. Usually the relationship referred to is between what the writer is characterizing as an independent variable and a dependent variable.

Contexts: mathematics; theory; estimation

Pigou effect: The wealth effect on consumption as prices fall. A lower price level leads to a greater existing private wealth of nominal value, leading to a rise in consumption. Contrast the Keynes effect.

Source: James Tobin. "Keynesian Models of Recession and Depression"
Contexts: macro; models

plant: a plant is an integrated workplace, usually all in one location.

platykurtic: An adjective describing a distribution with low kurtosis. 'Low' means the fourth central moment is less than three times the second central moment; such a distribution has less kurtosis than a normal distribution.
Platy- means 'fat' in Greek and refers to the central part of the distribution. Platykurtic distributions are not as common as leptokurtic ones.

Source: Davidson and MacKinnon, 1993, p 62-64
Contexts: statistics

PO: Pareto Optimal

Contexts: models

Poisson distribution: A discrete distribution. Possible values for x are the integers 1,2,3,...

Denoting mean as mu, the Poisson distribution has mean mu, variance mu, and pdf (e^-mumu^-x)/x!. Moment-generating function (mgf) is exp(mu(e^t-1)).

Source: Hogg and Craig
Contexts: statistics

Poisson process: In such a process, let n be the number of events that occur in a given time. n will have a Poisson distribution.

Contexts: statistics; models

political science: The academic subject centering on the relations between governments and other governments, and between governments and peoples.

polity: Group with an organized governance. Normally a politically organized population or can be a religious one.

Or, form of governance.

Examples needed. Use is very context-sensitive; that is, the definition is not too informative without examples.

Contexts: political science

polychotomous choice: Multiple choice. In the context of discrete choice econometric models, means that the dependent variable has more than two possible values.

Source: Maddala, 1983, 1996, p 275
Contexts: econometrics

pooling of interests: One of two ways to do the accounting for a U.S. firm after a merger. The alternative is purchase accounting.

A pooling of interests is the method usually taken for all-stock deals.

Contexts: accounting

poor: In poverty, which see.

Source: Blank, ITAN
Contexts: poverty

portmanteau test: a test for serial correlation in a time series, not just of one period back but of many. Standard reference is Ljung and Box (1978). The equation characterizing this test is given on page 18, footnote 15, of Bollerslev-Hodrick 1992 and will go in here when html has an equation format.

Source: Bollerslev-Hodrick 92 circa p 8
Contexts: finance; time series

poverty: As commonly defined by U.S. researchers: the state of living in a family with income below the federally defined poverty line.
Relevant terms: idle, poor, poverty, urban ghetto.

Source: Blank, ITAN
Contexts: data; poverty

power: "The power of a test statistic T is the probability that T will reject the null hypothesis when the hypothesis is not true.

Formally, it is the probability that a draw of T is in the rejection region given that the hypothesis is not true.

Source: Davidson and MacKinnon, 1993, p 78-79
Contexts: econometrics; statistics; estimation

power distribution: A continuous distribution with a parameter that we will denote k. Pdf is kx^k-1. Mean is k/(k+1). Variance is k/[(1+k)²(2+k)].

This distribution has not been found to correspond to natural or economic phenomena, but is useful in practice problems because it is algebraically tractable.

Source: Hogg and Craig
Contexts: statistics

PPF: Short for Production Possibilities Frontier.

PPP: Stands for purchasing power parity, a criterion for an appropriate exchange rate between currencies. It is a rate such that a representative basket of goods in country A costs the same as in country B if the currencies are exchanged at that rate.

Actual exchange rates vary from the PPP levels for various reasons, such as the demand for imports or investments between countries.

Contexts: international

Prais-Winsten transformation: An improvement to the original Cochrane-Orcutt algorithm for estimating time series regressions in the presence of autocorrelated errors. The implicit reference is to Prais-Winsten (1954).

The Prais-Winsten tranformation makes it possible to include the first observation in the estimation.

Source: SHAZAM manual
Contexts: estimation; time series; econometrics

pre-fisc: Means before taking account of the government's fiscal policy. Usually refers to personal incomes before taxes and government transfers between people. For example a researcher might take more interest in pre-fisc income inequality than in post-fisc income inequality because the effects of government transfers are designed specifically to reduce inequality.

Contexts: public

precautionary savings: Savings accumulated by an agent to prepare for future periods in which the agent's income is low.

Contexts: models; finance

precision: reciprocal of the variance

Source: Hamilton, p 355
Contexts: econometrics

predatory pricing: The practice of selling a product at low prices in order to drive competitors out, discipline them, weaken them for possible mergers, and/or to prevent firms from entering the market. It is an expensive strategy.

In the United States there is no legal (statutory) definition of predatory pricing, but pricing below marginal cost (the Areeda-Turner test) has been used by the Supreme Court in 1993 as a criterion for pricing that is predatory. (Salon magazine, 1998/11/11)

Contexts: IO

predetermined variables: Those that are known at the beginning of the current time period. In an econometric model, means exogenous variables and lagged endogenous variables.

Source: Johnston, p 440
Contexts: econometrics

preferences: A property of the agents (individuals) in many economics models. The property is the ability to compare any two bundles of goods and to prefer one over the other. Usually this ability is presumed to be stable over time. The ability is presumed to be behind the observed behavior of individuals who make choices, and we can then make theories about their preferences.

Preferences are often implicitly assumed to exist in a model by declaring that there is a utility function characterizing the preferences of the agents in the model. A continuous utility function exists which perfectly describes the preferences if the preferences are complete, reflexive, transitive, continuous, and strongly monotonic.
[ed: yes, someday I will define those terms too.]

Standard disputes about models in which perfectly defined preferences exist are about whether the agent is perfectly informed about the various bundles; about whether there are risks; and how stable over time the preference relations (responses to comparisons) are.

Contexts: utility theory

present-oriented: A present-oriented agent discounts the future heavily and so has a HIGH discount rate, or equivalently a LOW discount factor. See also 'future-oriented', 'discount rate', and 'discount factor'.

Contexts: models

price ceiling: Law requiring that a price for a certain good be kept below some level. May lead to shortage and a black market.

price complements: Two inputs i and j to a production function can be "price complements in production". Assume the demand for the output is decreasing in its price. Inputs i and j are price complements if when the price of i goes down the profit-maximizing use of both i and j go up.

Contexts: IO; labor

price elasticity: A measure of responsiveness of some other variable to a change in price. See elasticity for the the general equation.

Contexts: micro theory

price floor: Law requiring that a price for a certain good be kept above some level.

price index: A single number summarizing price levels.

A larger number conventionally represents higher prices. A variety of algorithms are possible and a precise specification (which is rare) requires both an algorithm (an example of which is a Laspeyres index) and a set of goods, fixed known quantities of each (the basket),

Contexts: macro; price indexes

price substitutes: Inputs i and j to a production function are "price substitutes in production" if when the price of i goes down the use of j goes up.

Contexts: IO; labor

pricing kernel: same as "stochastic discount factor" in a model of asset prices.

Source: Campbell, Lo, and MacKinlay p 294
Contexts: finance, macro

pricing schedule: A mapping from quantity purchased to total price paid

Contexts: IO

principal components: An approach to finding what mixture of underlying variables produces most of the variation in the dependent variable.

For a more complete discussion see http://www.statsoftinc.com/textbook/stfacan.html

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

Contexts: finance; business

principal-agent: The general name for a class of games faced by a player, called the principal, who by the nature of the environment does not act directly but instead by giving incentives to other players, called agents, who may have different interests.

Contexts: phrasing; game theory

principal-agent problem: A particular game-theoretic description of a situation. There is a player called a principal, and one or more other players called agents with utility functions that are in some sense different from the principal's. The principal can act more effectively through the agents than directly, and must construct incentive schemes to get them to behave at least partly according to the principal's interests. The principal-agent problem is that of designing the incentive scheme. The actions of the agents may not be observable so it is not usually sufficient for the principal just to condition payment on the actions of the agents.

Contexts: game theory

principle of optimality: The basic principle of dynamic programming, which was developed by Richard Bellman: that an optimal path has the property that whatever the initial conditions and control variables (choices) over some initial period, the control (or decision variables) chosen over the remaining period must be optimal for the remaining problem, with the state resulting from the early decisions taken to be the initial condition.

Contexts: models

priori: Not used separately; see phrase a priori.

Contexts: phrases

Prisoner's Dilemma: A classic game with two players. Imagine that the two players are criminals being interviewed separately by police. If either gives information to the police, the other will get a long sentence. Either player can Cooperate (with the other player) or Defect (by giving information to the police). Here is an example payoff matrix for a Prisoner's Dilemma game:

		Player Two
		C	D
Player One	C	3,3	0,4
Player One	D	4,0	1,1

(D,D) is the Nash equilibrium, but (C,C) is the Pareto optimum. That difference has been discussed extensively for various games in the research literature. Analogies to the prisoner's dilemma or some other game can support an argument about why in the real world some Pareto optima are observed not to be achieved.

If this same game is repeated more than once with a high enough discount factor, there exist Nash equilibria in which (C,C) is a possible outcome of the early stages.

Source: Varian, 1992, Ch 15
Contexts: game theory

pro forma: describes a presentation of data, typically financial statements, where the data reflect the world on an 'as if' basis. That is, as if the state of the world were different from that which is in fact the case. For example, a pro forma balance sheet might show the balance sheet as if a debt issue under consideration had already been issued. A pro forma income statement might report the transactions of a group on the basis that a subsidiary acquired partway through the reporting period had been a part of the group for the whole period. This latter approach is often adopted in order to ensure comparability between financial statements of the year of acquisition with those of subsequent years.

Source: Stephen Brown (stephenb@nwu.edu at the time) 7/24/2000, by email
Contexts: accounting; finance; business

probability:
Relevant terms: almost surely, convergence in quadratic mean, countable additivity property, expectation, Fatou's lemma, Jensen's inequality, mixing, notation, strong law of large numbers, support.

Contexts: fields

probability function: synonym for pdf.

Source: Newey-McFadden, Ch 36, Handbook of Econometrics
Contexts: econometrics; statistics

probit model: An econometric model in which the dependent variable y_i can be only one or zero, and the continuous indepdendent variable x_i are estimated in:
Pr(y_i=1)=F(x_i'b)
Here b is a parameter to be estimated, and F is the normal cdf. The logit model is the same but with a different cdf for F.

Source: Takeshi Amemiya, "Discrete Choice Models," The New Palgrave: Econometrics
Contexts: econometrics; estimation

process: see "stochastic process"

Contexts: statistics

product differentiation: This is a product market concept. Chamberlin (1933) defined it thus: "A general class of product is differentiated if any significant basis exists for distinguishing the goods of one seller from those of another."

Source: Chamberlin, E. 1933. The Theory of Monopolistic Competition. Harvard University Press. Cambridge, MA. 8th edition, 1962. as cited in: Brynjolfsson, Erik, Michael D. Smith, Yu (Jeffrey) Hu. "Consumer Surplus in the Digital Economy: Estimating the Value of Increased Product Variety." p.6. On the net as of Jan 7, 2003.
Contexts: IO

production function: Describes a mapping from quantities of inputs to quantities of an output as generated by a production process. Standard example is:

y = f(x₁, x₂)

Where f() is the production function, the x's are inputs, and the y is an output quantity.

Contexts: micro

production possibilities frontier: A standard graph of the maximum amounts of two possible outputs that can be made from a given list of input resources.

A basic outline of how to draw one.

production set: The set of possible input and output combinations. Often put into the notation of netputs, so that this set can be defined by restrictions on a collection of vectors with the dimension of the number of goods, one element for each kind of good, and a positive or negative real quantity in each element.

Contexts: general equilibrium; models

productivity: A measure relating a quantity or quality of output to the inputs required to produce it.

Often means labor productivity, which is can be measured by quantity of output per time spent or numbers employed. Could be measured in, for example, U.S. dollars per hour. For some more detail see this site.

Contexts: macro

productivity paradox: Standard measures of labor productivity in the U.S. suggest that computers, at least until 1995, were not improving productivity. The paradox is the question: why, then, were U.S. employers investing more and more heavily in computers?

Resolving the paradox probably requires an understanding of the gap between what the productivity statistics measure and the goals of the U.S. organizations getting computers. Sichel (1990), pp 33-36 lists these six:

the mismanagement hypothesis is that computers underestimate the costs of new computer technology, such as training, and therefore buy too many for optimum short-run profitability
the redistribution hypothesis is that private rates of return on computers are high enough, but the effect is only to compete over business with other firms in the same industry, which does not overall show greater productivity; the analogy is to an arms race, in which both players invest heavily but the overall effect is not to increase security
the long learning-lags hypothesis is that information technology will generate a substantial productivity effect when society is organized around its availability, but it is too soon for that
the mismeasurement hypothesis is that national economic accounts do not tend to measure the services brought by information technology such as quality, variety, customization, and convenience
the offsetting factors hypothesis is that other factors unrelated to computers have dragged down productivity measures
the small share of computers in the capital stock hypothesis is just that computers are too small a share of plant and equipment to make a difference.

Two other hypotheses on this subject are:

the externalities hypothesis is that computers in organization A improve the long-run productivity of organization B but this is not attributable in the national accounts to the computers in A.
the reorganization hypothesis is that computers in a firm do not raise much the quantity of capital stock but they cause a more productive long run organization of the capital stock within that firm and a more efficient split of tasks between that firm and other organizations.

Technophiles (such as this writer, or venture capitalists, or Silicon Valley publications) and technology historians tend to believe in the long learning-lags hypothesis, the mismeasurement hypothesis, the externalities/network-effects hypothesis, and the reorganization hypothesis. The gap in beliefs and understandings between technophiles and national accounts and pricing experts, such as Sichel and Robert J. Gordon (see e.g. the 1996 paper) is astonishing as of early 1999. They talk past one another. The national accounts experts tend to take the labor/capital models more seriously, and technology history less seriously, than do the technophiles. The Federal Reserve Bank under Greenspan has piloted between these views.

Note, March 2002: The national accounts experts have come now to the view of the technophiles and it is now commonly thought thtat the productivity measure lags the other indicators in the boom.

Source: Sichel, Daniel E. 1997. The computer revolution: an economic perspective. Brookings Institution Press, Washington D.C.
Paul David, May 1990, American Economic Review, p 355.
Contexts: macro; technology

proof: A mathematical derivation from axioms, often in principle in the form of a sequence of equations, each derived by a standard rule from the one above.

Contexts: mathematics; phrases; modelling

propensity score: An estimate of the probability that an observed entitiy like a person would undergo the treatment. This probability is itself a predictor of outcomes sometimes.

Contexts: empirical

proper equilibrium: Any limit of epsilon-proper equilibria as epsilon goes to zero. -- Myerson (1978), p 78

Source: Myerson, 1978, p 78, as cited by Pearce, 1984, p 1037
Contexts: game theory

property income: Nominal revenues minus expenses for variable inputs including labor, purchased materials, and purchased services. Property income can serve as an approximation to the services rendered by capital. It contains the returns to national wealth. It can be thought to include technology and organizational components as well as 'pure' returns to capital.

Source: Harper, 1999, p. 330
Contexts: macro; capital measurement

pseudoinverse: Also called Moore-Penrose inverse. The pseudoinverse of any matrix exists, is unique and satisfies four conditions shown on p 37 of Greene (1993).

Perhaps the most important case is when the matrix X has more rows than columns, and X is of full column rank. Then the pseudoinverse of X is: (X'X)^-1X'. Notice how much this equation looks like the equation for the OLS estimator.

Source: Greene, 1993, p 37
Contexts: econometrics

PSID: Panel Study of Income Dynamics. Data set often used in labor economics studies. Data is from U.S. and is put together at the University of Michigan.
Since 1968 the PSID has followed and interviewed annually a national sample that began with about 5000 families. Low-income families were over-sampled in the original design. Interviews are usually conducted with the 'head' of each family.
Includes a lot of income and employment variables, and continues to track children who grow up and move out. For more information see the PSID's Web site at http://www.isr.mich.edu/src /psid/index.html

Contexts: labor; data

public economics: A subfield that includes public goods and common pool resources, and public finance meaning taxes and public borrowing and spending.

Source: fields

public finance:
Relevant terms: AGI, contingent valuation, embedding effect, existence value, Lerman ratio, Lucas critique, nonuse value, SCF, Survey of Consumer Finances, Tobin tax.

Contexts: fields

purchase accounting: One of two ways to do the accounting for a U.S. firm after a merger. The alternative is the pooling of interests.

Contexts: accounting

put option: A put option is a security which conveys the right to sell a specified quantity of an underlying asset at or before a fixed date.

Contexts: finance; business

put-call parity: A relationship between the price of a put option and a call option on a stock according to a standard model.
Define:
r as the risk-free interest rate, constant over time, in an environment with no liquidity constraints
S as a stock's price
t as the current date
T as the expiration date of a put option and a call option
K as the strike price of the put option and call option
C(S,t) as the price of the call option when the current stock price is S and the current date is t
P(S,t) as the price of the put option when the current stock price is S and the current date is t
Then the relationship is:
P(S,t) = C(S,t) - S + Ke^-r(T-t)
The relationship is derived from the fact that combinations of options can make portfolios that are equivalent to holding the stock through time T, and that they must return exactly the same amount or an arbitrage would be available to traders.

Contexts: finance

putting-out system: "A condition for the putting-out system to exist was for labor to be paid a piece wage, since working at home made the monitoring of time impossible." -- Joel Mokyr, NU working paper: "The rise and fall of the factory system: technology, firms, and households since the industrial revolution" Carnegie-Rochester Conference on macreconomics, Nov 17-19, 2000.

Source: Joel Mokyr, NU working paper: "The rise and fall of the factory system: technology, firms, and households since the industrial revolution" Carnegie-Rochester Conference on macreconomics, Nov 17-19, 2000.

putty-putty: As in Romer, JPE, Oct 1990. This describes an attribute of capital in some models. Putty-putty capital can be transformed into durable goods then back into general, flexible capital. This contrasts with putty-clay capital which if I understand correctly can be converted into durable goods but which cannot then be converted back into re-investable capital. The algebraic modeler chooses one of these to make an argument or arrive at a conclusion within the model. The term is not normally interpreted empirically although empirical analogues to each kind of capital exist.

Source: Romer, 1990
Contexts: macro; models

Q ratio: Or, "Tobin's Q". The ratio of the market value of a firm to the replacement cost of everything in the firm. In Tobin's model this was the driving force behind investment decisions.

Contexts: macro; finance; models

Q-statistic: Of Ljung-Box. A test for higher-order serial correlation in residuals from a regression.

Source: RATS manual, p. 1-15
Contexts: time series; estimation; econometrics

QJE: Quarterly Journal of Economics

Contexts: journals

QLR: quasi-likelihood ratio statistic

Contexts: econometrics; time series

QML: Stands for quasi-maximum likelihood.

Contexts: econometrics; estimation

quango: Stands for quasi-non-governmental organization, such as the U.S. Federal Reserve. The term is British.

Contexts: phrases

quantity theory of money: There are multiple versions and interpretations of quantity theories of money. A central idea is that if there is more money in an economic system, prices will go up. Here, money includes cash and various kinds of credit which serve as intermediaries in purchases.

Date: Sat, 20 Feb 1999 14:13:35 +0000
From: Ronan Conroy 
Subject: Re: statalist: Standardizing Variables

Paul Turner said (19/2/99 9:54 pm)

>I have two variables--X1 and X2--measured on ordinal scales. X1 ranges
>from 0 to 10; X2 ranges from 0 to 12. What I want to do is to standardize
>X1 and X2 to a common metric in order to explore how differences between
>the two affect the dependent variable of interest. Converting values to
>percentages of the maximum values (10 and 12) is the first approach that
>occurs to me, but I don't know if there's something I'm forgetting

This sort of thing is possible, and called ridit scoring.  You replace
each of the original scale points with the percentage (or proportion) of
the sample who scored at or below that value.  This gives the scales a
common interpretation as percentiles of the sample, and means that they
are now expressed on an interval metric, though the data are still grainy.

_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/

    _/_/_/      _/_/     _/_/_/     _/     Ronan M Conroy
   _/    _/   _/   _/  _/          _/      Lecturer in Biostatistics
  _/_/_/    _/          _/_/_/    _/       Royal College of Surgeons
 _/   _/     _/              _/  _/        Dublin 2, Ireland
_/     _/     _/_/     _/_/_/   _/         voice +353 1 402 2431
             rconroy@rcsi.ie               fax   +353 1 402 2329
_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/
I'm not an outlier; I just haven't found my distribution yet

q_d=a₁p+a₂+e_d (Demand equation)
q_s=b₁p+e_s    (Supply equation)
q_d=q_s=q

Here the quantity supplied is q_s, quantity demanded is q_d, price is p, the e's are errors or residuals, and the a's and b's are parameters to be estimated. We have data on p and q, and the quantities supplied and demanded are conjectural.

Contexts: econometrics; estimation

single-crossing property: Distributions with cdfs F and G satisfy the single-crossing property if there is an x₀ such that: F(x) >= G(x) for x<=x₀ and G(x) >= F(x) for x>=x₀

Contexts: models; statistics

sink: "In a second-order [linear difference equation] system, if both roots are positive and less than one, then the system converges monotonically to the steady state. If the roots are complex and lie inside the unit circle then the system spirals into the steady state. If at least one root is negative, but both roots are less than one in absolute value, then the system will flip from one side of the steady state to the other as it converges. In all of these cases the steady state is called a sink." Contrast 'source'.

Source: Farmer, p. 29
Contexts: macro; dynamical systems; models

SIPP: The U.S. Survey of Income and Program Participation, which is conducted by the U.S. Census Bureau.

A tutorial is at: http://www.bls.census.gov/sipp/tutorial/SIPP_Tutorial_Beta_version/LAUNCHtutor ial.html

Source: http://www.sipp.census.gov/sipp
With thanks to: Dan Levy
Contexts: data

size: A synonym for significance level.

Source: Davidson and MacKinnon, 1993, p 78-79
Contexts: econometrics; estimation

skewness: An attribute of a distribution. A distribution that is symmetric around its mean has skewness zero, and is 'not skewed'. Skewness is calculated as E[(x-mu)³]/s³ where mu is the mean and s is the standard deviation.

Source: Hogg and Craig, p 57
Contexts: statistics

skill: In regular English usage means "proficiency". Sometimes used in economics papers to represent the experience and formal education. (Ed.: in this editor's opinion that is a dangerously misleading use of the term; it invites errors of thought and understanding.)

Contexts: labor

SLID: Stands for Survey of Labour and Income Dynamics. A Canadian government database going back to 1993 at least. Web pages on this subject can be searched from: http://www.statcan.ca/english/search/index.htm.

Contexts: data; labor

SLLN: Stands for strong law of large numbers.

Contexts: econometrics

SMA: Structural Moving Average model, which see

Contexts: econometrics

Smithian growth: Paraphrasing directly from Mokyr, 1990: Economic growth brought about by increases in trade.

Source: Mokyr, 1990, pp 4-6
Contexts: history; macro

smoothers: Smoothers are estimators that produce smooth estimates of regression functions. They are nonparametric estimators. The most common and implementable types are kernel estimators, k-nearest-neighbor estimators, and cubic spline smoothers.

Source: Hardle, 1990
Contexts: econometrics; nonparametrics; estimation

smoothing: Smoothing of a data set {X_i, Y_i} is the act of approximating m() in a regression such as:
Y_i = m(X_i) + e_i
The result of a smoothing is a smooth functional estimate of m().

Source: Hardle, 1990
Contexts: econometrics; estimation

SMR: Standardized mortality ratio

Contexts: demography; epidemiology

SMSA: Stands for Standard Metropolitan Statistical Area, a U.S. term for the standard boundaries of urban regions for purpose of measurement. Defined by the U.S. Census Bureau. There are 250-300 of these.

Contexts: data

SNP: abbreviation for 'seminonparametric', which means the same thing as semiparametric.

Contexts: econometrics

social capital: The relationships of a person which lead to economically productive consequences. E.g., they may produce something analogous to investment returns to that person, or socially productive consequences to a larger society. "'Social capital' refers to the benefits of strong social bonds. [Sociologist James] Coleman defined the term to take in 'the norms, the social interworks, the relationships between adults and children that are of value for the children's growing up.' The support of a strong community helps the child accumulate social capital in myriad ways; in the [1990s U.S.] inner city, where institutions have disintegrated, and mothers often keep children locked inside out of fear for their safety, social capital hardly exists." -- Traub (2000)

Source: Traub, James. The New York Times. January 16, 2000. Sunday, Late Edition, final. Article in section 6, starting page 52, column 1, Magazine Desk.
A World Bank publication suggests that James Coleman has a "classic 1987 article" called "Social Capital in the Creation of Human Capital" which was fundamental to the use of the term social capital in the social sciences.

With thanks to: Isaac McFarlin for finding this definition
Contexts: labor; sociology; education

social planner: One solving a Pareto optimality problem. The problem faced by a social planner will have as an answer an allocation, without prices.
Also, "the social planner is subject to the same information limitations as the agents in the economy." -- Cooley and Hansen p 185 That is, the social planner does not see information that is hidden by the rules of the game from some of the agents. If an agent happens not to know something, but it is not hidden from him by the rules of the game, then the social planner DOES see it.

Contexts: general equilibrium; models

social savings: A measurement of a new technology discussed in Crafts (2002). "How much more did [a new technology] contribute than an alternative investment might have yielded?" and cites Fogel (1979).

social welfare function: A mapping from allocations of goods or rights among people to the real numbers.
Such a social welfare function (abbreviated SWF) might describe the preferences of an individual over social states, or might describe outcomes of a process that made allocations, whether or not individuals had preferences over those outcomes.

Contexts: models; public economics

SOFFEX: Swiss Options and Financial Futures Exchange

Contexts: organizations

Solas: Software for imputing values to missing data, published by Statistical Solutions.

Contexts: data; estimation

Solovian growth: Paraphrasing from Mokyr (1990): Economic growth brought about by investment, meaning increases in the capital stock.

Source: Mokyr, 1990, p. 4-6.
Contexts: history; macro

Solow growth model: Paraphrasing pretty directly from Romer, 1996, p 7:
The Solow model is meant to describe the production function of an entire economy, so all variables are aggregates. The date or time is denoted t. Output or production is denoted Y(t). Capital is K(t). Labor time is denoted L(t). Labor's effectiveness, or knowledge, is A(t). The production function is denoted F() and is assumed to have constant returns to scale. At each time t, the production function is:
Y = F(K, AL)
which can be written: Y(t) = F(K(t), A(t)L(t))

AL is effective labor.

Note variants of the way A enters into the production function. This one is called labor-augmenting or Harrod-neutral. Others are capital-augmenting, e.g. Y=F(AK,L), or , like Y=AF(K,L). -------------------- From _Mosaic of Economic Growth_: DEFN of Solow-style growth models: They come from the seminal Solow (1956). "In Solow-style models, there exists a unique and globally stable growth path to which the level of labor productivity (and per capita output) will converge, and along which the rate of advance is fixed (exogenously) by the rate of technological progress." Many subsequent models of agg growth (like Romer 1986) have abandoned the assumption that all forms of kap accumulation run into diminishing marginal returns, and get different global convergence implications. (p22)

Source: Romer, 1996, p 7; Solow, 1956; that is: Solow, Robert. "A contribution to the theory of economic growth." Quarterly Journal of Economics. Feb. 1956
Contexts: macro

Solow residual: A measure of the change in total factor productivity in a Solow growth model. This is a way of doing growth accounting empirically either for an industry or more commonly for a macroeconomy. Formally, roughly following Hornstein and Krusell (1996):

Suppose that in year t an economy produces output quantity y_t with exactly two inputs: capital quantity k_t and labor quantity l_t. Assume perfectly competitive markets and that production has constant returns to scale. Let capital's share of income be fixed over time and denoted a. Then the change in total factor productivity between period t and period t+1, which is the Solow residual, is defined by:

Solow residual = (log TFP_t+1) - (log TFP_t) = (log y_t+1) - (log y_t)
- a(log k_t+1) - a(log k_t)
- (1-a)(log l_t+1) - (1-a)(log l_t)
Analogous definitions exist for more complicated models (with other factors besides capital and labor) or on an industry-by-industry basis, or with capital's share varying by time or by industry.

The equation may look daunting but the derivations are not difficult and students are sometimes asked to practice them until they are routine. Hulten (2000) says about the residual that:
-- it measures shifts in the implicit aggregate production function.
-- it is a nonparametric index number which measures that shift in a computation that uses prices to measure marginal products.
-- the factors causing the measured shift include technical innovation, organizational and institutional changes, fluctuations in demand, changes in factor shares (where factors are capital, labor, and sometimes measures of energy use, materials use, and purchased services use), and measurement errors.

From an informal discussion by this editor, it looks like the residual contains these empirical factors, among others: public goods like highways; externalities from networks like the Internet; some externalities and losses of capital services from disasters like September 11; theft; shirking; and technical / technological change.

Source: Hornstein, Andreas, and Per Krusell. 1996. "Can technology improvements cause productivity slowdowns?" NBER Macroeconomics Annual 1996. MIT Press. pp 214-215.
Hulten, 2000
Contexts: macro

solution concept: A phrase relevant to game theory. A game has a 'solution' which may represent a model's prediction. The modeler often must choose one of several substantively different solution methods, or solution concepts, which can lead to different game outcomes. A solution concept may be preferred to others in context where it makes a unique prediction. Game solution concepts include:

iterative elimination of strictly dominated strategies
Nash equilibrium
subgame perfect equilibrium
perfect Bayesian equilibrium

Contexts: phrases; game theory; modelling

source: "In a second-order [linear difference equation] system, ... if both roots are positive and greater than one, then the system diverges monotonically to plus or minus infinity. If the roots are complex and [lie] outside the unit circle then the system spirals out away from the steady state. If at least one root is negative, but both roots are greater than one in absolute value, then the system will flip from one side of the steady state to the other as it diverges to infinity. In each of these cases the steady state is called a source." Constrast 'sink'.

Source: Farmer, p. 29
Contexts: macro; dynamical systems; models

sparse: A matrix is sparse if many of its values are zero. A division of sample data into discrete bins (that is into a multinomial table) is sparse if many of the bins have no data in them.

Contexts: econometrics

spatial autocorrelation: Usually autocorrelation means correlation among the data from different time periods. Spatial autocorrelation means correlation among the data from locations. There could be many dimensions of spatial autocorrelation, unlike autocorrelation between periods. Nick J. Cox () wrote, in a broadcast to a listserv discussing the software Stata, this discussion of spatial autocorrelation. It is quoted here without any explicit permission whatsoever. (Parts clipped out are marked by 'snip'.) If 'Moran measure' and 'Geary measure' are standard terms used in economics I'll add them to the glossary.

Date: Thu, 15 Apr 1999 12:29:10 GMT
From: "Nick Cox" 
Subject: statalist: Spatial autocorrelation

[snip...]

First, the kind of spatial data considered here is data in two-dimensional
space, such as rainfall at a set of stations or disease incidence in a set of
areas, not three-dimensional or point pattern data (there is a tree or a
disease case at coordinates x, y).  Those of you who know time series might
expect from the name `spatial autocorrelation' estimation of a function,
autocorrelation as a function of distance and perhaps direction.  What is
given here are rather single-value measures that provide tests of
autocorrelation for problems where the possibility of local influences is of
most interest, for example, disease spreading by contagion. The set-up is that
the value for each location (point or area) is compared with values for its
`neighbours', defined in some way.

The names Moran and Geary are attached to these measures to honour the pioneer
work of two very fine statisticians around 1950, but the modern theory is due
to the statistical geographer Andrew Cliff and the statistician Keith Ord.

For a vector of deviations from the mean z, a vector of ones 1, and a matrix
describing the neighbourliness of each pair of locations W, the Moran measure
for example is

       (z' W z) / (z' z)
   I = -----------------
       (1' W 1) / (1' 1)

where ' indicates transpose. This measure is for raw data, not regression
residuals.

[snip; and the remainder discusses a particular implementation of a spatial
autocorrelation measuring function in Stata.]

For n values of a spatial variable x defined for various locations,
which might be points or areas, calculate the deviations
            _
    z = x - x

and for pairs of locations i and j, define a matrix

    W = ( w   )
           ij

describing which locations are neighbours in some precise sense.
For example, w   might be assigned 1 if i and j are contiguous areas
              ij
and 0 otherwise; or w   might be a function of the distance between
                     ij
i and j and/or the length of boundary shared by i and j.

The Moran measure of autocorrelation is

        n   n                      n   n         n   2
   n ( SUM SUM z  w   z  ) / ( 2 (SUM SUM w  )  SUM z  )
       i=1 j=1  i  ij  j          i=1 j=1  ij   i=1  i

and the Geary measure of autocorrelation is

             n   n               2           n   n         n   2
   (n -1) ( SUM SUM w   (z  - z )  ) / ( 4 (SUM SUM w  )  SUM z  )
            i=1 j=1  ij   i    j            i=1 j=1  ij   i=1  i

and these measures may used to test the null hypothesis of no spatial
autocorrelation, using both a sampling distribution assuming that x
is normally distributed and a sampling distribution assuming randomisation,
that is, we treat the data as one of n! assignments of the n values to
the n locations.

In a toy example, area 1 neighbours 2, 3 and 4  and has value 3
                       2            1 and 4                   2
                       3            1 and 4                   2
                       4            1, 2 and 3                1

This would be matched by the data

^_n^ (obs no)    ^value^ (numeric variable)  ^nabors^ (string variable)
- -----------    ------------------------  ------------------------
    1                      3                    "2 3 4"
    2                      2                      "1 4"
    3                      2                      "1 4"
    4                      1                    "1 2 3"

That is, ^nabors^ contains the observation numbers of the neighbours of
the location in the current observation, separated by spaces. Therefore,
the data must be in precisely this sort order when ^spautoc^ is called.

Note various assumptions made here:

1. The neighbourhood information can be fitted into at most a ^str80^
variable.

2. If i neighbours j, then j also neighbours i and both facts are
specified.

By default this data structure implies that those locations listed
have weights in W that are 1, while all other pairs of locations are not
neighbours and have weights in W that are 0.

If the weights in W are not binary (1 or 0), use the ^weights^ option.
The variable specified must be another string variable.

^_n^ (obs no)  ^nabors^ (string variable)  ^weight^ (string variable)
- -----------  ------------------------  ------------------------
    1                "2 3 4"             ".1234 .5678 .9012"
    etc.

that is, w   = 0.1234, and so forth. w   need not equal w  .
          12                          ij                 ji

[snip]

References
- ----------

Cliff, A.D. and Ord, J.K. 1973. Spatial autocorrelation. London: Pion.

Cliff, A.D. and Ord, J.K. 1981. Spatial processes: models and
applications. London: Pion.

Author
- ------
         Nicholas J. Cox, University of Durham, U.K.
         n.j.cox@@durham.ac.uk

- ------------------------- end spautoc.hlp

Nick
n.j.cox@durham.ac.uk

Source: statalist, Nick J. Cox (N.J.Cox@durham.ac.uk, as of 4/15/99)
With thanks to: Nicholas J. Cox, University of Durham, U.K. (n.j.cox@durham.ac.uk)
Contexts: statistics; econometrics; estimation

SPE: Abbreviation for: Subgame perfect equilibrium

Contexts: game theory; models

specie: A commodity metal backing money; historically specie was gold or silver.

Contexts: money; history

spectral decomposition: The factorization of a positive definite matrix A into A=CLC' where L is a diagonal matrix of eigenvalues, and the C matrix has the eigenvectors. That decomposition can be written as a sum of outer products:

A = (sum from i=1 to i=N of) L_ic_ic_i'

where c_i is the i^th column of C.

Source: Greene, 1993, p 34
Contexts: econometrics

spectrum: Summarizes the periodicity properties of a time series or time series sample x_t. Often represented in a graph with frequency, or period, (often denoted little omega) on the horizontal axis, and S_x(omega), which is defined below, on the vertical axis. S_x is zero for frequencies that are not found in the time series or sample, and is increasingly positive for frequencies that are more important in the data.

S_x(omega) = (2pi)^-1(sum for j from -infinity to +infinity of) g_je^-ijomega

where g_j is the jth autocovariance, omega is in the range [-pi, pi], and i is the square root of -1.

Example 1: If x_t is white noise, the spectrum is flat. All cycles are equally important. If they were not, the series would be forecastable.

Example 2: If x_t is an AR(1) process, with coefficient in (0, 1), the spectrum has a peak at frequency zero and declines monotonically with distance from zero. This process does not have an observable cycle.

Source: Wouter J. den Haan, April 1996, "The Comovements between real activity and prices at different business cycle frequencies", as presented at Northwestern, April 21, 1997. Possibly a UCSD or NBER working paper. Supported by NSF grant SBR-9514813. Another good reference is Priestly, 1994.
Contexts: time series; econometrics

speculative demand: The speculative demand for money is inversely related to the interest rate.

Source: Branson
Contexts: money

spline function: The kind of estimate producted by a spline regression in which the slope varies for different ranges of the regressors. The spline function is continuous but usually not differentiable.

Source: Greene, 1993, p 237
Contexts: econometrics

spline regression: A regression which estimates different linear slopes for different ranges of the independent variables. The endpoints of the ranges are called knots.

Source: Greene, 1993, p 237
Contexts: econometrics

spline smoothing: 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 the 'cubic spline' which seems to be the most common.

Source: Hardle, 1990
Contexts: econometrics; nonparametrics; estimation

SPO: stands for Strongly Pareto Optimal, which see.

Contexts: general equilibrium; models

SPSS: Stands for 'Statistical Product and Service Solutions', a corporation at www.spss.com

Contexts: data

SSEP: Social Science Electronic Publishing, Inc.

Contexts: data

SSRN: Social Science Research Network Their web site

Contexts: data

stabilization policy: "Macroeconomic stabilization policy consists of all the actions taken by governments to (1) keep inflation low and stable; and (2) keep the short-run (business cycle) fluctuations in output and employment small." Includes monetary and fiscal policies, international and exchange rate policy, and international coordination. (p129 in Taylor (1996)).

Source: Taylor, John B. 1996. "Stabilization Policy and Long-Term Economic Growth." In The Mosaic of Economic Growth, edited by Ralph Landau, Timothy Taylor, and Gavin Wright. Stanford University Press.
Contexts: macro

stable distributions: See Campbell, Lo, and MacKinlay pp 17-18. Ref to French probability theories Levy. The normal, Cauchy, and Bernoulli distrbutions are special cases. Except for the normal distrbituion, they have infinite variance.
There has been some study of whether continuously compounded asset returns could fit a stable distribution, given that their kurtosis is too high for a normal distribution.

Source: Campbell, Lo, and MacKinlay 1996, pp 17-18
Contexts: finance; statistics

stable steady state: in a dynamical system with deterministic generator function F() such that N_t+1=F(N_t), a steady state is stable if, loosely, all nearby trajectories go to it.

Source: J. Montgomery, social networks paper
Contexts: macro; dynamical systems; models

staggered contracting: A model can be constructed in which some agents, usually firms, cannot change their prices at will. They make a contract at some price for a specified duration, then when that time is up can change the price. If the terms of the contracts overlap, that is they do not all end at the same time, we say the contracts are staggered.

An important paper on this topic was Taylor (1980) which showed that staggered contracts can have an effect of persistence -- that is, that one-time shocks can have effects that are still evolving for several periods. This is a version of a new Keynesian, sticky-price model.

Contexts: models

standard normal: Refers to a normal distribution with mean of zero and variance of one.

Contexts: statistics

Stata: Statistical analysis software. Stata web site

Contexts: data; estimation

state price: the price at time zero of a state-contingent claim that pays one unit of consumption in a certain future state.

Source: Huang and Litzenberger, 1988, pp 123-4
Contexts: finance; models

state price vector: the vector of state prices for all states.

Contexts: macro; finance; models

state-space approach to linearization: Approximating decision rules by linearizing the Euler equations of the maximization problem around the stationary steady state and finding a unique solution to the resulting system of dynamic equations

Source: explained in King, Plosser, Rebelo (87); ref Merz 94, p 21 footnote
Contexts: macro; models

stationarity: The attribute of being covariance stationary, with reference to a stochastic process. Note that strict stationarity is not a superset or subset, but a different thing.

stationary: When used to describe a stochastic process, this is usually a synonym for covariance stationary.

Source: Enders, Walter. 1995. Applied Econometric Time Series. John Wiley & Sons, Inc.

Hamilton, J. Time Series Analysis.
Contexts: stochastic processes

statistic: a function of one or more random variables that does not depend upon any unknown parameter.
(The distribution of the statistic may depend on one or more unknown parameters, but the statistic can be calculated without knowing them just from the realizations of the random variables, e.g. the data in a sample.)
In general a statistic could be a vector of values, but often it is a scalar.

Source: adapted from Hogg & Craig.
Contexts: statistics; econometrics; estimation

Statistica: Statistical software. See http://www.statsoft.com.

Contexts: data; estimation

statistical discrimination: A theory of why minority groups are paid less when hired. The theory is roughly that managers, who are of one type (say, white), are more culturally attuned to the applicants of their own type than to applicants of another type (say, black), and therefore they have a better measure of the likely productivity of the applicants of their own type. (There is uncertainty in the manager's predictions about blacks and probably of whites too, but more uncertainty for blacks.) Because the managers are risk averse they bid more for a white applicant of a given apparent productivity than for a black one, since their measure of the white's productivity is better. This theory predicts that white managers would offer black applicants lower starting wages than whites of the same apparent ability, even if the manager is not prejudiced against the blacks.

Contexts: labor

statistics:
Relevant terms: acceptance region, adapted, almost surely, alternative hypothesis, ANOVA, AR, AR(1), ARCH, autoregressive process, b, bandwidth, Bayesian analysis, Bonferroni criterion, bootstrapping, Box-Cox transformation, Cauchy distribution, cdf, characteristic function, chi-square distribution, coefficient of variation, complete, consistent, correlation, Cramer-Rao lower bound, cross-validation, delta method, density function, diffuse prior, distribution function, efficiency, efficiency bound, efficient, EGARCH, essentially stationary, estimator, excess kurtosis, expected value, exponential distribution, exponential family, F distribution, fat-tailed, frequency function, gamma distribution, gamma function, GARCH, Gaussian, Gaussian white noise process, generalized Wiener process, GEV, Heaviside function, Hermite polynomials, heterogeneous process, Huber standard errors, Huber-White standard errors, iid, information number, Ito process, Jensen's inequality, Kolmogorov's Second Law of Large Numbers, kurtosis, LAN, leptokurtic, Lindeberg-Levy Central Limit Theorem, log-concave, log-convex, logistic distribution, lognormal distribution, MA, main effect, MANOVA, Markov process, Markov's inequality, martingale, martingale difference sequence, mesokurtic, MGF, moment-generating function, Monte Carlo simulations, multivariate, MVN, noncentral chi-squared distribution, normal distribution, Op(1), order statistic, Pareto distribution, pdf, platykurtic, Poisson distribution, Poisson process, power, power distribution, probability function, process, random, random process, random variable, random walk, Rao-Cramer inequality, Riemann-Stieltjes integral, second moment, semiparametric, significance, single-crossing property, skewness, spatial autocorrelation, stable distributions, standard normal, statistic, stochastic, stochastic process, strict stationarity, strictly stationary, strong law of large numbers, strongly consistent, Student t, sufficient statistic, support, t distribution, t statistic, tangent cone, Tukey boxplot, type I error, type I extreme value distribution, type II error, uniform distribution, uniform weak law of large numbers, unit root, unit root test, UWLLN, variance, wavelet, weak law of large numbers, weak stationarity, weakly consistent, weakly dependent, Weibull distribution, white noise process, White standard errors, WLLN, Wold's theorem.

Contexts: fields

stochastic: synonym for random.

Contexts: statistics; econometrics; time series

stochastic difference equation: A linear difference equation with random forcing variables on the right hand side. Here is a stochastic difference equation in k:
k_t+1 + k_t = w_t
where the k's and w's are scalars, and time t goes from 0 to infinity. The w's were exogenous forcing variables. Or:
Ak_t+1 + Bk_t + Ck_t-1 = Dw_t + e_t
where the k's are vectors, the w's and e's are exogenous vectors, and A, B, C, and D are constant matrices.

Source: Sargent, 1979
Contexts: macro; models

stochastic dominance: An abbreviation for first-order stochastic dominance. A possible comparison relationship between two stochastic distributions. Let the possible returns from assets A and B be described by statistical distributions A and B. Payoff distribution A first-order stochastically dominates payoff distribution B if for every possible payoff, the probability of getting a payoff that high is never better in B than in A.

Much more is in Huang and Litzenberger (1988), chapter 2.

Source: Huang and Litzenberger, (1988), p. 40

stochastic kernel: Another name for stochastic transition function.

stochastic process: A stochastic process is an ordered collection of random variables. The term is synonymous with random process. Discrete ones are indexed, often by the subscript t for time, e.g., y_t, y_t+1, although such a process could be spatial instead of temporal. Continuous ones can be described as continuous functions of time, e.g. y(t).

A stochastic process is specified by properties of the joint distribution for those random variables. Examples:

-- the random variables are independently and identically distributed (iid).
-- the process is a Markov process
-- the process is a martingale
-- the process is white noise
-- the process is autoregressive (e.g. AR(1))
-- the process has a moving average (e.g. see MA(1))

Contexts: models; statistics

stochastic transition function: A generalization of the Markov transition matrix which describes the probability of a transition by a system from one set of states to another set of states. A matrix may not describe the situation if the subsets are complicated or infinite in number.

Stolper-Samuelson theorem: In some models of international trade, trade lowers the real wage of the scarce factor of production, and protection from trade raises it. That is a Stolper-Samuelson effect, by analogy to their (1941) theorem in a Heckscher-Ohlin model context.

A notable case is when trade between a modernized economy and a developing one would lower the wages of the unskilled in the modernized economy because the developing country has so many of the unskilled.

Source: MIT Dictionary of Modern Economics, edited by David W Pearce;
Gordon H. Hanson and Matthew J. Slaughter, "The Rybczinski theorem, factor-price equalization, and immigration: evidence from U.S. states," NBER working paper 7074, April 1999. On Web at http://www.nber.org/papers/w7074
Stolper, Wolfgang, and Paul A. Samuelson. 1941. "Protection and real wages." Review of Economics and Statistics 9(1): 58-73.
Contexts: trade; macro

stopping rule: A stopping rule, in the context of search theory, is a mapping from histories of draws to one of two decisions: stop at this draw, or continue drawing.

Source: Wolinsky's D14 notes, Jan 1997
Contexts: information; search

storable: A good is storable to the degree that it does not degrade or lose its value over time. In models of money, storable goods dominate less storable goods as media of exchange.

Contexts: money

straddle: An options trading strategy of buying a call option and a put option on the same stock with the same strike price and expiration date. Such a strategy would result in a profitable position if the stock price is far enough from the strike price.

Source: Hull, 1997, p 187
Contexts: finance

strategic form: Synonym for normal form display of a game.

Source: Varian, 1992
Contexts: game theory

strategy-proof: A decision rule (a mapping from expressed preferences by each of a group of agents to a common decision) "is strategy-proof if in its associated revelation game, it is a dominant strategy for each agent to reveal its true preferences."

Source: Miyagawa, 1998, p 2
Contexts: game theory

strict stationarity: Describes a stochastic process whose joint distribution of observations is not a function of time. Contrast weak stationarity.

Source: Hoel, Port, and Stone, 1972, p. 122.
Contexts: statistics; econometrics; time series

strict version of Jensen's inequality: Quoting directly from Newey-McFadden: "[I]f a(y) is a stricly concave function [e.g. a(y)=ln(y)] and Y is a nonconstant random variable, then a(E[Y]) > E[a(Y)]."

Source: Newey-McFadden, Ch 36, Handbook of Econometrics, p. 2124
Contexts: models

strictly stationary: A random process {x_t} is strictly stationary if the joint distribution of elements is not a function of the index t. In one sense this is a stronger condition than covariance stationarity because it requires also that the third and higher moments of the distributions be stationary. But a process can be strictly stationary without being covariance stationary if it does not have a finite variance.

Contexts: time series; econometrics; statistics

strip financing: Corporate financing by selling "stapled" packages of securities together that cannot be sold separately. E.g., if a firm might sell bonds only in a package that includes a standard proportion of senior subordinated debt, convertible debt, preferred, and common stock. A benefit is reduced conflict. In principle bondholders and stockholders have different interests and that can impose costs on the firm. After a strip financing, however, those groups are each made up of all the same people, so their interests coincide.

Source: Jensen (86)
Contexts: finance

strips: securities made up of standardized proportions of other securities from the same firm. See strip financing.

U.S. Treasury bonds can be split into principal and interest components, and the standard name for the resulting securities is STRIPS (Separate Trading of Registered Interest and Principal of Securities). See coupon strip and principal strip.

Source: Jensen (86)
Contexts: finance

strong form: Can refer to the strong form of the efficient markets hypothesis, which is that any public or private information known to anyone about a security is fully reflected in its current price.
Fama (1991) renames tests of the strong form of the hypothesis to be 'tests for private information.' Roughly -- If individuals with private information can make trading gains with it, the strong form hypothesis does not hold.

Source: Fama, 1970.

Dow and Gorton (1996) cite this paper. Possibly it defined the term for th first time:

Roberts, Harry V. 1967. "Statistical versus clinical prediction of the stock market," working paper, University of Chicago.
Contexts: finance

strong incentive: An incentive that encourages maximization of an objective. For example, payment per unit of output produced encourages maximum production. Useful in design of a contract if the buyer knows exactly what is desired. Contrast weak incentive.

Source: Weisbrod's class 5/23/97
Contexts: public economics

strong law of large numbers: If {Z_t} is a sequence of n iid random variables drawn from a distribution with mean MU, then with probability one, the limit of sample averages of the Z's goes to MU as sample size n goes to infinity.

I believe that strong laws of large numbers are generally, or perhaps always, proved using some version of Chebyshev's inequality. (The proof is rarely shown; in most contexts in economics one can simply assume laws of large numbers).

Contexts: statistics; econometrics; probability

strongly consistent: An estimator for a parameter is strongly consistent if the estimator goes to the true value almost surely as the sample size n goes to infinity. This is a stronger condition than weak consistency; that is, all strongly consistent estimators are weakly consistent but the reverse is not true.

Contexts: econometrics; statistics

strongly dependent: A time series process {x_t} is strongly dependent if it is not weakly dependent; that is, if it is strongly autocorrelated, either positively or negatively.

Example 1: A random walk with correlation 1 between observations is strongly dependent.

Example 2: An iid process is not strongly dependent.

Source: Discussed in Wooldridge, 1995, p 2646 which cites Robinson 1991b in J of econometrics.
Contexts: time series; econometrics

strongly ergodic: A stochastic process may be strongly ergodic even if it is nonstationary. A strongly ergodic process is also weakly ergodic.

Contexts: time series; econometrics

strongly Pareto Optimal: A strongly Pareto optimal allocation is one such that no other allocation would be both (a) as good for everyone and (b) strictly preferred by some.

Contexts: general equilibrium; models

strongly stationary: Synonym for strictly stationary, regarding a stochastic process.

Source: Hoel, Port, and Stone, 1972
Contexts: time series

structural break: A structural change detected in a time series sample.

Contexts: time series; econometrics

structural change: A change in the parameters of a structure generating a time series. There exist tests for whether the parameters changed. One is the Chow test.

Examples: (planned)

Contexts: time series; econometrics

structural moving average model: The model is a multivariate, discrete time, dynamic econometric model. Let y_t be an n_y x 1 vector of observable economic variables, C(L) is a n_y x n_e matrix of lag polynomials, and e_t be a vector of exogenous unobservable shocks, e.g. to labor supply, the quantity of money, and labor productivity. Then:
y_t=C(L)e_t
is a structural moving average model.

Source: M.W. Watson, Ch 57, Handbook of Econometrics, p 2899.
Contexts: econometrics

structural parameters: Underlying parameters in a model or class of models.

If a theoretical model explains two effects of variable x on variable y, one of which is positive and one negative, they are structurally separate. In another model, in which only the net effect of x on y is relevant, one structural parameter for the effect may be sufficient.

So a parameter is structural if a theoretical model has a distinct structure for its effect. The definition is not absolute, but relative to a model or class of models which are sometimes left implicit.

Contexts: estimation; econometrics

structural unemployment: Unemployment that comes from there being an absence of demand for the workers that are available. Contrast frictional unemployment.

Source: Baumol & Blinder
Contexts: labor; macro

structure: A model with its parameters fixed. One can discuss properties of a model with various parameters, but 'structural' properties are those that are fixed unless parameters change.

Source: Davidson and MacKinnon, 1993, I think, but can't find the exact page.
Contexts: econometrics

Student t: Synonym for the t distribution. The name came about because the original researcher who described the t distribution wrote under the pseudonym 'Student'.

Contexts: statistics

stylized facts: Observations that have been made in so many contexts that they are widely understood to be empirical truths, to which theories must fit. Used especially in macroeconomic theory. Considered unhelpful in economic history where context is central.
Relevant terms: Engel's law.

Contexts: fields; phrases

subdifferential: A class of slopes. By example -- consider the top half of a stop sign as a function graphed on the xy-plane. It has well-defined derivatives except at the corners. The subdifferential is made up of only one slope, the derivative, at those points. At the corners there are many 'tangents' which define lines that are everywhere above the stop sign except at the corner. The slopes of those lines are members of the subdifferential at those points.

In general equilibrium usage, the subdifferential can be a class of prices. It's the set of prices such that expanding the total endowment constraint would not cause buying and selling, because the agents have optimized perfectly with respect to the prices. So if a set of prices is possible for a Walrasian equilibrium, it is in the subdifferential of that alocation.

Contexts: general equilibrium; models

subgame perfect equilibrium: An equilibrium in which the strategies are a Nash equilibrium, and, within each subgame, the parts of the strategies relevant to the subgame make a Nash equilibrium of the subgame.

Contexts: game theory; models

submartingale: A kind of stochastic process; one in which the expected value of next period's value, as projected on the basis of the current period's information, is greater than or equal to the current period's value.
This kind of process could be assumed for securities prices.

Source: Fama, 1970, p 386
Contexts: finance; time series

subordinated: Adjective. A particular debt issue is said to be subordinated if it was senior but because of a subsequent issue of debt by the same firm is no longer senior. One says, 'subordinated debt'.

Contexts: finance

substitution bias: A possible problem with a price index. Consumers can substitute goods in response to price changes. For example when the price of apples rises but the price of oranges does not, consumers are likely to switch their consumption a little bit away from apples and toward oranges, and thereby avoid experiencing the entire price increase. A substitution bias exists if a price index does not take this change in purchasing choices into account, e.g. if the collection ("basket") of goods whose prices are compared over time is fixed.

"For example, when used to measure consumption prices between 1987 and 1992, a fixed basket of commodities consumed in 1987 gives too much weight to the prcies that rise rapidly over the timespan and too little weight to the prices that have fall; as a result, using the 1987 fixed basket overstates the 1987-92 cost-of-living change. Conversely, because consumers substitute, a fixed basket of commodities consumed in 1992 gives too much weight to the prices that have fallen over the timespan and to little to the prices that have risen; as a result, the 1992 fixed based understates the 1987-92 cost-of-living change." (Triplett, 1992)

Source: Triplett, 1992, p. 50
Contexts: macro; prices

SUDAAN: A statistical software program designed especially to analyze clustered data and data from sample surveys. The SUDAAN Web site is at http://www.rti.org/patent s/sudaan/sudaan.html.

Contexts: data; estimation; code

sufficient statistic: Suppose one has samples from a distribution, does not know exactly what that distribution is, but does know that it comes from a certain set of distributions that is determined partly or wholly by a certain parameter, q. A statistic is sufficient for inference about q if and only if the values of any sample from that distribution give no more information about q than does the value of the statistic on that sample.

E.g. if we know that a distribution is normal with variance 1 but has an unknown mean, the sample average is a sufficient statistic for the mean.

Contexts: statistics

sunk costs: Unrecoverable past expenditures. These should not normally be taken into account when determining whether to continue a project or abandon it, because they cannot be recovered either way. It is a common instinct to count them, however.

sup: Stands for 'supremum'. A value is a supremum with respect to a set if it is at least as large as any element of that set. A supremum exists in context where a maximum does not, because (say) the set is open; e.g. the set (0,1) has no maximum but 1 is a supremum.

sup is a mathematical operator that maps from a set to a value that is syntactically like an element of that set, although it may not actually be a member of the set.

Contexts: real analysis

superlative index numbers: "What Diewert called 'superlative' index numbers were those that provide a good approximation to a theoretical cost-of-living index for large classes of consumer demand and utility function specifications. In addition to the Tornqvist index, Diewert classified Irving Fisher's 'Ideal' index as belong to this class." -- Gordon, 1990, p. 5

from harper (1999, p. 335): The term "superlative index number" was coined by W. Erwin Diewert (1976) to describe index number formulas which generate aggregates consistent with flexible specifications of the production function."

Two examples of superlative index number formulas are the Fisher Ideal Index and the Tornqvist index. These indexes "accomodate subsitution in consumer spending while holding living standards constant, something the Paasche and Laspeyres indexes do not do." (Triplett, 1992, p. 50).

Source: Diewert, 1976; Gordon, 1990, p. 5; Triplett, 1992, p. 50
Contexts: index numbers

superneutrality: Money in a model 'is said to be superneutral if changes in [nominal] money growth have no effect on the real equilibrium.' Contrast neutrality.

Source: Blanchard & Fischer, p. 207
Contexts: money; macro; models

supply curve: For a given good, the supply curve is a relation between each possible price of the good and the quantity that would be supplied for 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   |         / Supply
        |       /
        |     /
        |   /
        |________________________
                        Quantity

0    1    2    3    4
 |--[==+===]---|  * *      <= the first distribution
      |-[=+==]---|         <= the second distribution

The first distribution has a median around 1.3, and the main part of it ranges from .3 to 3.0. There are some outliers at the top. The second distribution has a median near 2.0, and is more narrowly concentrated than the first, with few outliers.

Source: Quah, 1997; Cleveland, 1993
Contexts: statistics; econometrics

tutorial: Matlab: From a Unix shell one can just type 'matlab' as a command on any computer that has it, and start to type interactive statements such as those below. One could also put them in a file with the .m extension to run them from within matlab with 'run file.m' or from the shell with 'matlab < file.m' This tutorial covers very little but you can see something of the language.

%  The percent sign begins comments.
%  The statements below can be typed interactively one per line to get
% clear responses from Matlab.  No need to type the comment part at the
% end of the lines.  Make sure to use upper and lower case in the
% same was as in the statements shown.

A=[1 2;3 4]   % defines matrix A as a 2x2 with first line [1 2]
B=A'          % transpose
B=A+A         % sum, element by element
Ainv=inv(A)   % takes inverse of a matrix
A*Ainv        % calculates and prints the result of a matrix multiplication
B=[A;A]       % stacked so B has twice as many rows as A
B=[A A]       % the A's are side by side.  B has twice as many columns as A.
B=A(1,1)      % B is a scalar now, the upper left element of A
B=A'*A        % matrix multiplication
B=A(:,1)      % B is set to first row of A
B=A.*A        % element by element multiplication
B=B./A        % element by element division
A=zeros(3,3)  % special definition of a matrix of zeros
B=ones(3,1)   % defines a matrix of ones
A=eye(5)      % defines identity matrix
B=A(1:2,1:3)  % takes part of matrix
more on       % may not be needed; prevents help screen from scrolling off
help *        % shows sample of the help available

Source: Chris Taber, Econ D83 at Northwestern 1996-7, Matlab tutorial handout
Contexts: data

two stage least squares: An instrumental variables estimation technique. Extends the IV idea to a situation where one has more instruments than independent variables in the model. 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. But the matrix of independent variables X may be correlated to the e's. Then using a matrix of independent variables Z, uncorrelated to the e's, that is T x r, where r>k:
Stage 1: By OLS, regress the X's on the Z's to get Xhat = (Z'X)^-1Z'y
Stage 2: By OLS, regress y on the Xhat's. This gives an unbiased estimate of b.
The stages can be combined into one for maximum speed:
b = (X'P_zX)^-1X'P_zy
where P_z, the projection matrix of Z, is defined to be:
P_z = Z(Z'Z)^-1Z'

Contexts: econometrics; estimation

two-factor model: suggests a production model with two factors of production, labor L and capital K.

tying: Tying is the vendor practice of requiring customers of one product to buy others.
Tying can be said to impede trade in that the customer's choices are restricted. If the customer were free to buy the product without further conditions, the customer would apparently be better off than if the product has strings attached. Tying could, however, be efficiency-enhancing by (1) reducing the number of market transactions (an efficiency of scale), or by (2) enabling a work-around of a regulation, such as offering a bargain in conjunction with a price-controlled product.
A historical example: years ago lessees of IBM mainframes had to agree to buy punch cards only from IBM. Those punch cards were sold at a higher price than on the open market. So the customer would have been better off with the same contract minus this clause. But one could argue that tying the products this way improved competition. It could be that IBM was trying to charge heavy users of the computer more than light users by putting a surcharge on the punch cards. If so, IBM found a way to bill customers for one of its costs, computer maintenance. The practice would theoretically encourage customers to optimize their use of the computer rather than use it excessively. In this case the practice might be pro-competitive.

Contexts: IO

type I error: That is, 'type one error.' This is the error in testing a hypothesis of rejecting a hypothesis when it is true.

Source: Davidson and MacKinnon, 1993, p 78-79
Contexts: econometrics; estimation; statistics

type I extreme value distribution: Has the cdf F(x)=exp(-exp(-x)).

(Devine and Kiefer write F(x)=exp(-exp(-x)); the difference may be in the range of x? must write this out)

Source: Amemiya, Takeshi. "Discrete Choice Models," The New Palgrave: Econometrics
Contexts: econometrics; statistics

type II error: That is, 'type two error.' This is the error in testing a hypothesis of failing to reject a hypothesis when it is false.

Source: Davidson and MacKinnon, 1993, p 78-79
Contexts: econometrics; estimation; statistics

ultimatum game: An experiment. There are two players, an allocator A and a recipient R, who in the experiment do not know one another. They have received a windfall, e.g., of $1. The allocator, moving first, proposes to split the windfall by proposing to take share x, so that A receives x and R receives 1-x. The recipient can accept this allocation, or reject it in which case both get nothing. The subgame perfect equilibrium outcome is that A would offer the smallest possible amount to R, e.g., the share $.99 for A and $.01 for R, and that the recipient should accept. The experimental evidence, however, is that A offers a relatively large share to R, often 50-50, and that R would often reject smaller positive amounts. We may interpret R's behavior has willingness to pay a cost to punish "unfair" splits. With regard to A's behavior -- does A care about fairness too? Or is A income-maximizing given R's likely behavior? See also Dictator Game.

Contexts: game theory; experimental

unbalanced data: In a panel data set, there are observations across cross-section units (e.g. individuals or firms), and across time periods. Often such a data set can be represented by a completely filled in matrix of N units and T periods. In the "unbalanced data" case, however, the number of observations per time period varies. (Equivalently one might say that the number of observations per unit is not always the same.) One might handle this by letting T be the total number of time periods and N_t be the number of observations in each period.

Contexts: econometrics; estimation

unbiased: An estimator b of a distribution's parameter B is unbiased if the mean of b's sampling distribution is B. Formally, if: E[b] = B.

Source: Greene, 1993, p 93
Contexts: econometrics

uncertainty: If outcomes will occur with a probability that cannot even be estimated, the decisionmaker faces uncertainty. Contrast risk.

This meaning to uncertainty is attributed to Frank Knight, and is sometimes referred to as Knightian uncertainty.

The decisionmaker can apply game theory even in such a circumstance, e.g. the choice of a dominant strategy.

Kreps (1988), p 31, writes that three standard ways of modeling choices made under conditions of uncertainty are with von Neumann-Morgenstern expected utility over objective uncertainty, the Savage axioms for modeling subjective uncertainty, and the Anscombe-Aumann theory which is a middle course between them.

A recent ad for a new book edited by Haim Levy (Stochastic Dominance: Investment Decision Making under Uncertainty) considers three ways of modeling investment choices under uncertainty: by tradeoffs between mean and variance, by choices made by stochastic dominance, and non-expected utility approaches using prospect theory.

Source: J. Montgomery, social networks paper;
Kreps, 1988
Contexts: models

uncorrelated: Two random variables X and Y are uncorrelated if E(XY)=E(X)E(y). Note that this does not guarantee they are independent.

Source: Greene, 1993, p 64-65
Contexts: econometrics

under the null: Means "assuming the hypothesis formally being tested is true." See null hypothesis.

Contexts: phrases; econometrics