 Students / Subjects  CAGR Cumulative Average Growth Rate Source: econterms 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: econterms 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. Source: econterms call option A call option conveys the right to buy a specified quantity of an underlying security. Source: econterms 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. Source: econterms 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: econterms 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 of a certain input (e.g. a certain kind of capital input, a recent key example being computer equipment) can be measured in the following way. Estimate the growth of the services provided by this input, per unit of labor input, in year T and in year T+1. The growth rate of that ratio is one common measure of the rate of capital deepening. Oulton, p. 31 Source: econterms capital intensity Amount of capital per unit of labor input. Source: econterms capital ratio A measure of a bank's capital strength used by U.S. regulatory agencies. Source: econterms capital structure The capital structure of a firm is broadly made up of its amounts of equity and debt. Source: econterms 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)aL1-a the effectiveness variable A is capital-augmenting but in the model Y=AKaL1-a it is not. Another example would be a capital utilization variable as measured say by electricity usage. (E.g., as in Eichenbaum). ----------------- An example: in the context of a railroad, automatic railroad signaling, track-switching, and car-coupling devices are capital-augmenting. From Moses Abramovitz and Paul A. David, 1996. 'Convergence and Deferred Catch-up: productivity leadership and the waning of American exceptionalism.' In Mosaic of Economic Growth, edited by Ralph Landau, Timothy Taylor, and Gavin Wright. Source: econterms 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: econterms CAPM Capital Asset Pricing Model Source: econterms CAR stands for Cumulative Average Return. A portfolio's abnormal return (AR) at each time is ARt=Sum from i=1 to N of each arit/N. Here arit is the abnormal return at time t of security i. Over a window from t=1 to T, the CAR is the sum of all the ARs. Source: econterms 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: econterms CARs cumulative average adjusted returns Source: econterms 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: econterms 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: econterms Category split effect Research on frequency estimation has shown that several factors can influence the subjective frequency of events. One of these factors is the category width. Splitting an event category into smaller subcategories can increase the subjective frequency of events: A total set of events may have less impact, or appear less frequent, subjectively, than the sum of its (exclusive) subsets. For example, imagine you are asked to judge the number of Japanese cars in your own country, or, in another condition, to judge the frequency of Honda, Nissan, Toyota, Mazda, Daihatsu and Mitshubishi cars. The sum of the judged component frequencies from the split-category condition will be higher, under many circumstances, than the compound frequency of the entire category. Source: SFB 504 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: econterms Cauchy sequence A sequence satisfies the Cauchy criterion iff for each positive real epsilon there exists a natural number N such that the distance between any two elements of the sequence past the Nth element is less than epsilon. 'Distance' must be defined in context by the user of the term. One sometimes hears the construction: 'The sequence is Cauchy' if the sequence satisfies the definition. Source: econterms CCAPM Stands for Consumption-based Capital Asset Pricing Model. A theory of asset prices. Formulated in Lucas, 1978, and Breeden, 1979. Source: econterms CDE Stands for Corporate Data Exchange, an organization which has data on the shareholdings of large U.S. companies. Source: econterms cdf cumulative distribution function. This function describes a statistical distribution. It has the value, at each possible outcome, of the probability of receiving that outcome or a lower one. A cdf is usually denoted in capital letters. Consider for example some F(x), with x a real number is the probability of receiving a draw less than or equal to x. A particular form of F(x) will describe the normal distribution, or any other unidimensional distribution. Source: econterms CDFC Stands for Concavity of distribution function condition. Source: econterms censored dependent variable A dependent variable in a model is censored if observations of it cannot be seen when it takes on vales in some range. That is, the independent variables are observed for such observations but the dependent variable is not. A natural example is that if we have data on consumers and prices paid for cars, if a consumer's willingness-to-pay for a car is negative, we will see observations with consumer information but no car price, no matter how low car prices go in the data. Price observations are then censored at zero. Contrast truncated dependent variables. Source: econterms central bank A government bank; a bank for banks. Source: econterms Centrality of typicality Items with greater family resemblance to a category are judged to be more typical of the category. Source: SFB 504 Certainty effect The reduction of the probability of an outcome by a constant factor has more impact when the outcome was initially certain than when it was merely probable (e.g. Allais paradox). Source: SFB 504 certainty equivalence principle Imagine that a stochastic objective function is a function only of output and output-squared. Then the solution to the optimization problem of choosing output will have the special characteristic that only the conditional means of the future forcing variables appear in the first order conditions. (By conditional means is meant the set of means for each state of the world.) Then the solution has the "certainty equivalence" property. "That is, the problem can be separated into two stages: first, get minimum mean squared error forecasts of the exogenous [variables], which are the conditional expectations...; second, at time t, solve the nonstochastic optimization problem," using the mean in place of the random variable. "This separation of forecasting from optimization.... is computationally very convenient and explains why quadratic objective functions are assumed in much applied work. For general [functions] the certainty equivalence principle does not hold, so that the forecasting and opt problems do not 'separate.'" Source: econterms certainty equivalent The amount of payoff (e.g. money or utility) that an agent would have to receive to be indifferent between that payoff and a given gamble is called that gamble's 'certainty equivalent'. For a risk averse agent (as most are assumed to be) the certainty equivalent is less than the expected value of the gamble because the agent prefers to reduce uncertainty. Source: econterms CES production function CES stands for constant elasticity of substitution. This is a function describing production, usually at a macroeconomic level, with two inputs which are usually capital and labor. As defined by Arrow, Chenery, Minhas, and Solow, 1961 (p. 230), it is written this way: V = (bK-r + aL-r) -(1/r) where V = value-added, (though y for output is more common), K is a measure of capital input, L is a measure of labor input, and the Greek letters are constants. Normally a>0 and b>0 and r>-1. For more details see the source article. In this function the elasticity of substitution between capital and labor is constant for any value of K and L. It is (1+r)-1. Source: econterms CES technology Example, adapted from Caselli and Ventura: For capital k, labor input n, and constant bS mapping S into itself, T is a contraction mapping if for some b ('b') in the range (0,1), d(Tx,Ty) is less than or equal to b*d(x,y) for all x and y in S. One often abbreviates the phrase 'contraction mapping' by saying simply that T is a contraction. The function resulting from the applications of a contraction could slope the opposite way of the original function as long as it is less steeply sloped. A standard way to prove that an operator T is a contraction is to prove that it satisfies Blackwell's conditions. Source: econterms contractionary fiscal policy A government policy of reducing spending and raising taxes. In the language of some first courses in macroneconomics, it shifts the IS curve (investment/saving curve) to the left. Source: econterms contractionary monetary policy A government policy of raising interest rates charged by the central bank. In the language of some first courses in macroeconomics, it shifts the LM curve (liquidity/money curve) to the left. Source: econterms control for As used in the following way: "The effect of X on Y disappears when we control for Z", the phrase means to regress Y on both X and Z, together, and to interpret the direct effect of X as the only effect. Here the effect of Z on X has been "controlled for". It is implied that X is not causing changes in Z. Source: econterms Control group In an experimental design, which is contrasting two or more groups, the control group of subjects is not given the treatment whose effect is under investigation. Source: SFB 504 control variable A variable in a model controlled by an agent in order to optimize something. Source: econterms convergence Multiple meanings: (1) a mathematical property of a sequence or series that approaches a value; In macro: ''Catch-up' refers to the long-run process by which productivity laggards close the proportional gaps that separate them from the productivity leader .... 'Convergence,' in our usage, refers to a reduction of a measure of dispersion in the relative productivity levels of the array of countries under examination.' Like Barro and Sala-i-Martin (92)'s 'sigma-convergence', a narrowing of the dispersion of country productivity levels over time. Source: econterms convergence in quadratic mean A kind of convergence of random variables. If xt converges in quadratic mean it converges in probability but it does not necessarily converge almost surely. The following is a best guess, not known to be correct. Let et be a stochastic process and Ft be an information set at time t uncorrelated with et: E[et|Ft-m] converges in quadratic mean to zero as m goes to infinity IFF: E[E[et|Ft-m]2] converges to zero as m goes to infinity. Source: econterms convolution The convolution of two functions U(x) and V(x) is the function: U*V(x) = (integral from 0 to x of) U(t)V(x-t) dt Source: econterms Cook's distance A metric for deciding whether a particular point alone affects regression estimates much. After a regression is run one can consider for each data point how far it is from the means of the independent variables and the dependent variable. If it is far from the means of the independent variables it may be very influential and one can consider whether the regression results are similar without it. [Need to add the equation defining the Cook's d here.] Source: econterms cooperative game A game structure in which the players have the option of planning as a group in advance of choosing their actions. Contrast noncooperative game. Source: econterms Coordination games Normal form game where the players have the same number of strategies, which can be indexed such that it is always a strict Nash equilibrium for both players to play strategies having the same index. Source: SFB 504 core Defined in terms of an original allocations of goods among agents with specified utility functions. The core is the set of possible reallocations such that no subset of agents could break off from the others and all do better just by trading among themselves. Equivalently: The intersection of individually rational allocations with the Pareto efficient allocations. Individually rational, here, means the allocations such that no agent is worse off than with his endowment in the original allocation. Source: econterms corner solution A choice made by an agent that is at a constraint, and not at the tangency of two classical curves on a graph, one characterizing what the agent could obtain and the other characterizing the imaginable choices that would attain the highest reachable value of the agents' objective. A classic example is the intersection between a consumer's budget line (characterizing the maximum amounts of good X and good Y that the consumer can afford) and the highest feasible indifference curve. If the agent's best available choice is at a constraint -- e.g. among affordable bundles of good X and good Y the agent prefers quantity zero of good X -- that choice is often not at a tangency of the indifference curve and the budget line, but at a "corner" Contrast interior solution. Source: econterms correlation Two random variables are positively correlated if high values of one are likely to be associated with high values of the other. They are negatively correlated if high values of one are likely to be associated with low values of the other. Formally, a correlation coefficient is defined between the two random variables (x and y, here). Let sx and xy denote the standard devations of x and y. Let sxy denote the covariance of x and y. The correlation coefficent between x and y, denoted sometimes rxy, is defined by: rxy = sxy / sxsy Correlation coefficients are between -1 and 1, inclusive, by definition. They are greater than zero for positive correlation and less than zero for negative correlations. Source: econterms cost curve A graph of total costs of production as a function of total quantity produced. Source: econterms cost function is a function of input prices and output quantity. Its value is the cost of making that output given those input prices. A common form: c(w1, w2, y) is the cost of making output quantity y using inputs that cost w1 and w2 per unit. Source: econterms cost-benefit analysis An approach to public decisionmaking. Quotes below from Sugden and Williams, 1978 p. 236, with some reordering: 'Cost-benefit analysis is a 'scientific' technique, or a way of organizing thought, which is used to compare alternative social states or courses of action.' 'Cost-benefit analysis shows how choices should be made so as to pursue some given objective as efficiently as possible.' 'It has two essential characteristics, consistency and explicitness. Consistency is the principle that decisions between alternatives should be consistent with objectives....Cost-benefit analysis is explicit in that it seeks to show that particular decisions are the logical implications of particular, stated, objectives.' 'The analyst's skill is his ability to use this technique. He is hired to use this skill on behalf of his client, the decision-maker..... [The analyst] has the right to refuse offers of employment that would require him to use his skills in ways that he believes to be wrong. But to accept the role of analyst is to agree to work with the client's objectives.' p. 241: Two functions of cost-benefit analysis: It 'assists the decision-maker to pursue objectives that are, by virtue of the community's assent to the decision-making process, social objectives. And by making explicit what these objectives are, it makes the decision-maker more accountable to the community.' 'This view of cost-benefit analysis, unlike the narrower value-free interpretation of the decision-making approach, provides a justification for cost-benefit analysis that is independent of the preferences of the analyst's immediate client. An important consequence of this is that the role of the analyst is not completely subservient to that of the decision-maker. Because the analyst has some responsibility of principles over and above those held by the decision-maker, he may have to ask questions that the decision-maker would prefer not to answer, and which expose to debate conflicts of judgement and of interest that might otherwise comfortably have been concealed.' Source: econterms cost-of-living index A cost-of-living price index measures the changing cost of a constant standard of living. The index is a scalar measure for each time period. Usually it is a positive number which rises over time to indicate that there was inflation. Two incomes can be compared across time by seeing whether the incomes changed as much as the index did. Source: econterms costate A costate variable is, in practice, a Lagrangian multiplier, or Hamiltonian multiplier. Source: econterms countable additivity property the third of the properties of a measure. Source: econterms coupon strip A bond can be resold into two parts that can be thought of as components: (1) a principal component that is the right to receive the principal at the end date, and (2) the right to receive the coupon payments. The components are called strips. The right to receive coupon payments is the coupon strip. Source: econterms Cournot duopoly A pair of firms who split a market, modeled as in the Cournot game. Source: econterms Cournot game A game between two firms. Both produce a certain good, say, widgets. No other firms do. The price they receive is a decreasing function of the total quantity of widgets that the firms produce. That function is known to both firms. Each chooses a quantity to produce without knowing how much the other will produce. Source: econterms Cournot model A generalization of the Cournot game to describe industry structure. Each of N firms will choose a quantity of output. Price is a commonly-known decreasing functions of total output. All firms know N and take the output of the others as given. Each firm has a cost function ci(qi). Usually the cost functions are treated as common knowledge. Often the cost functions are assumed to be the same for all firms. The prediction of the model is that the firms will choose Nash equilibrium output levels. Formally, from notes given by Michael Whinston to the Economics D50-1 class at Northwestern U. on Sept 23, 1997: Denote xi as a quantity that firm i considers, X as the total quantity (the sum of the xi's), xi* and X* as the Nash equilibrium levels of those quantities, X-i as the total quantity chosen by all firms other than firm i, and p(X) as the function mapping total quantity to price in the market. Each firm i solves: maxxi p(xi+X-i)-ci(xi) The first order conditions are, for i from 1 to N: p'(xi*+X-i)+p(X*)-ci'(xi*)=0 Assuming xi* is greater than 0 for all i, then the Nash equilibrium output levels are characterized by the N equations: p'(X*)xi* + p(X*) = ci'(xi*) for each i. Source: econterms covariance stationary A stochastic process is covariance stationary if neither its mean nor its autocovariances depend on the index t. Source: econterms Covered short call written call A covered short call consists of holding an underlying asset and simultaneously selling a call option (short call) of this underlying asset. Although in the literature exists the name call hedge, the covered short call is not an actual hedge strategy. It is only possible to hedge losses of the underelying asset to the amount of the option price, higher losses will be reduced to this amount. On the other hand it is not possible to participate on gains of the underlying asset, because in this case, the option will be exercised, i.e. the seller has to deliver the underlying asset. Source: SFB 504 Cowles Commission A 1950s, probably British, panel on econometrics which focussed attention on the problem of simultaneous equations. In some tellings of the history this had an impact on the field -- other problems such as errors-in-variables (measurement errors in the independent variables), were set aside or given lower priority elsewhere too because of the prestige and influence of the Cowles Commission. Source: econterms CPI The Consumer Price Index, which is a measure of the cost of goods purchased by average U.S. household. It is calculated by the U.S. government's Bureau of Labor Statistics. As a pure measure of inflation, the CPI has some flaws: 1) new product bias (new products are not counted for a while after the appear) 2) discount store bias (consumers who care won't pay full price) 3) substitution bias (variations in price can cause consumers to respond by substituting on the spot, but the basic measure holds their consumption of various goods constant) 4) quality bias (product improvements are under-counted) 5) formula bias (overweighting of sale items in sample rotation) Source: econterms CPS The Current Population Survey (of the U.S.) is compiled by the U.S. Bureau of the Census, which is in the Dept of Commerce. The CPS is the source of official government statistics on employment and unemployment in the U.S. Each month 56,500-59,500 households are interviewed about their average weekly earnings and average hours worked. The households are selected by area to represent the states and the nation. "Each household is interviewed once a month for four consecutive months in one year and again for the corresponding time period a year later" to make month-to-month and year-to-year comparisons possible. The March CPS is special. For one thing the respondents are asked about insurance then. Source: econterms Cramer-Rao lower bound Whenever the Fisher information I(b) is a well-defined matrix or number, the variance of an unbiased estimator B for b is at least as large as [I(B)]-1. Source: econterms criterion function Synonym for loss function. Used in reference to econometrics. Source: econterms critical region synonym for rejection region Source: econterms Cronbach's alpha A test for a model or survey's internal consistency. Called a 'scale reliability coefficient' sometimes. The remainder of this definition is partial and unconfirmed. Cronbach's alpha assesses the reliability of a rating summarizing a group of test or survey answers which measure some underlying factor (e.g., some attribute of the test-taker). A score is computed from each test item and the overall rating, called a 'scale' is defined by the sum of these scores over all the test items. Then reliability a is defined to be the square of the correlation between the measured scale and the underlying factor the scale was supposed to measure. (Which implies that one has another measure in test cases of that underlying factor, or that it's imputed from the test results.) (In Stata's examples it remains unclear what the scale is, and how it's measured; apparently alpha can be generated without having a measure of the underlying factor.) Source: econterms Cross-Price Elasticity of Demand The cross-price elasticity of demand measures the sensitivity of the demand for one good to a change in the price of another good. It is calculated as: (Percentage Change in Demand for Good X)/(Percentage Change in Price of Good Y) If two goods are independent (that is, the price of one good has no effect on the demand for the other good), the cross-price elasticity of demand is zero. If two goods are complements (they are typically consumed together) an increase in the price of one good will decrease the demand for the other good (and the reverse); therefore for complements the cross-price elasticity of demand is negative On the other hand, if two goods are substitutes, an increase in the price of one good will increase the demand for the other good (and the reverse); therefore for substitutes, the cross-price elasticity of demand is positive. Source: EconPort cross-section data Parallel data on many units, such as individuals, households, firms, or governments. Contrast panel data or time series data. Source: econterms cross-validation A way of choosing the window width for a kernel estimation. The method is to select, from a set of possible window widths, one that minimizes the sum of errors made in predicting each data point by using kernel regression on the others. Formally, let J be the number of data points, j an index to each one, from one to J, yj the dependent variable for each j, Xj the independent variables for that j, Yj the dependent variable for that j, and {hi} for i=1 to n the set of candidate window widths. The hi's might be a set of equally spaced values on a grid. The algorithm for choosing one of the hi's is: For each candidate window width hi { ..For each j from 1 to J ..{ ....Drop the data point (Xj, Yj) from the sample temporarily ....Run a kernel regression to estimate Yj using the remaining X's and Y's ....Keep track of the square of the error made in that prediction ..} ..Sum the squares of the errors for every j to get a score for candidate window width hi ..Record that in a list as the score for hi } Select as the outcome h of this algorithm the hi with the lowest score The grid approach is necessary because the problem is not concave. Otherwise one might try a simpler maximization e.g., with the first order conditions. Note however that a complete execution of the cross-validation method can be very slow because it requires as many kernel regressions as there are data points. E.g. in this author's experience, the cross-validation computation for one window width on 500 data points on a Pentium-90 in Gauss took about five seconds, 1000 data points took circa seventeen seconds, but for 15000 data points it took an hour. (Then it takes another hour to check another window width; so even the very simplest choice, between two window widths, takes two hours.) Source: econterms CRRA Stands for Constant Relative Risk Aversion, a property of some utility functions, also said to have isoelastic form. CRRA is a synonym for CES. Example 1: for any real a<1, u(c)=ca/a is a CRRA utility function. It is a vNM utility function. Source: econterms CRS Stands for Constant Returns to Scale. Source: econterms CRSP Center for Research in Security Prices, a standard database of finance information at the University of Chicago. Has daily returns on NYSE, AMEX, and NASDAQ stocks. Started in early 1970s by Eugene Fama among others. The data there was so much more convenient than alternatives that it drove the study of security prices for decades afterward. It did not have volume data which meant that volume/volatility tests were rarely done. Source: econterms cubic spline A particular nonparametric estimator of a function. Given a data set {Xi, Yi} it estimates values of Y for X's other than those in the sample. The process is to construct a function that balances the twin needs of (1) proximity to the actual sample points, (2) smoothness. So a 'roughness penalty' is defined. See Hardle's equation 3.4.1 near p. 56 for exact equation. The cubic spline seems to be the most common kind of spline smoother. Source: econterms current account balance The difference between a country's savings and its investment. "[If] positive, it measures the portion of a country's saving invested abroad; if negative, the portion of domestic investment financed by foreigners' savings." Defined by the sum of the value of imports of goods and services plus net returns on investments abroad, minus the value of exports of goods and services, where all these elements are measured in the domestic currency. Source: econterms