 Students / Subjects  t distribution Defined in terms of a normal variable and a chi-squared variable. Let z~N(0,1) and v~X2(n). (That is, v is drawn from a chi-squared distribution with n degrees of freedom.) Then t = z(n/v)1/2 has a t distribution with n degrees of freedom. The t distribution is a one-parameter family of distributions. n is that parameter here. The t distribution is symmetric around zero and asymptotically (as n goes to infinity) approaches the standard normal distribution. Mean is zero, and variance is n/(n-2). Source: econterms t statistic After an estimation of a coefficient, the t-statistic for that coefficient is the ratio of the coefficient to its standard error. That can be tested against a t distribution (which see) to determine how probable it is that the true value of the coefficient is really zero. Source: econterms tangent cone Informally: a set of vectors that is tangent to a specified point. Source: econterms Target return To measure the shortfall risk and the excess chance, the investor has to define a target return. This can be a deterministic one, for example a riskless attainable final wealth position or a minimum return, spezified by a controlling authority or by the market. Besides this, it is also interesting to consider a random target return, e.g. the return or the price of a stock- or a bond-index. Source: SFB 504 team production Defined by Alchian and Demsetz (1972) this way: "Team pproductive activity is that in which a union, or joint use, of inputs yields a larger output than the sum of the products of the separately used inputs." (p. 794) Source: econterms technical change A change in the amount of output produced from the same inputs. Such a change is not necessarily technological; it might be organizational, or the result of a change in a constraint such as regulation, prices, or quantities of inputs. According to Jorgenson and Stiroh (May 1999 American Economic Review p 110), sometimes total factor productivity (TFP) can be a synonym for technical change. A possible measure is output per unit of factor input. Jorgenson and Stiroh also have an explanation of how it is definitionally possible for how a technological revolution not to lead to technical change as measured in these ways. Source: econterms technological change A change in the set of feasible production possibilities. Contrast technical change. Source: econterms technology shocks An event, in a macro model, that changes the production function. Commonly this is modeled with a aggregate production function that has a scaling factor, e.g.: F(Kt,Nt) = AtKaN(1-a) where At a time series of technology shocks whose values can be estimated or whose stochastic process (joint distribution) might be conjectured to have certain properties. By this definition the oil shocks of the 1970s were technology shocks -- that is, for any given aggregate capital stock or labor stock, production was more expensive after an oil shock because energy would be more expensive. This interpretation explains why real business cycle theory drew interest in economics in the 1970s after the oil shocks had such a dramatic impact on Western economies. Source: econterms tenure In the context of studies of employees, length of time with current employer in current job. Contrast experience. Source: econterms term spreads "long-term minus short-term interest rates" Source: econterms terms of trade An index of the price of a country's exports in terms of its imports. The terms of trade are said to improve if that index rises. (Obstfeld and Rogoff, p 25) An analogous use is when comparing relative prices. If the cost of agricultural goods in terms of industrial goods goes up, one might say the 'terms of trade ... shifted in favor of agricultural products.' (North and Thomas, p 108). Source: econterms tertiary sector Literally, 'third sector'. Per Landes, 1969/1993, p 9, refers to the "administrative and service sector of the economy". In context of Williamson and Lindert, 1980, p 172, is defined more specifically to be the sector of production outside of agriculture and industry, and includes construction, trade, finance, real estate, private services, government, and sometimes transportation. Source: econterms test for structural change An econometric test to determine whether the coefficients in a regression model are the same in separate subsamples. Often the subsamples come from different time periods. See Chow test. Source: econterms test of identifying restrictions synonym for Hausman test, in practice. Only overidentifying restrictions (assumptions) can be tested. Source: econterms test statistic "A random variable [T, in this example] of which the probability distribution is known, either exactly or approximately, under the null hypothesis. We then see how likely the observed value of T is to have occurred, according to that probability distribution. If T is a number that could easily have occurred by chance [under the tested hypothesis], then we have no evidence against the null hypothesis H0. However if it is a number that would occur by chance only rarely, we do have evidence against the null, and may well decide to reject it." Source: econterms TFP Abbreviation for Total Factor Productivity. Source: econterms the standard model Has a variety of meanings, and can be a confusing phrase to outsiders to a discussion. Often implicitly contrasts the model at hand to a simpler, earlier one in the same literature, sometimes with the implication that variations from the earlier one ought, in the speaker's opinion, to be justified explicitly. A standard model of a firm is one in which it is strictly and always profit maximizing. Often 'profit' is interpreted in a short term way, but depending on context it may refer to a long run present-discounted value kind of profit. A standard model of individuals seeking jobs is that they are strictly consumption maximizing, and therefore wage maximizing. Occasionally a long run present discounted value of wages is the objective. If time away from work is relevant, the consumer maximizes some combination of consumption/ wage and time away from work, or 'leisure'. A standard model of international trade is one in which countries specialize toward their comparative advantages. A standard model of a product market is one in which (1) all producers (called firms) and consumers (thought of as individuals) are price takers and variations in any one actor's production or consumption have no effect on the price; (2) the demand curve is strictly increasing (that is the price and quantity are positively correlated); (3) the supply curve is strictly decreasing (that is, price and quantity are negatively correlated); (4) the good is infinitely divisible. Source: econterms Theory of subjective expected utility The theory of subjective (expected) utility (Savage, 1954) is the central element of the neoclassical theory of rational economic behavior. As such, it is the most important example of a theory of rational behavior. Its basic assumptions are that choices are made:• among a given, fixed set of alternatives; • with (subjectively) known probability distributions of outcomes for each alternative; and • in such a way as to maximize the expected value of a given utility function.While these assumptions are convenient for many purposes, they may not fit empirically many situations of economic choice. This is the subject of the theory of bounded rationality and the research interest of behavioral economics. Source: SFB 504 theory of the firm Subject is: What are the nature, extent, and purposes of firms? This organization of the answers comes from Hart's book. Categories of answers: Neoclassical theories of the firm identify it with its production technology, and usually define the driving objective of the firm as maximizing its profits given its technology. Principal-agent theories of firms -- that firms are organized to divide work among many people in ways that minimize principal agent problems. Transaction cost theories -- that comprehensive contracts with workers are unrealistic and that the structure of a firm (e.g., a hierarchical one) is useful for efficiently doing a job. First academic paper of this kind was Coase, 1937. Property rights theories -- that ownership is a source of power ... --------- theory of the firm: firm organization substitutes for contracts, firms reduce uncertainty and opportunistic behavior, and set incentives to elicit efficient responses from agents. -- Mokyr's rise and fall paper Source: econterms theta As used with respect to options: The rate of change of the value of a portfolio of derivatives with respect to time with all else held constant. Formally this is a partial derivative. Source: econterms tightness An attribute of a market. In securities markets, tightness is "the cost of turning around a position over a short period of time." (Kyle, 1985, p 1316). [Does 'cost' mean trading costs, alone? So does 'turning around' just mean 'trading'?] A labor market is said to be tight if employers have trouble filling jobs, or if there is a long wait to fill an available job. It is not evidence that the labor market is tight if potential employees have trouble finding jobs or must wait to get one. Source: econterms time consistency Opposite of time inconsistency or dynamic inconsistency. Source: econterms time deposits The money stored in the form of savings accounts at banks. Source: econterms time inconsistency Same as dynamic inconsistency. Source: econterms Time preference Intuitively, time preference describes the preference for present consumption over future consumption. It is a key concept underlying the theory of intertemporal choice. The strength of this preference is measured by the rate of time preference or, equivalently, by a discount factor.An number of studies have shown that the standard theory of intertemporal choice is frequently violated in experimental settings, just as standard (static) expected utility (EU) theory of choice is systematically violated. The main findings of such experiments are (see Camerer 1995, pp. 649-51):• Implicit discount rates decline with time horizon (formally, this implies that discount rates are hyperbolic rather than exponential); • discount rates are larger for gains than for losses of equal magnitude; • people demand more to delay consumption than to speed it up.How alternative models of intertemporal choice (such as hyperbolic discounting) can be incorporated in applied economic research is an important field of current research. Source: SFB 504 time preference A utility function may or may not have the property of time preference. Time preference is an intense preference to receive goods or services immediately. The discount factor preference to avoid delay must be more than multiplictavely linear in the delay time passed, or one would not use this term to describe the utility function. In theory this attribute is analytically distinct from other reasons to want something sooner, such as interest rates; the bounded rationality problem of remembering how and when to consume the good later; or discounting of future events for reasons of opportunity, risk, or uncertainty (e.g., the chance of surviving to a later time). There is evidence that human behavior exhibits great impatience which might be modeled well by time preference and perhaps can perhaps be distinguished from these other factors. So one may read references to empirical observations of time preference, though as far as this editor can tell the concept is quite theoretical and some jump is required to leave all other explanations aside and link it directly to an observation. Source: econterms time series A stochastic process where the time index takes on a finite or countably infinite set of values. Denoted, e.g. {Xt | for all integers t}. Relevant terms: time series See Editor's comment on time series. Source: econterms time-varying covariates Means the same thing as time-dependent covariates; that the covariates (regressors, probably) change over time. Source: econterms tit-for-tat A strategy in a repeated game (or a series of similar games). When a Prisoner's dilemma game is repeated between the same players, the tit-for-tat strategy is to choose the 'cooperate' action unless in the previous round, one's opponent chose to defect, in which case one responds by choosing to defect this round. This tends to induce cooperative behavior against an attentive opponent. Source: econterms Tobin tax A tax on foreign currency exchanges. Source: econterms Tobin's marginal q The ratio of the change in the value of the firm to the added capital cost for a small increment to the capital stock. If the firm is in equilibrium, it's marginal q is one; all investments that add more to the value of the firm than their cost have already been undertaken, and if we knew the replacement cost of capital we could look up the stock market value of a firm and calculate its average q directly. Source: econterms Tobin's q This description comes from Dow and Gorton, (1996): The ratio of the current market value of a firm's assets to their cost. If q is greater than 1, the firm should increase its capital stock. It follows that, according to "Fischer and Merton (1984), 'the stock market should be a predictor of the rate of corporate investment' (p 84-85)" -- that is,"rising stock prices cause higher investment [by firms]. The empirical evidence is consistent with this view: investment in plant and eqipment increases following a rise in stock prices in all countries that have been studied. In fact, lagged stock returns outperform q in predicting investment [at both] the macroeconomic level and in cross-sections of firms. See Barro (1990), Bosworth (1975), and Welch (1994)." Source: econterms tobit model An econometric model in which the dependent variable is censored; in the original model of Tobin (1958), for example, the dependent variable was expenditures on durables, and the censoring occurs because values below zero are not observed. The model is: yi*=bxi+ui where ui~N(0,s2) But yi* (e.g., durable goods desired by the consumer described by variables xi) is not observed. yi=yi* if yi*>y0, and yi=y0 otherwise yi is observed. y0 is known. s2 is often treated as known. xi's are observed for all i. Source: econterms top-coded For data recorded in groups, e.g. 0-20, 21-50, 50-100, 101-and-up, we do not know the average or distribution of the top category, just its lower bound and quantity. That data is 'top-coded.' We may adjust for it by scaling up the top-code and calling that the average. Source: econterms topological space A pair of sets (X, t) such that t is a topology in X. See topology. Source: econterms topology Is defined with respect to a set X. A 'topology in X' is a set of subsets of X satisfying several criteria. Let t denote a topology in X. The sets in t are by definition 'open sets' with respect to t, and sets outside of t are not. t satisfies the following: (1) X and the null set are in t. (2) Finite or infinite unions of open sets (that is, elements of t) are also in t. (3) Finite intersections of open sets are in t. Comments and related definitions: More than one topology in X may be possible for a given set X. The complement of a set in t is said to be a 'closed set'. Element of X may be called 'points'. A 'neighborhood' of a point x is any open set containing x. Let M be a subset of X. A point x in X is a 'contact point' of M if every neighborhood of x contains at least one point of M; and x would be a 'limit point' of M if every neighborhood of x contained infinitely many points of M. The set of all contact points of M is the 'closure' of M. A 'topological space' is a pair of sets (X, t) satisfying the above. All metric spaces are topological spaces. The sets one would call open in a metric space satisfy the criteria above; one could also label all subsets of X as open for purpose of listing the members of the topology and they would then satisfy the definition above. Given two topologies t1 and t2 on the same set X, we say that 't1 is stronger than t2', or equivalently that 't2 is weaker than t1' if every set in t2 is in t1. A stronger topology thus has at least as many elements as a weaker one. Source: econterms Tornqvist index Defined in Hulten to be a discrete-time approximation to a Divisia index, in which averages over time fill in the quantities of capital and labor. The Tornqvist index is a superlative index formula. It was developed in the 1930s at the Bank of Finland, according to Triplett (1992). Defined at length in Dean & Harper, 1998, pages 8-9. See also http://www.geocities.com/jeab_cu/paper2/paper2.htm. Source: econterms total factor productivity Given the macro model: Yt = ZtF(Kt,Lt), Total Factor Productivity (TFP) is defined to be Yt/F(Kt,Lt) Likewise, given Yt = ZtF(Kt,Lt,Et,Mt), TFP is Yt/F(Kt,Lt,Et,Mt) The Solow residual is a measure of TFP. TFP presumably changes over time. There is disagreement in the literature over the question of whether the Solow residual measures technology shocks. Efforts to change the inputs, like Kt, to adjust for utilization rate and so forth, have the effect of changing the Solow residual and thus the measure of TFP. But the idea of TFP is well defined for each model of this kind. TFP is not necessarily a measure of technology since the TFP could be a function of other things like military spending, or monetary shocks, or the political party in power. "Growth in total-factor productivty (TFP) represents output growth not accounted for by the growth in inputs." -- Hornstein and Krusell (1996). Disease, crime, and computer viruses have small negative effects on TFP using almost any measure of K and L, although with absolutely perfects measures of K and L they might disappear. Reason: crime, disease, and computer viruses make people AT WORK less productive. Source: econterms totally mixed strategy In a noncooperative game, a totally mixed strategy of a player is a mixed strategy giving positive probability weight to every pure strategy available to the player. For a more formal definition see Pearce, 1984, p 1037. This is a rough paraphrase. Source: econterms Townsend inefficiency a possible property of monetary exchange. One of the parties is evaluating the value of the money he gets in the transaction not the utility he generated in production. Source: econterms trace The trace of a square matrix A is the sum of the elements on its diagonal. Has the property that tr(AB)=tr(BA). Source: econterms Tragedy of the commons A metaphor for the public goods problem that it is hard to coordinate and pay for public goods. The term comes from Hardin (1968). The commons is a pasture held by a group. Each individual owns sheep and has the incentive to put more and more sheep on the pasture to gain, privately. The overall effect of many individuals do this overwhelms the carrying capacity of the pasture and the sheep cannot all survive. Source: econterms trajectory series of states in a dynamical system {N0, N1, N2, ...}. For a deterministic generator function F() such that Nt+1 = F(Nt), then N1=F(N0), N2=F(F(N0)), etc. Source: econterms transactions costs Made up of three types per North and Thomas (1973) p 93: -- search costs (the costs of locating information about opportunities for exchange) -- negotiation costs (costs of negotiating the terms of the exchange) -- enforcement costs (costs of enforcing the contract) Source: econterms transactions demand The transactions demand for money is positively related to income and negatively related to the interest rate. Source: econterms transient In the context of stochastic processes, "A state is called transient if there is a positive probability of leaving and never returning." -- Stokey and Lucas, p 322 Source: econterms transition economics Since about 1992 this term has come to mean the subject of the transition of post-Soviet economies toward a Western free market model. It almost never refers either to other kinds of transitions economies might undergo, nor to the subject labeled development economics. Source: econterms translog The translog production function is a generalization of the Cobb-Douglas production function. The name stands for 'transcendental logarithmic'. See Greene, 2nd edition, p 209-210. Cited to Berndt and Christensen (1972); elsewhere, said to have been introduced by Christensen, Jorgenson, and Lau, 1971, p 255-6. Applied to a case like Y=f(K,L), where f() is replaced by the translog. Its use always seems to be in estimation not in theory. Avoids strong assumptions about the functional form of the production function; can approximate any other production function to second degree. The regression run is, e.g. (from Greene p 209): ln Y = b1 + b2 (ln L) + b3 (ln K) + b4 (ln L)2/2 + b5 (ln K)2/2 + b6 (ln L)(ln K) + e The Cobb-Douglas estimation is like this but with the restriction that b4=b5=b6=0. Greene, p 210 says that the elasticity of output with respect to capital is in this model: (d ln Y)/(d ln K) = b3 + b5 (ln K) + b6 (ln L) -------------------- From Lau (1996) in _Mosaic_: Flexible functional forms such as the translog production function allow 'the production [function?] elasticies to change with differing relative factor proportions.' (p76) Source: econterms transpose A matrix operation. The transpose of an M x N matrix A is an N x M matrix, denoted A' or AT, in which the top row of A has been made into the first column of A', the second row of A has been made into the second column of A', and so forth. Source: econterms transversality condition Limits solutions to an infinite period dynamic optimization problem. Intuitively, it rules out those that involve accumulating, for example, infinite debt. The transversality condition (TC) can be obtained by considering a finite, T-period horizon version of the problem of maximizing present value, obtaining the first-order condition for nt+T, and then taking the limit of this condition as T goes to infinity. The form is often: (TC) lim bT.... = 0 Source: econterms treatment effects In the language of experiments, a treatment is something done to a person that might have an effect. In the absence of experiments, discerning the effect of a treatment like a college education or a job training program can be clouded by the fact that the person made the choice to be treated. The outcomes are a combined result of the person's propensity to choose the treatment, and the effects of the treatment itself. Measuring the treatment's effect while screening out the effects of the person's propensity to choose it is the classic treatment effects problem. A standard way to do this is to regress the outcome on other predictors that do not vary with time, as well as whether the person took the treatment or not. An example is a regression of wages not only on years-of-education but also on test scores meant to measure abilities or motivation. Both years-of-education and test scores are positively correlated with subsequent wages, and when interpreting the findings the coefficient found on years of education has been partly cleansed of the factors predicting which people would have chosen to have more education. A more advanced method is the Heckman two-step. Source: econterms trembling hand perfect equilibrium Defined by Selten (1975). Now perfect equilibrium is considered a synonym. Source: econterms trend stationary A time series process is trend stationary if after trends were removed it would be stationary. Following Phillips and Xiao (1998): iff a time series process yt can be decomposed into the sum of other time series as below, it is trend stationary: yt = gxt + st where g is a k-vector of constants, xt is a vector of deterministic trends, and st is a stationary time series. Phillips and Xiao (1998), p. 2, say that xt may be "more complex than a simple time polynomial. For example, time polynomials with sinusoidal factors and piecewise time polynomials may be used. The latter corresponds to a class of models with structural breaks in the deterministic trend." Whether all researchers would include statistical models with structural breaks in the class of those that are trend stationary, as Phillips and Xiao do, is not known to this writer. Note that this definition is designed to discuss the question of whether a statistical model is trend stationary. To decide if one should think of a particular time series sample as trend stationary requires imposing a statistical model first. Source: econterms triangular kernel The triangular kernel is this function: (1-|u|) for -1k: 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'PzX)-1X'Pzy where Pz, the projection matrix of Z, is defined to be: Pz = Z(Z'Z)-1Z' Source: econterms two-factor model suggests a production model with two factors of production, labor L and capital K. Source: econterms 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. Source: econterms 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: econterms 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: econterms 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: econterms Type of players In a game of incomplete information, the payoff-relevant private information of a player, like the numerical level of a certain parameter in his von Neumann-Morgenstern utility function, is called his type. In a game of incomplete information, each player has at least two possible types. Types also can be represented as varying continously. Source: SFB 504 Type1 Arbitrage is a trading strategy that generates a strictly positive cash flow between 0 and T in at least one state with positive probability and does not require an outflow of funds at any date, that is a trading strategy that produces something from nothing. A simple example of this kind of arbitrage is the opportunity to borrow and lend at two different rates of interest. Source: SFB 504 Type2 Arbitrage generates a net future cash flow of at least zero for sure, with the arbitrageur getting his profits up front. This kind of arbitrage is referred to as free lunch. The simultaneous purchase and sale of the same or essentially similar security in two different markets for advantageously different prices may illustrate this case.This text-book definition of arbitrage requires no capital and entails no risk. We do not expect such strategies to exist in the equilibrium state of efficient securities market. Source: SFB 504