 Students / Subjects  F distribution The F distribution is defined in terms of two independent chi-squared variables. Let u and v be independently distributed chi-squared variables with u1 and v1 degrees of freedom, respectively. Then the statistic: F=(u/u1)/(v/v1) has an F distribution with (u1,v1) degrees of freedom. As can be computed from the definition of the t distribution, the square of a t statistic may be written: t2=(z2/1)/(v/v1), where z2, being the square of a standard normal variable, has a chi-squared distribution. Thus the square of a t variable with v1 degrees of freedom is an F variable with (1,v1) degrees of freedom, that is: t2=F(1,v1). Source: econterms F test Normally a test for the joint hypothesis that a number of coefficients are zero. Large values (greater than two?) generally reject the hypothesis, depending on the level of significance required. Source: econterms f.o.b. Indicates which services come with a price. Stands for 'free on board.' Describes a price which includes goods plus the services of loading those goods onto some vehicle or vessel at a named location, sometimes put in parentheses after the f.o.b. Source: econterms factor loadings "A security's factor loadings are the slopes in a multiple regression of its return on the factors." Source: econterms factor price equalization An effect observed in models of international trade -- that the prices of inputs to ("factors of") production in different countries, like wages, are driven towards equality in the absence of barriers to trade. This happens among other reasons because price incentives cause countries to choose to specialize in the production of goods whose factors of production are abundant there, which raises the prices of the factors towards equality with the prices in countries where those factors are not abundant. Shocks to factor availability in a country would cause only a temporary departure from factor price equality. The basic theorem of this kind is attributed to Samuelson (1948) by Hanson and Slaughter (1999) who also cite Blackorby, Schworm, and Venables (1993). The context of the theorem is a Heckscher-Ohlin model. Source: econterms factory system factories may have been more efficient by reducing transactions costs, as argued by Oliver Williamson (1980). Source: econterms fads The conjecture that market prices for securities take long swings away from their fundamental values and tend to return to them. In a time series of data this suggests that "the market price differs from the fundamental price by a highly serially correlated fad.". This formulation attributed to Shiller(1981, 1994), Summers (1986) and Poterba and Summers (1988) by Bollerslev and Hodrick (1992) p. 13. Source: econterms fair trader Contrasted with free trader, a holder of the the point of view that one's country's government must prevent foreign companies from having artificial advantages over domestic ones. The term dates at least as far back as 1886 Britain, where tariffs were recommended by one point of view expressed in a Royal Commission report 'not to countervail any natural and legitimate advantage which foreign manufacturers may possess, but simply to prevent our own industries being placed at an artificial disadvantage by the interference of either home or foreign legislation....' (Carr and Taplin, p 122) Source: econterms Fama-MacBeth regression A panel study of stocks to estimate CAPM or APT parameters Source: econterms family two or more persons related by blood, marriage, or adoption, and residing together. Source: econterms FASB Financial Accounting Standards Board, which sets accounting rules for the US. (public? private?) Source: econterms fat-tailed describes a distribution with excess kurtosis. Source: econterms Fatou's lemma Let {Xn} for n=1,2,3,... be a sequence of nonnegative real random variables. Then lim infn->infinity E[Xn] ≥ E[lim infn->infinity Xn]. Source: econterms FCLT stands for 'functional central limit theorem', and is synonymous with Donsker's theorem. Briefly: if {et} is a series of independent and mean zero random variables, partial sums (from 1 to T) of the e's converge to a standard Brownian motion process on [0,1] as T goes to infinity. See other sources for a proper formal statement. Source: econterms FDI Foreign Direct Investment, a component of a country's national financial accounts. Foreign direct investment is investment of foreign assets into domestic structures, equipment, and organizations. It does not include foreign investment into the stock markets. Foreign direct investment is thought to be more useful to a country than investments in the equity of its companies because equity investments are potentially "hot money" which can leave at the first sign of trouble, whereas FDI is durable and generally useful whether things go well or badly. Source: econterms FE stands for Fixed Effects estimator. That is, a linear regression in which certain kinds of differences are subtracted out so that one can estimate the effects of another kind of difference. Source: econterms Fed Funds Rate The interest rate at which U.S. banks lend to one another their excess reserves held on deposit at the U.S. Federal Reserve. Source: econterms FGLS Feasible GLS. That is, the generalized least squares estimation procedure (see GLS), but with an estimated covariance matrix, not an assumed one. Source: econterms fiat money is intrinsically useless; is used only as a medium of exchange. Source: econterms fields Most terms are in one of these categories. You can click on one to see a list of terms relevant to it. fields Source: econterms filter A filter is a way of treating or adjusting data before it is analyzed. Examples are the Hodrick-Prescott filter or Kalman filter. More exactly, a filter is an algorithm or mathematical operation that is applied to a time series sample to get another sample, often called the 'filtered' data. For example a filter might remove some high-frequency effects from the data; or detrend it; or remove seasonal frequencies but leave monthly frequencies in. Source: econterms FIML Full Information Maximum Likelihood, an approach to the estimation of simultaneous equations. As portrayed in Johnston's book: Define A as the matrix of coefficients in the multiple-equation model, u as the vector of residuals for each choice of A, and s as the covariance matrix E(uu'). FIML consists of maximizing ln(L(A, s)) with respect to the elements of A and s. Source: econterms finance The study of securities, borrowing, and ownership. finance Source: econterms FIPS Federal Information Processing Standards. These are encodings defined by the U.S. government and used to encode some data (like states and counties) in U.S. data sets. Listings can be found at the NIST FIPS site. Source: econterms firm Defined by Alchian and Demsetz (1972) this way: "The essence of the classical firm is identified here as a contractual structure with: 1) joint input production [see team production]; 2) several input owners [e.g. the workers]; 3) one party [the firm or its owners] who is common to all the contracts of the joint inputs; 4) who has rights to renegotiate any input's contract independently of contracts with other input owners; 5) who holds the residual claim; and 6) who has the right to sell his central contractual residual status. The central agent is call the firm's owner and the employer. No authoritarian control is involved; the arrangement is simply a contractual structure subject to continuous renegotiation with the central agent. The contractual structure arises as a means of enhancing efficient organization of team production." ---------- a firm is a hierarchical organization attempting to make profits. Source: econterms First price sealed bid auction Simultaneous bidding game where the bidder that has submitted the highest bid is awarded the object and pays his own bid (which is the 'first highest' bid). The multi-object form of the first price auction is called discriminatory auction . The equilibrium bid functions of first price auctions balance the trade- off that a higher winning probability is 'bought' by a higher expected payment. As a result, the bidders' private information is revealed in the bids in shaded form only. Oligopolistic competition of price setting firms under incomplete information (Betrand competition) is an instance of a first price procurement auction. Source: SFB 504 First Welfare Theorem The statement that a Walrasian equilibrium is weakly Pareto optimal. Such a theorem is true in a large and important class of general equilibrium models (usually static ones). The standard case is if every agent has a positive quantity of every good, and every agent has a utility function that is convex, continuous, and strictly increasing, the then the First Welfare Theorem holds. Source: econterms first-order stochastic dominance Usually means stochastic dominance. Source: econterms fiscalist view An extreme Keynesian view, that money doesn't matter at all as aggregate demand policy. Assumes that investment demand does not respond to interest rate changes. Relevant only in depression conditions (Branson, p 386). Source: econterms Fisher consistency This is a necessary condition for maximum likelihood estimation to be consistent. Maximizing the likelihood function L gives an estimate for parameter b that is Fisher-consistent if: E[d(ln L)/db]=0 at b=b0, where b0 is the true value of b. Another interpretation or phrasing: "An estimation procedure is Fisher consistent if the parameters of interest solve the population analog of the estimation problem." (Wooldridge). Source: econterms Fisher effect That in a model where inflation is expected to be steady, the nominal interest rate changes one-for-one with the inflation rate; see Fisher equation. The empirical analogy is the Fisher hypothesis. Source: econterms Fisher equation nominal rate of interest = real rate of interest + inflation Source: econterms Fisher hypothesis That the real rate of interest is constant. So the nominal rate moves with inflation. The real rate of interest would be determined by the time preferences of the public and technological constraints determining the return on real investment. Source: econterms Fisher Ideal Index The 'geometric mean of the fixed-weighted Paasche and Laspeyres indexes.' Proposed as a price index by Irving Fisher in 1922. This is a superlative index number formula. -- Triplett, 1992. Source: econterms Fisher index A price index, computed for a given period by taking the square root of the product of the the Paasche index value and the Laspeyres index value. Source: econterms Fisher information The Fisher information is an attribute or property of a distribution with known form but uncertain parameter values. It is only well-defined for distributions satisfying certain assumptions. It is a (k x k) matrix, where k is the number of elements in a vector of parameters b. Thus, for parameter b of pdf f(x): I(b)=E{ [f'(x)/f(x)]2 | b} That's from DeGroot. I think this is the same as in Greene p 96: I(b)=E[{d/db(ln L(b))}2] =-E[d2/db2(ln L(b))] If the Fisher information is 'large' then the estimated distribution will change radically as new data (x) are incorporated into the estimate of the distribution by maximum likelihood. The Fisher information is the main ingredient in the Cramer-Rao lower bound, and in some maximum likelihood estimators. Source: econterms Fisher transformation Hypotheses about the value of r, the correlation coefficient between variables x and y of the underlying population, can be tested using the Fisher transformation of a sample's correlation coefficient r. Let N be the sample's size. This transformation is defined by: z = 0.5 * ln ( (1+r)/(1-r) ) z is approximately normally distributed with mean r, and standard error 1/((N-3)^0.5). This is a common way of testing whether a correlation coefficient is significantly different from 0, and hence ascribing a p-value. ------ [Editor: We suspect that for x and y bivariate normal the distribution works exactly in all sample sizes, otherwise only asymptotically.] [See Kennedy, p 369. Bickel and Dobson, 'Mathematical Statistics: Basic Ideas and selected topics' page 221 also gives derivation, but makes no mention of any distribution requirements.] Source: econterms Fisherian criterion for optimal investment by a firm -- that it should invest in real assets until their marginal internal rate of return equals the appropriately risk-adjusted rate of return on securities Source: econterms Fixed Cost A cost of production that is independent of the quantity produced; a fixed costs must be paid even if nothing is produced. For example, if a trucking company buys a new semi-truck by taking out a 5-year loan to buy the truck, the loan must be paid (i.e., the truck must be paid for) even if the company decides to shut down and not operate at all. This fixed cost of production must be paid whether the company shuts down, reduces its production, or operates at full capacity. Fixed costs such as this are the opposite of variable costs, which depend on the amount produced. In the example above, gasoline would be a variable cost â?? if the company does not operate, it does will not have to purchase any gasoline, and the amount of gasoline purchased depends on the amount produced. Source: EconPort See also: Variable Cost , fixed effects estimation A method of estimating parameters from a panel data set. The fixed effects estimator is obtained by OLS on the deviations from the means of each unit or time period. This approach is relevant when one expects that the averages of the dependent variable will be different for each cross-section unit, or each time period, but the variance of the errors will not. In such a case random effects estimation would give inconsistent estimates of b in the model: y = Xb + e The fixed effects estimator is: (X'QX)-1X'Qy where Q is the matrix that "partials out" the averages from the groups that have different variances. Example: Define L as IN x 1T, where x is the Kronecker cross product operator, T is the number of time periods, and N is the number of cross-section units (individuals, say). Now individual effects can be screened out by premultiplying the model's equation by Q and running OLS, or equivalently using the estimator equation above. Thus estimating b. Source: econterms flexible-accelerator model A macro model in which there is a variable relationship between the growth rate of out put and the level of net investment. The relation between the change in output and the level of net investment is the accelerator principle. Source: econterms fob An occasional compressed form of f.o.b.. Source: econterms Folk theorem The theorem is that a Nash equilibrium exists in repeated games in which sufficiently patient players to reach Pareto optimal payoffs in a Nash equilibrium. (Fudenberg and Tirole, p 150, describes the achievable payoffs as the individually rational ones, not the Pareto optimal ones.) The strategies that achieve this often have the pattern that they 'punish' the other player at length for any defection from the Pareto optimal choice. In equilibrium that encourages the other player not to defect for a short term gain. Source: econterms Frame framing effect A decision-frame is the decision-maker's subjective conception of the acts, outcomes and contingencies associated with a particular choice. The frame that a decision maker adopts is controlled partly by the formulation of the problem and by the norms, habits, and personal characteristics of the decision maker. It is often possible to frame a given decision problem in more than one way. A framing effect is a change of preferences between options as a function of the variation of frames, for instance through variation of the formulation of the problem. For example, a problem can be presented as a gain (200 of 600 threatened people will be saved) or as a loss (400 of 600 threatened people will die), in the first case people tend to adopt a gain frame, generally leading to risk-aversion, and in the latter people tend to adopt a loss frame, generally leading to risk-seeking behavior. Source: SFB 504 Frechet derivative Informally: A derivative (slope) defined for mappings from one vector space to another. The first e in Frechet should have an accent aigu. Formally (this taken more or less directly from Tripathi, 1996): Let T be a transformation defined on an open domain U in a normed space X and mapping to a range in a normed space Y. (Does normed space mean normed vector space? Or might it not?) Holding fixed an x in U and for each h in X, if a linear and continuous operator L (mapping from X to Y) exists such that: lim||h|| falls to 0 (1/||h||) * (||T(x+h)-T(x)-L(h)||) = 0 Then the operator L, often denoted T'(x), is the Frechet derivative of T() and we can say T is Frechet differentiable at x. (Ed.: I believe any such L is unique.) Source: econterms Frechet differentiable Informally: A possible property of mappings from one space to another. For such a transformation, a Frechet derivative may exist at each point and if so we say the transformation is Frechet differentiable at that point. Properly the first e in Frechet should have an accent aigu. See the entry at Frechet derivative for a formal definition. Source: econterms Freddie Mac Shorthand for U.S. Federal Home Loan Mortgage Corporation. Source: econterms free cash flow cash flow to a firm in excess of that required to fund all projects that have positive net present values when discounted at the relevant cost of capital. Free cash flow can be a source of principal-agent conflict between shareholders and managers, since shareholders would probably want it paid out in some form to them, and managers might want to control it, e.g. to use it for unprofitable projects, for perquisites, to make acquisitions, to create jobs for friends and allies, and so forth. A possible partial solution to the conflict for the shareholders is for the company to have heavy debts on which frequent, heavy payments are due. Those payments keep the managers focused on delivering consistent revenues and clear out the extra cash. Source: econterms free entry condition An assumption posited in a search and matching model of a market. The assumption is that there is no institutional constraint on firms entering the market (e.g. to hire workers). There is no fixed number of firms. The number of firms is determined in equilibrium, by the costs of starting up. Source: econterms free reserves excess reserves minus borrowed reserves (Branson, p 353). Source: econterms free trader Holder of the political point of view that the best policy is to allow free trade into one's own country. Source: econterms frequency function The frequency function is the probability of drawing each particular value from a discrete distribution: p(x) = Pr(X=x). Here X is the random variable and x is one of its possible values. Source: econterms frictional unemployment Unemployment that comes from people moving between jobs, careers, and locations. Contrast structural unemployment. Source: econterms Friedman rule In a cash-in-advance model of a monetary system, the Friedman rule for monetary policy is to deflate so that it is not costly to those who have money to continue to hold it. Then the cash-in-advance constraint isn't binding on them. Source: econterms FTC Abbreviaton for the U.S. national Federal Trade Commission, which rules in some circumstances on some antitrust regulations. See also FTC. Source: econterms FTC Act A 1914 U.S. law creating a regulatory body for antitrust, price discrimination, and regulation. Section five says "Unfair methods of competition in or affecting commerce, and unfair or deceptive acts or practices in or affecting commerce, are hereby declared unlawful." Source: econterms functional a mapping from paths of functions to the reals (e.g. a value function defined by a mapping from possible paths of choices) Source: econterms functional equation an equation where the unknown is a function. Example: a value function is the solution to the equation that sets the value function equal to the present discounted value of the current period's utility and the discounted value function of next period's state. Source: econterms fungible "Being of such a nature or kind that one unit or part may be exchanged or substituted for another unit or equal part to discharge an obligation." Examples: money or grain. Not examples: works of art. Source: econterms future-oriented A future-oriented agent discounts the future lightly and so has a LOW discount rate, or equivalently a HIGh discount factor. See also present-oriented, discount rate, and discount factor. Source: econterms FWL theorem Given a statistical model y = X1b1 + X2b2+ e wherey is a vector of values of a dependent variable,the X's are linearly independent matrices of predetermined variables, and the e's are errors, we could premultiply the equation by M1=I-X1(X1'X1)-1X' which projects vectors in the space spanned by X1 to zero, and run OLS on the resulting equation M1y = M1X2b2+ M1e and (the theorem says) would get exactly the same estimate of b2 that OLS on the first equation would have given. This use of premultiplying is used in the derivation of many estimators: notably IV estimators and FE estimators. Source: econterms