Knowledge that Transforms

On presente une definition formelle de l'identification dans un contexte non parametrique sur la base des travaux de Koopmans et Reiersol (1950)

The exact distribution of the regression t statistic for testing the value of the AR parameter in a Gaussian first ord er autoregressive model is investigated by Monte Carlo methods. The S tudent's t distribution is not a satisfactory approximation for sampl es typical in economic applications. The main problem is the location of the distribution of the t statistic rather than the shape. Once t he t statistic is adjusted so that it has the same mean and standard deviation as Student's t, the distribution of the adjusted t statisti c is accurately approximated by Student's t. Techniques are presented for mak-ing these adjustments in practice. Copyright 1988 by The Econometric Society.

ESTIMATION OF PARAMETERS in discrete-time, linear-quadratic, infinite-horizon, dynamic, optimization models (Hansen and Sargent, 1980, 1981) is a nonlinear estimation problem. An impediment to effectively computing parameter estimates and their covariances in these models with gradient algorithms (Kennedy and Gentle, 1980, pp. 425-512) has been the absence of expressions for computing analytic VoP, the gradient matrix of first-partial derivatives of the optimal policy matrix P with respect to parameters of the optimization problem collected in vector 0. Derivatives can always be approximated numerically, but gradient algorithms perform more reliably, accurately, and quickly when analytic derivatives are used. In this paper we derive linear systems whose solution yields analytic V P. We also express Vo P in a closed form, which, while not computationally recommended because it involves sparse, Kronecker-product, matrices, may be analytically useful. We consider a higher-order problem put into first-order, state-space, form. Present results can be used with Euler-equation solution methods after making the appropriate translation (Hansen and Sargent, 1981, pp. 134-135).

A measure of complexity for repeated game strategies is studied. This measure facilitates the investigation of some issues regarding finite and the structure of subgame perfect equilibria of repeated games with discounting. Specifically, the complexity of a strategy in a given repeated game is defined to be the cardinality of the induced strategy set, i.e., the number of distinct strategies induced by the original strategy in all possible subgames. We observe that this cardinality is equal to the size (cardinality of the state set) of the smallest automaton which can implement the strategy. Thus, in a sense, complexity is measured on the basis of the amount of computing power inherent in the strategy. A measure of strategic memory is also studied. The following results are obtained: (1) combining two notions of bounded rationality (epsilon equilibrium and finite complexity), we find that every subgame perfect equilibrium of the repeated game can be approximated (with regard to payoffs) by a subgame perfect epsilon equilibrium of finite complexity. (2) For a generic class of normal form stage games, at every discount robust subgame perfect (DRSP) equilibrium, there are necessary relationships among the complexities and memories of the players' strategies. In the two player case, strategies must be equally complex and must have equal memories. (3) For a second class of two pla-yer stage games, we show that the payoff vectors for all DRSP equilibria are obtainable via equilibria in which the players' strategies are equally complex and have equal memoiies.

Many electoral rules require a super-majority vote to change the status quo. Without some restriction on preferences, super-majority rules have paradoxical properties. For example, electoral cycles are possible with anything other than 100 percent majority rule. The auth ors show that these problems do not arise if there is sufficient simi larity of attitudes among the voting population. Their definition of social consensus involves two restrictions on domain: one on individu al preferences, the other on the distribution of preferences. When th is consensus exists, 64 percent majority rule has many desirable prop erties, including the elimination of all electoral cycles. Copyright 1988 by The Econometric Society.

Several partners jointly own an asset that may be traded among them.Each partner has a valuation for the asset; the valuations arc known privately and drawn independently from a common probability distribution.We characterize the set of all incentive-compatible and interim-individually-rational trading mechanisms, and give a simple necessary and sufficient condition for such mechanisms to dissolve the partnership ex post efficiently.A bidding game is constructed that achieves such dissolution whenever it is possible.Despite incomplete in- formation about the valuation of the asset, a partnership can be dissolved ex post efficiently provided no single partner owns too large a share; this contrasts with Myerson and Satterth- waite's result that ex post efficiency cannot be achieved when the asset is owned by a singlf party.

Under fairly general conditions, ordinary least squares and linear instrumental variables estimators are asymptotically normal when a regression equation has nonstationary right hand side variables. Standard formulas may be used to calculate a consistent estimate of the asymptotic variance-covariance matrix of the estimated parameter vector, even if the disturbances are conditionally heteroskedastic and autocorrelated. So inference may proceed in the usual way. The key requirements are that the nonstationary variables share a common unit root and that the unconditional mean of their first differences is nonzero. Copyright 1988 by The Econometric Society.

This paper derives necessary and sufficient conditions for Arrow-Debreu choices of contingent consumption to be compatibl e with the maximization of a state-independent expected utility funct ion that exhibits increasing or decreasing absolute risk aversion, or increasing or decreasing relative risk aversion. The conditions can be used to bound different measures of risk aversion based on a singl e observation of Arrow-Debreu portfolio choice. Copyright 1988 by The Econometric Society.

The idea that markets might aggregate and disseminate information and also resolve conflicts is central to the literature on decentralization (Hurwicz, 1972) and rational expectations (Lucas, 1972). We report on three series of experiments all of which were predicted to have performed identically by the theory of rational expectations. In two of the three series (one in which participants trade a complete set of Arrow-Debreu securities and a second in which all participants have identical preferences), double auction trading leads to efficient aggregation of diverse information and rational expectations equilibrium. Failure of the third series to exhibit such convergence demonstrates the importance of market institutions and trading instruments in achievement of equilibrium.