Knowledge that Transforms

This paper presents a theory of equilibrium asset pricing that generalizes the recent work of G. Connor (1984). Th e model extends Connor's results to more general sets of asset return s and consumer preferences; introduces production; and provides a fra mework for analyzing exact and approximate equilibrium asset pricing. The other major contribution of the paper is the introduction of geo metric arguments that exploit the properties of induced preferences o ver assets. This method of analyzing asset pricing provides an intuit ively appealing way of analyzing equilibrium asset pricing theories. Copyright 1988 by The Econometric Society.

The Helpman-Razin model of international trade under uncertainty is extended to allow for country-specific productivi ty shocks. It is shown that, for the multiple-sector multiple-factor case, there exists a set of interesting sufficient conditions under w hich it is possible to predict the pattern of international trade in securities, goods, and factor content on the basis of cross-country d ifferences in factor endowments. It is shown that, under these circum stances, some well-known empirical tests have to be modified. Copyright 1988 by The Econometric Society.

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

The author proves several versions of the second welfare theorem for exchange economies with non convex preferences. One theorem asserts that, given a Pareto optimum f, one can find income transfers and a Walrasian quasiequilibrium g s uch that all but k agents are indifferent between f and g, where k is the number of commodities. Another theorem shows that, with probabil ity one in a particular formulation of a random sequence of economies , every Pareto optimum is close to a Walrasian equilibrium with incom e transfers. Copyright 1988 by The Econometric Society.

The paper provides an intertemporal version of the capital asset pricing model (CAPM) of Sharpe and Lintner. Although we allow for general changes in the investment opportunity set and for general risk-averse preferences, there are conditions under which two mutual funds are sufficient to generate all optimal portfolios. In particular, we require that the Riesz claim, which represents the date O pricing functional for the marketed claims, should lie in a scalar Brownian information set. Then we obtain an instantaneous counterpart to the CAPM pricing formula: a linear relationship between the conditional mean returns on the securities and conditional covariances with the return on the market portfolio. Our use of option pricing techniques requires continuous trading but does not require continuous consumption. In addition, we consider a large economy with a factor structure, as in Ross' arbitrage pricing theory. The dividends are assumed to have an approximate factor structure, with the factor components lying in the information set generated by an N-dimensional Brownian motion, and with the covariance matrices of the idiosyncratic components having uniformly bounded eigenvalues. We obtain an N-factor version of the pricing formula and relate the factors to the gains processes {price change plus accumulated dividends) for well-diversified portfolios. An approximate factor structure for dividends implies an approximate factor structure for the gains processes of the securities. Furthermore, the assumption_that per.capita supply is well diversified can motivate our condition that the Riesz claim lies in an N-dimensional Brownian information set.

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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.