Knowledge that Transforms

To make high-quality research more accessible and easier to explore.

Microeconometric Demand System with Binding Nonnegativity Constraints: The Dual Approach

Econometrica 1986 54(5), 1237
[This paper considers the problem of specifying and estimating demand systems for samples which contain a significant proportion of observation with zero consumption of one or more goods. Our approach uses virtual prices, which are dual to the Kuhn-Tucker conditions, to select the set of goods consumed--the demand regime--and to transform binding nonnegativity constraints into nonbinding constraints. It has the advantage of permitting the use of indirect cost and utility functions such as the translog, and the analytic decomposition of demand effects for goods at the nonnegativity limit.]

Learning Procedures and Convergence to Rationality

Econometrica 1986 54(4), 845
[Macroeconomic models with rational expectations find a new justification if these models appear as limits of some learning procedures. In this paper we consider the case in which, during the learning period, the predictions are obtained by regression. We exhibit the necessary and sufficient condition on the parameter of the model ensuring the convergence of the learning process. The limit is the solution of a rational expectations model in which the information set only includes the exogenous variables used in the auxiliary regression.]

The Folk Theorem in Repeated Games with Discounting or with Incomplete Information

Econometrica 1986 54(3), 533
When either there are only two players or a full dimensionality condition holds, any individually rational payoff vector of a one-shot game of complete information can arise in a equilibrium of the infinitely-repeated game if players are sufficiently patient. In contrast to earlier work, mixed strategies are allowed in determining the individually rational payoffs (even when only realized actions are observable). Any individually rational payoffs of a one-shot game can be approximated by sequential equilibrium payoffs of a long but finite game of incomplete information, where players' payoffs are almost certainly as in the one-shot game. THAT STRATEGIC RIVALRY in a long-term relationship may differ from that of a one-shot game is by now quite a familiar idea. Repeated play allows players to respond to each other's actions, and so each player must consider the reactions of his opponents in making his decision. The fear of retaliation may thus lead to outcomes that otherwise would not occur. The most dramatic expression of this phenomenon is the celebrated for repeated games. An outcome that Pareto dominates the minimax point is called individually rational. The Folk Theorem asserts that any individually rational outcome can arise as a equilibrium in infinitely repeated games with sufficiently little discounting. As Aumann and Shapley [3] and Rubinstein [20] have shown, the same result is true when we replace the word Nash by (subgame) perfect and assume no discounting at all. Because the Aumann-Shapley/Rubinstein result supposes literally no discounting, one may wonder whether the exact counterpart of the Folk Theorem holds for equilibrium, i.e., whether as the discount factor tends to one, the set of equilibrium outcomes converges to the individually rational set. After all, agents in most games of economic interest are not completely patient; the no discounting case is of interest as an approximation. It turns out that this counterpart is false. There can be a discontinuity (formally, a failure of lower hemicontinuity) where the discount factor, 8, equals one, as we show in Example 3. Nonetheless the games in which discontinuities occur are quite degenerate, and, in the end, we can give a qualified yes (Theorem 2) to the question of whether the Folk Theorem holds with discounting. In particular, it always holds in two-player games (Theorem 1). This last result contrasts with the recent work of Radner-Myerson-Maskin [18] showing that, even in two-player games, the equilibrium set may not be continuous at 8 = 1 in

Mobility Indices in Continuous Time Markov Chains

Econometrica 1986 54(6), 1407
[The axiomatic derivation of mobility indices for first-order Markov chain models in discrete time is extended to continuous-time models. Many of the logical inconsistencies among axioms noted in the literature for the discrete time models do not arise for continuous time models. It is shown how mobility indices in continuous time Markov chains may be estimated from observations at two points in time. Specific attention is given to the case in which the states are fractiles, and an empirical example is presented.]

Power and Linear Income Taxes: An Example

Econometrica 1986 54(1), 87
[This paper amends the Aumann and Kurz single commodity "Power and Taxes" model in several ways: A linear production technology is assumed, incentive effects are introduced, and tax schedules are restricted to be linear. A theorem is stated which characterizes the linear tax schedules which are the NTU solutions of the model. The solutions of an example are computed, providing a perspective on a result of the Aumann and Kurz model that equilibrium marginal tax rates are not less than 50 per cent. For this example, equilibrium marginal tax rates are less than 50 per cent; incentive effects appear to be responsible for the low tax rates.]

Theoretic Models: Mathematical Form and Economic Content

Econometrica 1986 54(6), 1259
[Changes in the mathematical form of theoretic models of an economy during the past four decades and the growth of mathematical economics in that period are considered in relation to each other and to the development of the Econometric Society. The fit of the mathematical form to the economic content of theoretic models, their separation in a completed axiomatic theory and their interplay in its elaboration are examined. Consequences of the axiomatization of economic theory are analyzed.]