The model analyzed here constrains most work on the main job to be full time. Partial retirement requires a job change and a wage reduction.Estimates of utility function parameters and their distributions incorporate information on age of leaving the main job and of full retirement. These estimates determine the slope at different ages and the convexity of within period indifference curves between compensation and leisure. Even though age specific dummy variables are not used, the model closely tracks retirement behavior. Policy analysis based on earlier models with simpler structures is shown to be misleading.
[This paper establishes a simple existence result for solutions to variational problems of the form ∫_0^∞ G(x, ẋ, t) dt or ∫_0^∞ G(x, ẋ, ẍ, t) dt. The key assumptions are that G have an integrable upper bound, that it satisfy a growth condition, and that it be concave as a function of the highest order derivative in the problem, other arguments held constant. The discussion illustrates why three well known types of problems fail to have solutions. For two of these—chattering and cake eating—extended solution concepts are contrasted with simple modifications that restore the existence of a conventional solution. In a third case—state variables with jumps—the source of the difficulty is fundamental. For these problems a natural extended solution, analogous to the extension from probability density functions to general distribution functions, is suggested.]
The Nash equilibrium concept may be extended gradually when the rules of the game are interpreted in a wider and wider sense, so as to allow preplay or even intraplay communication. A well-known extension of the Nash equilibrium is Aumann's correlated equilibrium, which depends only on the normal form of the game. Two other solution concepts for multistage games are proposed here: the extensive form correlated equilibrium, where the players can observe private extraneous signals at every stage and the communication equilibrium, where the players are furthermore allowed to transmit inputs to an appropriate device at every stage. We show that the set of payoffs associated with each solution concept has a canonical representation (in the spirit of the revelation principle) and is a convex polyhedron. We also provide for each concept a super-canonical game such that the set of payoffs associated with the solution concept is precisely the set of Nash equilibrium payoffs of this game.
On considere differents aspects de la conception et de l'analyse. On compare des facons alternatives d'observer des individus en temps discret via la matrice d'information de Fisher
[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.]
[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.]
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