Knowledge that Transforms

The authors design and study an OLG experimental economy where the government finances a fixed real deficit through seigniorage. The economy has continua of nonstationary rational expectations equilibria and two stationary rational expectations equilibria. The authors do not observe nonstationary rational expectations paths. Observed paths tend to converge close to, or somewhat below, the low inflation stationary state. The adaptive learning hypothesis is consistent with the data in selecting the low inflation stationary state rational expectations equilibrium as a long-run stationary equilibrium. Nevertheless, simple adaptive learning models do not capture the market uncertainty or the biases observed in the data. Copyright 1993 by The Econometric Society.

We analyze an evolutionary model with a finite number of players and with noise or mutations.The expansion and contraction of strategies is linked-as usual-to their current relative success, but mutations-which perturb the system away from its deterministic evolution-are present as well.Mutations can occur in every period, so the focus is on the implications of ongoing mutations, not a one-shot mutation.The effect of these mutations is to drastically reduce the set of equilibria to what we term "long-run equilibria."For 2 x 2 symmetric games with two symmetric strict Nash equilibria the equilibrium selected satisfies (for large populations) Harsanyi and Selten's (1988) criterion of risk-dominance.In particular, if both strategies have equal security levels, the Pareto dominant Nash equilibrium is selected, even though there is another strict Nash equilibrium.

This paper examines how the possibility of renegotiation affects contractual outcomes in signaling games when an infinite number of rounds of renegotiations are allowed before contracts are executed. The main results of the paper are (1) contracts may still contain distortions, (2) the popular 'efficient' separating-equilibrium outcome is never an equilibrium outcome with renegotiation, (3) incentive-compatibility constraints can be generalized to incorporate renegotiation, (4) equilibrium outcomes can be separating and nevertheless depend on the uninformed player's prior, and (5) renegotiation in signaling games may lead to outcomes similar to equilibrium outcomes of screening games in which multiple contract purchases are allowed. Copyright 1993 by The Econometric Society.

Each of n players, in an infinitely repeated game, starts with subjective beliefs about his opponents' strategies. If the individual beliefs are compatible with the true strategies chose, then Bayesian updating will lead in the long run to accurate prediction of the future of play of the game. It follows that individual players, who know their own payoff matrices and choose strategies to maximize their expected utility, must eventually play according to a Nash equilibrium of the repeated game. An immediate corollary is that, when playing a Harsanyi-Nash equilibrium of a repeated game of incomplete information about opponents' payoff matrices, players will eventually play a Nash equilibrium of the real game, as if they had complete information.

First-order autoregressive/unit root models with independent identically distributed normal errors are considered, including those without an intercept, those with an intercept, and those with an intercept and time trend. The autoregressive parameter is allowed to lie in the interval (-1, 1], which includes the unit root case. Exactly median-unbiased estimators and exact confidence intervals of the autoregressive parameter are introduced. Corresponding exactly median-unbiased estimators and exact confidence intervals are also provided for the impulse response function, the cumulative impulse response, and the half life of a unit shock. An unbiased model selection procedure is discussed. The introduced procedures are applied to several data series. Copyright 1993 by The Econometric Society.

A player's strategy, for an n-person infinitely repeated game with discounting, is subjectively rational if it is a best response to his individual beliefs regarding opponents' strategies. A vector of such strategies is a subjective equilibrium if the play induced by it is realization equivalent to the play induced by each players' beliefs. Thus, any statistical updating can only reinforce the beliefs. It is shown that under perfect monitoring, the joint behavior at a subjective equilibrium approximates a behavior of a Nash equilibrium even when perturbations are allowed. Therefore, learning processes leading to subjective equilibrium result in approximate Nash behavior.(This abstract was borrowed from another version of this item.)

A dynamic model with many sellers and buyers is constructed. Agents failing to trade may trade in the next period. An equilibrium is found where sellers hold identical auctions and buyers randomize over the sellers they visit. The distribution of buyer valuations is endogenous. An auction with efficient reserve is an optimal mechanism from each seller's point of view, in spite of the ability of any seller to alter the distribution of buyer types participating in the seller's mechanism by altering the mechanism. Copyright 1993 by The Econometric Society.

This paper introduces the concept of standard risk aversion. A von Neumann-Morgenstern utility function has standard risk aversion if any risk makes a small reduction in wealth more painful (in the sense of an increased reduction in expected utility) also makes any undesirable, independent risk more painful. It is shown that, given monotonicity and concavity, the combination of decreasing absolute risk aversion and decreasing absolute prudence is necessary and sufficient for standard risk aversion. Standard risk aversion is shown to imply not only Pratt and Zeckhauser's 'proper risk aversion" (individually undesirable, independent risks always being jointly undesirable) , but also that being forced to face an undesirable risk reduces the optimal investment in a risky security with and independent return. Similar results are established for the effect of broad class of increases in one risk on the desirability of (or optimal investment in) a second, independent risk.

Efficient estimators of cointegrating vectors are presented for systems involving deterministic components and variables of differing, higher orders of integration. The estimators are computed using GLS or OLS, and Wald Statistics constructed from these estimators have asymptotic x2 distributions. These and previously proposed estimators of cointegrating vectors are used to study long-run U.S. money (Ml) demand. Ml demand is found to be stable over 1900-1989; the 95% confidence intervals for the income elasticity and interest rate semielasticity are (.88,1.06) and (-.13, -.08), respectively. Estimates based on the postwar data alone, however, are unstable, with variances which indicate substantial sampling uncertainty.