The authors analyze a continuous time model with a Walrasian labor market and a random search retail market with prices set on a take-it or leave-it basis. The equilibrium distribution of money holdings is the asymptotic steady state of this stochastic process. There is a unique uniform price steady state equilibrium. The faster the search process the higher the absolute price, wage, and real wage. The instantaneous effect of an equal per capita infusion of money is to raise the price, wage, real wage, and transactions rate. The immediate post-infusion price and wage can overshoot their new asymptotic values. Copyright 1990 by The Econometric Society.
New results on the exact small sample distribution of the instrumental variable estimator are presented by studying an important special case. The exact closed forms for the probability density and cumulative distribution functions are given. There are a number of surprising findings. The small sample distribution is bimodal. with a point of zero probability mass. As the asymptotic variance grows large, the true distribution becomes concentrated around this point of zero mass. The central tendency of the estimator may be closer to the biased least squares estimator than it is to the true parameter value. The first and second moments of the IV estimator are both infinite. In the case in which least squares is biased upwards, and most of the mass of the IV estimator lies to the right of the true parameter, the mean of the IV estimator is infinitely negative. The difference between the true distribution and the normal asymptotic approximation depends on the ratio of the asymptotic variance to a parameter related to the correlation between the regressor and the regression, error. In particular, when the instrument is poorly correlated with the regressor, the asymptotic approximation to the distribution of the instrumental variable estimator will not be very accurate.
An adaptive learning rule is exhibited for the Azariadis (1981) overlapping generations model of a monetary economy with multiple equilibria, under which the economy may converge to a stationary equilibrium, even if agents do not initially believe that outcomes are significantly different in different sunspot states. The learning rule studied is of the stochastic approximation form studied by H. Robbins and S. Monro (1951); methods for analyzing the convergence of this form of algorithm are presented that may be of use in many other contexts as well. Conditions are given under which convergence to a equilibrium occurs with probability one. Copyright 1990 by The Econometric Society. (This abstract was borrowed from another version of this item.)
This paper investigates pure strategy sequential equilibria of repeated games with imperfect monitoring. The approach emphasizes the equilibrium value set and the static optimization problems embedded in extremal equilibria. A succession of propositions, central among which is "self-generation, " allow properties of constrained efficient supergame equilibria to be deduced from the solutions of the static problems. The authors show that the latter include solutions having a "bang-bang" property; this affords a significant simplification of the equilibria that need be considered. These results apply to a broad class of asymmetric games, thereby generalizing their earlier work on optimal cartel equilibria. Copyright 1990 by The Econometric Society.
This paper develops asymptotic prediction functions that approximate the shape of the density of future observations and correct for parameter uncertainty. The functions are based on extensions to a definition of predictive likelihood originally suggested by Lauritzen and Hinkley. The prediction function is shown to possess efficiency properties based on the Kullback-Leibler measure of information loss. Examples of the application of the prediction function and the derivation of relative efficiency are shown for linearnormal models, nonnormal models, and ARCH models.
This paper explores the robustness of the essential economic conclusions of the Roy model of self-selection and income inequality to relaxation of its normality assumptions. A log concave version of the model reproduces most of the main results. Log convex cases offer counterexamples. The authors show that in a Roy economy, random assignment is inegalitarian and Pareto inefficient. They consider nonparametric identifiability of latent skill distributions with cross-section and panel data. The authors' analysis proves nonparametric identifiability for the closely related competing risks model. Copyright 1990 by The Econometric Society.
MUCH OF THE UNCERTAINTY concerning the likely outcome of a typical management-labor conflict pertains to the cost of possible conflict to the two sides. In this paper, we consider situations of this kind, where the cost of conflict is not known with certainty. However, we will assume the benefits from cooperation to be known. We place our analysis in the abstract framework formulated by Nash (1950): Nash described a bargaining problem as a pair consisting of a feasible set (the amount to be divided among management and labor) and a disagreement point (giving the payoffs to both sides when they fail to reach agreement on a division, that is, the strike). Nash investigated the existence of solutions to such problems that would satisfy a certain list of appealing properties. In his analysis both feasible set and disagreement point were assumed to be known. Here, we assume only the feasible set to be known. Several studies have appeared of bargaining situations where the feasible set is unknown but the disagreement point is known. While we are of course not denying the relevance of such studies, we believe that an analysis of situations where it is the consequences of conflict that are unknown might be equally, and perhaps even more, relevant to industrial experience. Indeed, consider a management-labor conflict over wages and benefits. In many industries, the future profitability of the enterprise can be predicted with reasonable accuracy on the basis of its performance in the previous years, whereas the impact of a strike might depend on a number of factors that are significantly harder to evaluate. This is because strikes are infrequent and conjectures about these factors are often not put to the test (a strike is a threat that is often not carried out), and because they involve a number of parameters that are difficult to quantify, such as the psychological readiness of the strikers, the support they might receive from the population and the media, and the likely response of competing and related industries. We impose on solutions a new condition of disagreement point concavity guaranteeing that agents will agree on a compromise before the uncertainty concerning the disagreement point is resolved. To illustrate this requirement somewhat more concretely, suppose that bargaining takes place today, without the precise location of the disagreement point being known, this uncertainty being resolved tomorrow. The bargainers have two options: the first option is simply to wait until tomorrow and solve then whatever problem has come up. Unfortunately, the resulting pair of contingent compromises, evaluated today, is in general strictly Pareto-dominated. The other possibility is to solve today the problem obtained by replacing the uncertain disagreement point by its expected value (this represents the cost of conflict evaluated today) and to solve the resulting problem today. This second option has the advantage of yielding Paretoundominated compromises (provided, of course, that agents would, in the case of no uncertainty, select such compromises), but unfortunately, it may make one of the agents worse off than under the first option. In order to ensure that all agents agree to reaching a compromise today, we require that the second option always Pareto-dominate the first one. We show that disagreement point concavity, when used in conjunction with three standard properties that are satisfied by virtually all of the solutions commonly discussed
The theory of precautionary saving is shown in this paper to be isomorphic to the Arrow-Pratt theory of risk aversion, making possible the application of a large body of knowledge about risk aversion to precautionary saving, and more generally, to the theory of optimal choice under risk. In particular, a measure of the strength of precautionary saving motive analogous to the Arrow-Pratt measure of risk aversion is used to establish a number of new propositions about precautionary saving, and to give a new interpretation of the Oreze-Modigliani substitution effect.
This paper endogenizes the frequency of major discoveries and the extent of their refinement.Four axioms deliver a one-parameter family of beliefs that guide exploratory effort.Such effort trades off the prospect of major new discovery against the chance of successfully refining discoveries made in the past.The only other parameter is the cost of making new discoveries relative to the cost of refining old ones.The paper derives time-series properties of inventive activity as they relate to the two parameters, and it discusses several specific inventions and their subsequent refinement.In doing so, the paper arguably enhances our understanding of the process of discovery.1 We thank the C. V. Starr Center for Applied Economics for technical and financial assistance.The second