Showing papers in "Econometrica in 1986"

The Folk theorem in repeated games with discounting or with incomplete information

Abstract: 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 perfect 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 "Folk Theorem" 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 Nash 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 perfect equilibrium, i.e., whether as the discount factor tends to one, the set of perfect 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

On the strategic stability of equilibria

Abstract: A basic problem in the theory of noncooperative games is the following: which Nash equilibria are strategically stable, i.e. self-enforcing, and does every game have a strategically stable equilibrium? We list three conditions which seem necessary for strategic stabilitybackwards induction, iterated dominance, and invariance-and define a set-valued equilibrium concept that satisfies all three of them. We prove that every game has at least one such equilibrium set. Also, we show that the departure from the usual notion of single-valued equilibrium is relatively minor, because the sets reduce to points in all generic games.

Optimal taxation of capital income in general equilibrium with infinite lives

Abstract: This paper analyzes the optimal tax on capital income in general equilibrium models of the second best. Agents have infinite lives and utility functions which are extensions from the Koopmans form. The population is heterogeneous. The important property of the models is the equality between the social and the private discount rates in the long run. I find that the optimal tax rate is zero in the long run. For a special case of additively separable utility functions, I then determine the tax rates along the dynamic path and conditions that are sufficient for the local stability of the steady state.

Wald criteria for jointly testing equality and inequality restrictions

Abstract: On montre comment le test de Wald s'applique a des ensembles de restrictions d'egalite et d'inegalite et on presente la distribution, pour de grands echantillons, du test sous l'hypothese nulle

An Exogeneity Test for a Simultaneous Equation Tobit Model with an Application to Labor Supply

Abstract: A test of weak exogeneity in the simultaneous equation Tobit model is proposed and illustrated using a female labour supply model estimated using cross-section data. The test statistic can be simply output from any standard Tobit maximum likelihood package, and is asymptotically efficient. The procedure provides consistent estimators for the simultaneous Tobit model whose asymptotic covariance matrix is a simple extension of the usual Tobit formula. We also provide the Lagrange Multiplier test of weak exogeneity. (This abstract was borrowed from another version of this item.)

Patents as Options: Some Estimates of the Value of Holding European Patent Stocks

Abstract: In many countries holders of patents must pay an annual renewal fee in order to keep their patents in force. This paper uses data on the proportion of patents renewed, and the renewal fees faced by, post World War II cohorts of patents in France, the United Kingdom, and Germany, in conjunction with a model of patent holders' renewal decisions, to estimate the returns earned from holding patents in these countries. Since patents are often applied for at a nearly stage in the innovation process, the model allows agents to be uncertain about the sequence of returns that will be earned if the patent is kept inforce. Formally, then, the paper presents and solves a discrete choice optimal stochastic control model, derives the implications of the model on aggregate behaviour, and then estimates the parameters of the model from aggregate data. The estimates enable a detailed description of the evolution of the distribution of returns earned from holding patents over their life spans,and calculations of both; the annual returns earned from holding the patents still in force (or the patent stocks) in the alternative countries, and the distribution of the discounted value of returns earned from holding the patents in a cohort.

The Encompassing Principle and its Application To Testing Nonnested Hypotheses

Abstract: The encompassing principle is used to develop a testing framework which unifies the literature on non-nested testing, allowing analysis of the relationship between alternative tests and in particular enabling asymptotic and finite sample equivalences and identities to be established easily when they exist, as well as embracing nested hypothesis testing. The concept of the implicit null hypothesis of a test is introduced to show that the effective acceptance region for some tests extends beyond the acceptance region corresponding to the null of interest, and so such tests can be inconsistent against fixed alternatives closely related to the nominal null and alternative. The analysis is illustrated by an application to two non-nested linear regression models, and it is shown that the conventional F test, as well as all the one degree of freedom non-nested tests, has an encompassing interpretation, and that the F test is a "complete" parametric encompassing test.

Multistage games with communication

Abstract: This paper considers multistage games with communication mechanisms that can be implemented by a central mediator. In a communication equilibrium, no player expects ex ante to gain by manipulating his reports or actions. A sequential communication equilibrium is a communication equilibrium with a conditional probability system under which no player could ever expect to gain by manipulation, even after zero-probability events. Codominated actions are defined. It is shown that a communication equilibrium is a sequential communication equilibrium if and only if it never uses codominated actions. Predominant communication equilibria are defined by iterative elimination of codominated actions and are shown to exist.

The Measurement and Decomposition of Multi-Dimensional Inequality

Abstract: you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is a not-for-profit organization founded in 1995 to build trusted digital archives for scholarship. We work with the scholarly community to preserve their work and the materials they rely upon, and to build a common research platform that promotes the discovery and use of these resources. For more information about JSTOR, please contact support@jstor.org.

Symmetrically Trimmed Least Squares Estimation for Tobit Models

Abstract: This paper proposes alternatives to maximum likelihood estimation of the censored and truncated regression models (known to economists as "Tobit" models). The proposed estimators are based upon symmetric censoring or truncation of the upper tail of the distribution of the dependent variable. Unlike methods based on the assumption of identically distributed Gaussian errors, the estimators are semiparametric, in the sense that they are consistent and asymptotically normal for a wide class of (symmetric) error distributions with heteroskedasticity of unknown form. The paper gives the regularity conditions and proofs of these large sample properties, demonstrates how to construct consistent estimators of the asymptotic covariance matrices, and presents the results of a simulation study for the censored case. Extensions and limitations of the approach are also considered.

A Structural Retirement Model

Abstract: The life cycle model analyzed here constrains most work on the main job to be full-time. Partial retirement entails a wage reduction and frequently a job change. Maximum likelihood estimates of utility function parameters are designed to incorporate information on the age of leaving full-time work and the age of full retirement. The model closely tracks retirement behavior, including peaks in retirement activity at 62 and 65. The paper explores the relation of these peaks to nonlinearities in the budget constraint created by various retirement programs. Policy analyses based on this and on earlier models with simpler structures are compared. THE RETIREMENT CHOICE is one of the more prominent manifestations of life cycle behavior. The decision is the result of an interplay between an individual's preferences and a set of incentives which change in complicated ways as the individual progresses through his or her late 50's and 60's. The purpose of this study is to formulate and estimate a structural model which incorporates in a fundamental way this interplay between lifetime preferences and incentives, and to illustrate how such a model may be used to investigate retirement behavior. A structural model of this type is essential for analyzing potential policy changes which can be expected to affect incentives in varying ways over a number of years in the life cycle. The current study incorporates two structural features which have frequently been omitted from previous studies. First, the model requires that an individual who wishes to reduce work effort below full-time must accept a reduced hourly wage rate in order to do so. This reflects empirical evidence from micro data sets which indicates that around one-third of older individuals engage in part-time work at one time or another and that regardless of whether or not these older workers change jobs to obtain part-time work, they usually take wage cuts as compared to their previous full-time work.2 The fact that an individual is willing to accept a lower wage rate in return for the opportunity to work fewer than full-time hours contains important information about the preferences of the

An approach to communication equilibria

Abstract: 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.

Competition of firms: discriminatory pricing and location1

Abstract: Two costlessly mobile firms are to be located in a market region, a subset of the plane. The firms compete by setting locations and delivered price schedules. To study this competitive stiuation an appropriate extensive form game is defined, along with an appropri- ate noncooperative solution concept. Existence and general properties of the equilibrium are demonstrated. Among the results are: Each firm increases its profit by locating so as to decrease total cost to both firms of serving the market. Firms will never locate coinciden- tally if they have identical production costs and transport cost rates, or if these are different and the firms are located in a circular market region having a uniform demand distribution. THIS PAPER STUDIES competition between two profit maximizing firms in space who are costlessly mobile and may discriminate in price. We will allow the firms to set locations and delivered price schedules and we will be concerned with the existence- and properties of equilibria in location and price. Starting with Hotelling (9), the spatial competition literature has focused on location on bounded linear markets by two or more firms. Hotelling assumed identical firms that produced a single good with constant cost of production and considered consumers to be uniformly distributed and to have inelastic demand. He also assumed that the consumers pay transport cost and purchase the good from the cheapest source. Hotelling claimed that a Nash equilibrium in locations for the two firm market existed and yielded "back-to-back" locations at the center of the market. Many authors, most recently, D'Aspremont, Gabszewicz, and Thisse (2) have noted that an equilbrium in prices and location does not exist for Hotelling's model. However, if the firms employ identical exogeneously specified prices, Hotelling's conclusions hold. Subsequent work by Smithies (14), Hartwick and Hartwick (7), and Eaton (3) claimed to show that a Nash equi- librium in f.o.b. prices and locations can exist in markets with a uniform distribu- tion of consumers each of whom have identical elastic demand functions for the two and three firm problems. The work of D'Aspremont et al. casts doubt on these conclusions without the adoption of restrictive conditions. Our work contrasts with these works and related research which has dealt with linear markets, with uniform distributions of customers and with identical firms. Our work will involve markets that are subsets of the plane having nonuniform distributions of customers. Our firms will be allowed to be different, that is, have differences in production and transport costs. However, the fundamental difference in our approach is that our firms will set discriminatory prices and not price f.o.b. In many ways our work will represent the discriminatory pricing

On the allocation of residents to rural hospitals: a general property of two-sided matching markets

Abstract: the positions they do fill are filled by foreign medical school graduates. It has been suggested that changes in the manner in which the clearinghouse treats hospitals and students might alter this situation.3 However it was shown in Roth [4] that any two outcomes that are stable-the relevant equilibrium notion4 for this kind of market-fill the same number of positions at any hospital. Since that paper also showed that the clearinghouse procedure yields a stable outcome, any change in procedure that preserves this property would thus have no effect on the perceived numerical maldistribution of physicians among hospitals. Here it is shown that any hospital that fails to fill all of its positions at some stable outcome will not only fill the same number of positions at any other stable outcome, but will fill them with exactly the same residents. Thus, while the staffs of other hospitals are determined by which of the multiple equilibria of such a market is reached, the situation of hospitals whose positions are not all filled remains unaffected. The maldistribution of phvsicians, and particularly of American educated physicians, is therefore a property of equilibria of this kind of market, and not an artifact of the particular equilibrium presently selected. The formal model:5 The agents in the hospital-intern market consist of two disjoint

A Theory of Exit in Duopoly

Abstract: We develop a duopoly model in which exit occurs because of the existence of fixed costs or opportunity costs. Each firm enters the market knowing its own cost, but not that of its opponent. As times goes on, each firm becomes increasingly pessimistic about the cost of its remaining rival. The time of exit is the only strategic variable, so that our model is a "war of attrition." In contrast to the classic war of attrition, however, we assume that with positive probability each firm's costs may be low enough that staying in forever is a dominant strategy. Thus our model, unlike the classic one, has a unique equilibrium.

Borrowing constraints and aggregate economic activity

Abstract: A model of aggregate economic activity is formulated which enmphasizes the effects of borrowing constraints in the presence of uninsurable risk. An important determinant of current income level is shown to be the cross-sectional distribution of wealth. As this distribution evolves endogenously, the model is capable of producing rich dynamics from a simple specification of exogenous shocks. The model shows that this phenomena can contribute to observed asset price volatility. IT IS COMMONLY THOUGHT that individuals have only limited opportunities to borrow against future labor income and cannot totally insure all types of risk. It has also been suggested that such departures from the presumptive norm of frictionless, complete information capital markets may have implications for aggregate economic activity. AlthLough there has been some work analyzing the implications of borrowing constraints for individual savings behavior (18, 2, 8), there has been no systematic analysis of how such borrowing constraints will affect the time series properties of output, prices, and interest rates. In this paper, we present a completely specified infinitely lived two agent equilibrium model which emphasizes the roles of borrowing constraint and uninsured risk for affecting aggregate outcomes. Specifically we assume that agents are prohibited from ever having negative nonhuman wealth. The model has the central feature that there is no aggregate uncertainty, but each agent's own productive opportunities are stochastic. If there were a full set of Arrow- Debreu contingent claim markets each agent could attain a certain consumption stream and the resulting allocation and (implicit) relative prices would be constant through time. However, we assume that such markets do not exist. Rather, we assume that at each point in time agents may trade only the single durable "asset" for the single perishable consumption good. This asset may be interpreted either as fiat mon ay with a fixed own nominal return of zero, or as claims to productive capital which emits a fixed exogenous flow of the consumption good. We assume also that output may be produced by labor. However, only one of the two agents is productive at any instant in time. The duration of time over which a single agent is productive is assumed to be random, and, for analytical simplicity, is assumed to be generated by a Poisson counting process. The resulting allocation has the property that the agent who is not productive exchanges some of his

Instrumental-variable estimation of an error-components model

Abstract: On propose des estimateurs efficaces en considerant des hypotheses alternatives sur les sources d'endogeneite et les proprietes de variance-covariance des perturbations

Bargaining power, fear of disagreement, and wage settlements: theory and evidence from u.s. industry

Abstract: The paper develops and estimates a theoretical model of wage determination and union-nonunion wage differentials. In order to overcome the institutional ctiticisms of the formal bargaining literature, the paper generalizes the Nash-Zeuthen-Harsanyi model by linking the solution to the institutional concepts of bargaining power and fear or cost of disagreement and by making the outcome depend not only on endogenous but also on exogenous factors. An operational specification of bargaining power and fear of disagreement allows the model to be estimated with data covering twelve companies and trade unions during the period from mid-1950's to the late 1970's. While giving limited support to the NashZeuthen-Harsanyi solution, the empirical analysis indicates that the bargaining outcome usually deviates from the Nash-Zeuthen-Harsanyi point and, in accordance with the institutionalist claim, that it varies significantly with exogenous factors. Contrary to the traditional labor economics view, the results do not support the general conclusion that the bargaining solution lies on the marginal revenue product curve of labor. Instead, the relevant coefficients suggest that for many firms and unions the outcome might be better characterized by the efficient contract (vertical contract curve).

An Analysis of the Health and Retirement Status of the Elderly

Abstract: in this paper we specify and estimate a structural limited dependent variable model with which we study both the health and retirement status of the elderly. Standard linear estimators, which assume that these variable sare continuous, are not appropriate and categorical estimation techniques are preferred. Our model differs from previous work in that we have longitudinal data and random effects that are correlated over time for different individuals. The problem is made more complicated because there is sample truncation, which could potentially bias coefficient estimates, since approximately twenty percent of the individuals in our sample die. We outline the full information maximum likelihood estimator for such a model and implement it in our empirical analysis. With our structural estimates we analyze, among other things, the degree to which endogeneously determined health status affects the probability of retirement and how changes in social security benefits and eligibility for transfer payments modify both healthiness and the demand for leisure.

An Examination of Multijurisdictional Corporate Income Taxes Under Formula Apportionment

Abstract: This paper examines how corporate taxation of multijurisdictional firms using formula apportionment affects the incentives faced by individual firms and individual states. Under formula apportionment, a firm's tax payments to a given state depend on its total profits nationally (or internationally) times an average of the fractions of the firm's total property, payroll, and sales located in that state. This apportionment of a firm's total profits among states, based on three separate factors, in effect creates three separate taxes, each with complicated incentive effects. A large part of our analysis is concerned with the component of the tax tied to the allocation of property. Under this tax, price distortions differ in general among firms within the same state, creating incentives for firms producing in different states to merge their operations. State tax policies are also affected by this apportionment formula: states choose inefficiently low tax rates and are encouraged to shift to direct taxation of property. The component of the tax based on payroll creates many similar incentives. With this tax, however, the merger of firms producing different goods is discouraged. When a sales component to the tax is added, there are incentives for the cross-hauling of output, with production in low tax rate states sold in high tax rate states, and conversely. None of the above distortions are created when the corporate tax uses separate accounting to divide a firm's profits among states. The final section presents an alternative apportionment formula which retains the administrative advantages of existing law, yet creates the same incentives as separate accounting as long as there are no economic profits.