Abstract: This paper considers tests for parameter instability and structural change with unknown change point. The results apply to a wide class of parametric models that are suitable for estimation by generalized method of moments procedures. The asymptotic distributions of the test statistics considered here are nonstandard because the change point parameter only appears under the alternative hypothesis and not under the null. The tests considered here are shown to have nontrivial asymptotic local power against all alternatives for which the parameters are nonconstant. The tests are found to perform quite well in a Monte Carlo experiment reported elsewhere. Copyright 1993 by The Econometric Society.

Abstract: The unit root hypothesis is examined allowing a possible one-time change in the level or in the slope of the trend function. When fluctuations are stationary around a breaking trend function, standard tests cannot reject the unit root, even asymptotically. Consistent tests are derived and applied to the Nelson-Plosser data set (allowing a change in level for the 1929 crash) and to the postwar quarterly real GNP series (allowing a change in slope after 1973). The unit root hypothesis is rejected at a high confidence level for most series. Fluctuations are stationary. The only persistent "shocks" are the 1929 crash and the 1973 oil price shock. Copyright 1989 by The Econometric Society.

Abstract: The author shows how a group of individuals can learn to play a coordination game without any common knowledge and with only a small amount of rationality. The game is repeated many times by different players. Each player chooses an optimal reply based on incomplete information about what other players have done in the past. Occasionally they make mistakes. When the likelihood of mistakes is very small, typically one coordination equilibrium will be played almost all of the time over the long run. This stochastically stable equilibrium can be computed analytically using a general theorem the author proves on perturbed Markov processes. Copyright 1993 by The Econometric Society.

Abstract: An evolutionary model with a finite number of players and with stochastic mutations is analyzed. The expansion and contraction of strategies is linked to their current relative success, but mutuation, perturbing the system from its deterministic evolution, are present as well. The focus is on the long run implications of ongoing mutations, which drastically reduce the set of equilibria. For 2 by 2 symmetric games with two symmetric strict Nash equilibria the risk dominant equilibrium is selected. In particular, if both strategies have equal security levels, the Pareto dominant Nash equilibrium is selected. In particular, if both strategies have equal security levels, the Pareto dominant Nash equilibrium is selected, even though there is another strict Nash equilibrium. Copyright 1993 by The Econometric Society.

Abstract: This lecture surveys recent models of growth and trade in search of descriptions of technologies that are consistent with episodes of very rapid income growth. Emphasis is placed on the on-the-job accumulation of human capital: learning by doing. Possib le connections between learning rates and international trade are discussed Copyright 1993 by The Econometric Society.

Abstract: ANY MODEL, BY ITS NATURE, is based on assumptions that schematize and simplify the phenomena under investigation. The basic assumption underlying main-stream game-theoretic models is that the rules of the game, including its payoff structure and the rationality of the players, are common knowledge. There seems to be almost general agreement that game theory's agents are excessively rational and well-informed in comparison with their real-life counterparts. One way of assessing the role of this kind of assumption is to compare the model with perturbed variants that are based on slightly modified assumptions. In this manner, Harsanyi's (1973) games with randomly disturbed payoffs and Selten's (1975) concept of trembling-hand perfection perturb certain aspects of game theory's information and rationality assumptions. Analyzing such richer models may yield considerable benefits: Harsanyi's approach produces a plausible justification and interpretation of mixed strategy equilibria while Selten's approach frequently leads to a drastic reduction in the number of possible solutions. The present paper pursues this line of research by analyzing an incomplete information model-to be called a global game-which is based on a perturbation of the players' payoff information in 2 x 2 games. The game to be played is determined by a random draw from some subclass of all 2 x 2 games. Each player observes the selected game with some noise and then chooses one of his two available actions. If the initial subclass of games is large enough and contains games with different equilibrium structures, iterated elimination of dominated strategies in the incomplete information game yields a surprising result: When the 2 x 2 game actually selected by Nature is one with two strict Nash equilibria, iterated dominance forces the players to coordinate on the equilibrium which is risk-dominant in the sense of Harsanyi and Selten (1988), 1This paper is a combination and substantial generalization of Carlsson (1989) and Carlsson and van Damme (1989). Some basic ideas on global games and their relation to risk dominance originate from a note written by Carlsson in 1988. The authors thank Reinhard Selten, Lars-Gunnar Svensson, J6rgen Weibull, and various seminar audiences for helpful comments. The constructive criticism from an editor and several referees considerably improved the paper's quality. Carlsson gratefully acknowledges financial support from the Swedish Council for Research in the Humanities and Social Sciences and the Jan Wallander Foundation.

Abstract: This paper discusses the dynamic implications of learning in a large population coordination game, focusing on the structure of the matching process which describes how players meet. As in Kandori, Mailath, and Rob (1993) a combination of experimentation and myopia creates "evolutionary" forces which lead players to coordinate on the risk dominant equilibrium. To describe play with finite time horizons it is necessary to consider the rates at which the dynamic systems converge. In large populations with uniform matching, play is determined largely by historical factors. In contrast, when players interact with small sets of neighbors it is more reasonable to assume that evolutionary forces may determine the outcome.

Abstract: This paper proposes an estimator for discrete choice models that makes no assumption concerning the functional form of the choice probability function, where this function can be characterized by an index. The estimator is shown to be consistent, asymptotically normally distributed, and to achieve the semiparametric efficiency bound. Monte-Carlo evidence indicates that there may be only modest efficiency losses relative to maximum likelihood estimation when the distribution of the disturbances is known, and that the small-sample behavior of the estimator in other cases is good.

Abstract: In a decision-theoretic model of a firm, the author represents managers as information processors of limited capacity; efficiency is measured in terms of (1) the number of processors and (2) the delay between the receipt of information by the organization and the implementation of the decision. The author characterizes efficient networks for both one-shot and repeated regimes, as well as the corresponding 'production function' relating the number of items processed to the number of processors and the delay. He sketches some applications to common decision paradigms, and implications for decentralization and organizational returns to scale. Copyright 1993 by The Econometric Society.

Abstract: Internal consistency of choice has been a central concept in economics, decision theory, and social choice. This idea is essentially confused. We cannot determine whether a choice function is consistent without referring to something external to choice (e.g., objectives, values). The standard results have to be reexamined in this light. Kenneth J. Arrow's general possibility theorem is extended in this paper without demanding any internal consistency of social choice or any notion of 'social rationality.' Copyright 1993 by The Econometric Society.

Abstract: This paper provides a simulated moments estimator (SME) of the parameters of dynamic models in which the state vector follows a time-homogeneous Markov process. Conditions are provided for both weak and strong consistency as well as asymptotic normality. Various tradeoffs among the regularity conditions underlying the large sample properties of the SME are discussed in the context of an asset-pricing model. THIS PAPER PROVIDES CONDITIONS for the consistency and asymptotic normality of a simulated moments estimator (SME) of the parameters of asset-pricing models with time-homogeneous Markov representations of the stochastic forc- ing process. SME's for economic models have been proposed by McFadden (1989) and Pakes and Pollard (1989) for i.i.d. environments, and by Lee and Ingram (1991) for a time series environment. The SME for time series models examined in this paper is as follows. The state vector Yt that determines asset prices is assumed to follow a time-homogeneous Markov process whose transi- tion function depends on an unknown parameter vector 3)0. Asset prices, and possibly other relevant data, are observed as f(Yt, ,0), for some given function f of the underlying state and parameter vector. In parallel, a simulated state process {Y)} is generated (analytically or numerically) from the economic model and corresponding simulated observations f(YJ3, 13) are taken, for a given parameter choice f3. The parameter , is chosen so as to "match moments," that is, to minimize the distance between sample moments of the data, f(Y,8030), and those of the simulated series f(Yt/, f3), in a sense to be made precise. The proposed SME extends the generalized method-of-moments (GMM) estimator (Hansen (1982)) to a large class of asset-pricing models for which the moment restrictions of interest do not have analytic representations in terms of observable variables and the unknown parameter vector. We provide conditions on the transition function of Yt and the observation function f under which the SME of 030 is consistent, and characterize the normalized asymptotic distribu- tion of the estimator. For two reasons, neither the regularity conditions underly- ing Hansen's (1982) analysis of GMM estimators for time-series models without

Abstract: 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 chosen, then Bayesian updating will lead in the long run to accurate prediction of the future 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.

Abstract: rium path of play. Thus, if a self-confirming equilibrium occurs repeatedly, no player ever observes play that contradicts his beliefs, even though beliefs about play at off-path information sets need not be correct. We characterize the ways in which self-confirming equilibria and Nash equilibria can differ, and provide conditions under which self-con- firming equilibria correspond to standard solution concepts. NASH EQUILIBRIUM AND ITS REFINEMENTS describe a situation in which (i) each player's strategy is a best response to his beliefs about the play of his opponents, and (ii) each player's beliefs about the opponents' play are exactly correct. We propose a new equilibrium concept, self-confirming equilibrium, that weakens condition (ii) by requiring only that players' beliefs are correct along the equilibrium path of play. Thus, each player may have incorrect beliefs about how his opponents would play in contingencies that do not arise when play follows the equilibrium, and moreover the beliefs of different players may be wrong in different ways. The concept of self-confirming equilibrium is motivated by the idea that noncooperative equilibria should be interpreted as the outcome of a learning process, in which players revise their beliefs using their observations of previous play. Suppose that each time the game is played, the players observe the actions chosen by their opponents, but that players do not observe the actions their opponents would have played at the information sets that were not reached along the path of play. Then, if a self-confirming equilibrium occurs repeatedly, no player ever observes play that contradicts his beliefs, so the equilibrium is "self-confirming" in the weak sense of not being inconsistent with the evidence. By analogy with the literature on the bandit problem (e.g., Rothschild (1974)) one might expect that a non-Nash self-confirming equilibrium can be the outcome of plausible learning processes. This point was made by Fudenberg and

Abstract: 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.

Abstract: Methods for nonlinear impulse response analysis are introduced. The methods are based on conditional moment profiles defined for a stationary time series. Comparing conditional moment profiles to baseline profiles is the nonlinear analog of conventional impulse-response analysis. The bootstrap may be used for statistical inference. Profile bundles may be examined for evidence of damping or persistence. Application to bivariate NYSE price and volume series from 1928 to 1987 finds evidence of a heavily damped 'leverage effect' and a differential response of trading volume to 'common-knowledge' price shocks. Copyright 1993 by The Econometric Society.

Abstract: 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.

Abstract: Han's maximum rank correlation (MRC) estimator is shown to be 4/_-consistent and asymptotically normal. The proof rests on a general method for determining the asymptotic distribution of a maximization estimator, a simple U-statistic decomposition, and a uniform bound for degenerate U-processes. A consistent estimator of the asymptotic covariance matrix is provided, along with a result giving the explicit form of this matrix for any model within the scope of the MRC estimator. The latter result is applied to the binary choice model, and it is found that the MRC estimator does not achieve the semiparametric efficiency bound.

Abstract: The purpose of this paper is to study the role and implications of price advertising when shopping trips are costly to consumers. To do so, we introduce advertising into an optimal sequential search model. Information about prices is both gathered by consumers and disseminated by firms. Consumers search sequentially and stores advertise (with various intensity) when it is in their interest to do so. Our model has a unique equilibrium exhibiting priee dispersion. The model generates predictions about the shape of the price distribution and firms' advertising behavior. We explore the effects of entry, and find that when initial advertising costs (at zero level of effort) are precisely zero, entry drives the equilibrium to the perfectly competitive outcome. However, when initial marginal advertising costs are positive, entry drives prices higher, and while the informed consumers almost surely locate competitive prices, welfare does not necessarily increase. Finally, we compare the effectiveness of the two informational channels. When advertising costs shrink, prices become competitive; however, when search costs shrink, prices remain bounded above marginal production costs.

Abstract: We study the steady states of a system in which players learn about the strategies their opponents are playing by updating their Bayesian priors in light of their observations. Players are matched at random to play a fixed extensive-form game, and each player observes the realized actions in his own matches, but not the intended off-path play of his opponents or the realized actions in other matches. Because players are assumed to live finite lives, there are steady states in which learning continually takes place. If lifetimes are long and players are very patient, the steady state distribution of actions approximates that of a Nash equilibrium.

Abstract: This paper reports estimates of the structural parameters of a stochastic control model that describcs the labor decisions of small farmers in Burkina Faso, West Africa. The focus of the estimation is on measuring flexibility in production and intertemporal substitutability in consumption. Full information maximum likelihood estimates of the primitive parameters of the model are computed even though optimal labor decision rules cannot be derived analytically. Vuong's non-nested model specification test shows that this method yields parameter estimates that are superior to those derived by assuming that farmers solve a deterministic control problem. The low levels of agricultural labor effort commonly observed in the survey area are shown to be a consequence both of the low productivity of labor in archaic rainfed agriculture and of farmers' awareness that, in the absence of a labor market, overly ambitious production plans lead to seasonal manpower constraints. To meet rainfed farmers' concerns, agricultural research institutes and extension services should factor flexibility into their research agendas.

Abstract: 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.)

Abstract: Weighted average derivatives are useful parameters for semiparametric index models and nonparametric demand analysis. This paper gives efficiency results for average derivative estimators, including formulating estimators that have high efficiency. Our analysis is carried out in three steps. First, we derive the efficiency bound for weighted average derivatives of conditional location functionals, such as the conditional mean and median. Second, we derive the efficiency bound for semiparametric index models, where the location measure depends only on indices, or linear combinations of the regressors. Third, we compare the bound for index models with the asymptotic variance of weighted average derivative estimators of the index coefficients. We characterize the form of the optimal weight function when the distribution of the regressors is elliptically symmetric. In more general cases, we discuss how to combine estimators with different weight functions to achieve efficiency. We derive a general condition for approximate efficiency of pooled (minimum chi square) estimators for index model coefficients, based on weighted average derivatives. Finally, we discuss ways of selecting the type and number of weighting functions to achieve high efficiency.

Abstract: Anecdotal and experimental evidence suggests that bargaining sessions subject to deadlines often begin with cheap talk and rejected proposals. Agreements, if they are reached at all, tend to be concluded near the deadline. We attempt to capture and explain these phenomena in a strategic bargaining model that incorporates a bargaining deadline, the possibility of strategic delay, and a lack of perfect player control over the timing of offers. Imperfect player control is generated by an exogenous uniformly-distributed random delay in offer transmission. Our model has a symmetric Markov-perfect equilibrium, unique at almost all nodes, in which players adopt strategic delay early in the game, make and reject offers later on, and reach agreements late in the game if at all. In equilibrium players miss the deadline with positive probability. The expected division of the surplus is unique and close to an even split.

Abstract: Perfect equilibria of finitely repeated games may be vulnerable to the possibility of renegotiation among players. The authors study the limiting properties of the set of payoffs from equilibria that are immune to renegotiation. Their main result is th at the limit of the set of payoffs from renegotiation-proof equilibria is either a singleton or a connected subset of the Pareto efficient frontier. A simple sufficient condition for the latter to occur is a lso provided. Copyright 1993 by The Econometric Society.

Abstract: Different extensive form games with the same reduced normal form can have different information sets and subgames. This generates a tension between a belief in the strategic relevance of information sets and subgames and a belief in the sufficiency of the reduced normal form. We identify a property of extensive form information sets and subgames which we term strategic independence. Strategic independence is captured by the reduced normal form, and can be used to define normal form information sets and subgames. We prove a close relationship between these normal form structures and their extensive form namesakes. Using these structures, we are able to motivate and implement solution concepts corresponding to subgame perfection, sequential equilibrium, and forward induction entirely in the reduced normal form, and show close relations between their implications in the normal and extensive form.

Abstract: Formulas are derived for computing asymptotic covariance matrices of sets of impulse responses, step responses, or variance decompositions of estimated dynamic simultane- ous-equations models in vector autoregressive moving-average (VARMA) form. Com- puted covariances would be used to test linear restrictions on sets of impulse responses, step responses, or variance decompositions. The results unify and extend previous formulas to handle any model in VARMA form, provide accurate computations based on analytic derivatives, and provide insights into the structures of the asymptotic covariances. FOLLOWING THE LEAD OF SIMS (1980), impulse responses, step responses, and variance decompositions have become standard tools for examining the empiri- cal validity of economic theories or interpreting the forecasting and policy implications of estimated linear dynamic models. Runkle (1987) demonstrated the importance of accounting for sampling variability in these exercises. He computed confidence bounds for impulse responses and variance decomposi- tions derived from estimated vector autoregressive (VAR) models with sto- chastic simulations and asymptotic normal approximations. The two methods produced comparable results, but the simulations took about 160 times longer to compute than normal approximations based on numerical derivatives. Whereas Runkle only reported confidence bounds for individual impulse re- sponses and decomposed variances of VAR models, the present paper derives equations for computing full asymptotic covariance matrices of sets of impulse responses, step responses, or variance decompositions of estimated dynamic simultaneous-equations models in autoregressive moving-average form. The computed covariances may be used to jointly test multiple linear restrictions-or linear approximations of differentiable nonlinear restrictions-on sets of im- pulse responses, step responses, or variance decompositions of estimated mod- els. Because the derived computational equations are based on analytical derivatives, they have at least two advantages: they lead to more accurate and often faster computations than those based on numerical derivatives; they provide insight into the structures of asymptotic covariances of the estimated quantities. By allowing for various identifying restrictions, the paper extends and unifies results of Schmidt (1973), Evans and Wells (1986), and Liutkepohl (1988, 1989,