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Full-Text Articles in Social and Behavioral Sciences

Sequential Equilibria In Bayesian Games With Communication, Dino Gerardi, Roger B. Myerson Dec 2005

Sequential Equilibria In Bayesian Games With Communication, Dino Gerardi, Roger B. Myerson

Cowles Foundation Discussion Papers

We study the effects of communication in Bayesian games when the players are sequentially rational but some combinations of types have zero probability. Not all communication equilibria can be implemented as sequential equilibria. We define the set of strong sequential equilibria (SSCE) and characterize it. SSCE differs from the concept of sequential communication equilibrium (SCE) defined by Myerson (1986) in that SCE allows the possibility of trembles by the mediator. We show that these two concepts coincide when there are three or more players, but the set of SSCE may be strictly smaller than the set of SCE for two-player …


Testing Linearity In Cointegrating Relations With An Application To Purchasing Power Parity, Seung Hyun Hong, Peter C.B. Phillips Dec 2005

Testing Linearity In Cointegrating Relations With An Application To Purchasing Power Parity, Seung Hyun Hong, Peter C.B. Phillips

Cowles Foundation Discussion Papers

This paper develops a linearity test that can be applied to cointegrating relations. We consider the widely used RESET specification test and show that when this test is applied to nonstationary time series its asymptotic distribution involves a mixture of noncentral chi-squared distributions, which leads to severe size distortions in conventional testing based on the central chi-squared. Nonstationarity is shown to introduce two bias terms in the limit distribution, which are the source of the size distortion in testing. Appropriate corrections for this asymptotic bias leads to a modified version of the RESET test which has a central chi-squared limit …


The Response Of Prices, Sales, And Output To Temporary Changes In Demand, Adam Copeland, George J. Hall Dec 2005

The Response Of Prices, Sales, And Output To Temporary Changes In Demand, Adam Copeland, George J. Hall

Cowles Foundation Discussion Papers

We determine empirically how the Big Three automakers accommodate shocks to demand. They have the capability to change prices, alter labor inputs through temporary layoffs and overtime, or adjust inventories. These adjustments are interrelated, non-convex, and dynamic in nature. Combining weekly plant-level data on production schedules and output with monthly data on sales and transaction prices, we estimate a dynamic profit-maximization model of the firm. Using impulse response functions, we demonstrate that when an automaker is hit with a demand shock sales respond immediately, prices respond gradually, and production responds only after a delay. The size of the immediate sales …


Grading In Games Of Status: Marking Exams And Setting Wages, Pradeep Dubey, John Geanakoplos Dec 2005

Grading In Games Of Status: Marking Exams And Setting Wages, Pradeep Dubey, John Geanakoplos

Cowles Foundation Discussion Papers

We introduce grading into games of status. Each player chooses effort, producing a stochastic output or score. Utilities depend on the ranking of all the scores. By clustering scores into grades, the ranking is coarsened, and the incentives to work are changed. We first apply games of status to grading exams. Our main conclusion is that if students care primarily about their status (relative rank) in class, they are often best motivated to work not by revealing their exact numerical exam scores (100,99,…,1), but instead by clumping them into coarse categories ( A,B,C ). When student abilities are disparate, the …


Grading In Games Of Status: Marking Exams And Setting Wages, Pradeep Dubey, John Geanakoplos Dec 2005

Grading In Games Of Status: Marking Exams And Setting Wages, Pradeep Dubey, John Geanakoplos

Cowles Foundation Discussion Papers

We introduce grading into games of status. Each player chooses effort, producing a stochastic output or score. Utilities depend on the ranking of all the scores. By clustering scores into grades, the ranking is coarsened, and the incentives to work are changed. We first apply games of status to grading exams. Our main conclusion is that if students care primarily about their status (relative rank) in class, they are often best motivated to work not by revealing their exact numerical exam scores (100,99,…,1), but instead by clumping them into coarse categories ( A,B,C ). When student abilities are disparate, the …


A Remark On Bimodality And Weak Instrumentation In Structural Equation Estimation, Peter C.B. Phillips Dec 2005

A Remark On Bimodality And Weak Instrumentation In Structural Equation Estimation, Peter C.B. Phillips

Cowles Foundation Discussion Papers

In a simple model composed of a structural equation and identity, the finite sample distribution of the IV/LIML estimator is always bimodal and this is most apparent when the concentration parameter is small. Weak instrumentation is the energy that feeds the secondary mode and the coefficient in the structural identity provides a point of compression in the density that gives rise to it. The IV limit distribution can be normal, bimodal, or inverse normal depending on the behavior of the concentration parameter and the weakness of the instruments. The limit distribution of the OLS estimator is normal in all cases …


A Credit Mechanism For Selecting A Unique Competitive Equilibrium, Cheng-Zhong Qin, Martin Shubik Nov 2005

A Credit Mechanism For Selecting A Unique Competitive Equilibrium, Cheng-Zhong Qin, Martin Shubik

Cowles Foundation Discussion Papers

The enlargement of the general-equilibrium structure to allow default subject to penalties to appririate credit limits and default penalties results in a construction of a simple mechanism for a credit using society. We show that there generically exists a price-normalizing bundle that determines a credit money along with appropriate credit limmits and default penalties for a credit mechanism to select a unique competitive equilibrium (CE). With some additional conditions, a common credit money can be applied such that any CE can be a unique selection by the credit mechanism with appropriate credit limits default penalties for the traders. This will …


Estimated Age Effects In Baseball, Ray C. Fair Oct 2005

Estimated Age Effects In Baseball, Ray C. Fair

Cowles Foundation Discussion Papers

Age effects in baseball are estimated in this paper using a nonlinear fixed-effects regression. The sample consists of all players who have played 10 or more “full-time” ’ years in the major leagues between 1921 and 2004. Quadratic improvement is assumed up to a peak-performance age, which is estimated, and then quadratic decline after that, where the two quadratics need not be the same. Each player has his own constant term. The results show that aging effects are larger for pitchers than for batters and larger for baseball than for track and field, running, and swimming events and for chess. …


A New Approach To Robust Inference In Cointegration, Sainan Jin, Peter C.B. Phillips, Yixiao Sun Oct 2005

A New Approach To Robust Inference In Cointegration, Sainan Jin, Peter C.B. Phillips, Yixiao Sun

Cowles Foundation Discussion Papers

A new approach to robust testing in cointegrated systems is proposed using nonparametric HAC estimators without truncation. While such HAC estimates are inconsistent, they still produce asymptotically pivotal tests and, as in conventional regression settings, can improve testing and inference. The present contribution makes use of steep origin kernels which are obtained by exponentiating traditional quadratic kernels. Simulations indicate that tests based on these methods have improved size properties relative to conventional tests and better power properties than other tests that use Bartlett or other traditional kernels with no truncation.


Prizes Versus Wages With Envy And Pride, Pradeep Dubey, John Geanakoplos, Ori Haimanko Oct 2005

Prizes Versus Wages With Envy And Pride, Pradeep Dubey, John Geanakoplos, Ori Haimanko

Cowles Foundation Discussion Papers

We show that if agents are risk neutral, prizes outperform wages when there is sufficient pride and envy relative to the noisiness of performance. If agents are risk averse, prizes are a necessary supplement to wages (as bonuses).


Perfect Competition In A Bilateral Monopoly (In Honor Of Martin Shubik), Pradeep Dubey, Dieter Sondermann Sep 2005

Perfect Competition In A Bilateral Monopoly (In Honor Of Martin Shubik), Pradeep Dubey, Dieter Sondermann

Cowles Foundation Discussion Papers

We show that if limit orders are required to vary smoothly, then strategic (Nash) equilibria of the double auction mechanism yield competitive (Walras) allocations. It is not necessary to have competitors on any side of any market: smooth trading is a substitute for price wars. In particular, Nash equilibria are Walrasian even in a bilateral monopoly.


Continuous Versus Discrete Market Games, Alexandre Marino, Bernard De Meyer Sep 2005

Continuous Versus Discrete Market Games, Alexandre Marino, Bernard De Meyer

Cowles Foundation Discussion Papers

De Meyer and Moussa Saley [4] provide an endogenous justification for the appearance of Brownian Motion in Finance by modeling the strategic interaction between two asymmetrically informed market makers with a zero-sum repeated game with one-sided information. The crucial point of this justification is the appearance of the normal distribution in the asymptotic behavior of V n ( P )// n . In De Meyer and Moussa Saley’s model [4], agents can fix a price in a continuous space. In the real world however, the market compels the agents to post prices in a discrete set. The previous remark raises …


Testing For Non-Nested Conditional Moment Restrictions Via Conditional Empirical Likelihood, Taisuke Otsu, Yoon-Jae Whang Sep 2005

Testing For Non-Nested Conditional Moment Restrictions Via Conditional Empirical Likelihood, Taisuke Otsu, Yoon-Jae Whang

Cowles Foundation Discussion Papers

We propose non-nested tests for competing conditional moment restriction models using a method of empirical likelihood. Our tests are based on the method of conditional empirical likelihood developed by Kitamura, Tripathi and Ahn (2004) and Zhang and Gijbels (2003). By using the conditional implied probabilities, we develop three non-nested tests: the moment encompassing, Cox-type, and efficient score encompassing tests. Compared to the existing non-nested tests which mainly focus on testing unconditional moment restrictions, our approach directly tests conditional moment restrictions which imply the infinite number of unconditional moment restrictions. We derive the null distributions and power properties of the proposed …


Inference With Weak Instruments, Donald W.K. Andrews, James H. Stock Aug 2005

Inference With Weak Instruments, Donald W.K. Andrews, James H. Stock

Cowles Foundation Discussion Papers

This paper reviews recent developments in methods for dealing with weak instruments (IVs) in IV regression models. The focus is more on tests (and confidence intervals derived from tests) than estimators. The paper also presents new testing results under “many weak IV asymptotics,” which are relevant when the number of IVs is large and the coefficients on the IVs are relatively small. Asymptotic power envelopes for invariant tests are established. Power comparisons of the conditional likelihood ratio (CLR), Anderson-Rubin, and Lagrange multiplier tests are made. Numerical results show that the CLR test is on the asymptotic power envelope. This holds …


Making Statements And Approval Voting, Enriqueta Aragones, Itzhak Gilboa, Andrew Weiss Aug 2005

Making Statements And Approval Voting, Enriqueta Aragones, Itzhak Gilboa, Andrew Weiss

Cowles Foundation Discussion Papers

We assume that people have a need to make statements, and construct a model in which this need is the sole determinant of voting behavior. In this model, an individual selects a ballot that makes as close a statement as possible to her ideal point, where abstaining from voting is a possible (null) statement. We show that in such a model, a political system that adopts approval voting may be expected to enjoy a significantly higher rate of participation in elections than a comparable system with plurality rule.


Information In Mechanism Design, Dirk Bergemann, Juuso Välimäki Aug 2005

Information In Mechanism Design, Dirk Bergemann, Juuso Välimäki

Cowles Foundation Discussion Papers

We survey the recent literature on the role of information for mechanism design. We specifically consider the role of endogeneity of and robustness to private information in mechanism design. We view information acquisition of and robustness to private information as two distinct but related aspects of information management important in many design settings. We review the existing literature and point out directions for additional future work.


Information In Mechanism Design, Dirk Bergemann, Juuso Välimäki Aug 2005

Information In Mechanism Design, Dirk Bergemann, Juuso Välimäki

Cowles Foundation Discussion Papers

We survey the recent literature on the role of information in mechanism design. First, we discuss an emerging literature on the role of endogenous payoff and strategic information for the design and the efficiency of the mechanism. We specifically consider information management in the form of acquisition of new information or disclosure of existing information. Second, we argue that in the presence of endogenous information, the robustness of the mechanism to the type space and higher order beliefs becomes a natural desideratum. We discuss recent approaches to robust mechanism design and robust implementation.


Robust Monopoly Pricing, Dirk Bergemann, Karl Schlag Jul 2005

Robust Monopoly Pricing, Dirk Bergemann, Karl Schlag

Cowles Foundation Discussion Papers

We consider a robust version of the classic problem of optimal monopoly pricing with incomplete information. In the robust version, the seller faces model uncertainty and only knows that the true demand distribution is in the neighborhood of a given model distribution. We characterize the optimal pricing policy under two distinct, but related, decision criteria with multiple priors: (i) maximin expected utility and (ii) minimax expected regret. The resulting optimal pricing policy under either criterion yields a robust policy to the model uncertainty. While the classic monopoly policy and the maximin criterion yield a single deterministic price, minimax regret always …


Branch Rickey’S Equation Fifty Years Later, Ray C. Fair, Danielle Catambay Jul 2005

Branch Rickey’S Equation Fifty Years Later, Ray C. Fair, Danielle Catambay

Cowles Foundation Discussion Papers

This paper analyzes Branch Rickey’s 1954 equation in a regression context. The results for 1934–1953 are consistent with Rickey’s conclusions, and the equation holds up well when extended 51 years. Two of the main conclusions are that on-base percentage dominates batting average and that offense and defense are equally important. Perhaps Rickey was as good as he thought he was?


Robust Monopoly Pricing: The Case Of Regret, Dirk Bergemann, Karl Schlag Jul 2005

Robust Monopoly Pricing: The Case Of Regret, Dirk Bergemann, Karl Schlag

Cowles Foundation Discussion Papers

We consider a robust version of the classic problem of optimal monopoly pricing with incomplete information. The robust version of the problem is distinct in two aspects: (i) the seller minimizes regret rather than maximizes revenue, and (ii) the seller only knows that the true distribution of the valuations is in a neighborhood of a given model distribution. We characterize the robust pricing policy as the solution to a minimax problem for small and large neighborhoods. In contrast to the classic monopoly policy, which is a single deterministic price, the robust policy is always a random pricing policy, or equivalently, …


Robust Monopoly Pricing, Dirk Bergemann, Karl Schlag Jul 2005

Robust Monopoly Pricing, Dirk Bergemann, Karl Schlag

Cowles Foundation Discussion Papers

We consider a robust version of the classic problem of optimal monopoly pricing with incomplete information. In the robust version of the problem the seller only knows that demand will be in a neighborhood of a given model distribution. We characterize the optimal pricing policy under two distinct, but related, decision criteria with multiple priors: (i) maximin expected utility and (ii) minimax expected regret. While the classic monopoly policy and the maximin criterion yield a single deterministic price, minimax regret always prescribes a random pricing policy, or equivalently, a multi-item menu policy. The resulting optimal pricing policy under either criterion …


Competition, Consumer Welfare, And The Social Cost Of Monopoly, Yoon-Ho Alex Lee, Donald J. Brown Jul 2005

Competition, Consumer Welfare, And The Social Cost Of Monopoly, Yoon-Ho Alex Lee, Donald J. Brown

Cowles Foundation Discussion Papers

Conventional deadweight loss measures of the social cost of monopoly ignore, among other things, the social cost of inducing competition and thus cannot accurately capture the loss in social welfare. In this Article, we suggest an alternative method of measuring the social cost of monopoly. Using elements of general equilibrium theory, we propose a social cost metric where the benchmark is the Pareto optimal state of the economy that uses the least amount of resources, consistent with consumers’ utility levels in the monopolized state. If the primary goal of antitrust policy is the enhancement of consumer welfare, then the proper …


Improved Har Inference Using Power Kernels Without Truncation, Peter C.B. Phillips, Yixiao Sun, Sainan Jin Jun 2005

Improved Har Inference Using Power Kernels Without Truncation, Peter C.B. Phillips, Yixiao Sun, Sainan Jin

Cowles Foundation Discussion Papers

Employing power kernels suggested in earlier work by the authors (2003), this paper shows how to refine methods of robust inference on the mean in a time series that rely on families of untruncated kernel estimates of the long-run parameters. The new methods improve the size properties of heteroskedastic and autocorrelation robust (HAR) tests in comparison with conventional methods that employ consistent HAC estimates, and they raise test power in comparison with other tests that are based on untruncated kernel estimates. Large power parameter (ρ) asymptotic expansions of the nonstandard limit theory are developed in terms of the usual limiting …


Gmm With Many Moment Conditions, Chirok Han, Peter C.B. Phillips Jun 2005

Gmm With Many Moment Conditions, Chirok Han, Peter C.B. Phillips

Cowles Foundation Discussion Papers

This paper provides a first order asymptotic theory for generalized method of moments (GMM) estimators when the number of moment conditions is allowed to increase with the sample size and the moment conditions may be weak. Examples in which these asymptotics are relevant include instrumental variable (IV) estimation with many (possibly weak or uninformed) instruments and some panel data models covering moderate time spans and with correspondingly large numbers of instruments. Under certain regularity conditions, the GMM estimators are shown to converge in probability but not necessarily to the true parameter, and conditions for consistent GMM estimation are given. A …


Nonstationary Discrete Choice: A Corrigendum And Addendum, Peter C.B. Phillips, Sainan Jin, Ling Hu Jun 2005

Nonstationary Discrete Choice: A Corrigendum And Addendum, Peter C.B. Phillips, Sainan Jin, Ling Hu

Cowles Foundation Discussion Papers

We correct the limit theory presented in an earlier paper by Hu and Phillips (Journal of Econometrics, 2004) for nonstationary time series discrete choice models with multiple choices and thresholds. The new limit theory shows that, in contrast to the binary choice model with nonstationary regressors and a zero threshold where there are dual rates of convergence ( n 1 /4 and n 3 /4 ), all parameters including the thresholds converge at the rate n 3 /4 . The presence of non-zero thresholds therefore materially affects rates of convergence. Dual rates of convergence reappear when stationary variables are present …


Limit Theory For Moderate Deviations From A Unit Root Under Weak Dependence, Peter C.B. Phillips, Tassos Magdalinos Jun 2005

Limit Theory For Moderate Deviations From A Unit Root Under Weak Dependence, Peter C.B. Phillips, Tassos Magdalinos

Cowles Foundation Discussion Papers

An asymptotic theory is given for autoregressive time series with weakly dependent innovations and a root of the form ρ n = 1 + c / n α , involving moderate deviations from unity when α in (0,1) and c in R are constant parameters. The limit theory combines a functional law to a diffusion on D[0,∞) and a central limit theorem. For c > 0, the limit theory of the first-order serial correlation coefficient is Cauchy and is invariant to both the distribution and the dependence structure of the innovations. To our knowledge, this is the first invariance principle of …


Sign Tests For Dependent Observations And Bounds For Path-Dependent Options, Rustam Ibragimov, Donald J. Brown Jun 2005

Sign Tests For Dependent Observations And Bounds For Path-Dependent Options, Rustam Ibragimov, Donald J. Brown

Cowles Foundation Discussion Papers

The present paper introduces new sign tests for testing for conditionally symmetric martingale-difference assumptions as well as for testing that conditional distributions of two (arbitrary) martingale-difference sequences are the same. Our analysis is based on the results that demonstrate that randomization over zero values of three-valued random variables in a conditionally symmetric martingale-difference sequence produces a stream of i.i.d. symmetric Bernoulli random variables and thus reduces the problem of estimating the critical values of the tests to computing the quantiles or moments of Binomial or normal distributions. The same is the case for randomization over ties in sign tests for …


Robust Implementation: The Role Of Large Type Spaces, Dirk Bergemann, Stephen Morris Jun 2005

Robust Implementation: The Role Of Large Type Spaces, Dirk Bergemann, Stephen Morris

Cowles Foundation Discussion Papers

A social choice function is robustly implemented if every equilibrium on every type space achieves outcomes consistent with a social choice function. We identify a robust monotonicity condition that is necessary and (with mild extra assumptions) sufficient for robust implementation. Robust monotonicity is strictly stronger than both Maskin monotonicity (necessary and almost sufficient for complete information implementation) and ex post monotonicity (necessary and almost sufficient for ex post implementation). It is equivalent to Bayesian monotonicity on all type spaces. It requires that there not be too much interdependence of types. We characterize robust monotonicity for some interesting economic environments. We …


The Evolution Of Our Preferences: Evidence From Capuchin-Monkey Trading Behavior, Keith M. Chen, Venkat Lakshminarayanan, Laurie Santos Jun 2005

The Evolution Of Our Preferences: Evidence From Capuchin-Monkey Trading Behavior, Keith M. Chen, Venkat Lakshminarayanan, Laurie Santos

Cowles Foundation Discussion Papers

Behavioral economics has demonstrated systematic decision-making biases in both lab and field data. But are these biases learned or innate? We investigate this question using experiments on a novel set of subjects — capuchin monkeys. By introducing a fiat currency and trade to a capuchin colony, we are able to recover their preferences over a wide range of goods and risky choices. We show that standard price theory does a remarkably good job of describing capuchin purchasing behavior; capuchin monkeys react rationally to both price and wealth shocks. However, when capuchins are faced with more complex choices including risky gambles, …


A Simple Approach To The Parametric Estimation Of Potentially Nonstationary Diffusions, Federico M. Bandi, Peter C.B. Phillips Jun 2005

A Simple Approach To The Parametric Estimation Of Potentially Nonstationary Diffusions, Federico M. Bandi, Peter C.B. Phillips

Cowles Foundation Discussion Papers

A simple and robust approach is proposed for the parametric estimation of scalar homogeneous stochastic differential equations. We specify a parametric class of diffusions and estimate the parameters of interest by minimizing criteria based on the integrated squared difference between kernel estimates of the drift and diffusion functions and their parametric counterparts. The procedure does not require simulations or approximations to the true transition density and has the simplicity of standard nonlinear least-squares methods in discrete-time. A complete asymptotic theory for the parametric estimates is developed. The limit theory relies on infill and long span asymptotics and is robust to …