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First Price Auctions With General Information Structures: Implications For Bidding And Revenue, Dirk Bergemann, Benjamin Brooks, Stephen Morris Aug 2015

First Price Auctions With General Information Structures: Implications For Bidding And Revenue, Dirk Bergemann, Benjamin Brooks, Stephen Morris

Cowles Foundation Discussion Papers

We explore the impact of private information in sealed-bid first-price auctions. For a given symmetric and arbitrarily correlated prior distribution over values, we characterize the lowest winning-bid distribution that can arise across all information structures and equilibria. The information and equilibrium attaining this minimum leave bidders indifferent between their equilibrium bids and all higher bids. Our results provide lower bounds for bids and revenue with asymmetric distributions over values. We also report further characterizations of revenue and bidder surplus including upper bounds on revenue. Our work has implications for the identification of value distributions from data on winning bids and …


Efficient Estimation Of Multivariate Semi-Nonparametric Garch Filtered Copula Models, Xiaohong Chen, Zhuo Huang, Yanping Yi Aug 2015

Efficient Estimation Of Multivariate Semi-Nonparametric Garch Filtered Copula Models, Xiaohong Chen, Zhuo Huang, Yanping Yi

Cowles Foundation Discussion Papers

This paper considers estimation of semi-nonparametric GARCH filtered copula models in which the individual time series are modelled by semi-nonparametric GARCH and the joint distributions of the multivariate standardized innovations are characterized by parametric copulas with nonparametric marginal distributions. The models extend those of Chen and Fan (2006) to allow for semi-nonparametric conditional means and volatilities, which are estimated via the method of sieves such as splines. The fitted residuals are then used to estimate the copula parameters and the marginal densities of the standardized innovations jointly via the sieve maximum likelihood (SML). We show that, even using nonparametrically filtered …


Introduction To Jet Symposium Issue On ‘Dynamic Contracts And Mechanism Design, Dirk Bergemann, Alessandro Pavan Aug 2015

Introduction To Jet Symposium Issue On ‘Dynamic Contracts And Mechanism Design, Dirk Bergemann, Alessandro Pavan

Cowles Foundation Discussion Papers

The Introduction to the Symposium Issue on “Dynamic Contract and Mechanism Design” of the Journal of Economic Theory provides an overview of the dynamic mechanism design literature. We then introduce the papers that are contained in the Symposium issue and finally conclude by discussing avenues for future research. Several of the papers contained in the Symposium issue were presented at the Economic Theory Workshop of the Cowles Foundation for Research in Economics at Yale University in June 2013.


First Price Auctions With General Information Structures: Implications For Bidding And Revenue, Dirk Bergemann, Benjamin Brooks, Stephen Morris Aug 2015

First Price Auctions With General Information Structures: Implications For Bidding And Revenue, Dirk Bergemann, Benjamin Brooks, Stephen Morris

Cowles Foundation Discussion Papers

This paper explores the consequences of information in sealed bid first price auctions. For a given symmetric and arbitrarily correlated prior distribution over valuations, we characterize the set of possible outcomes that can arise in a Bayesian equilibrium for some information structure. In particular, we characterize maximum and minimum revenue across all information structures when bidders may not know their own values, and maximum revenue when they do know their values. Revenue is maximized when buyers know who has the highest valuation, but the highest valuation buyer has partial information about others’ values. Revenue is minimized when buyers are uncertain …


Information And Market Power, Dirk Bergemann, Tibor Heumann, Stephen Morris Aug 2015

Information And Market Power, Dirk Bergemann, Tibor Heumann, Stephen Morris

Cowles Foundation Discussion Papers

We analyze demand function competition with a finite number of agents and private information. We show that the nature of the private information determines the market power of the agents and thus price and volume of equilibrium trade. We establish our results by providing a characterization of the set of all joint distributions over demands and payoff states that can arise in equilibrium under any information structure. In demand function competition, the agents condition their demand on the endogenous information contained in the price. We compare the set of feasible outcomes under demand function to the feasible outcomes under Cournot …


Information And Market Power, Dirk Bergemann, Tibor Heumann, Stephen Morris Aug 2015

Information And Market Power, Dirk Bergemann, Tibor Heumann, Stephen Morris

Cowles Foundation Discussion Papers

We consider demand function competition with a finite number of agents and private information. We analyze how the structure of the private information shapes the market power of each agent and the price volatility. We show that any degree of market power can arise in the unique equilibrium under an information structure that is arbitrarily close to complete information. In particular, regardless of the number of agents and the correlation of payoff shocks, market power may be arbitrarily close to zero (so we obtain the competitive outcome) or arbitrarily large (so there is no trade in equilibrium). By contrast, price …


First Price Auctions With General Information Structures: Implications For Bidding And Revenue, Dirk Bergemann, Benjamin Brooks, Stephen Morris Aug 2015

First Price Auctions With General Information Structures: Implications For Bidding And Revenue, Dirk Bergemann, Benjamin Brooks, Stephen Morris

Cowles Foundation Discussion Papers

We explore the impact of private information in sealed bid first price auctions. For a given symmetric and arbitrarily correlated prior distribution over values, we characterize the lowest winning bid distribution that can arise across all information structures and equilibria. The information and equilibrium attaining this minimum leave bidders uncertain whether they will win or lose and indifferent between their equilibrium bids and all higher bids. Our results provide lower bounds for bids and revenue with asymmetric distributions over values. We report further analytic and computational characterizations of revenue and bidder surplus including upper bounds on revenue. Our work has …


First Price Auctions With General Information Structures: Implications For Bidding And Revenue, Dirk Bergemann, Benjamin Brooks, Stephen Morris Aug 2015

First Price Auctions With General Information Structures: Implications For Bidding And Revenue, Dirk Bergemann, Benjamin Brooks, Stephen Morris

Cowles Foundation Discussion Papers

We explore the impact of private information in sealed-bid first-price auctions. For a given symmetric and arbitrarily correlated prior distribution over values, we characterize the lowest winning-bid distribution that can arise across all information structures and equilibria. The information and equilibrium attaining this minimum leave bidders indifferent between their equilibrium bids and all higher bids. Our results provide lower bounds for bids and revenue with asymmetric distributions over values. We report further analytic and computational characterizations of revenue and bidder surplus including upper bounds on revenue. Our work has implications for the identification of value distributions from data on winning …


Identification In Differentiated Products Markets, Steven T. Berry, Philip A. Haile Aug 2015

Identification In Differentiated Products Markets, Steven T. Berry, Philip A. Haile

Cowles Foundation Discussion Papers

Empirical models of demand for — and, often, supply of — differentiated products are widely used in practice, typically employing parametric functional forms and distributions of consumer heterogeneity. We review some recent work studying identification in a broad class of such models. This work shows that parametric functional forms and distributional assumptions are not essential for identification. Rather, identification relies primarily on the standard requirement that instruments be available for the endogenous variables — here, typically, prices and quantities. We discuss the kinds of instruments needed for identification and how the reliance on instruments can be reduced by nonparametric functional …


Team Production, Endogenous Learning About Abilities And Career Concerns, Evangelia Chalioti Aug 2015

Team Production, Endogenous Learning About Abilities And Career Concerns, Evangelia Chalioti

Cowles Foundation Discussion Papers

This paper studies career concerns in teams where the support a worker receives depends on fellow team members’ effort and ability. In this setting, by exerting effort and providing support, a worker can influence her own and her teammates’ performances in order to bias the learning process in her favor. To manipulate the market’s assessments, we argue that in equilibrium, a worker has incentives to help or even sabotage her colleagues in order to signal that she is of higher ability. In a multiperiod stationary framework, we show that the stationary level of work effort is above and help effort …


Identification Of Nonparametric Simultaneous Equations Models With A Residual Index Structure, Steven T. Berry, Philip A. Haile Jul 2015

Identification Of Nonparametric Simultaneous Equations Models With A Residual Index Structure, Steven T. Berry, Philip A. Haile

Cowles Foundation Discussion Papers

We present new results on the identifiability of a class of nonseparable nonparametric simultaneous equations models introduced by Matzkin (2008). These models combine exclusion restrictions with a requirement that each structural error enter through a “residual index.” Our identification results encompass a variety of special cases allowing tradeoffs between the exogenous variation required of instruments and restrictions on the joint density of structural errors. Among these special cases are results avoiding any density restriction and results allowing instruments with arbitrarily small support.


Inference In Near Singular Regression, Peter C.B. Phillips Jul 2015

Inference In Near Singular Regression, Peter C.B. Phillips

Cowles Foundation Discussion Papers

This paper considers stationary regression models with near-collinear regressors. Limit theory is developed for regression estimates and test statistics in cases where the signal matrix is nearly singular in finite samples and is asymptotically degenerate. Examples include models that involve evaporating trends in the regressors that arise in conditions such as growth convergence. Structural equation models are also considered and limit theory is derived for the corresponding instrumental variable estimator, Wald test statistic, and overidentification test when the regressors are endogenous.


Inference Based On Many Conditional Moment Inequalities, Donald W.K. Andrews, Xiaoxia Shi Jul 2015

Inference Based On Many Conditional Moment Inequalities, Donald W.K. Andrews, Xiaoxia Shi

Cowles Foundation Discussion Papers

In this paper, we construct confidence sets for models defined by many conditional moment inequalities/equalities. The conditional moment restrictions in the models can be finite, countably infinite, or uncountably infinite. To deal with the complication brought about by the vast number of moment restrictions, we exploit the manageability (Pollard (1990)) of the class of moment functions. We verify the manageability condition in five examples from the recent partial identification literature. The proposed confidence sets are shown to have correct asymptotic size in a uniform sense and to exclude parameter values outside the identified set with probability approaching one. Monte Carlo …


Efficiency And Stability In Large Matching Markets, Yeon-Koo Che, Olivier Tercieux Jul 2015

Efficiency And Stability In Large Matching Markets, Yeon-Koo Che, Olivier Tercieux

Cowles Foundation Discussion Papers

We study efficient and stable mechanisms in matching markets when the number of agents is large and individuals’ preferences and priorities are drawn randomly. When agents’ preferences are uncorrelated, then both efficiency and stability can be achieved in an asymptotic sense via standard mechanisms such as deferred acceptance and top trading cycles. When agents’ preferences are correlated over objects, however, these mechanisms are either inefficient or unstable even in an asymptotic sense. We propose a variant of deferred acceptance that is asymptotically efficient, asymptotically stable and asymptotically incentive compatible. This new mechanism performs well in a counterfactual calibration based on …


Identification Of Nonparametric Simultaneous Equations Models With A Residual Index Structure, Steven T. Berry, Philip A. Haile Jul 2015

Identification Of Nonparametric Simultaneous Equations Models With A Residual Index Structure, Steven T. Berry, Philip A. Haile

Cowles Foundation Discussion Papers

We present new identification results for a class of nonseparable nonparametric simultaneous equations models introduced by Matzkin (2008). These models combine traditional exclusion restrictions with a requirement that each structural error enter through a “residual index.” Our identification results are constructive and encompass a range of special cases with varying demands on the exogenous variation provided by instruments and the shape of the joint density of the structural errors. The most important of these results demonstrate identification even when instruments have limited variation. A genericity result demonstrates a formal sense in which the associated density conditions may be viewed as …


Inference Based On Many Conditional Moment Inequalities, Donald W.K. Andrews, Xiaoxia Shi Jul 2015

Inference Based On Many Conditional Moment Inequalities, Donald W.K. Andrews, Xiaoxia Shi

Cowles Foundation Discussion Papers

In this paper, we construct confidence sets for models defined by many conditional moment inequalities/equalities. The conditional moment restrictions in the models can be finite, countably in finite, or uncountably in finite. To deal with the complication brought about by the vast number of moment restrictions, we exploit the manageability (Pollard (1990)) of the class of moment functions. We verify the manageability condition in five examples from the recent partial identification literature. The proposed confidence sets are shown to have correct asymptotic size in a uniform sense and to exclude parameter values outside the identified set with probability approaching one. …


Sieve Semiparametric Two-Step Gmm Under Weak Dependence, Xiaohong Chen, Zhipeng Liao Jul 2015

Sieve Semiparametric Two-Step Gmm Under Weak Dependence, Xiaohong Chen, Zhipeng Liao

Cowles Foundation Discussion Papers

This paper considers semiparametric two-step GMM estimation and inference with weakly dependent data, where unknown nuisance functions are estimated via sieve extremum estimation in the first step. We show that although the asymptotic variance of the second-step GMM estimator may not have a closed form expression, it can be well approximated by sieve variances that have simple closed form expressions. We present consistent or robust variance estimation, Wald tests and Hansen’s (1982) over-identification tests for the second step GMM that properly reflect the first-step estimated functions and the weak dependence of the data. Our sieve semiparametric two-step GMM inference procedures …


Information Limits Of Aggregate Data, Ray C. Fair Jul 2015

Information Limits Of Aggregate Data, Ray C. Fair

Cowles Foundation Discussion Papers

This paper uses a small model in the Cowles Commission (CC) tradition to examine the limits of aggregate data. It argues that more can be learned about the macroeconomy following the CC approach than the reduced form and VAR approaches allow, but less than the DSGE approach tries to do.


Payoff Equivalence Of Efficient Mechanisms In Large Matching Markets, Yeon-Koo Che, Olivier Tercieux Jul 2015

Payoff Equivalence Of Efficient Mechanisms In Large Matching Markets, Yeon-Koo Che, Olivier Tercieux

Cowles Foundation Discussion Papers

We study Pareto efficient mechanisms in matching markets when the number of agents is large and individual preferences are randomly drawn from a class of distributions, allowing for both common and idiosyncratic shocks. We show that, as the market grows large, all Pareto efficient mechanisms — including top trading cycles, serial dictatorship, and their randomized variants — are uniformly asymptotically payoff equivalent “up to the renaming of agents,” yielding the utilitarian upper bound in the limit. This result implies that, when the conditions of our model are met, policy makers need not discriminate among Pareto efficient mechanisms based on the …


An Analysis Of Top Trading Cycles In Two-Sided Matching Markets, Yeon-Koo Che, Olivier Tercieux Jul 2015

An Analysis Of Top Trading Cycles In Two-Sided Matching Markets, Yeon-Koo Che, Olivier Tercieux

Cowles Foundation Discussion Papers

We study top trading cycles in a two-sided matching environment (Abdulkadiroglu and Sonmez (2003)) under the assumption that individuals’ preferences and objects’ priorities are drawn iid uniformly. The distributions of agents’ preferences and objects’ priorities remaining after a given round of TTC depend nontrivially on the exact history of the algorithm up to that round (and so need not be uniform iid ). Despite the nontrivial history-dependence of evolving economies, we show that the number of individuals/objects assigned at each round follows a simple Markov chain and we explicitly derive the transition probabilities


Investment Horizons And Price Indeterminacy In Financial Markets, Shinichi Hirota, Juergen Huber, Thomas Stöckl, Shyam Sunder Jun 2015

Investment Horizons And Price Indeterminacy In Financial Markets, Shinichi Hirota, Juergen Huber, Thomas Stöckl, Shyam Sunder

Cowles Foundation Discussion Papers

We examine how different investment horizons, and consequently the number of hands through which a security passes during its life, affect prices in a laboratory market populated by overlapping generations of investors. We find that (i) price deviations are larger in markets populated only by short-horizon investors compared to markets with long-horizon investors; (ii) for a given maturity of security, price deviations increase as investment horizons shrink (and frequency of transfers increases); and (iii) short investment horizons create upward pressure on prices when liquidity is high and downward pressure when liquidity is low.


Edmond Malinvaud: A Tribute To His Contributions In Econometrics, Peter C.B. Phillips Jun 2015

Edmond Malinvaud: A Tribute To His Contributions In Econometrics, Peter C.B. Phillips

Cowles Foundation Discussion Papers

This paper provides a tribute to Edmond Malinvaud’s contributions to econometrics. We overview the primary original contributions in Edmond Malinvaud’s masterful work The Statistical Methods of Econometrics . This advanced text developed a complete treatment of linear estimation theory using geometric methods and, for the first time, provided rigorous nonlinear regression asymptotics, using this theory as the basis of a rigorous development of the limit theory for simultaneous equations theory. Malinvaud’s treatise remained the most complete textbook study of econometric methods for several decades.


Pitfalls And Possibilities In Predictive Regression, Peter C.B. Phillips Jun 2015

Pitfalls And Possibilities In Predictive Regression, Peter C.B. Phillips

Cowles Foundation Discussion Papers

Financial theory and econometric methodology both struggle in formulating models that are logically sound in reconciling short run martingale behaviour for financial assets with predictable long run behavior, leaving much of the research to be empirically driven. The present paper overviews recent contributions to this subject, focussing on the main pitfalls in conducting predictive regression and on some of the possibilities offered by modern econometric methods. The latter options include indirect inference and techniques of endogenous instrumentation that use convenient temporal transforms of persistent regressors. Some additional suggestions are made for bias elimination, quantile crossing amelioration, and control of predictive …


Hot Property In New Zealand: Empirical Evidence Of Housing Bubbles In The Metropolitan, Ryan Greenaway-Mcgrevy, Peter C.B. Phillips Jun 2015

Hot Property In New Zealand: Empirical Evidence Of Housing Bubbles In The Metropolitan, Ryan Greenaway-Mcgrevy, Peter C.B. Phillips

Cowles Foundation Discussion Papers

Using recently developed statistical methods for testing and dating exhuberant behavior in asset prices we document evidence of episodic bubbles in the New Zealand property market over the past two decades. The results show clear evidence of a broad-based New Zealand housing bubble that began in 2003 and collapsed over mid 2007 to early 2008 with the onset of the worldwide recession and the financial crisis. New methods of analyzing market contagion are also developed and are used to examine spillovers from the Auckland property market to the other metropolitan centres. Evidence from the latest data reveals that the greater …


Business Cycles, Trend Elimination, And The Hp Filter, Peter C.B. Phillips, Sainan Jin Jun 2015

Business Cycles, Trend Elimination, And The Hp Filter, Peter C.B. Phillips, Sainan Jin

Cowles Foundation Discussion Papers

We analyze trend elimination methods and business cycle estimation by data filtering of the type introduced by Whittaker (1923) and popularized in economics in a particular form by Hodrick and Prescott (1980/1997; HP). A limit theory is developed for the HP filter for various classes of stochastic trend, trend break, and trend stationary data. Properties of the filtered series are shown to depend closely on the choice of the smoothing parameter (λ). For instance, when λ = O ( n 4 ) where n is the sample size, and the HP filter is applied to an I(1) process, the filter …


Minimum Distance Testing And Top Income Shares In Korea, Jin Seo Cho, Myung-Ho Park, Peter C.B. Phillips Jun 2015

Minimum Distance Testing And Top Income Shares In Korea, Jin Seo Cho, Myung-Ho Park, Peter C.B. Phillips

Cowles Foundation Discussion Papers

We study Kolmogorov-Smirnov goodness of fit tests for evaluating distributional hypotheses where unknown parameters need to be fitted. Following work of Pollard (1979), our approach uses a Cramér-von Mises minimum distance estimator for parameter estimation. The asymptotic null distribution of the resulting test statistic is represented by invariance principle arguments as a functional of a Brownian bridge in a simple regression format for which asymptotic critical values are readily delivered by simulations. Asymptotic power is examined under fixed and local alternatives and finite sample performance of the test is evaluated in simulations. The test is applied to measure top income …


Testing Mean Stability Of Heteroskedastic Time Series, Violetta Dalla, Liudas Giraitis, Peter C.B. Phillips Jun 2015

Testing Mean Stability Of Heteroskedastic Time Series, Violetta Dalla, Liudas Giraitis, Peter C.B. Phillips

Cowles Foundation Discussion Papers

Time series models are often fitted to the data without preliminary checks for stability of the mean and variance, conditions that may not hold in much economic and financial data, particularly over long periods. Ignoring such shifts may result in fitting models with spurious dynamics that lead to unsupported and controversial conclusions about time dependence, causality, and the effects of unanticipated shocks. In spite of what may seem as obvious differences between a time series of independent variates with changing variance and a stationary conditionally heteroskedastic (GARCH) process, such processes may be hard to distinguish in applied work using basic …


The Dynamics Of Capital Accumulation In The Us: Simulations After Piketty, Philippe De Donder, John E. Roemer Apr 2015

The Dynamics Of Capital Accumulation In The Us: Simulations After Piketty, Philippe De Donder, John E. Roemer

Cowles Foundation Discussion Papers

We calibrate a sequence of four nested models to study the dynamics of wealth accumulation. Individuals maximize a utility function whose arguments are consumption and investment. They desire to accumulate wealth for its own sake — this is not a life-cycle model. A competitive firm produces a single good from labor and capital; the rate of return to capital and the wage rate are market-clearing. The second model introduces political lobbying by the wealthy, whose purpose is to reduce the tax rate on capital income. The third model introduces differential rates of return to capitals of different sizes. The fourth …


The Dynamics Of Capital Accumulation In The Us: Simulations After Piketty, Philippe De Donder, John E. Roemer Apr 2015

The Dynamics Of Capital Accumulation In The Us: Simulations After Piketty, Philippe De Donder, John E. Roemer

Cowles Foundation Discussion Papers

We develop a dynamic model where a competitive firm produces a single good from labor and capital, with market clearing rates of return. Individuals are heterogeneous in skills, with an endowment in capital/wealth increasing in skill. Individuals aspire to a standard consumption level, with a constant marginal propensity to consume out of income above this level. We define a steady state of this model as an equilibrium where factor returns and wealth shares remain constant. We calibrate the model to the US economy and obtain that a steady state exists. We then study three variants of the model: one with …


Overidentification In Regular Models, Xiaohong Chen, Andres Santos Apr 2015

Overidentification In Regular Models, Xiaohong Chen, Andres Santos

Cowles Foundation Discussion Papers

In models defined by unconditional moment restrictions, specification tests are possible and estimators can be ranked in terms of efficiency whenever the number of moment restrictions exceeds the number of parameters. We show that a similar relationship between potential refutability of a model and semiparametric efficiency is present in a much broader class of settings. Formally, we show a condition we name local overidentification is required for both specification tests to have power against local alternatives and for the existence of both efficient and inefficient estimators of regular parameters. Our results immediately imply semiparametric conditional moment restriction models are typically …