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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 …


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 …


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 …


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 …


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


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. …


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.


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.


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 …


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 …


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 …


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 …


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.


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 …


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

Overidentification In Regular Models, Xiaohong Chen, Andres Santos

Cowles Foundation Discussion Papers

In the unconditional moment restriction model of Hansen (1982), specification tests and more efficient estimators are both available whenever the number of moment restrictions exceeds the number of parameters of interest. We show a similar relationship between potential refutability of a model and existence of more efficient estimators is present in much broader settings. Specifically, a condition we name local overidentification is shown to be equivalent to both the existence of specification tests with nontrivial local power and the existence of more efficient estimators of some “smooth” parameters in general semi/nonparametric models. Under our notion of local overidentification, various locally …


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 …


Optimal Design For Social Learning, Yeon-Koo Che, Johannes Hörner Apr 2015

Optimal Design For Social Learning, Yeon-Koo Che, Johannes Hörner

Cowles Foundation Discussion Papers

This paper studies the design of a recommender system for organizing social learning on a product. To improve incentives for early experimentation, the optimal design trades off fully transparent social learning by over-recommending a product (or “spamming”) to a fraction of agents in the early phase of the product cycle. Under the optimal scheme, the designer spams very little about a product right after its release but gradually increases the frequency of spamming and stops it altogether when the product is deemed sufficiently unworthy of recommendation. The optimal recommender system involves randomly triggered spamming when recommendations are public — as …


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 …


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 …


Innovation Adoption By Forward-Looking Social Learners, Mira Frick, Yuhta Ishii Mar 2015

Innovation Adoption By Forward-Looking Social Learners, Mira Frick, Yuhta Ishii

Cowles Foundation Discussion Papers

We build a model studying the effect of an economy’s potential for social learning on the adoption of innovations of uncertain quality. Provided consumers are forward-looking (i.e., recognize the value of waiting for information), we show how quantitative and qualitative features of the learning environment affect observed adoption dynamics, welfare, and the speed of learning. Our analysis has two main implications. First, we identify environments that are subject to a “saturation effect,” whereby increased opportunities for social learning can slow down adoption and learning and do not increase consumer welfare, possibly even being harmful. Second, we show how differences in …


Buying Locally, George J. Mailath, Andrew Postlewaite, Larry Samuelson Mar 2015

Buying Locally, George J. Mailath, Andrew Postlewaite, Larry Samuelson

Cowles Foundation Discussion Papers

“Buy local” arrangements encourage members of a community or group to patronize one another rather than the external economy. They range from formal mechanisms such as local currencies to informal “I’ll buy from you if you buy from me” arrangements, and are often championed on social or environmental grounds. We show that in a monopolistically competitive economy, buy local arrangements can have salutary effects even for selfish agents immune to social or environmental considerations. Buy local arrangements effectively allow firms to exploit the equilibrium price-cost gap to profitably expand their sales at the going price.


Learning To Disagree In A Game Of Experimentation, Alessandro Bonatti, Johannes Hörner Mar 2015

Learning To Disagree In A Game Of Experimentation, Alessandro Bonatti, Johannes Hörner

Cowles Foundation Discussion Papers

We analyse strategic experimentation in which information arrives through fully revealing, publicly observable “breakdowns.” With hidden actions, there exists a unique equilibrium that involves randomization over stopping times. This randomization induces belief disagreement on the equilibrium path. When actions are observable, the equilibrium is pure, and welfare improves. We analyse the role of policy interventions such as subsidies for experimentation and risk-sharing agreements. We show that the optimal risk-sharing agreement restores the first-best outcome, independent of the monitoring structure.


The Implementation Duality, Georg Nöldeke, Larry Samuelson Mar 2015

The Implementation Duality, Georg Nöldeke, Larry Samuelson

Cowles Foundation Discussion Papers

We use the theory of abstract convexity to study adverse-selection principal-agent problems and two-sided matching problems, departing from much of the literature by not requiring quasilinear utility. We formulate and characterize a basic underlying implementation duality. We show how this duality can be used to obtain a sharpening of the taxation principle, to obtain a general existence result for solutions to the principal-agent problem, to show that (just as in the quasilinear case) all increasing decision functions are implementable under a single crossing condition, and to obtain an existence result for stable outcomes featuring positive assortative matching in a matching …


The Implementation Duality, Georg Nöldeke, Larry Samuelson Mar 2015

The Implementation Duality, Georg Nöldeke, Larry Samuelson

Cowles Foundation Discussion Papers

Conjugate duality relationships are pervasive in matching and implementation problems and provide much of the structure essential for characterizing stable matches and implementable allocations in models with quasilinear (or transferable) utility. In the absence of quasilinearity, a more abstract duality relationship, known as a Galois connection, takes the role of (generalized) conjugate duality. While much weaker, this duality relationship still induces substantial structure. We show that this structure can be used to extend existing results for, and gain new insights into, adverse-selection principal-agent problems and two-sided matching problems without quasilinearity.


Insurance In Extended Family Networks, Orazio P. Attanasio, Costas Meghir, Corina Mommaerts Mar 2015

Insurance In Extended Family Networks, Orazio P. Attanasio, Costas Meghir, Corina Mommaerts

Cowles Foundation Discussion Papers

We investigate partial insurance and group risk sharing in extended family networks. Our approach is based on decomposing income shocks into group aggregate and idiosyncratic components, allowing us to measure the extent to which each component is insured. We apply our framework to extended family networks in the United States by exploiting the unique intergenerational structure of the Panel Study of Income Dynamics. We find that over 60% of shocks to household income are potentially insurable within extended family networks. However, we find little evidence that the extended family provides insurance for such idiosyncratic shocks.


The Marriage Market, Labor Supply And Education Choice, Pierre-André Chiappori, Monica Costa Dias, Costas Meghir Mar 2015

The Marriage Market, Labor Supply And Education Choice, Pierre-André Chiappori, Monica Costa Dias, Costas Meghir

Cowles Foundation Discussion Papers

We develop an equilibrium life cycle model of education, marriage and labor supply and consumption in a transferable utility context. Individuals start by choosing their investments in education anticipating returns in the marriage market and the labor market. They then match based on the economic value of marriage and on preferences. Equilibrium in the marriage market determines intrahousehold allocation of resources. Following marriage households (married or single) save, supply labor and consume private and public commodities under uncertainty. Marriage thus has the dual role of providing public goods and offering risk sharing. The model is estimated using the British HPS.


Relational Contracts With Subjective Peer Evaluations, Joyee Deb, Jin Li, Arijit Mukherjee Mar 2015

Relational Contracts With Subjective Peer Evaluations, Joyee Deb, Jin Li, Arijit Mukherjee

Cowles Foundation Discussion Papers

We study optimal contracting in a setting where a firm repeatedly interacts with multiple workers, and can compensate them based on publicly available performance signals as well as privately reported peer evaluations. If the evaluation and the effort provision are done by different workers (as in a supervisor/agent hierarchy), we show that, using both the private and public signals, the first best can be achieved even in a static setting. However, if each worker is required to both exert effort and report on his co-worker’s performance (as in a team setting), the worker’s effort incentives cannot be decoupled from his …


Insurance In Extended Family Networks, Orazio P. Attanasio, Costas Meghir, Corina Mommaerts Mar 2015

Insurance In Extended Family Networks, Orazio P. Attanasio, Costas Meghir, Corina Mommaerts

Cowles Foundation Discussion Papers

We investigate partial insurance and group risk sharing in extended family networks. Our approach is based on decomposing income shocks into group aggregate and idiosyncratic components, allowing us to measure the extent to which each is insured, having accounted for public insurance programs. We apply our framework to extended family networks in the United States by exploiting the unique intergenerational structure of the PSID. We find that over 60% of shocks to household income are potentially insurable within family networks. However, we find little evidence that the extended family provides insurance for such idiosyncratic shocks.


The Marriage Market, Labor Supply And Education Choice, Pierre-André Chiappori, Monica Costa Dias, Costas Meghir Mar 2015

The Marriage Market, Labor Supply And Education Choice, Pierre-André Chiappori, Monica Costa Dias, Costas Meghir

Cowles Foundation Discussion Papers

We develop an equilibrium lifecycle model of education, marriage and labor supply and consumption in a transferable utility context. Individuals start by choosing their investments in education anticipating returns in the marriage market and the labor market. They then match based on the economic value of marriage and on preferences. Equilibrium in the marriage market determines intrahousehold allocation of resources. Following marriage households (married or single) save, supply labor and consume private and public under uncertainty. Marriage thus has the dual role of providing public goods and offering risk sharing. The model is estimated using the British HPS.