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EL Inference for Partially Identified Models: Large Deviations Optimality and Bootstrap Validity
, 2008
"... This paper addresses the issue of optimal inference for parameters that are partially identified in models with moment inequalities. There currently exists a variety of inferential methods for use in this setting. However, the question of choosing optimally among contending procedures is unresolved. ..."
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Cited by 60 (5 self)
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This paper addresses the issue of optimal inference for parameters that are partially identified in models with moment inequalities. There currently exists a variety of inferential methods for use in this setting. However, the question of choosing optimally among contending procedures is unresolved. In this paper, I first consider a canonical large deviations criterion for optimality and show that inference based on the empirical likelihood ratio statistic is optimal. This finding is a direct analog to that in Kitamura (2001) for moment equality models. Second, I introduce a new empirical likelihood bootstrap that provides a valid resampling method for moment inequality models and overcomes the implementation challenges that arise as a result of nonpivotal limit distributions. Lastly, I analyze the finite sample properties of the proposed framework using Monte Carlo simulations. The simulation results are encouraging.
Inference in Models Defined by Conditional Moment Inequalities with Continuous Covariates,” Working Paper
, 2010
"... In this paper I present a novel approach to inference in models where the partially identified parameter is defined by a set of conditional moment inequalities with continuous covariates. This class of models covers many economic applications, including treatment response models and regression with ..."
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Cited by 12 (1 self)
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In this paper I present a novel approach to inference in models where the partially identified parameter is defined by a set of conditional moment inequalities with continuous covariates. This class of models covers many economic applications, including treatment response models and regression with missing or interval outcome data. Depending on the assumptions that a researcher is willing to make on conditional moment functions that define the inequalities, I propose inference procedure that is based on the distance between the set of conditional moment functions and the cone of nonpositive (or nonnegative) functions. If a researcher is reluctant to impose any assumptions about the shape of conditional moment functions except certain smoothness conditions, I offer a method that relies on bootstrapping of the simultaneous lower confidence bands for nonparametric estimators of conditional moments. In general, this inference procedure may lead to a conservative coverage. However, I show that under a particular set of shape restrictions on conditional moment functions one can construct confidence sets based on a Gaussian asymptotic approximation that is relatively easy to implement and attains accurate coverage in small samples. Finally, I conduct Monte Carlo simulations to illustrate both procedures. ∗I am indebted to Elie Tamer for his constant encouragement and support throughout this project. I am very grateful to Ivan Canay and Wenxin Jiang for valuable comments and suggestions. I want to thank Vasiliy Ponomarev and Daniil Manaenkov for helpful discussions.
Global identification in nonlinear semiparametric models. UCSD Working Paper
, 2008
"... Abstract. This paper derives primitive conditions for global identification in nonlinear simultaneous equations systems. Identification is semiparametric in the sense that it is based on a set of unconditional moment restrictions. Our contribution to the literature is twofold. First, we derive a se ..."
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Cited by 3 (2 self)
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Abstract. This paper derives primitive conditions for global identification in nonlinear simultaneous equations systems. Identification is semiparametric in the sense that it is based on a set of unconditional moment restrictions. Our contribution to the literature is twofold. First, we derive a set of unconditional moment restrictions on the observables that are the starting point for identification in nonlinear structural systems even in the presence of multiple equilibria. Second, we provide primitive conditions under which a parameter value that solves those restrictions is unique. We apply our results a nonlinear IV model with multiple equilibria and give sufficient conditions for identifiability of its parameters.
Consistency of PlugIn Estimators of Upper Contour and Level Sets ∗
"... This note studies the problem of estimating the set of finite dimensional parameter values defined by a finite number of moment inequality or equality conditions and gives conditions under which the estimator defined by the set of parameter values that satisfy the estimated versions of these conditi ..."
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This note studies the problem of estimating the set of finite dimensional parameter values defined by a finite number of moment inequality or equality conditions and gives conditions under which the estimator defined by the set of parameter values that satisfy the estimated versions of these conditions is consistent in Hausdorff metric. This note also suggests extremum estimators that with probability approaching to one agree with the set consisting of parameter values that satisfy the sample versions of the moment conditions. Finally, the note studies the model where the information at hand consists of inequality constraints on nonparametric regression functions and shows the consistency of the plugin estimator or Mestimators that agree with that estimator with probability approaching to one.
A TEST FOR MONOTONE COMPARATIVE STATICS
"... Abstract. In this paper we design an econometric test for monotone comparative statics (MCS) often found in models with multiple equilibria. Our test exploits the observable implications of the MCS prediction: that the extreme (high and low) conditional quantiles of the dependent variable increase m ..."
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Abstract. In this paper we design an econometric test for monotone comparative statics (MCS) often found in models with multiple equilibria. Our test exploits the observable implications of the MCS prediction: that the extreme (high and low) conditional quantiles of the dependent variable increase monotonically with the explanatory variable. The main contribution of the paper is to derive a likelihoodratio test, which to the best of our knowledge, is the first econometric test of MCS proposed in the literature. The test is an asymptotic “chibar squared ” test for order restrictions on intermediate conditional quantiles. The key features of our approach are: (1) it does not require estimating the underlying nonparametric model relating the dependent and explanatory variables to the latent disturbances; (2) it makes few assumptions on the cardinality, location or probabilities over equilibria. In particular, one can implement our test without assuming an equilibrium selection rule.
I S T
"... In this paper we design an econometric test for monotone comparative statics (MCS) often found in models with multiple equilibria. Our test exploits the observable implications of the MCS prediction: that the extreme (high and low) conditional quantiles of the dependent variable increase monotonical ..."
Abstract
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In this paper we design an econometric test for monotone comparative statics (MCS) often found in models with multiple equilibria. Our test exploits the observable implications of the MCS prediction: that the extreme (high and low) conditional quantiles of the dependent variable increase monotonically with the explanatory variable. The main contribution of the paper is to derive a likelihoodratio test, which to the best of our knowledge, is the first econometric test of MCS proposed in the literature. The test is an asymptotic “chibar squared ” test for order restrictions on intermediate conditional quantiles. The key features of our approach are: (1) it does not require estimating the underlying nonparametric model relating the dependent and explanatory variables to the latent disturbances; (2) it makes few assumptions on the cardinality, location or probabilities over equilibria. In particular, one can implement our test without assuming an equilibrium selection rule.
mann, and seminar participants at UCSD for their helpful comments. I also benefited from conversations with
, 2010
"... This paper considers inference for the set ΘI of parameter values that minimize a criterion function. Chernozhukov, Hong, and Tamer (2007) (CHT) develop a general theory of consistent set estimation using the levelset of a criterion function and inference based on their quasilikelihood ratio (QLR) ..."
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This paper considers inference for the set ΘI of parameter values that minimize a criterion function. Chernozhukov, Hong, and Tamer (2007) (CHT) develop a general theory of consistent set estimation using the levelset of a criterion function and inference based on their quasilikelihood ratio (QLR)type statistic. This paper proposes a tractable way to represent the levelset estimator by its support function. The properly normalized (scaled and centered) support function of the levelset estimator provides an alternative Waldtype inference method to conduct tests regarding the identified set and a point θ0 in the identified set. These tests can be inverted to obtain confidence collections and confidence sets for ΘI and θ0. We also propose a generic stepup algorithm to choose a tuning parameter, the level of the criterion function. For econometric models that involve finitely many moment inequalities, we show that our Waldtype statistic is asymptotically equivalent to CHT’s QLR statistic under some regularity conditions. JEL Classification: C12