Inference for the Identified Set in Partially Identified Econometric Models PDF Download
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Author: Joseph P. Romano
Publisher:
ISBN:
Category :
Languages : en
Pages : 41
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Author: Azeem M. Shaikh
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Category :
Languages : en
Pages : 194
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Author: Joseph P. Romano
Publisher:
ISBN:
Category :
Languages : en
Pages : 41
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Author: Hiroaki Kaido
Publisher:
ISBN: 9781124030555
Category : Capital assets pricing model
Languages : en
Pages : 402
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When a sample of data does not fully reveal the "true" data generating structure (or parameter) but gives information that bounds the set of observationally equivalent structures, an economic model is said to be partially identified. This dissertation develops and applies estimation and inference methods for economic models whose population features are only partially identified. In Chapter 1 (co-authored with Halbert White), I apply econometric techniques from the partial identification literature to address a fundamental problem in asset pricing theory. Namely, that the market price of risk is only identified as a set under incomplete markets. I construct a set estimator and confidence regions for the set of market risk prices. I further show that it is possible to test hypotheses of economic interest without fully identifying the market price of risk. The econometric techniques used in Chapter 1 are developed by Chapter 2 (co-authored with Halbert White). When the dimension of the parameter space is large, this is a particular challenge for set-valued estimators, as high dimensionality can create computational difficulties and seriously hamper the interpretation of estimation results. We study how the use of a natural two-stage extension of the Chernozhukov, Hong, and Tamer's (2007) (CHT) framework can exploit a priori knowledge about the data generating process to mitigate the problems otherwise associated with set estimation in high-dimensional parameter spaces. Chapter 3 unifies two general approaches recently proposed in the literature, the criterion function approach and support function approach. CHT develop a theory of set estimation and inference for the set [Theta]/I of parameter values that minimize a criterion function. The support function approach provides an alternative characterization of CHT's level-set estimator by its supporting hyperplanes. This results in an estimation and inference method that has the wide applicability of the criterion function approach and the computational tractability of the support function approach. By establishing the asymptotic distribution of the properly normalized support function of the level set estimator, I provide Wald-type inference tools to conduct tests regarding the identified set [Theta]/I and a point [Theta]0 in the identified set.
Author: Joseph P. Romano
Publisher:
ISBN:
Category :
Languages : en
Pages : 39
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Author: Frank Schorfheide
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Category : Economics
Languages : en
Pages : 34
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A large sample approximation of the posterior distribution of partially identified structural parameters is derived for models that can be indexed by a finite-dimensional reduced form parameter vector. It is used to analyze the differences between frequentist confidence sets and Bayesian credible sets in partially identified models. A key difference is that frequentist set estimates extend beyond the boundaries of the identified set (conditional on the estimated reduced form parameter), whereas Bayesian credible sets can asymptotically be located in the interior of the identified set. Our asymptotic approximations are illustrated in the context of simple moment inequality models and a numerical illustration for a two-player entry game is provided.
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Languages : en
Pages : 248
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This dissertation consists of two self-contained essays on partially identified econometric models, organized in the form of two chapters. The first chapter develops inference methods for conditional moment models in which the unknown parameter is possibly partially identified and may contain infinite-dimensional components. I consider testing the hypothesis that a given restriction on the parameter is satisfied by at least one element of the identification set. I propose using the sieve minimum of a Kolmogorov-Smirnov type statistic as the test statistic, derive its asymptotic distribution, and provide consistent bootstrap critical values. In this way a broad family of restrictions can be consistently tested, making the proposed procedure applicable to various types of inference. In particular, I show how to: (1) test the semiparametric model specification; (2) construct confidence sets for unknown parametric components; and (3) construct confidence sets for unknown functions at a given point. The specification test is consistent against fixed alternatives. The confidence sets have correct asymptotic coverage probability, excluding any value outside the identification set with asymptotic probability one. My methods are robust to partial identification, and allow for the moment functions to be nonsmooth. A Monte Carlo study demonstrates finite sample performance. In the second chapter, I consider estimation in dynamic discrete choice panel data models of short time series, in which neither the cross-sectional heterogeneity nor the initial condition is observed. The major challenges are: (1) point-identification often fails in these models as demonstrated by Honoré and Tamer (2006); and (2) the heterogeneity cannot be differenced out by the standard "within" or first difference transformations due to nonlinearity. I show that the parameter can be equivalently defined by a finite number of conditional moment equalities. And I propose set estimators that are fixed-T consistent with respect to a properly defined Hausdorff distance. Rates of convergence in the Hausdorff distance are derived.
Author: Victor Chernozhukov
Publisher:
ISBN:
Category :
Languages : en
Pages : 43
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This paper provides confidence regions for minima of an econometric criterion function Q([mu]). The minima form a set of parameters, [Theta]I, called the identified set. In economic applications, [Theta]I represents a class of economic models that are consistent with the data. Our inference procedures are criterion function based and so our confidence regions, which cover [Theta]I with a prespecified probability, are appropriate level sets of Qn([mu]), the sample analog of Q([mu]). When [Theta]I is a singleton, our confidence sets reduce to the conventional confidence regions based on inverting the likelihood or other criterion functions. We show that our procedure is valid under general yet simple conditions, and we provide feasible resampling procedure for implementing the approach in practice. We then show that these general conditions hold in a wide class of parametric econometric models. In order to verify the conditions, we develop methods of analyzing the asymptotic behavior of econometric criterion functions under set identification and also characterize the rates of convergence of the confidence regions to the identified set. We apply our methods to regressions with in terval data and set identified method of moments problems. We illustrate our methods in an empirical Monte Carlo study based on Current Population Survey data. Keywords: Set estimator, level sets, interval regression, subsampling bootsrap. JEL Classifications: C13, C14, C21, C41, C51, C53.
Author: Steven Durlauf
Publisher: Springer
ISBN: 0230280811
Category : Literary Criticism
Languages : en
Pages : 365
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Specially selected from The New Palgrave Dictionary of Economics 2nd edition, each article within this compendium covers the fundamental themes within the discipline and is written by a leading practitioner in the field. A handy reference tool.
Author: Herman B. Leonard
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Category :
Languages : en
Pages :
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