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25
Estimation of Nonparametric Simultaneous Equations
, 2005
"... This paper considers identification in parametric and nonparametric models, with additive or nonadditive unobservables, and with or without simultaneity among the endogenous variables. Several characterizations of observational equivalence are presented and conditions for identification are develope ..."
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Cited by 40 (7 self)
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This paper considers identification in parametric and nonparametric models, with additive or nonadditive unobservables, and with or without simultaneity among the endogenous variables. Several characterizations of observational equivalence are presented and conditions for identification are developed based on these. It is shown that the results can be extended to situations where the dependent variables are latent. We also demonstrate how the results may be used to derive constructive ways to calculate the unknown functions and distributions in simultaneous equations models, directly from the probability density of the observable variables. Estimators based on this do not suffer from the illposed inverse problem that other methods encounter.
Heterogeneity and the nonparametric analysis of consumer choice: conditions for invertibility”, cemmap Working Papers
, 2005
"... This paper considers structural nonparametric random utility models for continuous choice variables with unobserved heterogeneity. We provide sufficient conditions on random preferences to yield reducedform systems of nonparametric stochastic demand functions that allow global invertibility betwe ..."
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Cited by 12 (3 self)
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This paper considers structural nonparametric random utility models for continuous choice variables with unobserved heterogeneity. We provide sufficient conditions on random preferences to yield reducedform systems of nonparametric stochastic demand functions that allow global invertibility between demands and nonseparable unobserved heterogeneity. We distinguish between new classes of models in which heterogeneity is separable and nonseparable in the marginal rates of substitution, respectively. Invertibility is essential for global identification of structural consumer demand models, for the existence of wellspecified probability models of choice and for the nonparametric analysis of revealed stochastic preference.
Nonparametric Identification and Estimation of Random Coefficients in Nonlinear Economic Models
, 2010
"... We show how to nonparametrically identify and estimate the distribution of random coefficients that characterizes the heterogeneity among agents in a general class of economic choice models. We introduce an axiom that we term separability and prove that separability of a structural model ensures ide ..."
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Cited by 12 (4 self)
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We show how to nonparametrically identify and estimate the distribution of random coefficients that characterizes the heterogeneity among agents in a general class of economic choice models. We introduce an axiom that we term separability and prove that separability of a structural model ensures identification. Identification naturally gives rise to a nonparametric minimum distance estimator. We prove identification of distributions of utility functions in multinomial choice, distributions of labor supply responses to tax changes, and distributions of wage functions in the Roy selection model. We also reconsider the problem of endogeneity in economic choice models, leading to new results on the twostage least squares model.
Identification in Nonparametric Limited Dependent Variable Models with Simultaneity and Unobserved Heterogeneity”.
 Journal of Econometrics,
, 2012
"... Abstract We extend the identification results for nonparametric simultaneous equations models in ..."
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Cited by 11 (3 self)
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Abstract We extend the identification results for nonparametric simultaneous equations models in
Identifying Heterogeneity in Economic Choice and Selection Models Using Mixtures, working paper
, 2009
"... We show how to nonparametrically identify the distribution of heterogeneity in a general class of structural economic choice models. We state an economic property known as reducibility and prove that reducibility ensures identification. Reducibility makes verifying the identification of nonlinear mo ..."
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Cited by 8 (1 self)
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We show how to nonparametrically identify the distribution of heterogeneity in a general class of structural economic choice models. We state an economic property known as reducibility and prove that reducibility ensures identification. Reducibility makes verifying the identification of nonlinear models a straightforward task because it is a condition that is stated directly in terms of a choice model. We can allow for a nonparametric distribution over nonparametric functions of the data. We use our framework to prove identification in three classes of economic models: 1) nonparametric regressions including with endogenous regressors, 2) multinomial discrete choice including endogenous regressors as well as multiple purchases with complementarities, and 3) selection and mixed continuousdiscrete choice. Our identification strategy avoids identification at infinity. For selection, we allow for essential heterogeneity in both the selection and outcome equations and fully identify the joint distribution of outcomes.
2010a), “Estimation of Nonparametric Models with Simultaneity,” working paper
"... We introduce methods for estimating nonparametric, nonadditive models with simultaneity. The methods are developed by directly connecting the elements of the structural system to be estimated with features of the density of the observable variables, such as ratios of derivatives or averages of pro ..."
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Cited by 5 (2 self)
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We introduce methods for estimating nonparametric, nonadditive models with simultaneity. The methods are developed by directly connecting the elements of the structural system to be estimated with features of the density of the observable variables, such as ratios of derivatives or averages of products of derivatives of this density. The estimators are therefore easily computed functionals of a nonparametric estimator of the density of the observable variables. We consider in detail a model where to each structural equation there corresponds an exclusive regressor and a model with one equation of interest and one instrument that is included in a second equation. For both models, we provide new characterizations of observational equivalence on a set, in terms of the density of the observable variables and derivatives of the structural functions. Based on those characterizations, we develop two estimation methods. In the first method, the estimators of the structural derivatives are calculated by a simple matrix inversion and matrix multiplication, analogous to a standard Least Squares estimator, but with the elements of the matrices being averages of products of derivatives of nonparametric density estimators. In the second method, the
Semiparametric estimation of nonseparable models: a minimum distance from independence approach
 Econometrics Journal
, 2010
"... eScholarship provides open access, scholarly publishing services to the University of California and delivers a dynamic research platform to scholars worldwide. ..."
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Cited by 3 (0 self)
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eScholarship provides open access, scholarly publishing services to the University of California and delivers a dynamic research platform to scholars worldwide.
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.
From The New Palgrave Dictionary of Economics, Second Edition, 2008
"... The problem of identification is defined in terms of the possibility of characterizing parameters of interest from observable data. This problem occurs in many fields, such as automatic control, biomedical engineering, psychology, systems science, the design of experiments, and econometrics. This ar ..."
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Cited by 2 (1 self)
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The problem of identification is defined in terms of the possibility of characterizing parameters of interest from observable data. This problem occurs in many fields, such as automatic control, biomedical engineering, psychology, systems science, the design of experiments, and econometrics. This article focuses on identification in econometric models, which typically involve random variables. Identification in general parametric statistical models is defined, and its meaning in a number of specific econometric models is considered: regression (collinearity), simultaneous equations, dynamic models, and nonlinear models. Identification in nonparametric models, weak identification, and the statistical implications of identification failure are also discussed. Keywords Bayes ’ th; collinearity; endogeneity and exogeneity; identification; instrumental variable; linear models; multivariate regression models; nonparametric estimation; nonparametric models; probability; random variables; returns to schooling; separability; serial correlation; simultaneous equations models; treatment effect; weak identification; weak instruments Article In economic analysis, we often assume that there exists an underlying structure which has generated the observations of realworld data. However, statistical inference can relate only to characteristics of the distribution of the observed variables. Statistical models which are used to explain the behaviour of observed data typically involve parameters, and statistical inference aims at making statements about these parameters. For that
Identifying Demand with Multidimensional Unobservables: A Random Functions Approach
, 2011
"... We explore the identification of nonseparable models without relying on the property that the model can be inverted in the econometric unobservables. In particular, we allow for infinite dimensional unobservables. have multiple unobservables. In the context of a demand system, this allows each produ ..."
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Cited by 2 (1 self)
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We explore the identification of nonseparable models without relying on the property that the model can be inverted in the econometric unobservables. In particular, we allow for infinite dimensional unobservables. have multiple unobservables. In the context of a demand system, this allows each product to We identify the distribution of demand both unconditional and conditional on market observables, which allows us to identify several quantities of economic interest such as the (conditional and unconditional) distributions of elasticities and the distribution of price effects following a merger. Our approach is based on a significant generalization of the linear in random coefficients model that only restricts the random functions to be analytic in the endogenous variables, which is satisfied by several standard demand models used in practice. We assume an (unknown) countable support for the the distribution of the infinite dimensional unobservables.