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Identification and Inference of Nonlinear Models Using Two Samples with Arbitrary Measurement Errors

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Author Info
Xiaohong Chen (New York University)
Yingyao Hu (University of Texas at Austin)

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Abstract

This paper considers identification and inference of a general latent nonlinear model using two samples, where a covariate contains arbitrary measurement errors in both samples, and neither sample contains an accurate measurement of the corresponding true variable. The primary sample consists of some dependent variables, some error-free covariates and an error-ridden covariate, where the measurement error has unknown distribution and could be arbitrarily correlated with the latent true values. The auxiliary sample consists of another noisy measurement of the mismeasured covariate and some error-free covariates. We first show that a general latent nonlinear model is nonparametrically identified using the two samples when both could have nonclassical errors, with no requirement of instrumental variables nor independence between the two samples. When the two samples are independent and the latent nonlinear model is parameterized, we propose sieve quasi maximum likelihood estimation (MLE) for the parameter of interest, and establish its root-n consistency and asymptotic normality under possible misspecification, and its semiparametric efficiency under correct specification. We also provide a sieve likelihood ratio model selection test to compare two possibly misspecified parametric latent models. A small Monte Carlo simulation and an empirical example are presented.

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Paper provided by Cowles Foundation, Yale University in its series Cowles Foundation Discussion Papers with number 1590.

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Length: 58 pages
Date of creation: Nov 2006
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Handle: RePEc:cwl:cwldpp:1590

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Related research
Keywords: Data combination Nonlinear errors-in-variables model Nonclassical measurement error Nonparametric identification Misspecified parametric latent model Sieve likelihood estimation and inference

Find related papers by JEL classification:
C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods

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  1. Xiaohong Chen & Yingyao Hu & Arthur Lewbel, 2007. "Nonparametric Identification of Regression Models Containing a Misclassified Dichotomous Regressor Without Instruments," Boston College Working Papers in Economics 675, Boston College Department of Economics. [Downloadable!]
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