Identification and Inference of Nonlinear Models Using Two Samples with Arbitrary Measurement Errors
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.
Chen, Xiaohong and Hu, Yingyao, "Identification and Inference of Nonlinear Models Using Two Samples with Arbitrary Measurement Errors" (2006). Cowles Foundation Discussion Papers. 1883.