COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
COWLES FOUNDATION DISCUSSION PAPER NO. 1590 Identification and Inference of Nonlinear Models Using Two
Samples Xiaohong Chen November 2006 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. |
