Simulation-Based Estimation of the Structural Errors-in-Variables Negative Binomial Regression Model with an Application

This paper studies the effects and estimation of errors-in-variables negative binomial regression model. We prove that in the presence of measurement errors, in general, maximum likelihood estimator of the overdispersion using the observed data is biased upward. We adopt a structural approach assuming that the distribution of the latent variables is known and propose a simulation-based corrected maximum likelihood estimator and a simulation-based corrected score estimator to estimate the errors-in-variables negative binomial model. Though having similar asymptotic properties to the simulation-based corrected maximum likelihood estimator, the simulation-based corrected score estimator has a better finite sample performance as evidenced by the Monte Carlo studies. An application to the elderly demand for medical care using Medical Expenditure Panel Study is illustrated.