Identification and estimation of single-index models with measurement error and endogeneity

Economic variables are often measured with an error and may be endogenous. In this paper, we give new identification results for the ratio of partial effects in linear index models with measurement error and endogeneity. The identification restrictions include independence of covariates and error terms, and the derivative of some conditional mean functions being nonzero. We propose a local polynomial regression estimator to estimate the single-index parameters. We apply these tools to estimate the labour-supply elasticity and find that the labour-supply elasticity for married men is positive, while the coefficients for married women are negative for the full sample and positive for the working sample.