Estimation of cross sectional and panel data censored regression models with endogeneity

It is very difficult to deal with endogeneity in limited dependent variables models. Unless strong assumptions are made on the exact relationship between the endogenous regressors and the instruments, it is generally not possible to apply instrumental variable type techniques. This paper derives moment conditions that are useful in estimating censored regression models with endogenous regressors. These moment conditions are motivated by panel data censored regression models with predetermined (but not strictly exogenous) explanatory variables, but the main insight is also applicable to cross sectional models with endogenous explanatory variables.