Inference in Censored Models with Endogenous Regressors
Econometrica · 2003 · Volume 71 · Issue 3
Abstract
This paper analyzes the linear regression modely = xβ+εwith a conditional median assumption med (ε| z) = 0, wherezis a vector of exogenous instrument random variables. We study inference on the parameterβwhenyis censored andxis endogenous. We treat the censored model as a model with interval observation on an outcome, thus obtaining anincompletemodel with inequality restrictions on conditional median regressions. We analyze the identified features of the model and providesufficientconditions for point identification of the parameterβ. We use a minimum distance estimator to consistently estimate the identified features of the model. We show that under point identification conditions and additional regularity conditions, the estimator based on inequality restrictions is normal and we derive its asymptotic variance. One can use our setup to treat the identification and estimation of endogenous linear median regression models with no censoring. A Monte Carlo analysis illustrates our estimator in the censored and the uncensored case.
Keywords
Endogeneity, interval data, modified minimum distance estimator, censored regression model, endogenous median regression
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