Identification and estimation of partially linear censored regression models with unknown heteroscedasticity

In this paper, we introduce a new identification and estimation strategy for partially linear regression models with a general form of unknown heteroscedasticity, that is, Y = X ′ β 0 + m ( Z ) + U and U = σ ( X , Z ) ε , where ε is independent of ( X , Z ) and the functional forms of both m ( · ) and σ ( · ) are left unspecified. We show that in such a model, β 0 and m ( · ) can be exactly identified while σ ( · ) can be identified up to scale as long as σ ( X , Z ) permits sufficient nonlinearity in X. A two‐stage estimation procedure motivated by the identification strategy is described and its large sample properties are formally established. Moreover, our strategy is flexible enough to allow for both fixed and random censoring in the dependent variable. Simulation results show that the proposed estimator performs reasonably well in finite samples.