Open AccessIdentification and estimation of partially linear censored regression models with unknown heteroscedasticity
Author(s) -
Zhang Zhengyu,
Liu Bing
Publication year - 2015
Publication title -
the econometrics journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.861
H-Index - 36
eISSN - 1368-423X
pISSN - 1368-4221
DOI - 10.1111/ectj.12037
Subject(s) - heteroscedasticity , censoring (clinical trials) , estimator , mathematics , identification (biology) , linear regression , instrumental variable , scale (ratio) , estimation , regression analysis , statistics , econometrics , economics , botany , management , biology , physics , quantum mechanics
Summary 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.