Semiparametric estimation of a bivariate Tobit model

• Published in: Journal of econometrics Vol. 165; no. 2; pp. 266 - 274
• Main Authors: Chen, Songnian, Zhou, Xianbo
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.12.2011; Elsevier; Elsevier Sequoia S.A
• Subjects: Applications; Asymptotic methods; Distribution; Distribution theory; Econometric models; Economic models; Economic theory; Error; Estimation; Exact sciences and technology; Independence; Insurance, economics, finance; Mathematics; Multivariate analysis; Normal; Parameter estimation; Probability and statistics; Probability theory and stochastic processes; Sciences and techniques of general use; Semiparametric models; Simulation; Statistics; Studies; Instrumental variable; Error estimation; Independence; Finite sample; Tobit model; Statistical estimation; Multivariate analysis; Semiparametric method; Asymptotic convergence; Semiparametric model; Statistical method; Simulation; Distribution function; Econometrics
• ISSN: 0304-4076; 1872-6895
• DOI: 10.1016/j.jeconom.2011.07.005

The existing semiparametric estimation literature has mainly focused on univariate Tobit models and no semiparametric estimation has been considered for bivariate Tobit models. In this paper, we consider semiparametric estimation of the bivariate Tobit model proposed by Amemiya (1974), under the independence condition without imposing any parametric restriction on the error distribution. Our estimator is shown to be consistent and asymptotically normal, and simulation results show that our estimator performs well in finite samples. It is also worth noting that while Amemiya’s (1974) instrumental variables estimator (IV) requires the normality assumption, our semiparametric estimator actually outperforms his IV estimator even when normality holds. Our approach can be extended to higher dimensional multivariate Tobit models.