Asymptotic Variance and Extensions of A Density-Weighted-Response Semiparametric Estimator

다국어 초록 (Multilingual Abstract)

Building on some early works, Lewbel (2000) proposed estimators for binary
and ordered discrete response models with endogenous regressors. These estimators
have been extended for panel data and for truncated and censored models by later
papers. The estimators are particularly innovative in that the latent linear regression
functions are pulled out of the nonlinear limited dependent variable models, which are
then treated as if they were the usual linear models. But understanding the estimators
and their applications have been “hampered” by less-than-ideal expositions and
assumptions. For this problem, this short note reviews the estimators and makes the
following three points. First, the derivation and proper insight of the asymptotic
variances are provided. Second, the inefficiency of the ordered discrete response
version is pointed out and corrected. Third, assumptions in the panel data extension by
Honoré and Lewbel (2002) are relaxed.

다국어 초록 (Multilingual Abstract)

Building on some early works, Lewbel (2000) proposed estimators for binary
and ordered discrete response models with endogenous regressors. These estimators
have been extended for panel data and for truncated and censored models by later
papers. The estimators are particularly innovative in that the latent linear regression
functions are pulled out of the nonlinear limited dependent variable models, which are
then treated as if they were the usual linear models. But understanding the estimators
and their applications have been “hampered” by less-than-ideal expositions and
assumptions. For this problem, this short note reviews the estimators and makes the
following three points. First, the derivation and proper insight of the asymptotic
variances are provided. Second, the inefficiency of the ordered discrete response
version is pointed out and corrected. Third, assumptions in the panel data extension by
Honoré and Lewbel (2002) are relaxed.

참고문헌 (Reference)

1 Khan, S., "Weighted and two stage least squares estimation of semiparametric truncated regression models, Econometric Theory, forthcoming"

2 Maurin, E., "The impact of parental income on early schooling transitions: a reexamination using data over three generations" 85 : 301-332, 2002

3 Newey, W., "The asymptotic variance of semiparametric estimators" 62 : 1349-1382, 1994

4 Lewbel, A., "Semiparametric qualitative response model estimation with unknown heteroskedasticity or instrumental variables" 97 : 145-177, 2000

5 Lewbel, A., "Semiparametric latent variable model estimation with endogenous or mismeasured regressors" 66 : 105-121, 1998

6 Anton, A.A., "Semiparametric estimation of a duration model" 63 : 517-533, 2001

7 Honor큖, B., "Semiparametric binary choice panel data models without strictly exogenous regressors" 70 : 2053-2063, 2002

8 Lee, M.J., "Panel data econometrics: methods-of-moments and limited dependent variables" Academic Press 2002

9 Lee, M.J., "Nonparametric two stage estimation of simultaneous equations with limited endogenous regressors" 12 : 305-330, 1996

10 Blundell, R.W., "Endogeneity in semiparametric binary response models" 71 : 655-679, 2004

11 Blundell, R.W., "Endogeneity in nonparametric and semiparametric regression models, Advances in Economics and Econometrics: Theory and Applications, Eighth World Congress, Vol.II" Cambridge University Press 2003

12 Horowitz, J.L, "Direct semiparametric estimation of a single index model with discrete covariates" 91 : 1632-1640, 1996

13 Stewart, M.B., "A comparison of semiparametric estimators for the ordered response model" 49 : 555-573, 2005