Semiparametric qualitative response model estimation with unknown heteroscedasticity or instrumental variables

Optimal Bandwidth Choice for Estimation of Inverse Conditional–density–weighted Expectations

“…For Limited Dependent Variable models, examples of estimators belonging to this class are Lewbel (1998), Lewbel (2000b), Honoré and Lewbel (2002), Khan and Lewbel (2007), and Lewbel (2006). Results derived in this paper are directly applicable to these estimators.…”

“…The results in this paper are directly applicable to semiparametric estimators proposed in Lewbel (1998), Lewbel (2000b), Honoré and Lewbel (2002), Khan and Lewbel (2007), and Lewbel (2006). The optimal bandwidth is derived by minimizing the leading terms of a second-order mean squared error expansion of the resulting estimator with respect to h. The expansion also demonstrates that the bandwidth can be chosen on the basis of bias alone, and that a simple 'plug-in' estimator for the optimal bandwidth can be constructed.…”

“…By assuming e i ∼ N 0, σ 2 i , the first column from the left (σ 2 i = 1), and the second (σ 2 i = exp z ⊤ γ ) are obtained by maximum likelihood estimation. The third and fourth columns report results using estimators proposed by Lewbel (2000b) and Lewbel and Schennach (2007) respectively. Standard errors are in parenthesis.…”

“…Standard errors are in parenthesis. Lewbel's (2000b) estimator is equivalent to a standard linear least squares regression of…”

“…An important class of semiparametric estimators, first proposed by Lewbel (1998), involves the use of kernel-based nonparametric estimates in place of the true conditional density in objects of the form…”