Local NLLS estimation of semi‐parametric binary choice models

Abstract

In this paper, non-linear least squares (NLLS) estimators are proposed for semiparametric binary response models under conditional median restrictions. The estimators can be identical to NLLS procedures for parametric binary response models (e.g. probit), and consequently have the advantage of being easily implementable using standard software packages such as Stata. This is in contrast to existing estimators for the model, such as the maximum score estimator and the smoothed maximum score (SMS) estimator. Two simple bias correction methods-a proposed jackknife method and an alternative non-linear regression function-result in the same rate of convergence as SMS. The results from a Monte Carlo study show that the new estimators perform well in finite samples.

Informational content of special regressors in heteroskedastic binary response models

“…The model differs from that in Manski (1988), Horowitz (1992), Blevins and Khan (2013), and Khan (2013) in that one of the regressors V is independent from the error term conditional on the other regressors X . It also differs from that considered in Lewbel (2000) and Khan and Tamer (2010), for the error term is median-independent rather than mean-independent from X .…”

“…A partial list of other papers that discussed related topics include Chamberlain (1986), Chen and Khan (2003), Cosslett (1987), Horowitz (1992), Blevins and Khan (2013), Khan (2013), Magnac and Maurin (2007), Manski (1988) and Zheng (1995) (which studied semiparametric binary response models with various specifications of heteroskedastic errors); as well as Andrews (1994), Newey and McFadden (1994), Powell (1994) and Ichimura and Lee (2010) (which discussed asymptotic properties of semiparametric M-estimators).…”

Binary quantile regression and variable selection: A new approach

“…In a recent paper, Blevins and Khan (2013) demonstrated that for binary data the maximum score objective function in equation (5) is equivalent to the quadratic loss objective function under the median restriction, i.e for w = 0.5. Since quantile regression can be viewed as a generalisation of median regression, in this chapter this work is extended to the estimation of binary regression quantiles using a nonlinear least asymmetric weighted squares (LAWS) approach.…”

“…This is in contrast to the rate of h 2 n for the smoothed maximum score estimator. However, according to Blevins and Khan (2013) it improves the prediction performance of the predictors (iii) knowledge about the relevant variables can enhance the understanding of the underlying problem. Furthermore, multicollinearity and overfitting are areas of concern when a large number of independent variables are incorporated in a regression model.…”

“…Proof of theorem 1 Proof. To establish consistency we use the results of Blevins and Khan (2013), who applied the standard consistency theorem of Newey and McFadden (1994) (Theorem 2.1). The proof is similar to those in Manski (1985) and Horowitz (1992).…”