We discuss the relative advantages and disadvantages of four types of convenient estimators of binary choice models when regressors may be endogenous or mismeasured, or when errors are likely to be heteroskedastic. For example, such models arise when treatment is not randomly assigned and...

Dong and Lewbel have developed the theory of simple estimators for binary choice models with endogenous or mismeasured regressors, depending on a “special regressor” as defined by Lewbel (Journal of Econometrics, 2000). These estimators can be used with limited, censored, continuous, or...

This paper provides a few variants of a simple estimator for binary choice models with endogenous or mismeasured regressors, or with heteroskedastic errors, or with panel fixed effects. Unlike control function methods, which are generally only valid when endogenous regressors are continuous, the...

Suppose V and U are two independent mean zero random variables, where V has an asymmetric distribution with two mass points and U has a symmetric distribution. We show that the distributions of V and U are nonparametrically identified just from observing the sum V+U, and provide a rate root n...

This paper provides a few variants of a simple estimator for binary choice models with endogenous or mismeasured regressors, or with heteroskedastic errors. Unlike control function methods, which are generally only valid when endogenous regressors are continuous, the estimators proposed here can...

While most existing research concludes that grade retention generates no benefits for the retainees' academic performance, holding low-achieving children back has been a popular practice for decades. Drawing on a recently collected nationally representative dataset in the US, this paper...

This paper shows identification of a semiparametric binary choice model containing an endogenous regressor, when no outside instrumental variable is available. A simple estimator, an easy test for endogeneity, and an empirical application to US migration data are provided.

This paper provides simple estimators for binary choice models with endogenous or mismeasured regressors. Unlike control function methods, which are generally only valid when endogenous regressors are continuous, the estimators proposed here can be used with limited, censored, continuous, or...

Many empirical applications of regression discontinuity (RD) models use a running variable that is rounded and hence is discrete, e.g., age in years, or birth weight in ounces. This paper shows that standard RD estimation using a rounded discrete running variable leads to inconsistent estimates...