Cross Section and Panel Data Estimators for Nonseparable Models with Endogenous Regressors

Abstract

We propose two new methods for estimating models with nonseparable errors and endogenous regressors. The first method estimates a local average response. One estimates the response of the conditional mean of the dependent variable to a change in the explanatory variable while conditioning on an external variable and then undoes the conditioning. The second method estimates the nonseparable function and the joint distribution of the observable and unobservable explanatory variables. An external variable is used to impose an equality restriction, at two points of support, on the conditional distribution of the unobservable random term given the regressor and the external variable. Our methods apply to cross sections, but our lead examples involve panel data cases in which the choice of the external variable is guided by the assumption that the distribution of the unobservable variables is exchangeable in the values of the endogenous variable for members of a group. Copyright The Econometric Society 2005.

Estimation of nonseparable models with censored dependent variables and endogenous regressors

“…with endogenous X was proposed and studied in Altonji and Matzkin (2005). For example, Aaronson (1998) investigated the effects of average neighborhood income X on college attendance Y holding the distribution of U |X = x fixed.…”

“…Thus, β AM (x) is a parameter of interest in Aaronson's (1998) empirical analysis. See further discussions in Altonji and Matzkin (2005) for motivations of the local average response β AM (x). Our object of interest, β(x), in (1) shares similar motivations.…”

“…The rows labeled "No Censoring Control" report the mean for the nonparametric estimator without controlling for censoring. This estimator can be viewed as the nonparametric estimator developed in Altonji and Matzkin (2005). In this paper it refers to using onlyξ(x) as the estimator.…”

“…It has large upward bias at x = 2 and large downward bias at x = 5. Also, the "No Censoring Control" estimator proposed in Altonji and Matzkin (2005) shows severe downward biases. These results show that in the current setting, it is crucial to control for both endogeneity and censoring problems at the same time.…”

“…AIO focus on the exogenous case and only briefly introduce endogeneity as an extension to the model. Whilst Altonji and Matzkin (2005) discussed identification and estimation of the local average response in a nonseparable model without censoring.…”