Bounding the Effect of a Dichotomous Regressor With Arbitrary Measurement Errors

Abstract

This note considers a nonlinear regression model containing a 0-1 dichotomous regressor when it is subject to arbitrary measurement errors in the sample. The parameter of interest is the effect of the latent dichotomous variable on the dependent variable. Given that the measurement errors are arbitrary, the misreported values of the latent dichotomous variable may not contain any useful information. Therefore, our identification results are only based on the first three moments of the dependent variable conditional on other observed regressors. The key identification assumption requires that the third conditional moment of the regression error is zero. Such an assumption is reasonable when the regression error has a symmetric distribution. This note suggests that the effect of the latent dichotomous variable may be bounded away from zero using the observed moments. Such bounds may be useful to test the significance of the effect of the latent variable on the dependent variable. Bounds on the conditional mean of the latent dichotomous variable are also provided.

Keywords: arbitrary measurement error, bounds, dichotomous variable

JEL Classification: C1, C14