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st: Test for Endogeneity in a Tobit FE
I am working with a househol panel data set (a two year-panel), in order to control for household unobserved heterogeneity. My left hand side variable is truncated at 0, and given that the unobserved time-invariant effects are likely to be correlated with the regressors, I use tobit fixed effects estimators (developed by Honore 1992) to estimate the structural equation.
I would like to test for the endogeneity of one explanatory variable. I am aware of the Smith-Blundell two step procedure (see Wooldridge, 2002, p. 531) for a cross-section, that has been programmed by Christopher Baum under the command "tobexog". When I perform the 2-step procedure myself, and test for the normality of the error term after the second stage tobit estimation, the null hypothesis of normality is strongly rejected. I would expect this to happen, since my whole estimation strategy rests on controlling for unobserved heterogeneity that is likely to be correlated with some of the regressors.
Am I right in understanding that the estimates that I get in the 2nd-step are not consistent and that the Smith-Blundell test is not valid ?
Does someone know of a test for the endogeneity of a regressor in a panel data model using FE? Is it possible to extend the Smith-Blundell test to a panel data setting with FE ? I.e. to use linear FE estimator in the first-stage of the Smith-Blundell procedure, extract the residuals and incorporate them in the second-stage of the Smith-Blundell procedure, using a Tobit FE estimation ?
I am blocking on this issue, so your advice will be very much appreciated.
London School of Economics
Development Studies Institute
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