st: 1) Estimate a Correlated Random Coefficient Regression with an Endogenous Regressor for Panel Data?

[Mai Anh Ngo <maianh.ngo@gmail.com>]

Hello,

I need to estimate a regression for a panel data set where the
coefficients may be correlated with the regressors and some of the
regressors are endogenous. My model is something as follows:

Yit=a +bX1it +cX2it+dX3it + ui + eit

where ui is the individual unobserved heterogeneity, eit is an
idiosyncratic error term. The coefficients b, c, and d are correlated
with the regressors X1, X2, X3 respectively. In addition, X1 is
endogenous. Both Y and X1 are continuous and non-negative.

I don’t know which techniques I should use to obtain consistent
estimates. I’ve used the FE-2SLS technique outlined in Murtazashvili
and Wooldridge (2008) but the results are strange, probably because my
instrumental variable is weak and did not satisfy the conditions
outlined in that paper.

Is there any other method (besides instrumental variable method) to
estimate this model? Thank you for your consideration.

Mai Ngo

Reference: Murtazashvili, Irina and Jeffrey M. Wooldridge. 2008.
"Fixed Effects Instrumental Variables Estimation in Correlated Random
Coefficient Panel Data Models" Journal of Econometrics, 142(1):
539-552

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