Hi all,

Jeff Wooldridge
it's been a while that I am trying to apply the two stage procedure described in "Testing and correcting for endogeneity in nonlinear unobserved effects models" (Lin, Wei, and Jeffrey M. Wooldridge. Panel Data Econometrics. Academic Press, 2019. 21-43) which you can find here: http://www.weilinmetrics.com/uploads...g_20170309.pdf in pdf.
In particular I have a balanced panel dataset consisting of identifiers called idatc observed in Years from 2004 to 2010. From literature I know that when modeling innovation on size, one might incur in endogeneity of size. For this reason, since innovation is modeled by the number of clinical trials (and therefore a fixed effect poisson is needed) I am following the aforementioned procedure. Summarizing, I am estimating a "first stage" of the endogenous (called y in the following code) on the instrument (L.major_recalls_norm) and the other regressors (average_age_prodbyatc3 avg_prd_sq mean_agefirm_byatc mean_agefirm_squared hhi share_expired share_patented). Predicting the residuals of the fixed effects estimation and putting the residuals inside the "second stage" in a sort of control function approach. So in the second stage I am basically regressing the dependent (trials) on the residuals of thee first stage and the other regressors using a poisson f.e.:

Code:
xtreg y L.major_recalls_norm average_age_prodbyatc3 avg_prd_sq mean_agefirm_byatc mean_agefirm_squared hhi share_expired share_patented i.Year, fe vce(cluster newid)
        predict residuals, e
        xtpoisson trials y residuals average_age_prodbyatc3 avg_prd_sq mean_agefirm_byatc mean_agefirm_squared hhi share_expired share_patented i.Year, fe vce(robust)
The issue comes now: what I would like to do is to perform bootstrap on such a procedure (so that residuals are computed in every drawn sample each time), but when I do it, the coefficients seem not to be close to the ones that I obtain by simply applying the two step procedure without bootstrap. I am therefore concerned about the possibility (and reliability) of applying bootstrap procedure to the two step approach introduced by the authors. Can you please help me figuring out?

Thanks,

Federico