Divergence between the Mundlak model and -xtreg, fe-

[Ingo Brooks]

Dear all,

I would like to reproduce the results of -xtreg, fe- by aid of the Mundlak model estimated with pooled OLS. I tried the following:

webuse grunfeld, clear

by company: egen mvalue_mean = mean(mvalue)
sum mvalue_mean
replace mvalue_mean = mvalue_mean - r(mean)

by company: egen kstock_mean = mean(kstock)
sum kstock_mean
replace kstock_mean = kstock_mean - r(mean)

xtreg invest mvalue kstock, fe cluster(company)
reg invest mvalue kstock mvalue_mean kstock_mean, cluster(company)

Comparing the results from the two estimation commands shows that the coefficient estimates indeed match. However, the standard errors are different. Do I miss something, or is there an econometric reason for why the standard errors are different? If so, is it possible to adjust the standard errors in the pooled OLS estimation, such that they coincide with the FE estimates?

Thanks a lot for looking into this.

Best,
Ingo

[Daniel Schaefer]

I was not going to try to answer this question, but I did do a little reading just to learn a bit more about the Mundlak approach and, long story short, it looks like you may need to use the random effects panel model rather than the OLS regression model.

see: https://blog.stata.com/2015/10/29/fi...dlak-approach/

Edit: I'm probably misunderstanding something though. Also notice the vce(robust) option, which changes the way the standard errors are estimated.

[FernandoRios]

This seems to be a problem of degrees of freedom
If you use gmm (where no DF adjustments are made) you get almost the same (except for rounding errors)
Using the code you had earlier:

gmm (invest-{beta:_cons mvalue kstock i.company}), instrument(mvalue kstock i.company) vce(cluster company) onestep
gmm (invest-{beta:_cons mvalue kstock mvalue_mean kstock_mean}), instrument(mvalue kstock mvalue_mean kstock_mean) vce(cluster company)