corr (u_i, Xb)

[Pvunderink]

Can someone explain to me if corr (u_i, Xb) unequal to zero violates a fixed effects assumption?
Does this refer to 'strict exogeneity'?

[Alfonso Sánchez-Peñalver]

Can you explain to me what is the fixed effects assumption you refer to? Also why are you checking the correlation with the predicted values and not with the explanatory variables themselves? At least that is what I assume Xb represents.

As far as I know you favor fixed effects over random effects when the unobserved heterogeneity across clusters is correlated with the explanatory variables, and random effects when it's not. As to the correlation of the errors and the regressors being strict exogeneity, I would say it's quite the opposite: it reflects endogeneity of the explanatory variables.

[Pvunderink]

Thank you Alfonso Sanchez-Penalver.
Well, corr (u_i, Xb) is an ouput feature of the fixed effects model in Stata. I'm not really sure how to interpret my result. I wasn't sure if a non-zero outcome would be a problem?

[Martin Bresslein]

It is not a problem using a fixed-effects model. It is actually quite nicely described in the Stata manual on panel data (pp. 371-374). To further Alfonso's point, the u_i represent the unobserved heterogeneity. Using a RE model you assume that the u_i are not correlated with your explanatory variables - hence in the output you find:

corr(u_i, X) = 0 (assumed)

The FE model is still consistent if this assumption fails. Hence, a high corr (u_i, Xb) may indicate that a RE model is not appropriate.

Martin

[Pvunderink]

It is not a problem using a fixed-effects model. It is actually quite nicely described in the Stata manual on panel data (pp. 371-374). To further Alfonso's point, the u_i represent the unobserved heterogeneity. Using a RE model you assume that the u_i are not correlated with your explanatory variables - hence in the output you find:

corr(u_i, X) = 0 (assumed)

The FE model is still consistent if this assumption fails. Hence, a high corr (u_i, Xb) may indicate that a RE model is not appropriate.

Martin

I have still one question.
Isn't the alpha(i) the fixed unknown constants, which are allowed to be correlated with the explanatory variables in the FE model but not in RE?
I thought that u(i) was part of the error term in RE, and assumed to be i.i.d. over individuals and time in FE.
Because if so, I thought that in RE the explanatory variables are not allowed to correlated with either part, and with FE X is allowed to correlate with alpha, but not with u(i): E {x(it)u(is)} = 0; (A strictly exogenous variable is not allowed to depend upon current, future and past values of the error term.)


Or is u_1 of the code not the same as the u(i) of the error term? Is it the fixed effects part (alpha)?

[Martin Bresslein]

I am not sure but the confusion might stem from the fact that the u_i from Stata's output (which I am also referring to) is not the idiosyncratic error term, but the individual_specific part - hence only the index i and not it. If that is not the point, I am missing something here but I would still suggest you take a look at the manual - which is part of Stata's installation package - and get back if the issue is still unclear...

[Pvunderink]

Thank you. That was the word I was looking for (idiosyncratic). Now I understand it.