st: residual in the same specification

["Khieu, Hinh" <Hdkhieu@usi.edu>]

Dear statalist members,

I have a dependent variable derived as the residual of a regression below:

(1) Y = f(control variables, called X's)  - dep and independent all at time t.

Then, I run the following regression:

(2) Residual from  (1) above = f(same control variables above + 2 new variables of interest) - this time, all dependent and independent variables are at time t+1.

Could someone tell me what could be wrong with regression (2)?

In particular,

Question 1: is the residual serving as dependent variable in (2) supposed to be orthogonal to the set of control variables X's theoretically? Note that they are at 2 different times and that in reality, the results from regression (2) still show significant coefficients of a bunch of X's.

Question 2: what if regression (2) is also at time t?

I greatly appreciate any help in explaining the problem.

Thanks,
Hinh

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