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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