# st: first-differenced model with time-invariant variables

 From "Brent Fulton" To Subject st: first-differenced model with time-invariant variables Date Fri, 25 Jul 2008 23:18:25 -0700

```Dear Statalist,

I am using Stata 9.2 estimating a first-differenced regression model. I
first-difference the variables myself, so am using -regress-. For a key
time-varying independent variable (x), I want to estimate whether its
association with the dependent variable varied by a person's sex.

Because sex is time-invariant, it dropped out of the model. If I interact
sex with x, I was wondering if the estimators would remain being consistent
and their standard errors would remain being asymptotically valid? This
issue was touched on in a previous thread,
http://www.stata.com/statalist/archive/2006-10/msg00352.html, which refers
to Plumper and Troeger (2007), which uses a three-stage model to estimate
parameters for time-invariant  variables in a fixed effects (or
time-demeaned) model. Hence, if I simply use specification (1) below, I'm
concerned about that I might not be estimating consistent estimators with
valid standard errors.

Let "d" be the delta symbol e.g., dy(i) = y(i,t) - y(i,t-1)
Let u be the error term

(1) dy = B0 + B1dx + B2dx * male + B3 male + time dummies + du

Below is another specification (2) that includes dx*male, but removes male
by itself. However, now each variable within the interaction term is not
separately included in the model. I assume this doesn't solve the problem?

(2) dy = B0 + B1dx + B2dx * male + time dummies + du

Thanks,
Brent Fulton

Plumper, Thomas and Vera E. Troeger. 2007. "Efficient Estimation of
Time-Invariant and Rarely Changing Variables in Finite Sample Panel Analyses
with Unit Fixed Effects." Political Analysis 15:124-139.

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