st: Explanatories that vary only over time in panel data

[ARDE DE <wsbbarde@gmail.com>]

Dear All:

Our question is about both, the theory of panel data analysis and
(later on) its implementation in Stata.

The model we have in mind is:
Y_it = a_i + b*X_it + c*t + u_it,
i.e. the standard FE/RE framework but with a linear time trend.
One of our explanatory variables in X_it does not vary across
individuals, it only varies across time (it is a price variable that
is assumed to be the same across all districts i within the country we
consider).
How do we tell Stata about this?
If we just repeat the price entries for all i districts in our input
data we assume that Stata will think that there are in fact multiple
observations. So the standard errors can not be correct.
The same question applies to our linear time trend c*t. Can we just
include the "year" variable repeatedly (although it does not vary
across the index i)?

We were not able to find an answer in Wooldridge (2001): Econometric
Analysis of Cross Section and Panel Data, nor in Matyas et al. (2008):
The Econometrics of Panel Data, 3rd ed.

Has someone used a similar model?
Any help/hints will be highly appreciated

Arde
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