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# re: st: time trend or year effect for pooled data

 From Kit Baum To statalist@hsphsun2.harvard.edu Subject re: st: time trend or year effect for pooled data Date Fri, 12 Mar 2010 10:23:07 -0500

```<>
Yan said

> 1)	I have a equation as this: y=a+b1*X1+b2*X2+b3*X3+...+ c*T +
> error, where a, b, c are coefficients;
> 2)	Y is a couple of dependent variables, which could be binary or
> continuous;
> 3)	T is a time trend and I use it to capture year effect;
> 4)	My observation is user groups which were visited in different
> years and I pool them together, treating them as cross-sectional data.
>
> My question: how should I treat T? Should I value it as 1, 2, 3, ..., OR
> just yearly (eg., 1990, 1991, 1992, ....). I run regressions (both
> Probit and OLS) using both methods, and the regression results give me
> different coefficients ad t statistics  for "T".
>
> Could anyone explain why and which method is appropriate for pooled
> data?

In a pooled setting, I would include time fixed effects (i.e. i.year in factor-variable notation) which will estimate a coefficient for each year. This set of variables will absorb all time-specific (or "macro') variation.

If you use instead a time trend, it does not matter whether it starts from 1 or starts from 1990; any variable for which D.time is a constant will yield the same results, in terms of explanatory power. But using a linear time trend constrains the time-effect coefficients to lie on a straight line, whereas estimating i.time allows the coefficient pattern over years to be whatever the data chooses. If you have ten years, it is a difference between estimating nine coefficients and one coefficient. Are those eight constraints accepted by the data? That is an easily testable hypothesis.

Kit Baum   |   Boston College Economics & DIW Berlin   |   http://ideas.repec.org/e/pba1.html
An Introduction to Stata Programming  |   http://www.stata-press.com/books/isp.html
An Introduction to Modern Econometrics Using Stata  |   http://www.stata-press.com/books/imeus.html

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