# time trend or year effect for pooled data

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## time trend or year effect for pooled data

 Dear Statalist, 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? Thank you very much for your help. Yan Sun IFPRI * *   For searches and help try: *   http://www.stata.com/help.cgi?search*   http://www.stata.com/support/statalist/faq*   http://www.ats.ucla.edu/stat/stata/
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## re: time trend or year effect for pooled data

 <> 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* *   For searches and help try: *   http://www.stata.com/help.cgi?search*   http://www.stata.com/support/statalist/faq*   http://www.ats.ucla.edu/stat/stata/
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## re: time trend or year effect for pooled data

 In reply to this post by Sun, Yan (IFPRI) To professor Kit Baum, thank you very much for your help. Would you please let me know what is the test you mentioned at the end of your last email (are those eight constraints accepted by the data? That is an easily testable hypothesis.) Thanks. Yan * *   For searches and help try: *   http://www.stata.com/help.cgi?search*   http://www.stata.com/support/statalist/faq*   http://www.ats.ucla.edu/stat/stata/