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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 12:37:09 -0500

```<>
> 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.

Say you estimate the model

y_it = b_0 + b1_t,  t=1,2,3

then the effects of time are b1, 2 b1, 3 b1, respectively. You estimate two parameters.

Instead consider the model (sans constant)

y_it = d_0 + d_1 T2 + d_2 T3

where T2, T3 are dummies for time=2 and time=3 respectively. You estimate three parameters.

d_0 is the conditional mean of y | time=1. If the effect of time is linear, d_2 should be twice d_1. That is one constraint which can
be tested or imposed.

Run the enclosed, in which the effect of time is constructed to be nonlinear, and you can see the difference.

------------------------------
webuse grunfeld, clear
drop if year>1937
tsset
g y = year + 0.5*(year-1935)^2 + rnormal(0,1)
// allow for time effects => three coeffs to be estimated
reg y i.year
test 2*1936.year = 1937.year
// force linear trend => two coefficients to be estimated
reg y year
// enforce the linearity constraint
const def 1 2*1936.year=1937.year
cnsreg y i.year, c(1)
--------------------------------

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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```