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

From   Kit Baum <>
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
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   |
                              An Introduction to Stata Programming  |
   An Introduction to Modern Econometrics Using Stata  |

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