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st: Difference-in-difference regression models


From   "riti@ucla.edu" <riti@ucla.edu>
To   statalist@hsphsun2.harvard.edu
Subject   st: Difference-in-difference regression models
Date   Tue, 23 Oct 2007 14:38:20 -0700

Dear STATA users,

When I use the following to estimate a difference-in-difference model:

Score = constant + a0bonus + a1bonusbaseline + a2baseline + e

score bonus control baseline bonusbaseline controlbaseline
0.4 1 0 1 1 0
0.2 1 0 1 1 0
0.1 1 0 0 0 0
0.9 1 0 0 0 0
0.5 0 1 1 0 1
0.6 0 1 1 0 1
0.7 0 1 0 0 0
0.76 0 1 0 0 0
*bonusbaseline=bonus x baseline
** controlbaseline=control x baseline

The OLS estimates are:
Number of obs = 8
Source SS df MS F( 3, 4) = 0.72
Model 0.1876 3 0.0625 Prob > F = 0.5895
Residual 0.3468 4 0.0866 R-squared = 0.351
Total 0.5344 7 0.0763 Adj R-squared = -0.1357
Root MSE = 0.2944
score Coef. Std. Err. t P>t [95% ConfInterval]
bonus -0.23 0.2944 -0.78 0.478 -1.0472 0.5875
bonusbasel~e -0.02 0.4164 -0.05 0.964 -1.1761 1.1361
baseline -0.18 0.2944 -0.61 0.574 -0.9975 0.6375
_cons 0.73 0.2082 3.51 0.025 0.15192 1.3080

If instead I estimate:
Score = constant + b0bonus + b1bonusbaseline + b2controlbaseline + u

The OLS estimates are:
Number of obs = 8
Source SS df MS F( 3, 4) = 0.72
Model 0.1876 3 0.0625 Prob > F = 0.5895
Residual 0.3468 4 0.0866 R-squared = 0.351
Total 0.5344 7 0.0763 Adj R-squared = -0.1357
Root MSE = 0.2944
score Coef. Std. Err. t P>t [95% ConfInterval]
bonus -0.23 0.2944 -0.78 0.478 -1.0475 0.5875
bonusbasel~e -0.2 0.2944 -0.68 0.534 -1.0175 0.6175
controlbas~e -0.18 0.2944 -0.61 0.574 -0.9975 0.6375
_cons 0.73 0.2082 3.51 0.025 0.1519 1.3080

As seen above, I get the same coefficients and standard errors for bonus and _cons in the two regressions. Moreover, the coefficient and standard error for controlbaseline are the same as baseline in the first regression. Both sets of regressions have the same goodness of fit measures. Both sets also yield the same predicted means and marginal effects. However, the coefficients for bonusbaseline are different across regressions.

Question: What explains the difference in the coefficients for bonusbaseline across regression models?

Thanks,
Riti

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