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Re: st: Difference-in-difference regression models


From   "Austin Nichols" <austinnichols@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Difference-in-difference regression models
Date   Wed, 24 Oct 2007 10:24:28 -0400

Riti--
This looks a lot like a homework question, disallowed by the Statalist
FAQ, but I think you can find an answer reading
http://www.ats.ucla.edu/stat/stata/webbooks/reg/chapter3/statareg3.htm

On 10/23/07, riti@ucla.edu <riti@ucla.edu> wrote:
> 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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