st: Difference-in-difference regression models

["riti@ucla.edu" <riti@ucla.edu>]

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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