st: Modelling of categorical-continuous variable interaction

[Daniel Yue <xyrixx@hotmail.com>]

Dear Statalisters,

I would love your advice my model of the following specifications:

y = i + t + (I*x1) + (I*x2) + (I*x3)

where i and t are firm- and time-fixed effects, respectively, “I” is an indicator variable with values 0-2 and x1-x3 are the three IVs. “I” are supposed to illustrate three “categories” the firms are put into, depending on firm performance relative to two reference points: I==1 if performance of the firm is below a both reference points, I==2 if it is in between, I==3 if it is above. What I want to find out is whether y’s reaction to  x1 x2 x3 differs in strength, i.e. if the slope of the coefficients for x1-x3 are different, depending on the “category” of the firm (hence the indicators), 
The data is in panel format. I – xtset – the dataset and ran the following in Stata 12:

xtreg y I#c.x1 I#c.x2 I#c.x3, fe

My questions:

1.Do the coefficients for I#x1 I#x2 I#x3 really measure what I want them to, as described above?

2.If I instead run

xtreg y I##c.x1 I##c.x2 I##c.x3, fe

the results seem to differ by a lot, although I had expected them to be the same. What is wrong?

3.	I also ran

by I: xtreg y x1 x2 x3, fe

because I thought the results there should be the same as with the original equation. Again, there are not. Why not? What am I missing?

Thanks for your consideration!

Daniel 		 	   		  
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