Test difference between coefficients across multiple regressions

[Srini Nagaraj]

Hi,

Is there a simple way to test if a common coefficient is equal across multiple regressions? I have a long panel data with 50 individuals(id) in 120 time periods(t). I am interested in running a time series regression, expenditure vs income for each individual : exp_i=a_i+b_i*inc_i, and test if the coefficient on income is equal for all 50 individuals, that is b1=b2=....=b50

It is straightforward to obtain 50 coefficients on inc for each individual, using statsby:

 statsby beta_inc=_b[inc] , sa(`results',replace) by(id) verbose nodots : regress exp inc

test command in stata may be appropriate for 2 or 3 equations. But how do I test equality of 50 coefficients?

Any advice is much appreciated.

Thank you

[Joseph Coveney]

I suppose, depending on how you look at it, you could do either something like

mixed exp c.inc || id: inc
estimates store Slopes
mixed exp c.inc || id:
lrtest Slopes

or something like

glm exp i.id##c.inc
estimates store Slopes
glm exp i.id c.inc
lrtest Slopes

[Srini Nagaraj]

Thanks for your response. Yes that works. But, doesn't lrtest do b1=b2=...b50=0? I'm interested in equality of coefficients, rather than equality to zero. Thank you

[Joseph Coveney]

. . . doesn't lrtest do b1=b2=...b50=0?

No.

The first looks at the variance of the slopes between individuals. Neglecting that failure to reject the null hypothesis is not the same as proving it, if there is no variance in the slopes, then the slopes are all equal.

The second looks at the interaction of slope and individual. Ditto; if there is no interaction, then all id's slopes can be represented by a common slope, i.e., they are equal.

I would be surprised to find that the individuals' slopes do not differ. I would have assumed that there is nonzero variance in the slopes, and have gone from there.