Testing whether coefficient differs in one year from another

[Carl Isaac]

Suppose I have a panel dataset over two years, and I run a regression model of Y = a + X*B1 + e separately for year 1 and year 2. I want to understand whether the parameter B1 is different in year 1 from year 2 at a statistically significant level. Based on my online search, it appears that I can use "estimates store" along with the "suest" command to run this comparison, as shown below. I was wondering if this is the proper command to be used for a task such as this? If so, what description would be used for such a test (is it a t-test, chow test, etc.)? Thanks!

reg y x if y == 2002
estimates store y2002
reg y x if y == 2003
estimates store y2003

suest y2002 y2003
test _b[y2002_mean:x] = _b[y2003_mean:x]

[Clyde Schechter]

Surely you do not mean -reg y x if y == 2002- (resp. 2003)! You would be constraining the dependent variable to be constant, and the coefficient of x will necessarily be zero.

I think you meant -reg y x if year == 2002- (resp. 2003). With that correction, and on the assumption that year is the time variable in your panel, then this way of comparing the cross-sectional coefficients of x in those two years would be OK.

I won't pretend to advise you about what to call it. The term Chow test, at least originally, referred to a specific way to test for equality of coefficients across two regressions that was developed in the 1960's. It had the advantage that it could be calculated just from sums of squares, so that it was relatively easy to carry out by hand after inspecting the two regression outputs. In an era when computing power and access to computing facilities were very limited, and very expensive, you would strongly prefer a test that you could carry out by hand to one that you had to run on a computer. (By the way, there were no pocket calculators back then either.)

The results you get from what you are doing with -suest- are asymptotically equivalent to the original Chow test, but they are not exactly the same thing. Today the -suest- approach would be more commonly used than the original Chow test. But the meaning of the phrase "Chow test" has generalized over time and it is sometimes used to refer to any test of equality of coefficients in two regressions having the same variables. That would include, by the way, yet another popular way of doing this which would be

reg y i.year##c.x if inlist(year, 2002, 2003)

and looking at the output for 2003.year#x. (Replace c.x by i.x if x is a discrete variable.) This approach, actually, will still be equivalent to the original Chow test even in small samples, though the calculation is done very differently.

Getting away from the messy issue of just what constitutes a "Chow test," the actual test statistic in the -suest- approach is a chi square statistic. So, no, you couldn't call it a t-test. If you were to use the interaction term approach I have shown above, you would in fact get a t-statistic, so you could call it a t-test if you wanted to. Frankly, I'd probably just describe the actual approach used, "Contrast of coefficients across linear regressions using seemingly unrelated estimation."

[Carl Isaac]

Yes, sorry, I meant to say "if year == 2002". This addresses my question. I think the interaction term approach is more useful for my purposes. Thanks, Clyde!