# How do you compare coefficients and variances across sub sample regressions

Forgive the simple question. I have divided up the sample population into quartiles based on initial house price. I have regressed the same econometric model on each quartile, so for example for regression (2) I dropped all observations with initial house prices above the 25th percentile then ran the regression then repeated the same process for each quartile.

If now want to see if the coefficients of different quartiles are significantly different how do I do this? e.g. if in (3) I want to see if house price growth 0.025 is significantly different from -0.005 in (5), how do I test this?

Also the underlying distributions are not normal.

Is it appropriate to use Mann Whitney U for the means, and Levene to compare the variances?

Thank you for any help.

Chris

Two approaches immediately come to mind:

Solution 1: Pool your data and re-estimate your model with interactions between the quartiles and covariates of interest.

Solution 2: Try suest.

If the coefficients themselves (rather than the variables) have an asymptotic normal distribution then you should be able to use t-tests. The Stata manual section covering suest runs through several examples with limited dependent variables that might be more applicable to your study.

• Thank you Paul. With the second solution using suest, do you know if there is a module to test if the asymptotic distribution of the coefficients is normal? If not how would I determine this? – user9903833 Apr 1 '18 at 17:25
• And to clarify I am just running a fixed effects regression with the controls that you can see in the picture. – user9903833 Apr 1 '18 at 20:01
• Asymptotic normality is a property of an estimator (like OLS). If you you're running OLS regressions, and the assumptions underlying OLS are appropriate for your data, then OLS coefficients may be treated as having an asymptotically normal distribution. See this link for technical details. – Paul Spin Apr 1 '18 at 20:12