# What is the best technique for panel regressions (ols, fixed, between, random effects)?

I have panel data which includes American states (1-48) and years (1900-1917). All the variables are time-varying with one exception. This exception is time invariant and a three level categorical variable measuring regional designations for the states tested using two dummy variables. I also want look at interactions between one of the dummies and several of the time-varying variables. OLS estimates of this model indicate heteroscedasticity. So given the organization of the data my question is which of the panel techniques is best and why? I am using Stata. Thanks, RB

## 1 Answer

I would say it depends on the data. But there are some general ideas about model specification. Fixed effects method is consistent and therefore should be used to control subject-level confounders. If there is no subject-level confounders, random effects method is efficient to account for correlated errors.

• OLS vs. Fixed effects: F-test of the joint significance of the fixed effects intercepts. The null hypothesis is that all of the fixed effect intercepts are zero. If the null is rejected, then we need to use fixed effects method. The F-test is automatically conducted when we run xtreg in Stata. It appears at the bottom of regression output.
• Fixed vs. random effects: Hausman test. The null hypothesis is that the slope coefficients of the two models being compared do not differ significantly. If the estimates are different then we reject romdom effects and must use fixed effects, otherwise we use the more efficient random effects method. There is a command hausman in Stata.
• I think the wrinkle is the time invariant variable (3 levels, 2 dummies) which is created using aggregations of the cross-sectional data (states). So if I run the fixed effects model in Stata the two dummies drop out. Is the solution to drop the two dummies and just look at the individual states which comprise these two dummies? Thanks again, RB – user36830 Jan 3 '14 at 16:28
• You are right, @user36830. Generally speaking, fixed effects method cannot handle time-invariant covariates, but the recent paper may be of your interest. If you are really interested in the effects of time-invariant covariates, you can turn to random effects method. There is also another longitudinal/panel data model called population average (or marginal) models (e.g. generalized estimating equations models), as compared to subject specific models. See my clarification here. – Randel Jan 3 '14 at 16:49
• Thanks for your help. Will check out paper and other answer. RB – user36830 Jan 3 '14 at 17:45