Solved – the best technique for panel regressions (ols, fixed, between, random effects)

panel data

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

Best 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.

Related Solutions

Solved – Fixed Effects Gravity Model for forecasting..with time constant variables Stata

What they do in the paper is that they estimate their gravity model, say equation 5.2, using the fixed effects estimator and they estimate the fixed effects directly to use them later in equation 6. You can do this with the predict command after xtreg. In Stata this would be:

xtreg IX lYi lYj lNi lNj lD  lIi lIj Pij1 - Pijh
predict IE, u

In the fixed effects regression all the time-invariant variables drop out as the authors stated. The predict command then gives you the individual effects $\text{IE}$ which they use in equation 6.

With regards to your note I'm not sure if the same procedure applies to xtpoisson given that the interpretation of the estimated fixed effects changes. For this have a look at a similar question on the Statalist with the corresponding answer by Maarten Buis. He is also active on CV so if you're lucky he can provide you with guidance on this. Otherwise I would guess that Martinez-Zarzoso and Nowak-Lehmann had the same problem with the many zeros (I suppose their data is similar to yours given the similarity of the application) and yet the had their reasons to stick to linear models.
I hope this helps.

Solved – Too many significant dumthe variables in fixed-effect panel model

No, that's not a problem.

If you have an intercept term in your model, one of the state dummies will be dropped, and the others then give the state means relative to the omitted state. In this case, statistically significant state dummies just mean that those states have means that are statistically significantly different from the omitted state. I can't see how this would be a problem.

If you instead have dropped your intercept term, and therefore can include dummies for all states, the state dummies simply capture the mean for each state. In this case, statistically significant dummies just mean that those states have means that are statistically significantly different from zero. I can't see how this would be a problem, either.

Best Answer

Related Solutions

Solved – Fixed Effects Gravity Model for forecasting..with time constant variables Stata

Solved – Too many significant dumthe variables in fixed-effect panel model

Related Question