of the fixed-effects models cannot be biased because of omitted time-invariant characteristics…[like culture,religion, gender, race, etc] One side effect of the features of fixed-effects models is that they cannot be used to investigate time-invariant causes of the dependent variables. Technically, time-invariant characteristics of the individuals are perfectly collinear with the person [or entity] dummies. Substantively, fixed-effects models are designed to study the causes of changes within a person [or entity]. A time-invariant characteristic cannot cause such a change, because it is constant for each person.”
One alternative to a fixed effects model is a random effects model. The rationale behind random effects model is that, unlike the fixed effects model, the variation across entities is assumed to be random and uncorrelated with the predictor or independent variables included in the model: “…the crucial distinction between fixed and random effects is whether the unobserved individual effect embodies elements that are correlated with the regressors in the model, not whether these effects are stochastic or not” [Green, 2008, p.183] If you have reason to believe that differences across entities have some influence on your dependent variable then you should use random effects. An advantage of random effects is that you can include time invariant variables (i.e. gender). In the fixed effects model these variables are absorbed by the intercept. The random effects model is:
Yit = βXit + α + uit + εit (“u” is the between entity error and “e” is the within entity error)
Random effects assume that the entity’s error term is not correlated with the predictors which allows for time-invariant variables to play a role as explanatory variables. In random-effects you need to specify those individual characteristics that may or may not influence the predictor variables. The problem with this is that some variables may not be available therefore leading to omitted variable bias in the model.
The between estimator uses only between or cross-section variation in the data. Because only cross-section variation in the dta is used, the coefficients of any individual-invariant regressors, such as time dummies, cannot be identified. It is seldom used.
To decide between fixed or random effects you can run a Hausman test where the null hypothesis is that the preferred model is random effects vs. the alternative the fixed effects (see Green, 2008, chapter 9). It basically tests whether the unique errors (ui) are correlated with the regressors, the null hypothesis is they are not. Run a fixed effects model and save the estimates, then run a random model and save the estimates, then perform the test. (Hausman test is near the beginning of TSCS material)
Older Discussion/Comments from Neal Beck:
I think it is desirable to use the panel corrected standard errors that Beck and Katz (APSR, 1995) developed. STATA has the necessary commands. The