Panel Data Models: Fixed Effects Models

We define fixed effects models in terms of the density of the observed random variable and an index function,

           

There is one dummy variable coefficient for each individual or group. Familiar treatments in the literature are the linear regression model, in which the dummy variables are removed by deviations or by first differences, or in the binary logit or Poisson regression, in which the dummy variables are conditioned out and not estimated. LIMDEP's implementation of this model is unconditional. All the dummy variable coefficients are actually estimated, with up to 50,000 groups, as well as the other model parameters. This is a new estimation method in LIMDEP that does not appear in any other software. This allows a far wider range of models than the conditional estimator:

• Linear regression model
• Probit, logit, Gompertz, complementary log log binary choice
• Tobit, truncated regression, categorical data
• Stochastic frontier
• Survival models: exponential, Weibull, lognormal, loglogistic
• Loglinear models: Weibull, gamma, exponential, inverse Gauss
• Bivariate probit, partial observability
• Ordered probit, ordered logit, ordered Gompertz, ordered complementary log log
• Sample selection
• Poisson, negative binomial, zero inflated Poisson
• Conditional logit (multinomial logit - discrete choice)

Compare the preceding list to the list of conditional fixed effects estimators in LIMDEP and other programs: linear regression, binary logit, Poisson, negative binomial.

Other features of the unconditional fixed effects estimator include:

• Full maximum likelihood estimation
• Automatic data check for groups of one and groups with no variation
• Dummy variable coefficients are retained
• Predictions
• Marginal effects