The error component model is relevant when the slopes, i.e., the marginal effects of the covariates on the response, are the same for all the individuals, the intercepts being a priori different. Note that for some authors, the error component model is a byword for the “random‐effects model” as opposed to the “fixed‐effects model.” These two estimators will be analyzed in this chapter as two different ways to consider the individual component of the error terms for the same error component model (assuming no correlation and correlation with the regressors, respectively).
This is the landmark model of panel data econometrics, and this chapter presents the main results about it.
2.1 Notations and Hypotheses
For the observation of individual at period , we can write the model to be estimated, denoting by the response, the vector of covariates, the error, the intercept, and the vector of parameters associated to the covariates: