Panel data analysis: fixed effects or random effects?

Fixed-effects explore the relationship between the independent and dependent variables within an entity (e.g. country, company, etc.). Each entity in the panel dataset has certain individual characteristics that may or may not influence the independent variable. For instance, your thesis or assignment is about analysing the effect that the political system of a specific country (independent variable) will have on GDP growth (dependent variable) under ceteris paribus conditions.

Fixed-effects techniques assume that individual heterogeneity in a specific entity (e.g. country) may bias the independent or dependent variables. Therefore, a fixed-effects model will be most suitable to control for the above-mentioned bias. In this respect, fixed effects models remove the effect of  time-invariant characteristics. For instance, if the political system remains the same for a particular country over the data period, then this is a time-invariant characteristic. Hence, these types of models make it possible to analyse the net effect of the independent variable (e.g. political system) on the dependent variable (e.g. GDP growth).

However, fixed-effects models cannot be applied if the entity (or time-invariant) characteristics are correlated with other entity characteristics and are not unique to a particular entity. This is because fixed-effects models are run under the assumption that each entity (e.g. country) is different and therefore the entity’s error term and the constant term (which captures specific country characteristics) should not be correlated with the others. This is the key rationale when performing the Hausman test and testing whether to apply fixed-effects or random-effects.

The random-effects model is most suitable when the variation across entities (e.g. countries) is assumed to be random and uncorrelated with the independent variable. Green (2008) states that “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”. Hence, if you have reasons to believe that differences across entities (e.g. countries) have any influence on your dependent variable, then fixed-effects models should not be used; but random-effects models are the most appropriate. Under random-effects models, any time-invariant characteristics (e.g. political system remains the same over the whole of the data period for a particular country) are taken into consideration when analysing the data. However, in the case of fixed-effects techniques such time-invariant characteristics are merely captures by the intercept.