In one of my earlier posts, I discussed panel data modeling and my intentions to use it as my capstone. A panel data model is rather general, however, and thus I want to consider specific variations of it. The first variation that I have decided to take a closer look at is the fixed effects model.

The fixed effects model operates under the assumption that unobserved variables are correlated with variables included in the regression. Consequently, studies conducted using this model can only be used to describe the effects of the included independent variables on the dependent variable, and thus cannot extend their results to explain the effects of other variables on the dependent variable.

Recall the general form of a panel data model: $y_{it} = \alpha_i + \beta'x_{it} + \epsilon_{it}$. The fixed effects model assumes that the individual effects coefficients ($\alpha_i$) vary across each cross-sectional unit, while the $\beta'$ coefficient is held constant.  As a result of the variability in the individual effects coefficients, it becomes necessary to use dummy variables representing each cross-sectional unit in order to properly estimate the regression. The resulting equation is $y_{it} = D \alpha_i + \beta'x_{it} + \epsilon_{it}$ where $D$ is the set of dummy variables.