Chapter 4 FE and RE Models

In panel data analysis, we often face a fundamental question: how to model systematic differences between individuals that do not change over time? For example, when explaining the impact of education on income, different individuals may exhibit stable fiddrences in ability, family background, or attitudes. These factors, though unobservable, may simultaneously influence educational choices and income levels, thereby introducing bias into estimation results.

To identify the true iimpact of expanatory variables on the outcomes variable, we must address this unit specific heterogeneity.

1 Fixed Effects Model

1.1 Model Specification

$$Y_{it}=\alpha_i + \beta X_{it}+u_{it }$$

2 Random Effects Model

2.1 Model Specification

$$Y_{it}=\alpha + \beta X_{it}+c_i+u_{it }$$

Y_{it}=\alpha + \beta X_{it}+c_i+u_{it }