Final answer:
The first difference model in panel data analysis is used to focus on within-entity variations over time, correcting for any time-invariant characteristics by estimating the changes in variables across time, which differs from the OLS regression's approach.
Step-by-step explanation:
In the context of panel data analysis, the first difference model controls for any time-invariant characteristics of individuals by using the difference in the variables between two time periods. Unlike the Ordinary Least Squares (OLS) regression, which simply involves a linear relationship between a set of explanatory variables and the outcome variable, the first difference model estimates the change in the dependent variable that is associated with changes in the independent variables from one time period to the next. This is particularly useful in panel data where we observe the same entities over multiple time periods.
To estimate a first difference model using the plm command in R, you specify the model as model="fd" in the command structure, which stands for first difference. When reviewing the results, standard errors can be clustered by groups to correct for any within-group error correlations using the coeftest function with the option cluster="group".
The first difference model is different from OLS because it focuses on the within-entity (such as individuals, companies, countries, etc.) variation over time, removing the effects of unobserved variables that do not change over time. This method is often used when panel data is available, to account for potential autocorrelation and unobserved individual heterogeneity that commonly violate the OLS assumptions.