In statistics and econometrics, the first-difference (FD) estimator is an estimator used to address the problem of omitted variables with panel data. It is consistent under the assumptions of the fixed effects model. In certain situations it can be more efficient than the standard fixed effects (or "within") estimator.

What is a first difference model?

The first-differenced (FD) estimator is an approach that is used to address the problem of omitted variables in econometrics and statistics by using panel data. The estimator is obtained by running a pooled OLS estimation for a regression of the differenced variables.

Is first difference the same as difference in difference?

Difference-in-differences combines these two methods to compare the before-and-after changes in outcomes for treatment and control groups and estimate the overall impact of the program. Difference-in-differences takes the before-after difference in treatment group's outcomes. This is the first difference.