Question

In a fixed effects model, we can consider several ways to control for the individual effects which may be correlated with the regressors. Three cases being the within estimator, least-squares dummy variable estimator (LSDV) and the first difference estimator. Consider the three methods, show that (2) The within estimator and the LSDV estimator are equivalent. (b) When T=2, the within estimator and the first difference estimator are equivalent.

Answer 1

a. The within estimator and the LSDV estimator are equivalent because they both control for individual effects in the same way. The within estimator uses information within each individual, while the LSDV estimator uses information across individuals where the same regressor is measured multiple times. Therefore, both methods control for individual effects in a similar fashion.

b. When T=2, both the within estimator and the first difference estimator are equivalent because they both control for changes that take place within individuals over time. This is because the first difference estimator measures change over time, while the within estimator controls for differences within individuals.