PANEL Procedure

Two-Way Fixed-Effects Model, First Differencing (FDTWO Option)

You perform two-way fixed-effects estimation via first differencing by specifying the FDTWO option in the MODEL statement. The method of first differencing offers an alternative to the within estimator ModifyingAbove bold-italic beta With caret Subscript f. Consider the following two-way fixed-effects model:

y Subscript i t Baseline equals alpha plus bold x Subscript i t Baseline bold-italic beta plus nu Subscript i Baseline plus lamda Subscript t Baseline plus e Subscript i t

For this model, the fixed effects are removed by the transformations normal upper Delta y Subscript i t Baseline equals y Subscript i t Baseline minus y Subscript i minus 1 comma t Baseline minus y Subscript i comma t minus 1 Baseline plus y Subscript i minus 1 comma t minus 1 and normal upper Delta bold x Subscript i t Baseline equals bold x Subscript i t Baseline minus bold x Subscript i minus 1 comma t Baseline minus bold x Subscript i comma t minus 1 Baseline plus bold x Subscript i minus 1 comma t minus 1. You obtain the two-way first-differenced estimator, ModifyingAbove bold-italic beta With caret Subscript f d, and its variance by performing OLS regression of normal upper Delta y Subscript i t on normal upper Delta bold x Subscript i t.

The estimation and parameterization of left-parenthesis alpha comma nu Subscript i Baseline comma lamda Subscript t Baseline right-parenthesis are identical to that described in the section Two-Way Fixed-Effects Model (FIXTWO Option), with ModifyingAbove bold-italic beta With caret Subscript f replaced by ModifyingAbove bold-italic beta With caret Subscript f d.

Last updated: June 19, 2025