An Algorithm to Estimate the Two-Way Fixed Effect Model

We present an algorithm to estimate the two-way fixed effect linear model. The algorithm relies on the Frisch-Waugh-Lovell Theorem and applies to ordinary least squares (OLS), two-stage least squares (TSLS) and generalized method of moments estimators (GMM). The coefficients of interest are computed using the residuals from the projection of all variables on the two sets of fixed-effects. Our algorithm has three important advantages. First, it manages memory and computational resources efficiently which speeds up the computation of the estimates. Second, it allows the researcher to estimate multiple specifications using the same set structure of fixed effects at a very low computational cost. Third, the asymptotic variance of the parameters of interest can be consistently estimated using standard routines on the residualized data.