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An Algorithm to Estimate the Two-Way Fixed Effects Model

Author

Listed:
  • Somaini Paulo

    (Department of Economics, MIT, Cambridge, MA, USA)

  • Wolak Frank A.

    (Department of Economics, Stanford University, Stanford, CA, USA)

Abstract

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 (GMM) estimators. 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 desirable features. 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 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.

Suggested Citation

  • Somaini Paulo & Wolak Frank A., 2016. "An Algorithm to Estimate the Two-Way Fixed Effects Model," Journal of Econometric Methods, De Gruyter, vol. 5(1), pages 143-152, January.
    • Handle: RePEc:bpj:jecome:v:5:y:2016:i:1:p:143-152:n:4
    DOI: 10.1515/jem-2014-0008
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    References listed on IDEAS

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    4. Sergio Correia, 2014. "REGHDFE: Stata module to perform linear or instrumental-variable regression absorbing any number of high-dimensional fixed effects," Statistical Software Components S457874, Boston College Department of Economics, revised 21 Aug 2023.
    5. Amine Ouazad, 2008. "A2REG: Stata module to estimate models with two fixed effects," Statistical Software Components S456942, Boston College Department of Economics.
    6. Anabela Carneiro & Paulo Guimarães & Pedro Portugal, 2012. "Real Wages and the Business Cycle: Accounting for Worker, Firm, and Job Title Heterogeneity," American Economic Journal: Macroeconomics, American Economic Association, vol. 4(2), pages 133-152, April.
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