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Interactions in Fixed Effects Regression Models

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  • Giesselmann, Marco
  • Schmidt-Catran, Alexander

Abstract

An interaction in a fixed effects (FE) regression is usually specified by demeaning the product term. How-ever, algebraic transformations reveal that this strategy does not yield a within-unit estimator. Instead, the standard FE interaction estimator reflects unit-level differences of the interacted variables. This property allows interactions of a time-constant variable and a time-varying variable in FE, but may yield unwanted results if both variables vary within units. In such cases, Monte Carlo experiments confirm that the standard FE estimator of z∙x is biased if x is correlated with an unobserved unit-specific moderator of z (or vice-versa). A within estimator of an interaction can be obtained by first demeaning each variable and then demeaning their product. This “double-demeaned” estimator is not subject to bias caused by unobserved effect heterogeneity. It is, however, less efficient than standard FE and only works with T > 2.

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  • Giesselmann, Marco & Schmidt-Catran, Alexander, 2020. "Interactions in Fixed Effects Regression Models," SocArXiv m78qf, Center for Open Science.
    • Handle: RePEc:osf:socarx:m78qf
    DOI: 10.31219/osf.io/m78qf
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    10. Jungkunz, Sebastian & Marx, Paul, 2021. "Income changes do not influence political participation: Evidence from comparative panel data," ifso working paper series 11, University of Duisburg-Essen, Institute for Socioeconomics (ifso).
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    12. Sebastian Jungkunz & Paul Marx, 2021. "Income Changes Do Not Influence Political Participation: Evidence from Comparative Panel Data," SOEPpapers on Multidisciplinary Panel Data Research 1129, DIW Berlin, The German Socio-Economic Panel (SOEP).
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    JEL classification:

    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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