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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.

Suggested Citation

  • Giesselmann, Marco & Schmidt-Catran, Alexander, 2020. "Interactions in Fixed Effects Regression Models," SocArXiv m78qf_v1, Center for Open Science.
    • Handle: RePEc:osf:socarx:m78qf_v1
    DOI: 10.31219/osf.io/m78qf_v1
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    References listed on IDEAS

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