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Interactions in Fixed Effects Regression Models

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  • Marco Giesselmann
  • Alexander W. Schmidt-Catran

Abstract

An interaction in a fixed effects (FE) regression is usually specified by demeaning the product term. However, 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 to be estimated but may yield unwanted results if both variables vary within units. In such cases, Monte Carlo experiments confirm that the standard FE estimator of x ⋅ z 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

  • Marco Giesselmann & Alexander W. Schmidt-Catran, 2022. "Interactions in Fixed Effects Regression Models," Sociological Methods & Research, , vol. 51(3), pages 1100-1127, August.
    • Handle: RePEc:sae:somere:v:51:y:2022:i:3:p:1100-1127
    DOI: 10.1177/0049124120914934
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    References listed on IDEAS

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    1. Jeffrey M Wooldridge, 2010. "Econometric Analysis of Cross Section and Panel Data," MIT Press Books, The MIT Press, edition 2, volume 1, number 0262232588, December.
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    3. Burra, Lavan T. & Sommer, Stephan & Vance, Colin, 2024. "Policy complementarities in the promotion of electric vehicles," Energy Policy, Elsevier, vol. 192(C).
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    7. Ning Meng & Yining Ni & Yeqing Ma, 2024. "The ripple effect: How trade policy shocks impact innovation of Chinese firms," Review of International Economics, Wiley Blackwell, vol. 32(4), pages 1868-1900, September.
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