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Interactions in Fixed Effects Regression Models

Marco Giesselmann and Alexander W. Schmidt-Catran

Sociological Methods & Research, 2022, vol. 51, issue 3, 1100-1127

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.

Keywords: panel data; fixed effects; interaction; within estimator; quadratic terms; nonlinearities; double demeaning; FEIS (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:sae:somere:v:51:y:2022:i:3:p:1100-1127

DOI: 10.1177/0049124120914934

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