Interactions in Fixed Effects Regression Models

22 Pages Posted: 8 Aug 2018

See all articles by Marco Giesselmann

Marco Giesselmann

German Institute for Economic Research (DIW Berlin)

Alexander Schmidt-Catran

Goethe University Frankfurt

Date Written: July 2018

Abstract

An interaction in a fixed effects (FE) regression is usually specified by demeaning the product term. However, this strategy does not yield a genuine within estimator. Instead, an estimator is produced that reflects unit-level differences of interacted variables whose moderators vary within units. This is desirable if the interaction of one unit-specific and one time-dependent variable is specified in FE, but it may yield problematic results if both interacted variables vary within units. Then, as algebraic transformations show, the FE interaction estimator picks up unit-specific effect heterogeneity of both variables. Accordingly, Monte Carlo experiments reveal that it is biased if one of the interacted variables is correlated with an unobserved unit-specific moderator of the other interacted variable. In light of these insights, we propose that a within interaction of two timedependent variables be estimated by first demeaning each variable and then demeaning the product term. 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, quadratic terms, polynomials, within estimator

JEL Classification: C33,C51

Suggested Citation

Giesselmann, Marco and Schmidt-Catran, Alexander, Interactions in Fixed Effects Regression Models (July 2018). DIW Berlin Discussion Paper No. 1748, Available at SSRN: https://ssrn.com/abstract=3227779

Marco Giesselmann (Contact Author)

German Institute for Economic Research (DIW Berlin) ( email )

Mohrenstraße 58
Berlin, 10117
Germany

Alexander Schmidt-Catran

Goethe University Frankfurt

Theodor-W.-Adorno-Platz 3
Frankfurt am Main, 60323
Germany

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