Interactions in Fixed Effects Regression Models

Marco Giesselmann and Alexander Schmidt-Catran

No 1748, Discussion Papers of DIW Berlin from DIW Berlin, German Institute for Economic Research

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 (search for similar items in EconPapers)
JEL-codes: C33 C51 (search for similar items in EconPapers)
Pages: 16 : Anh. p.
Date: 2018
New Economics Papers: this item is included in nep-ecm
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Citations: View citations in EconPapers (8)

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Working Paper: Interactions in Fixed Effects Regression Models (2020)
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