Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/181033 
Year of Publication: 
2018
Series/Report no.: 
DIW Discussion Papers No. 1748
Publisher: 
Deutsches Institut für Wirtschaftsforschung (DIW), Berlin
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.
Subjects: 
panel data
fixed effects
interaction
quadratic terms
polynomials
within estimator
JEL: 
C33
C51
Document Type: 
Working Paper

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