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Interactions in Fixed Effects Regression Models

Author

Listed:
  • Marco Giesselmann
  • Alexander Schmidt-Catran

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.

Suggested Citation

  • Marco Giesselmann & Alexander Schmidt-Catran, 2018. "Interactions in Fixed Effects Regression Models," Discussion Papers of DIW Berlin 1748, DIW Berlin, German Institute for Economic Research.
  • Handle: RePEc:diw:diwwpp:dp1748
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    File URL: http://www.diw.de/documents/publikationen/73/diw_01.c.594675.de/dp1748.pdf
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    References listed on IDEAS

    as
    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, January.
    2. repec:zbw:espost:180822 is not listed on IDEAS
    3. Chris Frost & Simon G. Thompson, 2000. "Correcting for regression dilution bias: comparison of methods for a single predictor variable," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 163(2), pages 173-189.
    4. repec:zbw:espost:167662 is not listed on IDEAS
    5. Daniel Oesch & Oliver Lipps, 2011. "Does Unemployment Hurt Less if There Is More of It Around?: A Panel Analysis of Life Satisfaction in Germany and Switzerland," SOEPpapers on Multidisciplinary Panel Data Research 393, DIW Berlin, The German Socio-Economic Panel (SOEP).
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    panel data; fixed effects; interaction; quadratic terms; polynomials; within estimator;

    JEL classification:

    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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