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Interactions in Fixed Effects Regression Models

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  • 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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    References listed on IDEAS

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    Cited by:

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    2. Morgenroth, Nicolas & Schels, Brigitte & Teichler, Nils, 2021. "Are Men or Women More Unsettled by Fixed-Term Contracts? Gender Differences in Affective Job Insecurity and the Role of Household Context and Labour Market Positions," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics.
    3. Bellia, Mario & Heynderickx, Wouter & Maccaferri, Sara & Schich, Sebastian, 2020. "Do CDS markets care about the G-SIB status?," Working Papers 2020-02, Joint Research Centre, European Commission.
    4. Enrico Bergamini & Georg Zachmann, 2020. "Exploring EU’s Regional Potential in Low-Carbon Technologies," Sustainability, MDPI, vol. 13(1), pages 1-28, December.
    5. Lieb, Lenard & Schuffels, Johannes, 2019. "Inflation expectations and consumer spending: the role of household balance sheets," Research Memorandum 022, Maastricht University, Graduate School of Business and Economics (GSBE).
    6. Jungkunz, Sebastian & Marx, Paul, 2021. "Income changes do not influence political participation: Evidence from comparative panel data," ifso working paper series 11, University of Duisburg-Essen, Institute for Socio-Economics (ifso).
    7. Giesselmann, Marco & Brady, David & Naujoks, Tabea, 2021. "The social consequences of the increase in refugees to Germany 2015-2016," Discussion Papers, Research Professorship Inequality and Social Policy SP I 2021-502, WZB Berlin Social Science Center.
    8. Alexander Deryigin & Irina Filippova & Igor Arlashkin, 2021. "Impact of intraregional tax decentralization on the development of the income base of the regions [Влияние Внутрирегиональной Налоговой Децентрализации На Развитие Доходной Базы Регионов]," Economic Policy, Russian Presidential Academy of National Economy and Public Administration, vol. 2, pages 8-33, April.
    9. Sebastian Jungkunz & Paul Marx, 2021. "Income Changes Do Not Influence Political Participation: Evidence from Comparative Panel Data," SOEPpapers on Multidisciplinary Panel Data Research 1129, DIW Berlin, The German Socio-Economic Panel (SOEP).

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    More about this item

    Keywords

    panel data; fixed effects; interaction; quadratic terms; polynomials; within estimator;
    All these keywords.

    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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