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On Marginal and Interaction Effects: The Case of Heckit and Two-Part Models

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  • Frondel, Manuel
  • Vance, Colin

Abstract

Interaction effects capture the impact of one explanatory variable x1 on the marginal effect of another explanatory variable x2. To explore interaction effects, so-called interaction terms x1x2 are typically included in estimation specifications. While in linear models the effect of a marginal change in the interaction term is equal to the interaction effect, this equality generally does not hold in non-linear specifications (AI, NORTON, 2003). This paper provides for a general derivation of marginal and interaction effects in both linear and non-linear models and calculates the formulae of the marginal and interaction effects resulting from HECKMAN's sample selection model as well as the Two-Part Model, two commonly employed censored regression models. Drawing on a survey of automobile use from Germany, we argue that while it is important to test for the significance of interaction effects, their size conveys limited substantive content. More meaningful, and also more easy to grasp, are the conditional marginal effects pertaining to two variables that are assumed to interact.

Suggested Citation

  • Frondel, Manuel & Vance, Colin, 2009. "On Marginal and Interaction Effects: The Case of Heckit and Two-Part Models," Ruhr Economic Papers 138, RWI - Leibniz-Institut für Wirtschaftsforschung, Ruhr-University Bochum, TU Dortmund University, University of Duisburg-Essen.
    • Handle: RePEc:zbw:rwirep:138
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    References listed on IDEAS

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    1. Edward C. Norton & Hua Wang & Chunrong Ai, 2004. "Computing interaction effects and standard errors in logit and probit models," Stata Journal, StataCorp LP, vol. 4(2), pages 154-167, June.
    2. White, Michelle J, 1986. "Sex Differences in Urban Commuting Patterns," American Economic Review, American Economic Association, vol. 76(2), pages 368-372, May.
    3. Bun Song Lee & John F. McDonald, 2003. "Determinants of Commuting Time and Distance for Seoul Residents: The Impact of Family Status on the Commuting of Women," Urban Studies, Urban Studies Journal Limited, vol. 40(7), pages 1283-1302, June.
    4. Manuel Frondel & Jorg Peters & Colin Vance, 2008. "Identifying the Rebound: Evidence from a German Household Panel," The Energy Journal, International Association for Energy Economics, vol. 0(Number 4), pages 145-164.
    5. Ai, Chunrong & Norton, Edward C., 2003. "Interaction terms in logit and probit models," Economics Letters, Elsevier, vol. 80(1), pages 123-129, July.
    6. Manuel Frondel & Colin Vance, 2009. "Do High Oil Prices Matter? Evidence on the Mobility Behavior of German Households," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 43(1), pages 81-94, May.
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    Cited by:

    1. Ramachander, Sangamitra, 2016. "The price sensitivity of mobile use among low income households in six countries of Asia," Telecommunications Policy, Elsevier, vol. 40(7), pages 673-691.
    2. Parcero, Osiris J. & Papyrakis, Elissaios, 2016. "Income inequality and the oil resource curse," Resource and Energy Economics, Elsevier, vol. 45(C), pages 159-177.

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    More about this item

    Keywords

    Censored regression models; interaction terms;

    JEL classification:

    • C34 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Truncated and Censored Models; Switching Regression Models

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