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

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  • Frondel Manuel

    (Leiter des Bereichs Umwelt und Ressourcen, Head of Department Environment and Resources, Rheinisch-Westfälisches Institut für Wirtschaftsforschung (RWI), Hohenzollernstr. 1-3, 45128 Essen, Germany)

  • Vance Colin

    (Rheinisch-Westfälisches Institut für Wirtschaftsforschung (RWI), Hohenzollernstraße 1-3, 45128 Essen, Germany)

Abstract

Interaction effects capture the impact of one explanatory variable on the marginal effect of another explanatory variable. To explore interaction effects, so-called interaction terms 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 interaction effects in both linear and non-linear models and calculates the formulae of the interaction effects resulting from Heckman’s sample selection model as well as the Two- Part Model, two regression models commonly applied to data with a large fraction of either missing or zero values in the dependent variable. 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, 2013. "On Interaction Effects: The Case of Heckit and Two-Part Models," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 233(1), pages 22-38, February.
    • Handle: RePEc:jns:jbstat:v:233:y:2013:i:1:p:22-38
    DOI: 10.1515/jbnst-2013-0104
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    References listed on IDEAS

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    1. Colin Vance, 2009. "Marginal effects and significance testing with Heckman's sample selection model: a methodological note," Applied Economics Letters, Taylor & Francis Journals, vol. 16(14), pages 1415-1419.
    2. Heckman, James, 2013. "Sample selection bias as a specification error," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 31(3), pages 129-137.
    3. repec:zbw:rwidps:0039 is not listed on IDEAS
    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. Greene, William, 2010. "Testing hypotheses about interaction terms in nonlinear models," Economics Letters, Elsevier, vol. 107(2), pages 291-296, May.
    7. 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.
    8. Duan, Naihua, et al, 1984. "Choosing between the Sample-Selection Model and the Multi-part Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 2(3), pages 283-289, July.
    9. Frondel, Manuel & Vance, Colin, 2010. "Driving for fun? Comparing the effect of fuel prices on weekday and weekend fuel consumption," Energy Economics, Elsevier, vol. 32(1), pages 102-109, January.
    10. White, Michelle J, 1986. "Sex Differences in Urban Commuting Patterns," American Economic Review, American Economic Association, vol. 76(2), pages 368-372, May.
    11. 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.
    12. 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.
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    More about this item

    Keywords

    Truncated regression models; interaction terms; Truncated regression models; interaction terms;
    All these keywords.

    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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