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

  • 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)

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.

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Article provided by De Gruyter in its journal Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik).

Volume (Year): 233 (2013)
Issue (Month): 1 (February)
Pages: 22-38

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Handle: RePEc:jns:jbstat:v:233:y:2013:i:1:p:22-38
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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. Greene, William, 2010. "Testing hypotheses about interaction terms in nonlinear models," Economics Letters, Elsevier, vol. 107(2), pages 291-296, May.
  3. 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.
  4. Heckman, James, 2013. "Sample selection bias as a specification error," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 31(3), pages 129-137.
  5. 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.
  6. 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 283-89, July.
  7. White, Michelle J, 1986. "Sex Differences in Urban Commuting Patterns," American Economic Review, American Economic Association, vol. 76(2), pages 368-72, May.
  8. 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.
  9. repec:zbw:rwidps:0039 is not listed on IDEAS
  10. Ai, Chunrong & Norton, Edward C., 2003. "Interaction terms in logit and probit models," Economics Letters, Elsevier, vol. 80(1), pages 123-129, July.
  11. 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.
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