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

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  • Manuel Frondel

    ()
    (RWI Essen)

  • Colin Vance

    ()
    (RWI Essen)

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.

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Bibliographic Info

Article provided by Justus-Liebig University Giessen, Department of Statistics and Economics in its journal Journal of Economics and Statistics.

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

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Handle: RePEc:jns:jbstat:v:233:y:2013:i:1:p:22-38

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Keywords: Truncated regression models; interaction terms;

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References

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  1. Manuel Frondel & Colin Vance, 2008. "Do High Oil Prices Matter? – Evidence on the Mobility Behavior of German Households," Ruhr Economic Papers 0072, Rheinisch-Westfälisches Institut für Wirtschaftsforschung, Ruhr-Universität Bochum, Universität Dortmund, Universität Duisburg-Essen.
  2. White, Michelle J, 1986. "Sex Differences in Urban Commuting Patterns," American Economic Review, American Economic Association, vol. 76(2), pages 368-72, May.
  3. 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.
  4. 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.
  5. 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.
  6. Manuel Frondel & Jörg Peters & Colin Vance, 2007. "Identifying the Rebound - Evidence from a German Household Panel," Ruhr Economic Papers 0032, Rheinisch-Westfälisches Institut für Wirtschaftsforschung, Ruhr-Universität Bochum, Universität Dortmund, Universität Duisburg-Essen.
  7. Ai, Chunrong & Norton, Edward C., 2003. "Interaction terms in logit and probit models," Economics Letters, Elsevier, vol. 80(1), pages 123-129, July.
  8. William H. Greene, 2009. "Testing Hypotheses About Interaction Terms in Nonlinear Models," Working Papers 09-08, New York University, Leonard N. Stern School of Business, Department of Economics.
  9. Colin Vance, 2006. "Marginal Effects and Significance Testing with Heckman’s Sample Selection Model: A Methodological Note," RWI Discussion Papers 0039, Rheinisch-Westfälisches Institut für Wirtschaftsforschung.
  10. 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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Cited by:
  1. Birte Pohl & Peter Mulder, 2013. "Explaining the Diffusion of Renewable Energy Technology in Developing Countries," GIGA Working Paper Series 217, GIGA German Institute of Global and Area Studies.

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