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

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  • Manuel Frondel

    ()

  • Colin Vance

Abstract

Interaction effects capture the impact of one explanatory variable x1 on the marginal effect of another explanatory variable x2. To explore interaction effects, socalled 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 specifi cations (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, respectively. 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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Paper provided by Rheinisch-Westfälisches Institut für Wirtschaftsforschung, Ruhr-Universität Bochum, Universität Dortmund, Universität Duisburg-Essen in its series Ruhr Economic Papers with number 0309.

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Length: 24 pages
Date of creation: Jan 2012
Date of revision:
Handle: RePEc:rwi:repape:0309

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Keywords: Truncated regression models; interaction terms;

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  1. Greene, William, 2010. "Testing hypotheses about interaction terms in nonlinear models," Economics Letters, Elsevier, vol. 107(2), pages 291-296, May.
  2. Manuel Frondel & Colin Vance, 2009. "Do High Oil Prices Matter? Evidence on the Mobility Behavior of German Households," Environmental & Resource Economics, European Association of Environmental and Resource Economists, vol. 43(1), pages 81-94, 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. Ai, Chunrong & Norton, Edward C., 2003. "Interaction terms in logit and probit models," Economics Letters, Elsevier, vol. 80(1), pages 123-129, July.
  6. White, Michelle J, 1986. "Sex Differences in Urban Commuting Patterns," American Economic Review, American Economic Association, vol. 76(2), pages 368-72, May.
  7. 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.
  8. 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.
  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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