Skip to main content
Log in

On dependency in double-hurdle models

  • Articles
  • Published:
Statistical Papers Aims and scope Submit manuscript

Abstract

In microeconometrics, consumption data is typically zero-inflated due to many individuals recording, for one reason or another, no consumption. A mixture model can be appropriate for statistical analysis of such data, with the Dependent Double-Hurdle model (DDH hereafter) one specification that is frequently adopted in econometric practice. Essentially, the DDH model is designed to explain individual demand through a simultaneous two-step process: a market participation decision (first hurdle), and a consumption level decision (second hurdle)—a non-zero correlation/covariance parameter allows for dependency between the hurdles. A significant feature of the majority of empirical DDH studies has been the lack of support for the existence of dependency. This empirical phenomenon is studied from a theoretical perspective using examples based on the bivariate normal, bivariate logistic, and bivariate Poisson distributions. The Fisher Information matrix for the parameters of the model is considered, especially the component corresponding to the dependency parameter. The main finding is that the DDH model contains too little statistical information to support estimation of dependency, even when dependency is truly present. Consequently, the paper calls for the elimination of attempts to estimate dependency using the DDH framework. The advantage of this strategy is that it permits flexible modelling: some possibilities are proposed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Aalen OO (1992), Modelling heterogeneity in survival analysis by the compound Poisson distribution.The Annals of Applied Probability 2, 951–972

    Article  MATH  MathSciNet  Google Scholar 

  2. Blaylock JR, Blisard WN (1992), U.S. cigarette consumption: the case of low-income women.American Journal of Agricultural Economics 74, 698–705

    Article  Google Scholar 

  3. Blundell R, Meghir C (1987), Bivariate alternatives to the Tobit model.Journal of Econometrics 34, 179–200

    Article  MATH  Google Scholar 

  4. Burton M, Tomlinson M, Young T (1994), Consumers' decisions whether or not to purchase meat: a double hurdle analysis of single adult households.Journal of Agricultural Economics 45, 202–212

    Article  Google Scholar 

  5. Cragg JG (1971), Some statistical models for limited dependent variables with applications to the demand for durable goodsEconometrica 39, 829–844

    Article  MATH  Google Scholar 

  6. Dionne G, Artis M, Guillen M (1996), Count data models for a credit scoring system.Journal of Empirical Finance 3, 303–325

    Article  Google Scholar 

  7. Gao XM, Wailes EJ, Cramer GL (1995), Double-hurdle model with bivariate normal errors: an application to U.S. rice demand.Journal of Agricultural and Applied Economics 27, 363–376

    Google Scholar 

  8. Garcia J, Labeaga JM (1996), Alternative approaches to modelling zero expenditure: an application to Spanish demand for tobacco.Oxford Bulletin of Economics and Statistics 58, 489–506

    Google Scholar 

  9. Gould BW (1992), At-home consumption of cheese: a purchase-infrequency model.American Journal of Agricultural Economics 72, 453–459

    Article  Google Scholar 

  10. Jones AM (1989), A double-hurdle model of cigarette consumption.Journal of Applied Econometrics 4, 23–39

    Article  Google Scholar 

  11. Jones AM (1992), A note on computation of the double-hurdle model with dependence with an application to tobacco expenditure.Bulletin of Economic Research 44, 67–74.

    Article  Google Scholar 

  12. Jones AM (2000), A Box-Cox double-hurdle model.The Manchester School of Economic and Social Studies 68, 203–221

    Article  Google Scholar 

  13. Lambert D (1992), Zero-inflated Poisson regression, with an application to defects in manufacturing.Technometrics 34, 1–14

    Article  MATH  Google Scholar 

  14. Pudney S (1989),Modelling Individual Choice: the Econometrics of Corners, Kinds, and Holes, London: Basil Blackwell

    Google Scholar 

  15. Shonkwiler JS, Shaw WD (1996), Hurdle count-data models in recreation demand analysis.Journal of Agricultural and Resource Economics 21, 210–219.

    Google Scholar 

  16. Spanier J, Oldham KB (1987),An Atlas of Functions, Washington: Hemisphere

    MATH  Google Scholar 

  17. Yen ST, Boxall PC, Adamowicz WL (1997), An econometric analysis of donations for environmental conservation in Canada.Journal of Agricultural and Resource Economics 22, 246–263

    Google Scholar 

  18. Yen ST, Jensen HH, Wang Q (1996), Cholesterol information and egg consumption in the US: a nonnormal and heteroscedastic double-hurdle model.European Review of Agricultural Economics 23, 343–356

    Google Scholar 

  19. Yen ST, Jones AM (1997), Household consumption of cheese: an inverse hyperbolic sine double-hurdle model with dependent errors.American Journal of Agricultural Economics 79, 246–251

    Article  Google Scholar 

  20. Zorn CJW (1998), An analytic and experimental examination of zero-inflated and hurdle Poisson specifications.Sociological Methods and Research 26, 368–400

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Murray D. Smith.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Smith, M.D. On dependency in double-hurdle models. Statistical Papers 44, 581–595 (2003). https://doi.org/10.1007/BF02926011

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02926011

Key words

Navigation