Statistical Papers

, 44:581 | Cite as

On dependency in double-hurdle models

  • Murray D. SmithEmail author


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.

Key words

Dependency Weak identification Fisher's information 


  1. [1]
    Aalen OO (1992), Modelling heterogeneity in survival analysis by the compound Poisson distribution.The Annals of Applied Probability 2, 951–972zbMATHCrossRefMathSciNetGoogle Scholar
  2. [2]
    Blaylock JR, Blisard WN (1992), U.S. cigarette consumption: the case of low-income women.American Journal of Agricultural Economics 74, 698–705CrossRefGoogle Scholar
  3. [3]
    Blundell R, Meghir C (1987), Bivariate alternatives to the Tobit model.Journal of Econometrics 34, 179–200zbMATHCrossRefGoogle Scholar
  4. [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, 202–212CrossRefGoogle Scholar
  5. [5]
    Cragg JG (1971), Some statistical models for limited dependent variables with applications to the demand for durable goodsEconometrica 39, 829–844zbMATHCrossRefGoogle Scholar
  6. [6]
    Dionne G, Artis M, Guillen M (1996), Count data models for a credit scoring system.Journal of Empirical Finance 3, 303–325CrossRefGoogle Scholar
  7. [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, 363–376Google Scholar
  8. [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, 489–506Google Scholar
  9. [9]
    Gould BW (1992), At-home consumption of cheese: a purchase-infrequency model.American Journal of Agricultural Economics 72, 453–459CrossRefGoogle Scholar
  10. [10]
    Jones AM (1989), A double-hurdle model of cigarette consumption.Journal of Applied Econometrics 4, 23–39CrossRefGoogle Scholar
  11. [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.CrossRefGoogle Scholar
  12. [12]
    Jones AM (2000), A Box-Cox double-hurdle model.The Manchester School of Economic and Social Studies 68, 203–221CrossRefGoogle Scholar
  13. [13]
    Lambert D (1992), Zero-inflated Poisson regression, with an application to defects in manufacturing.Technometrics 34, 1–14zbMATHCrossRefGoogle Scholar
  14. [14]
    Pudney S (1989),Modelling Individual Choice: the Econometrics of Corners, Kinds, and Holes, London: Basil BlackwellGoogle Scholar
  15. [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. [16]
    Spanier J, Oldham KB (1987),An Atlas of Functions, Washington: HemispherezbMATHGoogle Scholar
  17. [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, 246–263Google Scholar
  18. [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, 343–356Google Scholar
  19. [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, 246–251CrossRefGoogle Scholar
  20. [20]
    Zorn CJW (1998), An analytic and experimental examination of zero-inflated and hurdle Poisson specifications.Sociological Methods and Research 26, 368–400CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2003

Authors and Affiliations

  1. 1.Econometrics and Business StatisticsUniversity of SydneySydneyAustralia

Personalised recommendations