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Truncation and Endogenous Stratification in Various Count Data Models for Recreation Demand Analysis

Author

Listed:
  • Nakatani, Tomoaki

    () (Dept. ofAgricultural Economics, Hokkaido University)

  • Sato, Kazuo

    (Dept. of Dairy Science, Rakuno Gakuen University)

Abstract

This paper extends the truncated and endogenously stratified Poisson and negative binomial models to three alternative discrete distributions, namely the generalized Poisson, geometric, and Borel distributions. Our primary intention here is to demonstrate how improper treatment of the data generates divergent outcomes by applying those distributions to recreation trip data gathered from surveys of visitors to an indigenous horse park in Japan. Our empirical application shows that failure to account for overdispersion, truncation, and endogenous stratification leads to substantial changes in parameter estimates and their standard errors. The parameter on the travel cost tends to be underestimated in absolute value in the standard setups. This results in serious overestimation of the economic benefit that the recreation site offers to society. Even when the endogenous stratification is incorporated, ignoring overdispersion causes the per capita per trip consumer's surplus to be over seven times larger than that obtained when endogenous stratification and overdispersion are considered.

Suggested Citation

  • Nakatani, Tomoaki & Sato, Kazuo, 2005. "Truncation and Endogenous Stratification in Various Count Data Models for Recreation Demand Analysis," SSE/EFI Working Paper Series in Economics and Finance 615, Stockholm School of Economics.
  • Handle: RePEc:hhs:hastef:0615
    as

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    References listed on IDEAS

    as
    1. J. M. C. Santos Silva, 2001. "A score test for non-nested hypotheses with applications to discrete data models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(5), pages 577-597.
    2. Englin, Jeffrey & Shonkwiler, J S, 1995. "Estimating Social Welfare Using Count Data Models: An Application to Long-Run Recreation Demand under Conditions of Endogenous Stratification and Truncation," The Review of Economics and Statistics, MIT Press, vol. 77(1), pages 104-112, February.
    3. Rakhal Sarker & Yves Surry, 2004. "The Fast Decay Process in Outdoor Recreational Activities and the Use of Alternative Count Data Models," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 86(3), pages 701-715.
    4. Grogger, J T & Carson, Richard T, 1991. "Models for Truncated Counts," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 6(3), pages 225-238, July-Sept.
    5. Gurmu, Shiferaw, 1991. "Tests for Detecting Overdispersion in the Positive Poisson Regression Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(2), pages 215-222, April.
    6. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    7. Shaw, Daigee, 1988. "On-site samples' regression : Problems of non-negative integers, truncation, and endogenous stratification," Journal of Econometrics, Elsevier, vol. 37(2), pages 211-223, February.
    8. Cameron, A Colin & Trivedi, Pravin K, 1986. "Econometric Models Based on Count Data: Comparisons and Applications of Some Estimators and Tests," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 1(1), pages 29-53, January.
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    More about this item

    Keywords

    Count data models; Endogenous stratification; Overdispersion; Recreation demand analysis; Consumer's surplus;

    JEL classification:

    • C34 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Truncated and Censored Models; Switching Regression Models
    • C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions
    • D12 - Microeconomics - - Household Behavior - - - Consumer Economics: Empirical Analysis
    • Q26 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Renewable Resources and Conservation - - - Recreational Aspects of Natural Resources

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