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Estimating Willingness to Pay from Count Data When Survey Responses are Rounded


  • Ian B. Page

    () (University of Maryland)

  • Erik Lichtenberg

    () (University of Maryland)

  • Monica Saavoss

    () (United States Department of Agriculture)


Recall data of visits to recreational sites often contain reported numbers that appear to be rounded to nearby focal points (e.g., the closest 5 or 10). Failure to address this rounding has been shown to produce biased estimates of marginal effects and non-linear combinations of coefficients such as willingness to pay. We investigate the relative performance of three count data models used with data of the kind typically found in survey data. We create a dataset based on observed recreational trip counts and associated trip costs that exhibits substantial rounding. We then conduct a Monte Carlo simulation exercise to compare the estimated parameters, willingness to pay, and the average consumer surplus per trip for three alternative estimators: a standard Poisson model with no adjustment for rounding, a censored Poisson model, a grouped Poisson model, and a latent class Poisson model with rounding and non-rounding classes. The standard Poisson model with no adjustment for rounding exhibits significant and persistent bias, especially in estimates of non-linear effects. The grouped and latent class Poisson models, in contrast, show little to no bias in estimates.

Suggested Citation

  • Ian B. Page & Erik Lichtenberg & Monica Saavoss, 2020. "Estimating Willingness to Pay from Count Data When Survey Responses are Rounded," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 75(3), pages 657-675, March.
  • Handle: RePEc:kap:enreec:v:75:y:2020:i:3:d:10.1007_s10640-020-00403-6
    DOI: 10.1007/s10640-020-00403-6

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    References listed on IDEAS

    1. Martin Browning & Thomas F. Crossley & Guglielmo Weber, 2003. "Asking consumption questions in general purpose surveys," Economic Journal, Royal Economic Society, vol. 113(491), pages 540-567, November.
    2. Robert A. Androkovich, 2015. "Recreational Visits to the Adam's River during the Annual Sockeye Run: A Travel Cost Analysis," Marine Resource Economics, University of Chicago Press, vol. 30(1), pages 35-49.
    3. Ferrini, Silvia & Scarpa, Riccardo, 2007. "Designs with a priori information for nonmarket valuation with choice experiments: A Monte Carlo study," Journal of Environmental Economics and Management, Elsevier, vol. 53(3), pages 342-363, May.
    4. Baltas, George & Argouslidis, Paraskevas C. & Skarmeas, Dionysis, 2010. "The Role of Customer Factors in Multiple Store Patronage: A Cost–Benefit Approach," Journal of Retailing, Elsevier, vol. 86(1), pages 37-50.
    5. Hoderlein, Stefan & Winter, Joachim, 2010. "Structural measurement errors in nonseparable models," Journal of Econometrics, Elsevier, vol. 157(2), pages 432-440, August.
    6. Luceri, Beatrice & Latusi, Sabrina, 2012. "The importance of consumer characteristics and market structure variables in driving multiple store patronage," Journal of Retailing and Consumer Services, Elsevier, vol. 19(5), pages 519-525.
    7. Moeltner, Klaus, 2003. "Addressing aggregation bias in zonal recreation models," Journal of Environmental Economics and Management, Elsevier, vol. 45(1), pages 128-144, January.
    8. Craig E. Landry & Kenneth E. McConnell, 2007. "Hedonic Onsight Cost Model of Recreation Demand," Land Economics, University of Wisconsin Press, vol. 83(2), pages 253-267.
    9. Smith, Jordan W. & Seekamp, Erin & McCreary, Allie & Davenport, Mae & Kanazawa, Mark & Holmberg, Kerry & Wilson, Bruce & Nieber, John, 2016. "Shifting demand for winter outdoor recreation along the North Shore of Lake Superior under variable rates of climate change: A finite-mixture modeling approach," Ecological Economics, Elsevier, vol. 123(C), pages 1-13.
    10. Blair, Edward & Burton, Scot, 1987. "Cognitive Processes Used by Survey Respondents to Answer Behavioral Frequency Questions," Journal of Consumer Research, Oxford University Press, vol. 14(2), pages 280-288, September.
    11. Hindsley, Paul & Landry, Craig E. & Gentner, Brad, 2011. "Addressing onsite sampling in recreation site choice models," Journal of Environmental Economics and Management, Elsevier, vol. 62(1), pages 95-110, July.
    12. John Whitehead & Daniel Phaneuf & Christopher Dumas & Jim Herstine & Jeffery Hill & Bob Buerger, 2010. "Convergent Validity of Revealed and Stated Recreation Behavior with Quality Change: A Comparison of Multiple and Single Site Demands," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 45(1), pages 91-112, January.
    13. Richard C. Bishop & Kevin J. Boyle, 2019. "Reliability and Validity in Nonmarket Valuation," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 72(2), pages 559-582, February.
    14. Kenneth A. Baerenklau, 2010. "A Latent Class Approach to Modeling Endogenous Spatial Sorting in Zonal Recreation Demand Models," Land Economics, University of Wisconsin Press, vol. 86(4), pages 800-816.
    15. Kuminoff, Nicolai V. & Parmeter, Christopher F. & Pope, Jaren C., 2010. "Which hedonic models can we trust to recover the marginal willingness to pay for environmental amenities?," Journal of Environmental Economics and Management, Elsevier, vol. 60(3), pages 145-160, November.
    16. Stephen Hynes & William Greene, 2013. "A Panel Travel Cost Model Accounting for Endogenous Stratification and Truncation: A Latent Class Approach," Land Economics, University of Wisconsin Press, vol. 89(1), pages 177-192.
    17. Wen, Hefei & Hockenberry, Jason M. & Cummings, Janet R., 2015. "The effect of medical marijuana laws on adolescent and adult use of marijuana, alcohol, and other substances," Journal of Health Economics, Elsevier, vol. 42(C), pages 64-80.
    18. Carpio, Carlos E. & Wohlgenant, Michael K. & Boonsaeng, Tullaya, 2008. "The Demand for Agritourism in the United States," Journal of Agricultural and Resource Economics, Western Agricultural Economics Association, vol. 33(2), pages 1-16.
    19. Wei Shi & Ju-Chin Huang, 2018. "Correcting On-Site Sampling Bias: A New Method with Application to Recreation Demand Analysis," Land Economics, University of Wisconsin Press, vol. 94(3), pages 459-474.
    20. Manski, Charles F. & Molinari, Francesca, 2010. "Rounding Probabilistic Expectations in Surveys," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(2), pages 219-231.
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    More about this item


    Coarsened data; Count data; Heaped data; Poisson; Recreation demand; Rounding;

    JEL classification:

    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities
    • Q26 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Renewable Resources and Conservation - - - Recreational Aspects of Natural Resources


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