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

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.