ERRORS OF TRUNCATION IN APPROXIMATIONS TO EXPECTED CONSUMER SURPLUS

Consumer surplus and other welfare measures calculated from demand curves are random variables. Increasingly, this realization has been incorporated into studies which assess such benefit measures. Unfortunately, consumer surplus measures usually involve the ratio of random variables, and the expected value of a ratio of random variables is not equal to the ratio of the expected values. Indeed in small samples the expectation of consumer surplus often does not have a closed-form representation. In this case, one must resort to an approximation or a cumbersome Monte Carlo analysis. In our example, the magnitude of the error due to truncation of the approximation varies markedly across functional forms for the demand function. Our illustration of this error is conducted using consumer surplus estimates for a travel cost model of recreation demand. We investigate three functional forms for a model with the number of visits in a season regressed on a constant and travel cost. The exact model used in our analysis is quite simple; we do not intend to offer a convincing model of recreation demand as much as we wish to illustrate the size of the potential errors that can be made by truncating an approximation to expected consumer surplus. -from Authors