The support search is repeated R = 3 times, and both the AMMSE and MAP estimates are calculated.
On different conditions, the performances of the two modified-BMP estimators (AMMSE and MAP) are clearly superior to those of BPDN and OMP.
Here we still adopt the AMMSE estimate in the two BMP methods.
An argument similar to that of Farebrother (1975) can be used to demonstrate the consistency of the AMMSE.
The differences between the MELO estimator and AMMSE arise because his marginal posterior for [Mathematical Expression Omitted] is based on a diffuse prior that has been updated with sample information assumed to be generated by a process that has independently distributed normal errors with zero mean and constant variance. Zellner's (1978) MELO for ratios of random variables would be applicable to the case of a linear demand model using the consumer surplus per trip for the expression (see Table 1), provided the quantity term was treated simply.
Nonetheless, because the semi-log specification is one of the most popular forms for travel cost demand models and because consumer surplus per trip (or unit of use) is frequently an important focus of benefit transfer analyses for policy, a comparison of benefit measures derived from "tailored" estimators designed to fit a specific objective (such as the AMMSE) to those from general purpose estimates of demand models remains of interest.
To fully describe the comparative performance of OLS versus AMMSE in small samples would require extensive research along the lines of Kling's recent experimental comparisons (1988a, 1988b) of random utility versus conventional travel cost demand models.
Each experiment involves 500 independent replications where OLS and AMMSE (with the OLS estimates as the starting values) are applied to the task of estimating s using samples of 100 observations.
In terms of mean squared error, the AMMSE estimator of consumer surplus offers an improvement over both the OLS and the inequality-constrained OLS estimates for all but the case of the smallest (in absolute magnitude) own-price coefficient.
However, this improvement develops because the AMMSE estimator accepts a large bias.
On the basis of these findings, using AMMSE for cases where the semi-log can be treated as the correct form for the site demand seems to offer a conservative strategy for estimating per-trip benefits.