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Welfare Analysis using Logsum Differences versus Rule of Half: Series of Case Studies

Logsum differences and rule-of-half (ROH) calculations are two methods for estimating consumer surplus in transport economics. As a traditional and relatively straightforward (and potentially more robust) procedure, ROH is widely used in project investment and policy analysis, and much of the literature agrees that logsums are somewhat superior to ROH when user benefits are valued, at least when true travel behaviors stem from random-utility maximization with Gumbel error terms. This paper explores the differences in both methods through a careful review of literature and many case study results. The comparison of ROH and logsum methods relies on three specifications in order of increasing complexity: binary logit, multinomial logit, and nested logit models under a variety of settings and scenarios. This work offers a closer look at three numerical examples and concludes that the difference between ROH and logsum solutions rises with increases in travel times or costs and with changes in parameters. The monetized differences in logsums is usually smaller than the ROH solution for welfare changes under most situations and gives a more exact result for consumer surplus than ROH (which assumes a linear demand relationship with respect to cost). Larger coefficients on affected variables (such as travel time and cost) in the random-utility expressions tend to increase differences between logsum-and ROH-based estimates. Such findings should be of interest to policy makers and planners when they are developing transportation planning and land use models and interpreting their results for more accurate and rigorous and behaviorally defensible project evaluations.