The logsum as an evaluation measure - review of the literature and new results
Transport infrastructure projects in The Netherlands are appraised ex ante by using cost-benefit analysis (CBA) procedures following the so-called ‘OEI-guidelines’. The project benefits for travellers are incorporated in the form of changes in demand (e.g. from the Dutch national model system, LMS, or the regional models, NRM) and changes in the generalised travel costs (using values of time from Stated Preference studies to monetise travel time savings), and applying the rule of half. While a number of short-term improvements to the current procedures have been improved, it is also interesting to consider a more radical approach using explicit measures of consumer surplus, obtained by integrating the demand models directly. These measures are called logsums, from their functional form. The advantages that the logsums would give to the appraisal procedure would be that logsums can incorporate a degree of heterogeneity in the population, while also being theoretically more correct and in many cases easier to calculate. In this context, the Transport Research Centre (AVV) of the Dutch Ministry of Transport, Public Works and Water Management has commissioned RAND Europe to undertake a study comparing the conventional approach to the use of the logsum change as a measure of the change in consumer surplus that would result from a transport infrastructure project. The paper is based on the work conducted in the study. The paper opens with a review of the literature on the use of logsums as a measure of consumer surplus change in project appraisal and evaluation. It then goes on to describe a case study with the Dutch National Model System (LMS) for transport in which three methods are compared for a specific project (a high speed magnetic hover train that would connect the four main cities in the Randstad: Amsterdam, The Hague, Rotterdam and Utrecht): a.the ‘classical’ CBA approach as described above, b.the improved ‘classical’ CBA approach (introducing a number of short-term improvements) and c.the logsum approach (as a long term improvement). The direct effects of a particular policy on the travellers can be measured as the change in consumer surplus that results from that policy (there can also be indirect and external effects that may not be covered in the consumer surplus change). The consumer surplus associated with a set of alternatives is, under the logit assumptions, relatively easy to calculate. By definition, a person’s consumer surplus is the utility, in money terms, that a person receives in the choice situation. If the unobserved component of utility is independently and identically distributed extreme value and utility is linear in income, then the expected utility becomes the log of the denominator of a logit choice probability, divided by the marginal utility of income, plus arbitrary constants. This if often called the ‘logsum’. Total consumer surplus in the population can be calculated as a weighted sum of logsums over a sample of decision-makers, with the weights reflecting the number of people in the population who face the same representative utilities as the sampled person. The change in consumer surplus is calculated as the difference between the logsum under the conditions before the change and after the change (e.g. introduction of a policy). The arbitrary constants drop out. However, to calculate this change in consumer surplus, the researcher must know the marginal utility of income. Usually a price or cost variable enters the representative utility and, in case that happens in a consistent linear additive fashion, the negative of its coefficient is the marginal utility of income by definition. If the marginal utility of income is not constant with respect to income, as is the case in the LMS and NRM, a far more complex formula is needed, or an indirect approach has to be taken. This paper will review the theoretical literature on the use of the logsum as an evaluation measure, including both the original papers on this from the seventies and the work on the income effect in the nineties. Also recent application studies that used the logsum for evaluation purposes will be reviewed. Finally outcomes of runs with the LMS will be reported for the three different approaches (including the logsum approach) mentioned above for evaluating direct effect of transport policies and projects. Different methods for monetising the logsum change will be compared.
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- Joseph A. Herriges & Catherine L. Kling, 1999.
"Nonlinear Income Effects in Random Utility Models,"
The Review of Economics and Statistics,
MIT Press, vol. 81(1), pages 62-72, February.
- H C W L Williams, 1977. "On the Formation of Travel Demand Models and Economic Evaluation Measures of User Benefit," Environment and Planning A, , vol. 9(3), pages 285-344, March.
- H C W L Williams, 1977. "On the formation of travel demand models and economic evaluation measures of user benefit," Environment and Planning A, Pion Ltd, London, vol. 9(3), pages 285-344, March.
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