Use of Logsums in Welfare Estimation: Application in PRISM

Use of Logsums in Welfare Estimation: Application in PRISM


Serbjeet Kohli, ITS, University of Leeds, U K and Mott MacDonald, UK; Andrew Daly, ITS, University of Leeds, U K and RAND Europe, UK


In this paper we examine a number of applications of the logsum technique to evaluate consumer surplus under different scenarios. West Midlands strategic model-PRISM is used to test the applications of the logsum measure.


Welfare estimation lies at the heart of most appraisal processes. A number of techniques are used for the estimation of consumer surplus gained or lost due to the implementation of a project. The use of random utility maximisation (RUM) based on logit models opens up a new dimension in the welfare estimation techniques with the use of the ?logsum? as an evaluation measure.

In this paper we examine a number of applications of the logsum technique to evaluate consumer surplus under different scenarios. The model used for the applications is PRISM, the new strategic transport model of the West Midlands in the U.K. (described in a paper presented to the 2004 ETC (by van Vuren et. al)).

The theory behind the use of logsum measures for the calculation of consumer surplus is quite comprehensive, however applications of this measure in real life models remain sparse. It is this link between theory and application of the logsum technique that we have tried to bring forward in this paper.

While the theory behind logsum provides significant support in the development of a welfare calculation methodology, a number of theoretical and practical issues arise in the application of this measure, when dealing with models like PRISM; they are highlighted in this paper and solutions are proposed.

The issues are covered in the paper include:

? Non-linear formulation: Inclusions of cost in a non-linear form, such as the logarithmic functional form used in the PRISM models presents a specific problem of calculating the welfare benefits. This logcost formulation causes problems in two particular cases:
- Monetisation of the benefits: To convert the benefits calculated in utils into money terms requires an assessment of the average marginal utility of cost implied by the models.
- Inclusion of slow modes (walking and cycling): Use of slow modes presents another issue where zero cost for some of the alternatives. This problem is resolved using an approximation.

Welfare estimates are generated using the logsum technique with three trip purposes applied to the travel demand sub models of PRISM:

? home based work trips
? home based shopping trips
? home based other trips

The test studies the impact of a particular set of network interventions which improve the transport infrastructure in the West Midlands. The strength of the logsum technique in being able to evaluate the welfare benefits simultaneously for each of the market segments that exist in the structure of the models is discussed in detail. Market segmentation based on attributes of the consumer (traveller) in the model structure, like employment status, car-ownership and age in some cases, facilitates a detailed analysis of the impacts on consumer surplus for different sections of society. An extension of the results could be interpreted as social exclusion indicators for e.g. welfare benefits to different age groups or the unemployed.

A particular feature of the consumer surplus calculation is that the logsum formulation is no longer correct when household income is included in a non-linear functional form in the RUM models. A more rigorous theoretical approach needs to be taken in this case for the evaluation of welfare benefits. As in PRISM household income only appears as one of the market segmenting attributes the logsum technique is appropriate.

This paper provides:
? extension to the logsum theory to make it applicable in the models like PRISM;
? results of the welfare estimates generated using the logsum technique for three different trip purpose demand models;
? discussions based on the results on the strengths of the logsum technique in being used for welfare estimation; and
? further directions of research in the use of logsum in more wider areas of application within the transport planning field.


Association for European Transport