APPLIED WELFARE ECONOMICS WITH DISCRETE CHOICE MODELS IN THE PRESENCE OF INCOME EFFECTS
R Batley, ITS University of Leeds, UK; J Ibanez, European Commission's Joint Research Centre (IPTS), ES
Small & Rosen (1981) established the basis upon which discrete choice models could be applied to welfare analysis. The present paper will reveal new insights on their work, and strengthen the implications for discrete choice modelling practice.
Small & Rosenâ??s 1981 paper in Econometrica has played an influential role in promoting the application of discrete choice models to the welfare analysis of public policy interventions. Batley & Ibanezâ??s paper at ETC2010 reviewed the theoretical basis of Small & Rosen, with a view to strengthening practical advice. They found that Small & Rosenâ??s welfare measure is applicable only to demand problems not subject to income effects, and where the specification of deterministic utility observes four requirements: (i) for each alternative, equivalence (in absolute terms) between the conditional marginal utilities of income and price; (ii) common conditional marginal utility of income across alternatives; (iii) common conditional marginal utility of price across alternatives; and (iv) independence of the conditional marginal utility of income from prices.
Arising from the above findings, it becomes clear that, where income effects are prevalent and/or the specification requirements are not observed, Small & Rosenâ??s welfare measure is inappropriate. Our submission to ETC2011 is motivated by an interest in exploring the theory behind welfare measures in the presence of income effects, and especially its implications for the practical specification of discrete choice models. We begin by reviewing relevant literature by Hau (1985, 1987), Jara-DÃaz & Farah (1988), Jara-DÃaz (1990), KarlstrÃ¶m (1999) and KarlstrÃ¶m & Morey (2004), rehearsing the intuition behind the notion of income effects in discrete choice models, and noting that welfare measures in the presence of income effects seek, in essence, to relax requirements (ii) and (iv) above.
The substantive contribution of the paper is to identify the minimal set of assumptions necessary to derive a theoretically valid probabilistic demand function, both in the absence, and in the presence, of income effects. We interpret theoretical validity to mean compliance with the Random Utility Model, whilst at the same time observing the fundamental properties of demand functions, namely adding-up, negativity, homogeneity and symmetry. To these ends, we generalise previous work by Hau (which focussed on the absence of income effects), draw clear and unambiguous prescription for the practical specification of discrete choice models, and (on the basis of the model specifications adopted) comment upon the implied properties of exemplar studies reported in the extant literature.
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