A Nonparametric Revealed Preference Approach to Measuring the Value of Environmental Quality

Environ Resource Econ (2018) 69:503–527 https://doi.org/10.1007/s10640-018-0229-9 A Nonparametric Revealed Preference Approach to Measuring the Value of Environmental Quality Laura Blow1,2 · Richard Blundell2,3 Published online: 26 February 2018 © The Author(s) 2018. This article is an open access publication Abstract We develop an approach to valuing non-market goods using nonparametric revealed preference analysis. We show how nonparametric methods can also be used to bound the welfare effects of changes in the provision of a non-market good. Our main context is one in which the non-market good affects the marginal utility of consuming a related market good. This can also be framed as a shift in the taste for, or quality of, the market good. A systematic approach for incorporating quality/taste variation into a revealed preference framework for heterogeneous consumers is developed. This enables the recovery of the minimal variation in quality required to rationalise observed choices of related market goods. The variation in quality appears as a adjustment to the price for related market goods which then allows a revealed preference approach to bounding compensation measures of welfare effects to be applied. Keywords Revealed preference · Bounds · Public good valuation · Inequality restrictions · Semiparametric regression · Changing tastes Guest Editor: V. Kerry Smith. We would like to thank Kerry Smith, two anonymous commentators and participants at the conference for comments on an earlier draft. The authors also gratefully acknowledge financial support from the Economic and Social Research Council Centre for the Microeconomic Analysis of Public Policy at IFS. B Laura Blow Richard Blundell 1 Surrey University, Guildford, UK 2 IFS, London, UK 3 UCL, London, UK 123 504 L. Blow, R. Blundell 1 Introduction In this article, we use a common method of valuing non-market environmental goods whereby information about the valuation of a public good is extracted from its relationship with a marketed good. Existing specific examples of this method include household production theory where the household combines market goods with an environmental good to produce the service from which they ultimately derive utility, and the assumption of weak complementarity or substitutability between the surrogate market good and the environmental good. We develop a new approach to this general method that uses nonparametric revealed preference analysis. We believe this could be a helpful approach for two main reasons: firstly it does not rely on particular functional forms for demand which have the potential to influence heavily the valuation estimates; secondly the marginal valuation of changes in the quality of the environmental good are allowed to differ in a very flexible way across consumers. This second point means that this approach could also be very flexible and useful from a benefit transfer point of view, provided we have information on the distribution of relevant characteristics for the transfer population. We now discuss both these points in a little more detail. Revealed preference theory was pioneered by Samuelson (1948). At that time, the traditional approach to demand theory (still widely used today) was parametric; a particular functional form for demand functions was estimated and then consideration was given to the restrictions those functions must satisfy if they had been generated by utility maximisation. One problem endemic to parametric demand estimation is that predictions can be heavily dependent on the functional form used to estimate demands. Indeed this has been discussed by Crooker and Kling (2000) in the case of environmental valuation. This has potential to be a significant issue in applications using weak complementarity, for example, since the demand curve for the weakly complementary market good must be extrapolated to zero. Nonparametric revealed preference theory generates elegant nonparametric tests that can be used to assess whether data on observed consumer choices is consistent with having been generated by utility maximisation without having to impose a particular functional form on preferences. Building on the work of Samuelson (1948), Houthakker (1950) and Afriat (1967), Varian (1982, 1983) solved or simplified many of the most important computational aspects of revealed preference. He also showed that if the data satisfies revealed preference tests of maximising behaviour, then revealed preference theory can be used to recover information about the utility function and to forecast choices at new budgets or prices. Blundell et al. (2003, 2008) developed a method for choosing a sequence of total expenditures that maximize the power of tests of generalized axiom of revealed preference (GARP) with respect to a given preference ordering. They term this the sequential maximum power (SMP) path and present some simulation evidence showing that these GARP tests have considerable power against some key alternatives. From this idea it is possible to develop a method of generating best bounds on the welfare costs of relative price or tax changes. In particular, Blundell et al. obtain the tightest upper and lower bounds for indifference curves passing through any chosen point in the commodity space. The tightness of these bounds depends on the closeness of the new prices to the sets of previously observed prices and the restrictions placed on cross-price effects. If environmental quality was a marketed good (bad) then the welfare gain from reducing the level of the environmental quality across the income distribution could be measured nonparametrically using this nonparametric revealed preference bounds analysis. Crooker and Kling (2000) outline the use of the Varian bounds approach for this case in the particular 123 A Nonparametric Revealed Preference Approach to Measuring the… 505 situation where observed data are generated under fixed nominal income and a varying price for the environmental good. The more usual case is where the environmental good is not marketed. Typically we also cannot perfectly observe and quantify an environmental good in the same way as a market good; we have some indicators of water quality, say, but that it is a different situation from being able to say the household has consumed a certain number of apples. Suppose first that its level can be measured. In that case we can think of the environmental good as being a special case of a rationed good. Hicks (1940) and Rothbarth (1941) and more recently Neary and Roberts (1980) discuss the question of how to deal with rationed goods in economic problems, and in particular how to price goods when the consumer is free to purchase goods in some markets, but forced to purchase certain levels of other goods in other markets. They show how the properties of demands under these circumstances can be expressed in terms of unrationed demands by allowing free choice over a (...truncated)