Using structural restrictions to achieve theoretical consistency in benefit transfers

Analysts often extrapolate estimates of the value of environmental improvements reported in prior studies to evaluate new policy proposals, a practice sometimes referred to as "benefit transfer." Benefit transfer functions are frequently specified based on statistical considerations alone. However, such a purely statistical approach can lead to willingness-to-pay functions that fail to satisfy some aspects of theoretical consistency that may be especially important for policy evaluations. In this paper, we examine several previous meta-analyses of nonmarket valuation studies in light of the adding-up condition, which is one important aspect of theoretical validity. We then use meta-regression to estimate a new willingness-to-pay function for surface water quality improvements intended to be used for benefit transfers. We estimate the meta-regression model using summary results from 51 previously published stated preference studies. An important feature of our approach is that we develop the meta-regression estimating equation to ensure that the resulting benefit transfer function will necessarily comply with the adding-up condition. This is achieved by first specifying a marginal willingness-to-pay function and then deriving an expression for total willingness-to-pay. This leads to a non-linear estimating equation, so we estimate the parameters of the model using non-linear least squares. We discuss the advantages and disadvantages of our approach relative to other structural approaches, and we compare our empirical results to a more traditional nonstructural meta-regression model. Finally, we examine the quantitative importance of imposing the adding-up condition in our case study by performing some illustrative calculations of willingness-to-pay for hypothetical water quality improvements using both structural and non-structural models.