Determining the Optimal Sample Size for Contingent Valuation Surveys

Abstract

Fundamentally, this paper is about the value of information. Whenever a cost-benefit analysis has to be undertaken using benefits that are estimated from household survey data the size of the survey sample must be specified. The most obvious case in the valuation of environmental amenity improvements through contingent valuation (CV) surveys of willingness to pay. One of the first questions that has to be answered in the survey design process is "How many subjects should be interviewed?" The answer can have significant implications for the cost of project preparation. Traditionally, the sample size question has been answered in an ad hoc way either be dividing an exogenously fixed survey budget by the cost per interview or employing some variant of a standard statistical tolerance interval formula. Neither of these approaches can balance the gains to additional sampling effort against the extra interviewing costs. A better answer if not to be found in the environmental economics literature, though it can be developed by adapting a Bayesian decision analysis approach from business statistics. The paper explains and illustrates, with a worked example, the rationale for and mechanics of a sequential Bayesian optimization technique, which is applicable when there is some monetary payoff to alternative courses of action that can be linked to the sample data. In this sense, unlike pure valuation studies that are unconnected to a policy decision, investigators who use contingent valuation results directly in cost-benefit analysis have a hidden advantage that can be exploited to optimize the sample size. The advantage lies in the link between willingness to pay and the decision variable, the net present value of the prospective investment. The core objective of the paper is practical. Readers without a statistical background can easily implement the method. An Appendix shows how, with just six key pieces of information, anyone can solve the optimal sample size problem in a spreadsheet. An automated spreadsheet algorithm is available from the authors on request. To run the program all the users has to do is enter the key data and then activate a macro that automatically computes the optimum number of additional observations needed to augment any initial "small" survey sample.