PROCEDURAL INVARIANCE TESTING OF THE ONE-AND-ONE- HALF-BOUND DICHOTOMOUS CHOICE ELICITATION METHOD Ian J. Bateman, Brett H. Day, Diane P. Dupont, and Stavros Georgiou* Abstract—The contingent valuation method for estimating willingness to pay for public goods typically adopts a single referendum question format, which is relatively statistically inefficient. As an alternative, Cooper, Hanemann, and Signorello (2002) propose the one-and-one-half bound (OOHB) format, allowing researchers to question respondents about both a lower and higher limit on project costs, thereby securing substantial gains in statistical efficiency. Using an experimental design, we find that responses to OOHB valuation questions fail crucial tests of procedural invariance. We test various competing models of observed response patterns including strategic misrepresentation of standard preferences and nonstandard models of preference formation. I. Introduction M ORE than fifty years ago, Ciriacy-Wantrup (1947, 1952) suggested that “appropriately constructed in- terviews” may be capable of obtaining information about people’s preferences for goods not ordinarily priced in the market. Since then, the contingent valuation (CV) method has become the most widely used approach for obtaining willingness to pay (WTP) values for an assortment of environmental and other nonmarket public goods (Carson, 2007). However, the issue of how WTP questions should be phrased and responses elicited has been and remains one of the most consistent themes in CV research (Cummings, Brookshire, & Schulze, 1986; Mitchell & Carson, 1989; Arrow et al., 1993; Bateman et al., 1995, 2002). An ideal WTP elicitation method would have three de- fining characteristics: (a) incentive compatibility, such that the dominant strategy for survey respondents is the truthful revelation of their WTP; (b) procedural invariance, such that respondents’ expressions of WTP are invariant to changes in decision-irrelevant features of the elicitation procedure; and (c) statistical efficiency, such that respondents provide suf- ficient information regarding their WTP to enable its accu- rate estimation. It was the issue of incentive compatibility that dominated the landmark NOAA blue-ribbon panel report on CV (Ar- row et al., 1993) and guided its endorsement of the single- bound (SB) dichotomous choice elicitation technique. Un- der the SB approach, each survey respondent is presented with a single referendum-style question asking whether he or she would endorse a project providing a public good if that project were to cost a specified sum, $ X. Varying this bid amount across respondents allows the analyst to esti- mate decision-relevant characteristics of the WTP distribu- tion. Strategic behavior arguments suggest that the dichot- omous nature of SB responses makes the approach incentive compatible (Gibbard, 1973; Satterthwaite, 1975; Carson & Groves, 2007). However, it is statistically inefficient, deter- mining only whether a respondent’s WTP lies above or below the bid amount. Hanemann, Loomis and Kanninen (1991) propose a so- lution to the inefficiency of the SB format in the form of their double-bound (DB) elicitation method. Here, follow- ing an initial binary choice question, a second bid amount is offered as a follow-up question. The elicitation of a second binary choice response yields substantial gains in terms of statistical efficiency. 1 Subsequent empirical testing, how- ever, has revealed that DB respondents are significantly less likely to accept a given bid amount when that amount is presented in the follow-up (as compared to initial) question (McFadden, 1994; Cameron & Quiggen, 1994; Herriges & Shogren, 1996; Alberini, Kanninen, & Carson, 1997; Bate- man et al., 2001; DeShazo, 2002; Carson et al., 2003). This difference in acceptance rates violates a fundamental re- quirement for procedural invariance, constituting a major problem for the DB method. Cooper, Hanemann, and Signorello (2002; hereafter CHS) conjecture that the inconsistency in acceptance rates arises when respondents react adversely to the surprise of the unanticipated follow-up question. They suggest that “eliminating the element of surprise has the potential to remove discrepancies in the responses to the two valuation questions” (p. 742). To that end, they propose the one-and- one-half-bound (OOHB) elicitation format. Here, survey respondents are initially informed that the cost of the good in question lies between some lower and some higher amount (which we shall denote $ L and $ H respectively). This simultaneous presentation of two cost levels is in- tended to avoid the surprise induced by an unanticipated follow-up question. CHS employ a prior random process to assign respondents to either an ascending or descending presentation sequence. In an ascending sequence, survey respondents are initially asked whether they would vote in favor of a project that would provide the public good at the Received for publication May 13, 2004. Revision accepted for publica- tion April 2, 2008. *Centre for Social and Economic Research on the Global Environment (Bateman and Day); Brock University, Canada (Dupont); and Economic Analysis Unit, Health and Safety Executive, London (Georgiou). Funding for this research was provided by the ChREAM project, which is funded by the ESRC and other research councils under the RELU project (RES-227-25-0024) and the Economics for the Environment Consultancy. We thank Graham Loomes and the participants at Heartland Conference, University of Iowa, September 2003; Envecon 2004, Royal Society, London, March 2004; the Thirteenth Annual Conference of the European Association of Environmental and Resource Economists, BUESPA, Budapest, June 2004; and three anonymous referees for their very helpful comments. We also thank Nuno Matias and Loga Subrama- nian for assistance in collecting data. Ian Bateman is also adjunct profes- sor in the Department of Agricultural and Resource Economics at the University of Western Australia, Perth, and the Department of Economics, Waikato University, New Zealand, and is grateful to Lincoln University, New Zealand, for hosting him while this paper was completed. 1 These gains may be extended through the addition of further bounds (Langford, Bateman, & Langford, 1996; Scarpa & Bateman, 2000). The Review of Economics and Statistics, November 2009, 91(4): 806–820 © 2009 by the President and Fellows of Harvard College and the Massachusetts Institute of Technology