The scope test revisited

Abstract

Sensitivity to scope has become an acid test for the validity of responses to non-market valuation scenarios. The theoretical relationship between whether a subject's responses exhibit sensitivity to scope and whether consistent preferences underlie those responses is examined. It is found that sensitivity to scope is neither necessary nor sufficient for preference consistency. Moreover, while continuous, strongly monotonic and total preferences yield scope, the converse fails to hold. The results suggest caution in scope's application as a survey validation tool.

Acknowledgements

The authors thank Glenn Harrison and Jorge Martinez for helpful comments, James Andreoni and Jim Miller for access to their data and Georgia State University and Western Carolina University for grant support.

Notes

 Formal definitions are given in Section III.

 For empirical purposes, responses are deemed to satisfy scope if values differ across different quantitative or qualitative levels of a good. For instance, the split sample scope test asks separate population groups to value differently-sized changes of a good. Imposing the representative consumer assumption, the analyst pools subjects’ responses and estimates a willingness-to-pay (WTP) function. The test is considered satisfied if the coefficient of the quantity (or quality) variable is positive and significant (Carson, 1995).

 Assuming away measurement issues, such preferences yield responses which empirically fail scope when the initial level of the good in question is large (and consequently, the marginal utility of an increase is small) and the sample size is inadequate.

 Respondents who check no … indicate [e] that they would vote not even if it cost their household nothing to create the new park …’ (Rollins and Lyke, 1998, p. 341).

 Twenty-three subjects satisfied both monotonicity and consistency; two failed both; six satisfied consistency but not monotonicity; three satisfied monotonicity, but were inconsistent. A one-tailed Chi-squared test fails to reject the null that subjects with monotonic choice are as or less likely to be consistent than non-monotonic ones at the 0.1 level of significance.

Consistent, non-monotonic choice was most frequently associated with the decision-maker receiving a minority of the overall gains her decisions yielded; consequently, Andreoni and Miller termed the underlying preference as ‘jealous’ ones. In the context of environmental valuation such sentiments could be expressed as, ‘Yes, I’d like to see more South American rainforest preserved, but why should I pay for it? Shouldn’t the locals pitch in?’.

 Note that this counterexample is monotonic (Definition 2.1), but not strongly monotonic (Definition 2.2).

 Note that reflexivity and transitivity, the two other properties required for regularity, are not needed.

 If the analyst's expectations include consistency and diminishing marginal WTP, then reflexivity, transitivity and strict convexity (guaranteeing a strictly diminishing marginal rate of substitution) would also be required.