Scale factors and hypothetical referenda: A clarifying note

In this note we explore in detail the importance of, and problems associated with, correcting for variance differences between data sets obtained from hypothetical and real referenda. We show that a previous discussion in the literature rests on a problematic estimation of the relative scale factor. The implications are illustrated with data from Cummings et al. (1997) [5], as well as with simulated data. Moreover, we propose a concrete methodology for how to analyze cases where it is difficult, or even impossible, to estimate the relative scale factor due to informational limitations, such as when there is no variation of the bid. We conclude that it is valuable to be able to separate behavioral differences into variance differences and parameter differences in the underlying objective function. Yet, we argue that when using the results to interpret the results of other hypothetical referenda, it is sometimes the net effect, i.e., without correction for scale differences, that matters.