Rejoinder---Temporal Stochastic Inflation in Choice-Based Research
Marketing Science
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The implications of Salisbury and Feinberg's (2010) paper [Salisbury, L. C., F. M. Feinberg. 2010. Alleviating the constant stochastic variance assumption in decision research: Theory, measurement, and experimental test. Marketing Sci.29(1) 1--17] for the process of model development and testing in the field of intertemporal choice analysis is explored. Although supporting the overall thrust of Salisbury and Feinberg's critique of previous empirical work in the area, we also see their paper as illustrating the dangers of drawing strong inferences about the behavioral interpretation of statistical model parameters without seeking convergent empirical evidence. In particular, we are skeptical about the extent to which the reported effects of temporal distance on the estimated scale parameter, σc, are uniquely, or even primarily, due to unobserved error inflation that reflects consumer's uncertainty about future utility. This interpretation is brought into question by several lines of reasoning. Conceptually, we note that “uncertainty” is different from “error” and that, for choice data, the error inflation model is mathematically identical to a model in which the scale parameter is a deterministic function of the temporal discount rate. Empirically, a reanalysis of data from previously published experiments does not consistently support temporal error inflation, temporal convergence of choice shares, or the scale parameter as an explanation of variety seeking in choice sequences. In our opinion, the cumulative results of research on intertemporal choice require models in which the attributes of choice alternatives are differentially discounted over time. Despite these findings, we advocate that choice researchers should indeed follow Salisbury and Feinberg's advice to not assume that error variances will be unaffected by experimental manipulations, and such effects should be explicitly modeled. We also agree that uncovering effects on error variance is just the first step, and the ultimate goal should be to rigorously explain the reasons for such effects.