The Robustness and Pervasiveness of Sub-Additivity in Intertemporal Choice

A large literature has used choice experiments involving time-dated monetary rewards, to test whether time discounting is exponential or hyperbolic, with mixed results. One explanation, proposed by the psychologist Daniel Read (2001), is that the observed choice patterns reflect a type of framing effect, known as sub-additivity, rather than hyperbolic or exponential discounting. An alternative explanation, however, has emerged from a recent literature in economics, which points out various confounds that might affect the traditional intertemporal choice experiment, as well as challenges of inference from typically small or idiosyncratic samples. This paper makes two main contributions: (1) It re-visits the sub-additivity hypothesis, but using a design that addresses the key methodological confounds; (2) it uses large representative samples, to assess the pervasiveness and importance of anomalous choice patterns like sub-additivity. The analysis finds intertemporal choices that are consistent with sub-additivity, and rules out explanations based on confounds. Furthermore, subadditivity is pervasive, being observed across all sub-populations studied in the analysis, and constituting the majority choice pattern at the individual level. The results underline that sub-additivity is an important feature of intertemporal choice, they raise caveats about how intertemporal choice experimens have often been interpreted, and they suggest some directions for methodological improvements.