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This article investigates the roles of psychological biases for deviations between subjective survival beliefs (SSBs) and objective survival probabilities. We model these deviations through age-dependent inverse S-shaped probability weighting functions. Our estimates suggest that implied measures for cognitive weakness increase and relative optimism decrease with age. Direct measures of cognitive weakness and optimism share these trends. Our regression analyses confirm that these factors play strong quantitative roles in the formation of SSBs. Our main finding is that cognitive weakness instead of optimism becomes with age an increasingly important contributor to the well-documented overestimation of survival chances in old age.

This paper investigates the roles psychological biases play in empirically estimated deviations between subjective survival beliefs (SSBs) and objective survival probabilities (OSPs). We model deviations between SSBs and OSPs through age-dependent inverse S-shaped probability weighting functions (PWFs), as documented in experimental prospect theory. Our estimates suggest that the implied measures for cognitive weakness, likelihood insensitivity, and those for motivational biases, relative pessimism, increase with age. We document that direct measures of cognitive weakness and motivational attitudes share these trends. Our regression analyses confirm that these factors play strong quantitative roles in the formation of subjective survival beliefs. In particular, cognitive weakness is an increasingly important contributor to the overestimation of survival chances in old age.

On average young people \undersave" whereas old people \oversave" with respect to the rational expectations model of life-cycle consumption and savings. According to numerous studies on subjective survival beliefs, young people also \underestimate" whereas old people \overestimate" their objective survival chances on average. We take a structural behavioral economics approach to jointly address both empirical phenomena by embedding subjective survival beliefs that are consistent with these biases into a rank-dependent utility (RDU) model over life-cycle consumption. The resulting consumption behavior is dynamically inconsistent. Considering both naive and sophisticated RDU agents we show that within this framework underestimation of young age and overestimation of old age survival probabilities may (but need not) give rise to the joint occurrence of undersaving and oversaving. In contrast to this RDU model, the familiar quasi-hyperbolic discounting (QHD), which is nested as a special case, cannot generate oversaving.

On average, "young" people underestimate whereas "old" people overestimate their chances to survive into the future. We adopt a Bayesian learning model of ambiguous survival beliefs which replicates these patterns. The model is embedded within a non-expected utility model of life-cycle consumption and saving. Our analysis shows that agents with ambiguous survival beliefs (i) save less than originally planned, (ii) exhibit undersaving at younger ages, and (iii) hold larger amounts of assets in old age than their rational expectations counterparts who correctly assess their survival probabilities. Our ambiguity-driven model therefore simultaneously accounts for three important empirical findings on household saving behavior.

Based on a cognitive notion of neo-additive capacities reflecting likelihood insensitivity with respect to survival chances, we construct a Choquet Bayesian learning model over the life-cycle that generates a motivational notion of neo-additive survival beliefs expressing ambiguity attitudes. We embed these neo-additive survival beliefs as decision weights in a Choquet expected utility life-cycle consumption model and calibrate it with data on subjective survival beliefs from the Health and Retirement Study. Our quantitative analysis shows that agents with calibrated neo-additive survival beliefs (i) save less than originally planned, (ii) exhibit undersaving at younger ages, and (iii) hold larger amounts of assets in old age than their rational expectations counterparts who correctly assess their survival chances. Our neo-additive life-cycle model can therefore simultaneously accommodate three important empirical findings on household saving behavior.

This paper studies discrete time finite horizon life-cycle models with arbitrary discount functions and iso-elastic per period power utility with concavity parameter θ. We distinguish between the savings behavior of a sophisticated versus a naive agent. Although both agent types have identical preferences, they solve different utility maximization problems whenever the model is dynamically inconsistent. Pollak (1968) shows that the savings behavior of both agent types is nevertheless identical for logarithmic utility (θ = 1). We generalize this result by showing that the sophisticated agent saves in every period a greater fraction of her wealth than the naive agent if and only if θ ≥ 1. While this result goes through for model extensions that preserve linearity of the consumption policy function, it breaks down for non-linear model extensions.

We consider an additively time-separable life-cycle model for the family of power period utility functions u such that u0(c) = c−θ for resistance to inter-temporal substitution of θ > 0. The utility maximization problem over life-time consumption is dynamically inconsistent for almost all specifications of effective discount factors. Pollak (1968) shows that the savings behavior of a sophisticated agent and her naive counterpart is always identical for a logarithmic utility function (i.e., for θ = 1). As an extension of Pollak’s result we show that the sophisticated agent saves a greater (smaller) fraction of her wealth in every period than her naive counterpart whenever θ > 1 (θ < 1) irrespective of the specification of discount factors. We further show that this finding extends to an environment with risky returns and dynamically inconsistent Epstein-Zin-Weil preferences.