Jawwad Noor

Non-Bayesian Learning

A series of experiments suggest that, compared to the Bayesian benchmark, people may either underreact or overreact to new information. We consider a setting where agents repeatedly process new data. Our main result shows a basic distinction between the long-run beliefs of agents who underreact to information and agents who overreact to information. Like Bayesian learners, non-Bayesian updaters who underreact to observations eventually forecast accurately. Hence, underreaction may be a transient phenomenon. Non-Bayesian updaters who overreact to observations eventually forecast accurately with positive probability but may also, with positive probability, converge to incorrect forecasts. Hence, overreaction may have long-run consequences.

Uphill self-control

This paper extends the theory of temptation and self-control introduced by Gul and Pesendorfer (2001) to allow for increasing marginal costs of resisting temptation, that is, convex self-control costs. It also proves a representation theorem that admits a general class of self-control cost functions. Both models maintain the Order, Continuity, and Set Betweenness axioms but violate Independence.

Intertemporal choice and the magnitude effect

A robust finding in experiments on time preference is the magnitude effect: subjects tend to be more patient towards larger rewards. Using a calibration theorem, we argue against standard curvature-based explanations for the finding. We axiomatize a model of preferences over dated rewards that generalizes the standard exponential discounting model by permitting the discount factor to depend on the reward being discounted. The model is shown to behaviorally subsume the hyperbolic discounting model as a special case. When embedded in a sequential bargaining game the model gives rise to multiple stationary subgame perfect equilibria. There may exist equilibria in which the first mover gets a smaller share despite also being the more patient player.

Decreasing impatience and the magnitude effect jointly contradict exponential discounting

The experimental literature on time preference finds that the manner in which subjects discount money (as opposed to utility) exhibits properties known as Decreasing Impatience and the Magnitude Effect. While these findings are often referred to as anomalies for the Exponential Discounting model, several authors have demonstrated that each of these qualitative findings can be explained by the curvature of utility and thus are not anomalies. We prove that, under basic regularity conditions, the two findings jointly imply the existence of Preference Reversals, and thus jointly contradict the Exponential Discounting model.

Supplemental Appendix for 'Non-Bayesian Updating: A Theoretical Framework'

This appendix applies the model in ”Non-Bayesian Updating: A Theoretical Frame-Work” to address the question: What do non-Bayesian updaters learn?

Compensated Discount Functions: An Experiment on the Influence of Expected Income on Time Preferences

This paper examines the empirical question of whether subjects? static choices among rewards received at different times are influenced by their expected income levels at those times. Moreover, we recover time preferences after compensating for possible income effects. Besides eliciting subjects? preference between standard delayed rewards, the experimental design also elicited their preferences over delayed rewards that are received only if the subject?s income remains approximately constant. These preferences, along with elicited subjective probabilities of satisfying the condition, make the correction possible. We conducted the experiments in Iceland, where our prompt access to income tax records enabled us to condition delayed rewards on income realizations. We find that background income is associated with preferences over unconditional delayed rewards. While most people exhibited present bias when comparing unconditional delayed rewards, subjects with stable income did not. The results are similar for the entire sample once we correct subjects? discount functions for income effects. This suggests that income expectations have an effect on choices between future rewards, and that this may account for some of the present-bias observed in experiments.