Mislearning from Censored Data: The Gambler's Fallacy and Other Correlational Mistakes in Optimal-Stopping Problems

TL;DR

This paper examines how biased agents with incorrect beliefs about correlations in random sequences learn from censored data in optimal-stopping problems, leading to systematic misestimations and early stopping.

Contribution

It introduces a model of endogenous learning with misperceptions about intertemporal correlations, highlighting the effects of the gambler's fallacy on beliefs and stopping behavior.

Findings

Agents with gambler's fallacy underestimate streak likelihoods.

They develop over-pessimistic beliefs about the mean, stopping prematurely.

Overestimation of variance depends on stopping thresholds.

Abstract

I study endogenous learning dynamics for people who misperceive intertemporal correlations in random sequences. Biased agents face an optimal-stopping problem. They are uncertain about the underlying distribution and learn its parameters from predecessors. Agents stop when early draws are "good enough," so predecessors' experiences contain negative streaks but not positive streaks. When agents wrongly expect systematic reversals (the "gambler's fallacy"), they understate the likelihood of consecutive below-average draws, converge to over-pessimistic beliefs about the distribution's mean, and stop too early. Agents uncertain about the distribution's variance overestimate it to an extent that depends on predecessors' stopping thresholds. I also analyze how other misperceptions of intertemporal correlation interact with endogenous data censoring.