Mislearning from Censored Data: The Gambler's Fallacy and Other Correlational Mistakes in Optimal-Stopping Problems
For economists and behavioral scientists, the paper identifies a novel mechanism by which cognitive biases distort learning from endogenous data censoring in sequential decision-making.
The paper studies how biased agents who misperceive intertemporal correlations (e.g., gambler's fallacy) in optimal-stopping problems learn from censored data, leading to over-pessimistic beliefs and early stopping. It shows that such agents underestimate streak probabilities, converge to incorrect distribution parameters, and that the bias magnitude depends on predecessors' thresholds.
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.