Inference from Streaks in Random Outcomes: Experimental Evidence on Beliefs in Regime Shifting and the Law of Small Numbers

Abstract

Using data generated from laboratory experiments, we test and compare the empirical accuracy of two models that focus on judgment errors associated with processing information from random sequences. We test for regime-shifting beliefs of the type theorized in Barberis et al. (Barberis, N., A. Shleifer, R. Vishny. 1998. A model of investor sentiment. J. Financial Econom. 49(3) 307–343) and for beliefs in the “law of small numbers” as modeled in Rabin (Rabin, M. 2002. Inference by believers in the law of small numbers. Quart. J. Econom. 117(3) 775–816). In our experiments, we show subjects randomly generated sequences of binary outcomes and ask them to provide probability assessments of the direction of the next outcome. Inconsistent with regime-shifting beliefs, we find that subjects are not more likely to predict that the current streak will continue the longer the streak. Instead, consistent with Rabin (2002), subjects are more likely to expect a reversal following short streaks and continuation after long streaks. Results of a “test-of-fit” analysis based on structural estimation of each model also favor the model in Rabin. To provide more insight on Rabin, we use an additional experimental treatment to show that as the perception of the randomness of the outcome-generating process increases, subjects are more likely to predict reversals of current streaks.