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, Shleifer, and Vishny (1998) (BSV) and for beliefs in the "law of small numbers" as modeled in Rabin (2002). 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, 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.2

Predicting Lotto Numbers

“…From Figure 2 we see that at Streak jt = 1 there are 2% fewer moves toward numbers than at Streak jt = 0, meaning that there are 2% fewer bets on numbers drawn only in the previous week (and not in consecutive weeks) than on numbers not drawn. Our finding is in the same ballpark as the one found in the lab by Asparouhova et al (2009). They find that, on average, players reduce their probability estimate of continuation by approximately 0.9% for each unit increase in streak length for streaks of length up to three.…”

“…The authors argue that people who are prone to the gambler's fallacy but are absolutely certain about the true probability underlying random events will continue to act according to the gambler's fallacy even when observing long streaks. 1 Recently, Asparouhova et al (2009) found support for the prediction that the gambler's fallacy turns into the hot hand fallacy for some players in a laboratory experiment where participants are asked to predict the next observation in a random walk process. The authors also show that people are more likely to exhibit the hot hand fallacy as the perception of randomness of the data-generating process decreases.…”

Can Firms See into the Future? Survey Evidence from Germany

“…The evidence comes from laboratory experiments (Haruvy et al, 2007;Asparouhova et al, 2009;Hommes et al, 2008;Beshears et al, 2013;Frydman and Nave, 2016) and survey data (Tortorice, 2012;Greenwood and Shleifer, 2014;Massenot and Pettinicchi, 2017). We suggest that overextrapolation is pervasive as it also applies to expectations formed by firms and about a variable more familiar than, say, inflation or asset prices.…”

Disentangling Two Causes of Biased Probability Judgment Cognitive Skills and Perception of Randomness

“…Ayton and Fischer (2004) propose that the hot hand fallacy arises from the experience of positive serial correlations in human action sequences, while the gambler's fallacy arises from the experience of negative recency in sequences of natural events. An experimental study by Asparouhova et al (2009) finds support for the Rabin (2002) model that predicts agents to expect short sequence-ending streaks to reverse (gambler's fallacy) but longer streaks to continue (hot hand fallacy). An increase in perceived randomness increases expectations of reversal to the mean of subjects in this study as well.…”