Correlation Neglect in Belief Formation Benjamin Enke Florian Zimmermann Bonn Graduate School of Economics University of Zurich NYU Bounded Rationality in Choice Conference May 31, 2015 Benjamin Enke (Bonn) Correlation Neglect in Belief Formation NYU BRIC 1 / 26
Motivation Many natural information structures generate correlated rather than mutually independent signals News media: press agencies, well-known journalists Social networks: well-connected people Akerlof / Shiller (2009) have argued that the resulting telling and re-telling of stories leads people to overract to information and hence generates aggregate booms or busts Benjamin Enke (Bonn) Correlation Neglect in Belief Formation NYU BRIC 2 / 26
Motivation So how do people process correlated information when the data-generating process is transparent and known? If they neglect correlations,...... do they learn from others through market interaction?... what are the cognitive underpinnings of such a bias? Benjamin Enke (Bonn) Correlation Neglect in Belief Formation NYU BRIC 3 / 26
We show A considerable fraction of people neglects correlations in an individual decision-making task The cognitive error generates pronounced and predictable price distortions in an experimental asset market Correlation neglect has its cognitive roots in selective attention, so that exogenous shifts in subjects focus have large effects on beliefs Benjamin Enke (Bonn) Correlation Neglect in Belief Formation NYU BRIC 4 / 26
Outline 1 Individual Decision-Making Experiments 2 Market Experiments 3 The Sources of Correlation Neglect Benjamin Enke (Bonn) Correlation Neglect in Belief Formation NYU BRIC 5 / 26
Outline 1 Individual Decision-Making Experiments 2 Market Experiments 3 The Sources of Correlation Neglect Benjamin Enke (Bonn) Correlation Neglect in Belief Formation NYU BRIC 6 / 26
Experimental setup Subjects are asked to estimate hypothetical continuous true state Payment via precision (quadratic scoring rule) 10 independent tasks Key idea of between-subjects design: Construct two sets of signals (one with and one without a known and simple correlation), which result in the same Bayesian posterior Benjamin Enke (Bonn) Correlation Neglect in Belief Formation NYU BRIC 7 / 26
Experimental setup Computer D Intermediary 3 Computer D Intermediary 3 Computer C Intermediary 2 Computer C Intermediary 2 Computer B Intermediary 1 Computer B Intermediary 1 Computer A Subject Computer A Subject Figure : Uncorrelated (left panel) and correlated (right panel) information structure Computers A-D generate four unbiased iid signals about state (drawn from truncated normal) For example, in one task: true state=10, signals A-D=12, 9, 10, 0 Benjamin Enke (Bonn) Correlation Neglect in Belief Formation NYU BRIC 8 / 26
Experimental setup Extensive instructions and control questions Robustness check to ensure that results are robust to slight variations in experimental frame, information structure, and payment method Experiments conducted in BonnEconLab, 94 subjects, average earnings $15 Benjamin Enke (Bonn) Correlation Neglect in Belief Formation NYU BRIC 9 / 26
Results Individual Decision-Making In 9 out of 10 tasks, beliefs significantly differ in the direction predicted by correlation neglect at 5% (Wilcoxon ranksum test) Does not depend on magnitude of true state (10 vs. 46,422) Significant difference in earnings across treatments ( $3.50) Clear patterns in subjects responses allow estimation of naïveté types : 0 = Bayesian, 1 = Full correlation neglect Benjamin Enke (Bonn) Correlation Neglect in Belief Formation NYU BRIC 10 / 26
Results Individual Decision-Making Density 0.5 1 1.5 -.5 0.5 1 1.5 2 Median naïveté parameter Correlated treatment Uncorrelated treatment kernel = epanechnikov, bandwidth = 0.1500 Figure : Kernel density estimates of median naïveté parameters Similar picture emerges when estimating subjects updating rules through finite mixture model Benjamin Enke (Bonn) Correlation Neglect in Belief Formation NYU BRIC 11 / 26
Outline 1 Individual Decision-Making Experiments 2 Market Experiments 3 The Sources of Correlation Neglect Benjamin Enke (Bonn) Correlation Neglect in Belief Formation NYU BRIC 12 / 26
Market experiments experimental setup Incorporate belief elicitation task into standard continuous double auction with uncertainty over value of the assets; value equals true state from individual-level design Four buyers obtain monetary endowment, four sellers four assets each Identical signals for each subject; everybody received either correlated or uncorrelated information 10 trading periods, full reset after each period 288 subjects, average earnings $25 Note that magnitude of signal A relative to the other signals predicts direction of price distortion Benjamin Enke (Bonn) Correlation Neglect in Belief Formation NYU BRIC 13 / 26
Results Market Across periods / true states, prices are significantly distorted away from the Bayesian benchmark In 9 out of 10 periods, prices significantly differ across treatments at 5% (Wilcoxon ranksum test) Again, data relatively clean: Price trajectory closely tracks correlation neglect prediction Benjamin Enke (Bonn) Correlation Neglect in Belief Formation NYU BRIC 14 / 26
Results Market Ordering of rounds # 2-1 -.5 0.5 1 1 2 3 4 5 6 7 8 9 10 Trading period Bayes Correlated minus uncorrelated treatment Correlation neglect Figure : Difference between median normalized market prices in the correlated and uncorrelated treatments across trading rounds Benjamin Enke (Bonn) Correlation Neglect in Belief Formation NYU BRIC 15 / 26
Results Market We measured individual-level beliefs, which allows us to identify who is naïve / sophisticated This naïveté parameter predicts what it should predict, both across markets and across individuals within markets... Benjamin Enke (Bonn) Correlation Neglect in Belief Formation NYU BRIC 16 / 26
Results Market Table : Determinants of prices, asset holdings, and profits in the correlated market treatment Group-level median 1.00 0.95 correlation neglect (χ) (0.16) (0.20) Dependent variable: Normalized Median asset holdings Median asset holdings Median market price if underpricing if overpricing profit (1) (2) (3) (4) (5) (6) (7) (8) Individual median -1.53-1.30 0.64 0.26-0.12-0.11 correlation neglect (χ) (0.17) (0.19) (0.12) (0.14) (0.05) (0.05) Constant -0.089-0.95 2.85 2.37 1.43 4.04 10.1 10.2 (0.12) (1.04) (0.12) (0.94) (0.14) (1.31) (0.03) (0.28) Additional controls No Yes No Yes No Yes No Yes Observations 167 167 143 143 143 143 143 143 R 2 0.17 0.31 0.31 0.42 0.20 0.43 0.04 0.13 OLS estimates, standard errors clustered at the market group level. p < 0.10, p < 0.05, p < 0.01 Benjamin Enke (Bonn) Correlation Neglect in Belief Formation NYU BRIC 17 / 26
Outline 1 Individual Decision-Making Experiments 2 Market Experiments 3 The Sources of Correlation Neglect Benjamin Enke (Bonn) Correlation Neglect in Belief Formation NYU BRIC 18 / 26
Potential Mechanisms Clearly, there is some bounded rationality happening But what exactly is it, i.e., what are the cognitive mechanisms underlying correlation neglect? Important to know not just to de-bias people, but also to develop an empirical understanding of the potential ingredients (micro-foundations) of a general theory of boundedly rational updating Benjamin Enke (Bonn) Correlation Neglect in Belief Formation NYU BRIC 19 / 26
Potential Mechanisms 1 Conceptual or mathematical problems: Why would double-counting introduce a bias? How can I invert the messages in any case? 2 Cognitive effort costs: I could do it, but the stakes are too low. 3 Face value bias: This is not about correlations per se: Regardless of which feature distorts the signal, I m overwhelmed by the complexity and simply take the average of whatever I see. 4 Selective Attention: There s a lot going on in this problem. I m thinking about the information structure, but which feature do I actually need to focus on? In total, 11 treatments with almost 500 subjects Benjamin Enke (Bonn) Correlation Neglect in Belief Formation NYU BRIC 20 / 26
Conceptual or Mathematical Problems Computer B Computer B Intermediary Intermediary Computer A Subject Computer A Subject Figure : Simple uncorrelated (left panel) and correlated (right panel) information structure Requires the same conceptual understanding of double-counting, but virtually everybody gets it right When we explicitly ask people to invert the messages, almost everybody can do it Conceptual or mathematical problems do not drive correlation neglect Benjamin Enke (Bonn) Correlation Neglect in Belief Formation NYU BRIC 21 / 26
Cognitive Effort Costs We triple the stake size (maximum variable earnings $40) Effort as proxied for by response times goes up by 25%...... but subjects beliefs are unaffected Suggests that subjects try harder, but do not reflect upon their problem-solving strategy Benjamin Enke (Bonn) Correlation Neglect in Belief Formation NYU BRIC 22 / 26
Face Value Bias If subjects take all information at face value, they should also make mistakes in settings in which the signals are distorted by an external source, rather than through the interdependence of multiple signals Treatment 1: Independent signals get multiplied by 1.5 Treatment 2: Add known constant to correlated messages In both treatments, subjects un-do the external distortions, showing that the bias is indeed about correlations per se Treatment Multiply Treatment Face value Benjamin Enke (Bonn) Correlation Neglect in Belief Formation NYU BRIC 23 / 26
Selective Attention If subjects intuitively focus too little on the mechanics generating the correlation, they should perform significantly better when we (exogenously) shift their attention towards the correlation Treatment 1: We presented the correlated and uncorrelated information structure alternately (within subject) Treatment 2: Think carefully about what the intermediaries do! What does that imply for the estimates of the intermediaries? Benjamin Enke (Bonn) Correlation Neglect in Belief Formation NYU BRIC 24 / 26
Selective Attention Density 0.4.8 1.2 1.6 Treatment Alternating Density 0.4.8 1.2 1.6 Treatment Intermediaries -1 0 1 2 Median normalized belief Correlated Uncorrelated Alternating kernel = epanechnikov, bandwidth = 0.1500-1 0 1 2 Median normalized belief Correlated Uncorrelated Intermediaries kernel = epanechnikov, bandwidth = 0.1500 Beliefs significantly differ from correlated treatment, indistinguishable from uncorrelated condition Once subjects allocate their attention to the critical feature of the environment at hand, they correctly solve the problem Benjamin Enke (Bonn) Correlation Neglect in Belief Formation NYU BRIC 25 / 26
Conclusion and Relation to Literature Clean evidence for people s neglect of correlations in information sources Support for key assumption underlying naïve social learning theories (e.g., DeMarzo et al., 2003; Eyster and Rabin, 2010) or applications in political economy (Levy and Razin, 2015; Ortoleva and Snowberg, 2015) Bias persists in simple experimental market and generates predictable price distortions Findings regarding sources of correlation neglect highlight importance of attentional mechanisms in supplying selective inputs into belief formation process Conceptually related to recent efforts to model the mental process of belief formation through selective attention (Gennaioli and Shleifer, 2010; Bordalo et al., 2014; Schwartzstein, 2014) Benjamin Enke (Bonn) Correlation Neglect in Belief Formation NYU BRIC 26 / 26
Treatment Multiply Computer D Computer C Computer B Intermediary 3 Intermediary 2 Intermediary 1 Computer A Subject Figure : Treatment Multiply. The intermediaries multiply the reports of the intermediaries with 1.5. Back Benjamin Enke (Bonn) Correlation Neglect in Belief Formation NYU BRIC 27 / 26
Treatment Face value Computer D Intermediary 3 Machine 3 Computer C Intermediary 2 Machine 2 Computer B Intermediary 1 Machine 1 Computer A Subject Figure : Treatment Face value. The machines add X to the reports of the intermediaries. Back Benjamin Enke (Bonn) Correlation Neglect in Belief Formation NYU BRIC 28 / 26