Learning from Unknown Information Sources

When an agent receives information generated by a source whose accuracy might either be high or low, standard economic theory dictates that she update as if the source has medium accuracy. In a lab experiment, I find that subjects' updating behaviors deviate from this benchmark. First, subjects under-react to information when the source is uncertain. Second, the under-reaction is more pronounced for good news than for bad news. These two patterns, under-reaction and pessimism, are consistent with a theory of belief updating where agents are insensitive and averse to compound uncertainty and ambiguity. I also find that subjects' reactions to information with uncertain accuracy are uncorrelated with their evaluations of bets with uncertain odds. This suggests that people have distinct attitudes toward uncertainty in information accuracy and uncertainty in economic fundamentals. The experimental results are validated using observational data on stock price reactions to analyst earnings forecasts, where analysts with no forecast records are classified as uncertain information sources.e distinct attitudes toward uncertainty in fundamentals and uncertainty in information accuracy.

[1]  Mohammed Abdellaoui,et al.  The Rich Domain of Uncertainty: Source Functions and Their Experimental Implementation , 2011 .

[2]  I. Gilboa,et al.  Maxmin Expected Utility with Non-Unique Prior , 1989 .

[3]  A. Tversky,et al.  Prospect theory: an analysis of decision under risk — Source link , 2007 .

[4]  Roland G. Fryer,et al.  Updating Beliefs When Evidence Is Open to Interpretation: Implications for Bias and Polarization , 2018, Journal of the European Economic Association.

[5]  R. H. Willis,et al.  Do security analysts improve their performance with experience , 1997 .

[6]  M. Kocher,et al.  Ambiguity aversion is not universal , 2018 .

[7]  David Porter,et al.  Reaction to Public Information in Markets: How Much Does Ambiguity Matter? , 2013 .

[8]  M. Bradshaw,et al.  Analysts’ Forecasts: What Do We Know after Decades of Work? , 2011 .

[9]  Frank Zhang,et al.  Information Uncertainty and Stock Returns , 2004 .

[10]  Ben Greiner,et al.  Subject pool recruitment procedures: organizing experiments with ORSEE , 2015, Journal of the Economic Science Association.

[11]  D. Prelec The Probability Weighting Function , 1998 .

[12]  Justin M. Rao,et al.  The Good News-Bad News Effect: Asymmetric Processing of Objective Information about Yourself , 2011 .

[13]  Cristi A. Gleason,et al.  Analyst Forecast Revisions and Market Price Discovery , 2003 .

[14]  Peter Duersch,et al.  A dynamic Ellsberg urn experiment , 2012, Games Econ. Behav..

[15]  Philippe Jehiel,et al.  Non-Bayesian updating in a social learning experiment , 2018, J. Econ. Theory.

[16]  Martin Schneider,et al.  Recursive multiple-priors , 2003, J. Econ. Theory.

[17]  D. Ellsberg,et al.  Risk, ambiguity, and decision , 2001 .

[18]  M. Bar-Hillel The base-rate fallacy in probability judgments. , 1980 .

[19]  Larry G. Epstein,et al.  Hard-to-Interpret Signals , 2019 .

[20]  Uzi Segal,et al.  Two Stage Lotteries Without the Reduction Axiom , 1990 .

[21]  I. Gilboa,et al.  Advances in Economics and Econometrics: Ambiguity and the Bayesian Paradigm , 2011 .

[22]  A. Tversky,et al.  On the psychology of prediction , 1973 .

[23]  Mohammed Abdellaoui,et al.  Experiments on Compound Risk in Relation to Simple Risk and to Ambiguity , 2015, Manag. Sci..

[24]  Daniel L. Chen,et al.  oTree - An Open-Source Platform for Laboratory, Online, and Field Experiments , 2016 .

[25]  Stefan T. Trautmann,et al.  Sampling experience reverses preferences for ambiguity , 2014 .

[26]  T. Sargent,et al.  Robust Control and Model Uncertainty , 2001 .

[27]  D. Schmeidler Subjective Probability and Expected Utility without Additivity , 1989 .

[28]  Glenn Shafer,et al.  A Mathematical Theory of Evidence , 2020, A Mathematical Theory of Evidence.

[29]  Information Rigidity and the Expectations Formation Process : A Simple Framework and New Facts , 2012 .

[30]  Faruk Gul,et al.  Evaluating Ambiguous Random Variables and Updating by Proxy , 2017 .

[31]  Peter Klibanoff,et al.  Updating Ambiguity Averse Preferences , 2009 .

[32]  Haluk Ergin,et al.  A theory of subjective compound lotteries , 2009, J. Econ. Theory.

[33]  Larry G. Epstein,et al.  Ambiguity, Information Quality and Asset Pricing , 2008 .

[34]  Yaroslav Rosokha,et al.  Learning under compound risk vs. learning under ambiguity – an experiment , 2015, Journal of Risk and Uncertainty.

[35]  Faruk Gul,et al.  EXPECTED UNCERTAIN UTILITY THEORY , 2014 .

[36]  K. Barron Belief updating: does the ‘good-news, bad-news’ asymmetry extend to purely financial domains? , 2020 .

[37]  D. M. Grether,et al.  Bayes Rule as a Descriptive Model: The Representativeness Heuristic , 1980 .

[38]  Earl K. Stice,et al.  Analyst Forecasting Ability and the Stock Price Reaction to Forecast Revisions , 2000 .

[39]  Arthur P. Dempster,et al.  Upper and Lower Probabilities Induced by a Multivalued Mapping , 1967, Classic Works of the Dempster-Shafer Theory of Belief Functions.

[40]  D. Benjamin,et al.  Errors in Probabilistic Reasoning and Judgment Biases , 2018 .

[41]  Massimo Marinacci,et al.  Recursive smooth ambiguity preferences , 2009, J. Econ. Theory.

[42]  A. Tversky,et al.  Preference and belief: Ambiguity and competence in choice under uncertainty , 1991 .

[43]  Alain Chateauneuf,et al.  Choice under uncertainty with the best and worst in mind: Neo-additive capacities , 2007, J. Econ. Theory.

[44]  Marciano M. Siniscalchi,et al.  Ambiguity and Ambiguity Aversion , 2014 .

[45]  Tanya Rosenblat,et al.  Managing Self-Confidence ∗ , 2014 .

[46]  Faruk Gul,et al.  Hurwicz expected utility and subjective sources , 2015, J. Econ. Theory.

[47]  Jonathan Weinstein,et al.  THE AMBIGUITY AVERSION LITERATURE: A CRITICAL ASSESSMENT , 2009, Economics and Philosophy.

[48]  C. Pires A Rule For Updating Ambiguous Beliefs , 2002 .

[49]  Jean-Yves Jaffray Bayesian Updating and Belief Functions , 2008, Classic Works of the Dempster-Shafer Theory of Belief Functions.

[50]  Gideon Keren,et al.  The Wiley Blackwell handbook of judgement and decision making , 2015 .

[51]  Qi Chen,et al.  Investor Learning About Analyst Predictive Ability , 2003 .

[52]  Lawrence D. Brown,et al.  How Important Is Past Analyst Forecast Accuracy? , 2001 .

[53]  J. Eichberger,et al.  Updating Choquet Beliefs , 2007 .

[54]  David S. Ahn Ambiguity without a state space , 2004 .

[55]  Alice Hsiaw,et al.  Distrust in Experts and the Origins of Disagreement , 2016, J. Econ. Theory.

[56]  Massimo Marinacci,et al.  Differentiating ambiguity and ambiguity attitude , 2004, J. Econ. Theory.

[57]  Uzi Segal,et al.  The Ellsberg Paradox and Risk Aversion: An Anticipated Utility Approach , 1987 .

[58]  M. Degroot,et al.  Measuring utility by a single-response sequential method. , 1964, Behavioral science.

[59]  J. Quiggin A theory of anticipated utility , 1982 .

[60]  A. Baillon,et al.  Measuring Ambiguity Attitudes for All (Natural) Events , 2018 .

[61]  Ben Lourie,et al.  Decision Fatigue and Heuristic Analyst Forecasts , 2019, Journal of Financial Economics.

[62]  F. Knight The economic nature of the firm: From Risk, Uncertainty, and Profit , 2009 .

[63]  Jean-Yves Jaffray,et al.  An Experimental Study of Updating Ambiguous Beliefs , 1999, ISIPTA.

[64]  Wojciech Olszewski,et al.  Preferences over Sets of Lotteries , 2006 .

[65]  P. C. O'brien,et al.  Financial Analysts and Their Contribution to Well-Functioning Capital Markets , 2017 .

[66]  Eran Hanany,et al.  Updating Preferences with Multiple Priors , 2006 .

[67]  Sandro Ambuehl,et al.  Belief updating and the demand for information , 2018, Games Econ. Behav..

[68]  M. Kathleen Ngangoué,et al.  Learning under ambiguity: An experiment in gradual information processing , 2021, J. Econ. Theory.

[69]  Stefan T. Trautmann,et al.  Ambiguity Attitudes , 2014 .

[70]  Marciano M. Siniscalchi,et al.  Vector Expected Utility and Attitudes Toward Variation , 2008 .

[71]  Sundaresh Ramnath,et al.  Financial Analysts’ Forecasts and Stock Recommendations: A Review of the Research , 2010 .

[72]  A. Baillon,et al.  Experimental elicitation of ambiguity attitude using the random incentive system , 2015, Experimental Economics.

[73]  Alexander Coutts Good news and bad news are still news: experimental evidence on belief updating , 2019 .

[74]  Chen Li,et al.  The Effect of Learning on Ambiguity Attitudes , 2017, Manag. Sci..

[75]  Itzhak Gilboa,et al.  Updating Ambiguous Beliefs , 1992, TARK.

[76]  M. Marinacci,et al.  A Smooth Model of Decision Making Under Ambiguity , 2003 .

[77]  Yoram Halevy Ellsberg Revisited: An Experimental Study , 2005 .

[78]  Pietro Ortoleva,et al.  Ambiguous information and dilation: An experiment , 2023, J. Econ. Theory.

[79]  O. Mitchell,et al.  Ambiguity Attitudes About Investments: Evidence from the Field , 2019 .

[80]  Zhihua Li,et al.  The Rich Domain of Ambiguity Explored , 2017, Manag. Sci..

[81]  A. Rustichini,et al.  Ambiguity Aversion, Robustness, and the Variational Representation of Preferences , 2006 .

[82]  Eric C. So,et al.  Analysts’ Forecasts and Asset Pricing: A Survey , 2016 .

[83]  Ambiguity Attitudes in a Large Representative Sample , 2015 .

[84]  Gilles Hilary,et al.  Analyst Forecast Consistency , 2012 .

[85]  D. Ellsberg Decision, probability, and utility: Risk, ambiguity, and the Savage axioms , 1961 .

[86]  Massimo Marinacci,et al.  Revealed Ambiguity and Its Consequences: Updating , 2008 .

[87]  Debraj Ray,et al.  LEARNING, ADAPTATION, AND CLIMATE UNCERTAINTY: EVIDENCE FROM INDIAN AGRICULTURE , 2017 .

[88]  Craig R. Fox,et al.  Ambiguity Aversion and Comparative Ignorance , 1995 .