Competing Models

We develop a model in which different agents compete to predict a variable of interest. This variable is related to observables via an unknown data generating process. All agents are Bayesian, but may have `misspecified models' of the world, i.e., they consider different subsets of observables to make their prediction. After observing a common dataset, who has the highest confidence in her predictive ability? We characterize it and show that it crucially depends on the size of the dataset. With big data, we show it is typically `large-dimensional,' possibly using more variables than the true model. With small data, we show (under additional assumptions) that it is an agent using a model that is `small-dimensional,' in the sense of considering fewer covariates than the true data generating process. The theory is applied to auctions of assets where bidders observe the same information but hold different priors.

[1]  Dennis J. Moberg,et al.  The Ethics of Organizational Politics , 1981 .

[2]  Ran Spieglery.  The Market for Quacks , 2005 .

[3]  J. Shaver.  Testing for Mediating Variables in Management Research: Concerns, Implications, and Alternative Strategies , 2005 .

[4]  J. Poon,et al.  Situational antecedents and outcomes of organizational politics perceptions , 2003 .

[5]  Stephen Morris,et al.  TRADE WITH HETEROGENEOUS PRIOR BELIEFS AND ASYMMETRIC INFORMATION , 1994 .

[6]  Van Der Vaart,et al.  UvA-DARE ( Digital Academic Repository ) The Bernstein-Von-Mises theorem under misspecification , 2012 .

[7]  R. L. Dipboye,et al.  Multi-level theorizing about perceptions of organizational politics , 2002 .

[8]  Mohammed Saqib,et al.  Quality Minus Junk , 2014 .

[9]  Amos Drory,et al.  Perceived Political Climate and Job Attitudes , 1993 .

[10]  T. S. Bateman,et al.  Job Satisfaction and the Good Soldier: The Relationship Between Affect and Employee “Citizenship” , 1983 .

[11]  Elizabeth Wolfe Morrison,et al.  Role Definitions and Organizational Citizenship Behavior: The Importance of the Employee's Perspective , 1994 .

[12]  Ken Parry,et al.  Leadership, culture and performance: The case of the New Zealand public sector , 2002 .

[13]  Lu Zhang,et al.  Digesting Anomalies: An Investment Approach , 2012 .

[14]  E. Fama,et al.  Risk, Return, and Equilibrium: Empirical Tests , 1973, Journal of Political Economy.

[15]  Michael J. Kofler,et al.  Do programs designed to train working memory, other executive functions, and attention benefit children with ADHD? A meta-analytic review of cognitive, academic, and behavioral outcomes. , 2013, Clinical psychology review.

[16]  David R. Anderson,et al.  Model selection and multimodel inference : a practical information-theoretic approach , 2003 .

[17]  R. Hackett,et al.  Leader-Member Exchange as a Mediator of the Relationship Between Transformational Leadership and Followers' Performance and Organizational Citizenship Behavior , 2005 .

[18]  Alan J. Dubinsky,et al.  Transformational leadership theory: Using levels of analysis to determine boundary conditions. , 1994 .

[19]  Hülya Eraslan,et al.  Information-Based Trade , 2007, J. Econ. Theory.

[20]  P. Perrewé,et al.  Do Politics Perceptions Relate to Political Behaviors? Tests of an Implicit Assumption and Expanded Model , 2000 .

[21]  Yuval Salant,et al.  Statistical Inference in Games , 2020 .

[22]  Peter C. B. Phillips,et al.  Towards a Unified Asymptotic Theory for Autoregression , 1987 .

[23]  Wouter Dessein,et al.  When Does Coordination Require Centralization? , 2006 .

[24]  Mark G Ehrhart,et al.  Leadership and Procedural Justice Climate as Antecedents of Unit-Level Organizational Citizenship Behavior. , 2004 .

[25]  Eran Vigoda,et al.  Internal Politics in Public Administration Systems , 2000 .

[26]  Lyman W. Porter,et al.  Organizational Politics: An Exploration of Managers' Perceptions , 1980 .

[27]  Philipp Strack,et al.  Unrealistic Expectations and Misguided Learning , 2017 .

[28]  K. M. Kacmar,et al.  Organizational politics: The state of the field, links to related processes, and an agenda for future research. , 1999 .

[29]  Mallesh M. Pai,et al.  Coarse decision making and overfitting , 2014, J. Econ. Theory.

[30]  Zhiguo He,et al.  Intermediary Asset Pricing: New Evidence from Many Asset Classes , 2016 .

[31]  Daron Acemoglu,et al.  Fragility of Asymptotic Agreement Under Bayesian Learning , 2008 .

[32]  Lyman W. Porter,et al.  Organizational Politics , 1979 .

[33]  Edgar Erdfelder,et al.  G*Power 3: A flexible statistical power analysis program for the social, behavioral, and biomedical sciences , 2007, Behavior research methods.

[34]  G. Mailath,et al.  The Wisdom of a Confused Crowd: Model-Based Inference , 2019, SSRN Electronic Journal.

[35]  Joshua Schwartzstein,et al.  Using Models to Persuade , 2019, American Economic Review.

[36]  H. Akaike.  A new look at the statistical model identification , 1974 .

[37]  Ulrich K. Müller.  RISK OF BAYESIAN INFERENCE IN MISSPECIFIED MODELS, AND THE SANDWICH COVARIANCE MATRIX , 2013 .

[38]  P. Sørensen,et al.  Price Reaction to Information with Heterogeneous Beliefs and Wealth Effects: Underreaction, Momentum, and Reversal† , 2015 .

[39]  J. P. Near,et al.  ORGANIZATIONAL CITIZENSHIP BEHAVIOR: ITS NATURE AND ANTECEDENTS , 1983 .

[40]  David M. Kreps,et al.  Speculative Investor Behavior in a Stock Market with Heterogeneous Expectations , 1978 .

[41]  Gregory A. Rich,et al.  Transformational and transactional leadership and salesperson performance , 2001 .

[42]  B. Kőszegi,et al.  Convergence in models of misspecified learning , 2021 .

[43]  Gail S. Russ,et al.  The Dimensions of Politics Perceptions and Their Organizational and Individual Predictors1 , 1998 .

[44]  V. Vroom.  Work and motivation , 1964 .

[45]  Gerald R. Ferris,et al.  Perceptions of Organizational Politics , 1992 .

[46]  A. Baddeley.  Working Memory, Thought, and Action , 2007 .

[47]  Carolyn Y. Woo,et al.  Entrepreneurs' perceived chances for success , 1988 .

[48]  Alicia A. Grandey,et al.  The relationship of organizational politics and support to work behaviors, attitudes, and stress , 1997 .

[49]  Matias D. Cattaneo,et al.  Inference in Linear Regression Models with Many Covariates and Heteroscedasticity , 2015, Journal of the American Statistical Association.

[50]  F. Thomas Eggemeier,et al.  Workload assessment methodology. , 1986 .

[51]  R. Spiegler.  Bayesian Networks and Boundedly Rational Expectations , 2014 .

[52]  Dacheng Xiu,et al.  Taming the Factor Zoo: A Test of New Factors , 2017, The Journal of Finance.

[53]  Ignacio Esponda,et al.  Berk-Nash Equilibrium: A Framework for Modeling Agents with Misspecified Models , 2014, 1411.1152.

[54]  J. Steyrer,et al.  Transformational Leadership and Objective Performance in Banks , 1998 .

[55]  K. M. Kacmar,et al.  Discriminating among organizational politics, justice, and support , 2001 .

[56]  Nabil I. Al-Najjar.  Decision Makers as Statisticians: Diversity, Ambiguity, and Learning , 2009 .

[57]  Working Paper,et al.  Auctions , actions , and the failure of information aggregation , 2012 .

[58]  Muhamet Yildiz.  BARGAINING WITHOUT A COMMON PRIOR¿AN IMMEDIATE AGREEMENT THEOREM , 2003 .

[59]  J. Aislinn Bohren,et al.  Bounded Rationality and Learning: A Framework and a Robustness Result , 2017 .

[60]  Dawn S. Carlson,et al.  Interactive effects of personality and organizational politics on contextual performance , 2002 .

[61]  K. Jöreskog.  A General Method for Estimating a Linear Structural Equation System. , 1970 .

[62]  T. Achenbach.  Integrative Guide for the 1991 CBCL/4-18, Ysr, and Trf Profiles , 1991 .

[63]  G. Graen.  Role-making processes within complex organizations , 1976 .

[64]  M. Bensebti,et al.  Statistical Model , 2005 .

[65]  Dwight D. Frink,et al.  Reactions of Diverse Groups to Politics in the Workplace , 1996 .

[66]  P. Bentler,et al.  Significance Tests and Goodness of Fit in the Analysis of Covariance Structures , 1980 .

[67]  Eran Vigoda,et al.  Stress-related aftermaths to workplace politics: The relationships among politics, job distress, and aggressive behavior in organizations. , 2002 .

[68]  D. Fudenberg,et al.  Limit Points of Endogenous Misspecified Learning , 2020, Econometrica.

[69]  Patricia M. Fandt,et al.  Politics in organizations. , 1989 .

[70]  E. Fama,et al.  Common risk factors in the returns on stocks and bonds , 1993 .

[71]  F. Black,et al.  The Capital Asset Pricing Model: Some Empirical Tests , 2006 .

[72]  R. Engle,et al.  Individual differences in working memory capacity and what they tell us about controlled attention, general fluid intelligence, and functions of the prefrontal cortex. , 1999 .

[73]  M. Rabin,et al.  Channeled Attention and Stable Errors , 2018 .

[74]  Alwyn Young,et al.  Misspecified Politics and the Recurrence of Populism , 2022, American Economic Review.

[75]  Drew Fudenberg,et al.  Active learning with a misspecified prior , 2017 .

[76]  S. Morris.  The Common Prior Assumption in Economic Theory , 1995, Economics and Philosophy.

[77]  M. J. Emerson,et al.  The Unity and Diversity of Executive Functions and Their Contributions to Complex “Frontal Lobe” Tasks: A Latent Variable Analysis , 2000, Cognitive Psychology.

[78]  Deanne N. Den Hartog,et al.  Transactional versus transformational leadership: An analysis of the MLQ. , 1997 .

[79]  Inference in Linear Regression Models with Many Covariates and Heteroscedasticity , 2018, Journal of the American Statistical Association.

[80]  Sylvain Chassang.  Calibrated Incentive Contracts , 2011 .

[81]  Gordon D Logan,et al.  Horse-race model simulations of the stop-signal procedure. , 2003, Acta psychologica.

[82]  Philippe Jehiel,et al.  Analogy-based expectation equilibrium , 2004, J. Econ. Theory.

[83]  J. Aislinn Bohren,et al.  Informational Herding with Model Misspecification , 2013, J. Econ. Theory.

[84]  Jonathan Libgober,et al.  Evolutionarily Stable (Mis)specifications: Theory and Applications , 2021, EC.

[85]  D. Bergemann,et al.  Robust Mechanism Design , 2003 .

[86]  Darren C. Treadway,et al.  Perceptions of organizational politics: Additional thoughts, reactions, and multi-level issues , 2002 .

[87]  Annie Liang,et al.  Games of Incomplete Information Played by Statisticians , 2016, ArXiv.

[88]  R. Berk,et al.  CONSISTENCY A POSTERIORI , 1970 .

[89]  Daniel G. Bachrach,et al.  Organizational Citizenship Behaviors: A Critical Review of the Theoretical and Empirical Literature and Suggestions for Future Research , 2000 .

[90]  N. Ryan,et al.  Schedule for Affective Disorders and Schizophrenia for School-Age Children-Present and Lifetime Version (K-SADS-PL): initial reliability and validity data. , 1997, Journal of the American Academy of Child and Adolescent Psychiatry.

[91]  Jeffrey Gandz,et al.  The Experience of Workplace Politics , 1980 .

[92]  R. Spiegler,et al.  A Model of Competing Narratives , 2018, American Economic Review.

[93]  Kristóf Madarász,et al.  Sellers with Misspecified Models , 2016 .

[94]  Robert L. Dipboye,et al.  Perceptions of Organizational Politics: An Investigation of Antecedents and Consequences , 1995 .

[95]  B. Pennington,et al.  Validity of the Executive Function Theory of Attention-Deficit/Hyperactivity Disorder: A Meta-Analytic Review , 2005, Biological Psychiatry.

[96]  V. Sims,et al.  Working Memory Deficits in Boys with Attention-deficit/Hyperactivity Disorder (ADHD): The Contribution of Central Executive and Subsystem Processes , 2008, Journal of abnormal child psychology.

[97]  G D Logan,et al.  Response inhibition in AD/HD, CD, comorbid AD/HD + CD, anxious, and control children: a meta-analysis of studies with the stop task. , 1998, Journal of child psychology and psychiatry, and allied disciplines.

[98]  J. Stock,et al.  Instrumental Variables Regression with Weak Instruments , 1994 .

[99]  Wei Xiong,et al.  Overconfidence and Speculative Bubbles , 2003, Journal of Political Economy.

[100]  Pietro Ortoleva.  Modeling the Change of Paradigm: Non-Bayesian Reactions to Unexpected News † , 2012 .

[101]  Serhiy Kozak,et al.  Interpreting Factor Models , 2017 .

[102]  Barbara M. Byrne,et al.  Structural equation modeling with AMOS , 2010 .

[103]  Ryota Iijima,et al.  Misinterpreting Others and the Fragility of Social Learning , 2019, Econometrica.

[104]  P. Koellinger,et al.  "I Think I Can, I Think I Can": Overconfidence and Entrepreneurial Behavior , 2007 .

[105]  Henry Mintzberg.  The Nature of Managerial Work , 1974, Operational Research Quarterly (1970-1977).

[106]  B. Avolio,et al.  Impact of Transformational Leadership on Follower Development and Performance: A Field Experiment , 2002 .

[107]  E. Snowberg,et al.  Overconfidence in Political Behavior , 2013 .

[108]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[109]  Eran Vigoda.  Organizational Politics, Job Attitudes, and Work Outcomes: Exploration and Implications for the Public Sector. , 2000 .

[110]  Andrew Ang,et al.  Using Stocks or Portfolios in Tests of Factor Models , 2018, Journal of Financial and Quantitative Analysis.

[111]  R. R. Blake,et al.  The Managerial Grid , 1994 .

[112]  R. Nishii.  Asymptotic Properties of Criteria for Selection of Variables in Multiple Regression , 1984 .

[113]  S. J. Motowidlo,et al.  Occupational stress: its causes and consequences for job performance. , 1986, The Journal of applied psychology.

[114]  B. Bass.  LEADERSHIP AND PERFORMANCE BEYOND EXPECTATIONS , 1985 .

[115]  C. Huang-Pollock,et al.  ADHD Subtype Differences in Motivational Responsivity but not Inhibitory Control: Evidence From a Reward-Based Variation of the Stop Signal Paradigm , 2007, Journal of clinical child and adolescent psychology : the official journal for the Society of Clinical Child and Adolescent Psychology, American Psychological Association, Division 53.

[116]  T. Morrison,et al.  A Comparison of Situational and Dispositional Predictors of Perceptions of Organizational Politics , 2001, The Journal of psychology.

[117]  Eld,et al.  Cursed Equilibrium , 2000 .

[118]  O. Bunke,et al.  Asymptotic behavior of Bayes estimates under possibly incorrect models , 1998 .

[119]  Terrance Odean.  Do Investors Trade Too Much? , 1998 .

[120]  K Konrad,et al.  Neuropsychological and behavioural disinhibition in adult ADHD compared to borderline personality disorder , 2007, Psychological Medicine.

[121]  Dwight D. Frink,et al.  Perceptions of Organizational Politics: Prediction, Stress-Related Implications, and Outcomes , 1996 .

[122]  D. Fudenberg,et al.  Which Misperceptions Persist? , 2020 .

[123]  Nils Lid Hjort,et al.  Model Selection and Model Averaging , 2001 .

[124]  Chester A. Schriesheim,et al.  Fairness Perceptions and Trust as Mediators for Transformational and Transactional Leadership: A Two-Sample Study , 1999 .

[125]  Steven Thorley,et al.  Investor Overconfidence and Trading Volume , 2003 .

[126]  Amos Drory,et al.  Political behavior in organizations—A cross-cultural comparison , 1988 .

[127]  Gabriel D. Carroll.  Robustness and Linear Contracts , 2015 .

[128]  Anthony P. Ammeter,et al.  Toward a political theory of leadership , 2002 .

[129]  L. Tierney,et al.  The validity of posterior expansions based on Laplace''s method , 1990 .

[130]  R. Spiegler.  Placebo Reforms † , 2013 .

[131]  Guofu Zhou,et al.  Fama-MacBeth Two-Pass Regressions: Improving Risk Premia Estimates , 2015 .

[132]  Gerald R. Ferris,et al.  Perceptions of Organizational Politics Scale (POPS): Development and Construct Validation , 1991 .

[133]  Ryota Iijima,et al.  Dispersed Behavior and Perceptions in Assortative Societies , 2018, SSRN Electronic Journal.