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Decision Making under Uncertainty 서경원 2014 조락교 신진경제학상 강연 Probability • Probability is widely accepted and used in physics, statistics, economics and so on • No one can observe/verify probability A coin turns up head with probability 1/2 Frequentist’s view: out of an infinite number of coin tosses, exactly half of them turn head Not observable • Probability is an assumption rather than a result • Today, I will discuss cases where probability is not enough for modeling uncertainty in economics 2 Uncertainty • Uncertainty = Risk + Ambiguity Risk: probabilities are known Ambiguity: probabilities are unknown (or unknown risk) • sometimes referred to as Knightian uncertainty • Frank Knight (1921) “[…] a measurable uncertainty, or ‘risk’ proper, as we shall use the term, is so far different from an unmeasurable one […]” 3 Ellsberg Paradox ? ? 10 balls … … # of blue balls is unknown 10 balls # of black balls is 5 • Choose one: 1) between bet on blue vs. bet on black 2) between bet on yellow vs. bet on white • Typical choice: 1) black 2) white • Probability model can’t explain the choices 1) black: prob(blue)<50% 2) white: prob(yellow)<50% prob(blue or yellow) is less than 100% 4 • Probability is not enough to model the choice • Real world example – stock markets The box may be viewed as a firm • Blue: new product, innovation, cost reduction, … • Yellow: failure to invent a new product, cost increases, … Bet on green: buying the stock Bet on red: selling the stock Blue-yellow box: more ambiguity in the firm • small firms, new firms, venture firms … Black-white box: less ambiguity (or no ambiguity) in the firm • big firms, old firms, … 5 Model of Ambiguity: Multiple Priors • Multiple priors: Gilboa and Schmeidler (1989) Instead of a single probability, an agent considers a set of probabilities When betting on blue, 3 blue balls When betting on yellow, 7 blue balls 10 balls … 10 balls 10 balls or … 6 Model of Ambiguity: Probability over Probabilities • Probability over probabilities: Segal (1987), Klibanoff, Marinacci and Mukerji (2005), Ergin and Gul (2004), Nau (2006), Seo (2009) 3 blue balls with probability ½ 7 blue balls with probability ½ 10 balls with probability 1/2 10 balls … … 10 balls with probability 1/2 7 Financial Market Participation • Consider a stock market and an investor The current stock price is 2000 The investor has a belief on the price from a month now The future price is expected to be higher than, lower than or exactly equal to 2000 • Future price expected to be >2000: buy the asset (long position) • Future price expected to be <2000: sell the asset (short position) • Future price expected to be exactly 2000: do nothing (neutral position) 8 Effect of Risk • Does risk (or risk aversion) change the behavior? When buying, buy less When selling, sell less When doing nothing, doing nothing • Except the knife-edge case, people should participate in stock markets (and bond markets as well) Not true in the real world (Transaction cost can’t explain this for wealthy people (VissingJorgenson (2003))) 9 Effect of Ambiguity • People do not participate in stock markets if she feels ambiguity and behaves pessimistically: if I buy, price is expected to drop if I sell, price is expected to rise • Effect of ambiguity is qualitatively different from effect of risk 10 • Mukerji & Tallon (2001): ambiguity generates incomplete markets • Caballero & Krishnamurthy (2008), Caballero& Simsek (2012): market freeze under ambiguity in financial crises • Condie & Ganguli (2009): private information may not be fully revealing due to ambiguity • Trojani & Vanini (2004): ambiguity averse group might have no effect on the asset price • Condie (2010): ambiguity averse agents affect prices • Easley & O'hara (2011): market design reducing ambiguity to promote participation 11 Statistical Decision Making under Uncertainty • Observe a series of observations. Make decisions regarding future realizations For example, collect and analyze economic data, and choose an economic policy • Does the above procedure make sense under risk? Yes: De Finetti Theorem If ordering of a dataset does not matter, statistical procedure makes sense Probabilities are assumed • Does the above procedure make sense under ambiguity? Yes: Epstein and Seo (2010, 2014), Klibanoff, Mukerji and Seo (2013), Al-Najjar and De Castro (2014) 12