Keynes’ Beauty Contest: Speculative Price Bubbles in the Absence of Common Knowledge in Experimental Stock Markets Shin’ichi Hirota and Shyam Sunder Osaka University (ISER) Workshop, March 6, 2002 Speculative Bubbles

The Purpose of Our Study Explore why the price bubble occurs in stock markets What investors believe about others’ beliefs Experimental study Speculative Bubbles

John Maynard Keynes (1936) Stock Market is like a newspaper beauty contest Speculative Bubbles

Newspaper Beauty Contest Which Face is the prettiest? Speculative Bubbles

Which face they will choose as the prettiest? Speculative Bubbles

Which face they will believe that they will choose as the prettiest? Speculative Bubbles

Newspaper Beauty Contests I believe that A is the prettiest. others choose B others believe that B is the prettiest others choose B … So, I choose B Speculative Bubbles

Stock Markets So, I consider XB I believe that others believe that F (fundamental value) = XA others consider XB others believe that F (fundamental value) = XB others consider XB … So, I consider XB Stock price = XB even if every investor believes F = XA Speculative Bubbles

Plausible Story?? Well-known to practitioners and economists True in real world? 証券レディ (フィナンシャル・プランナー) 「みんなそう思ってますよ」 Central role of beliefs about others, and about others’ beliefs Emperor’s Clothes, 日本の大学？ Speculative Bubbles

Common Knowledge When XA = XB the value of the stock is common knowledge. In a great deal of modeling, common knowledge is routinely assumed What happens when it breaks down? When our higher order beliefs differ from first order belief, do they converge? (Aumann (1976)). Speculative Bubbles

Speculative Bubbles

Irrational Exuberance Less-than-rational behavior People do not know fundamentals (XA) People trade without considering fundamentals Bubble occurs due to investors’ error and emotional behavior (psychology) Drawbacks definition of bubbles, inconsistent exploration, useful exploration ? “Jack got lost because he is foolish” Speculative Bubbles

Beauty Contest Bubble “Rational behavior” Investor need not be irrational in decisions or beliefs, and need not believe the others to be irrational. Bubbles generated by gap between the first and second (higher) order beliefs. Do not depend on investor heterogeneity Speculative Bubbles

How to verify? In the field it is difficult enough to know the first order investor beliefs (fundamental value), and their diversity Second and higher order beliefs are also unobservable and practically out of reach In lab we might have a better, though still limited, chance to know beliefs, perhaps even open a gap between the first and higher order beliefs and observe their consequences under controlled conditions Speculative Bubbles

Experimental Design Double auction market for multiple units of a single security Multiple trading periods (3 minutes each) Each investor endowed with 10 shares, 10,000 points in “cash” Liquidation by dividend or predicted price Predictors knew the rules, no endowments, no ability to trade, could watch trading, knew the range of terminal dividends Speculative Bubbles

2 Types of Keynes’ Bubble Type I A gap between 1st and higher order beliefs Absence of common knowledge about dividends Type II Self-floating Is this same as ‘rational bubble’?? Blanchard & Watson (1982), Tirole (1982)(1985) Occurs in infinite maturity securities Speculative Bubbles

F=S sessions FS sessions Dividend Value = Dividend Range Common Knowledge F=S No Type I bubble Dividend Value  Dividend Range Absence of Common Knowledge F<S Type I bubble may be observed Speculative Bubbles

Finite Maturity Securities Sessions 15 periods. Single liquidating dividend is paid at the end of Period 15 By design, second order beliefs have the chance of being higher than the first order beliefs Type I bubbles may be observed. Bubbles continue until period T-1 and crash crash in the last period Speculative Bubbles

Indefinite Maturity Securities Sessions Investors do not know ex ante how many periods they will have. Dividend is paid at the end of Period 30, but session is likely to end before Period 30. Terminal payoff by endogenous prediction game Type II bubble may be observed. The price is totally dependent on market expectations Speculative Bubbles

Trading Screen Speculative Bubbles

Speculative Bubbles Table 2: Experimental Design 09/21/01 1 Type I M/D/Y Session Final Payoff on Stock Type of Bubble Predicted to Observe Dividends on cards given to investors Range of Dividend Announced Number of Subjects (Investors) $/point Conv. Rate Actual # of Periods Announced # of Periods Q&A/ V&C 09/21/01   1 Predicted Value Type I Type II 40 for 2, 75 for 3 [10, 300] 7 (5) 0.025 12 ≤ 30 No/ No 09/29/01 2 70 for 3, 130 for 3 [70, 130] 8 (6) 0.015 15 09/30/01 3 Dividend 80 for 3, 150 for 3 [40, 300] 11/16/01 4 120 for 2, 205 for 3 [120-205] 0.01 Yes/ Speculative Bubbles

Speculative Bubbles 12/01/01 5* Type I 105 for 2, 175 for 3 [55-350] 7 M/D/Y Session Final Payoff on Stock Type of Bubble Predicted to Observe Dividends on cards given to investors Range of Dividend Announced Number of Subjects $/point Conv. Rate Actual # of Periods Announced # of Periods Q&A/ V&C   12/01/01 5* Dividend Type I 105 for 2, 175 for 3 [55-350] 7 (5) 0.012 15 Yes/ No 02/15/02 6 150 for 5 [40, 300] 0.015 Yes 02/22/02 105 for 3, 8 (6) 03/01/02 Predicted Value Type II 40 for 2, 75 for 3 [10, 300] 5 (4) [Points/ Average]  $25 17 ≤ 30 * One predictor violated instructions Speculative Bubbles

Tentative Results Type I bubble ?? Type II bubble Keynes is right?! Bubble occurred in 1 of 4 sessions Type II bubble Bubble occurred in all of 3 sessions Keynes is right?! Bubble did not occur in Session 4. Market expectations tend to follow the market price. Speculative Bubbles

Discussion Significant part of market returns realized as capital gains, not dividends Valuation models should incorporate second order beliefs Link between uncertainty and bubbles Link between low dividend securities (larger duration) and bubbles Difference between stock and debt Exchange rate bubbles French and Roll: Market trading itself creates volatility (possibly through formation of second order beliefs?) Speculative Bubbles