Absence of Common Knowledge as A Source of Speculative Bubbles Shin’ichi Hirota (Waseda University) Shyam Sunder (Yale University) 10/12/2001

The purpose of our study Explore why the price bubble occurs in stock markets Investor’s belief on other’s belief Stock market experiments

Stock market bubble in the real world Internet Bubble e.g. Yahoo 10$ now, $250 in the peak Japan late 80’s e.g. Nikkei 225 Average 10,000 yen now, 40, 000 yen in the peak Must be bubbles Why bubbles occur

Investor should expect ... Infinitely lived investor Discounted value of future dividends Finite horizon investor Resale price Others’ valuation Others’ expectation for the future Future dividends Future price

If he believes that … Others will believe high future dividends or high future price, What should he do? Even if he does not believe high future dividends or high future price.

If every investor believes that Others will believe high future dividends or high future price, What will happen? Even if every investor himself does not believe high future dividends or high future price

Stock prices are determined by not investors’ own beliefs (first-order-beliefs) but investors’ beliefs on others’ beliefs (second-order-beliefs) Any Price can be observed depending on second-order-beliefs

Bubbles Price  Fundamental Value Second-order-belief Fundamental Value First-order-belief Second-order-belief  First-order-belief

Keynes Newspaper beauty contests How to verify? Well-known and popular story True in real world? How to verify? Fundamental value is unobservable Gap is unobservable

Experimental Study Laboratory Experimental Results Fundamental value is observable Create the gap between FOB and SOB See the effect of the gap on the stock price Experimental Results Bubbles occurred due to the gap Keynes is right!

Experimental Markets Stock market in the laboratory Trade a single stock 15 (12) periods of 3 minutes each Stocks has a life during the experiment

How to create the gap between FOB and SOB Each investor knows dividends (FOB) But… SOB may be different from FOB [Market 1] Dividends may not be received in the investment life. Dividends are paid only if the session lasts for 30 periods The subjects can easily guess that the session ends earlier The stock at the last period is evaluated at the predicted price of the next period They have to expect what the market expects the price

How to create the gap between FOB and SOB (continued) [Market 2] 15 periods. Dividends are paid at the end of Period 15. Each knows his dividend, but does not know others’ dividends Investors draws the dividend card Private information The dividend range is informed to everyone Investors have to guess others’ dividends, i.e., others’ valuation of the stock.

Investrors and Predictors Investors 10 stocks, 10,000 cash trade stocks using caplabTM system receive money depending on profits Predictors predict the next period’s price receive money depending on the accuracy

Conducted Experiments what, who, where, when 2 sessions for Market 1 (Session 1, 2) 1 session for Market 2 (Session 3) Yale university, undergraduate students Yale School of Management, B-74 Room September 21, 29, 30, 2001

Conclusion (from preliminary experimental results) The investors’ beliefs on other’s belief (SOB) significantly affect the stock prices. The gap between FOB and SOB seems to create bubbles in stock markets.