Bayesian Inference and Decision Techniques, edited by P. Goel and A. Zellner Elsevier Science Publishers B.V., 1986, pp. 217-231. Edward E. Leamer University of California Chapter 14 Bid-Ask Spreads for Subjective Probabilities 1. Introduction ... (p.220) The final section offers the suggestion that authors of scientific reports be expected to select bid and asking prices for lotteries contingent on interesting and decidable events, and be required to back up those claims with currency issued by the government or bye the journal. The intent of this scheme is to provide a clear incentive for authors to report what they believe, but only what they believe. ... (p.230) 5. A proposal for scientific reporting The interpretation of inferences reported in scientific journals is made difficult by the muddled incentives of the authors. An economist, after reviewing the data, forms a judgment about, say, the probability that the Treasury bill rate will rise over a one-year period in which the rate of money growth increases. Readers of research results would like to know what that probability is, but no writer of research results has an incentive currently to reveal it. The probability elicitation devices we have just discussed might be helpful. The writer of a report could be required to select a sharp price to buy or sell lottery tickets a la de Finetti, or name an offer price a la Marschak, or announce a bid-ask spread. But because of the unfairness of de Finetti's game to the price setter, authors are not likely to be forthcoming if they are compelled to buy or sell lottery tickets at a price of their choosing. And journals are unlikely to be willing to play Marschak's game because of the resources needed to support it, and because there is no disincentive to publication by relatively uninformed writers. The publication of bid-ask spreads for lotteries contingent on interesting and decidable events is feasible, however, and might have a remarkable effect on the quality of empirical work that gets published. Authors would be expected to propose new lotteries or to offer new bid-ask spreads for existing lotteries. Journals would make editorial decisions concerning the degree of interest in new lotteries and would commit journal space only if they anticipate sufficient interest. Lower selling prices or higher buying prices would be automatically published. If the analysis which led to these prices were sufficiently amusing and if the author were willing, an article describing the method could be published as well. Subscribers would be allowed to contract with authors at the stated prices, though authors would be free to retract prices at any time, in which case the price reverts to the most recent outstanding price. The journal holds the stakes until the issue is decided, and reports all contracts, and all payments. The ideal outcome would be a narrow interval of prices accurately representing the available social information. Whether this is the best institutional arrangement for achieving this goal can be questioned since complicated strategic considerations will affect the announcement of the bid and asking prices. Another problem with this half-baked scheme is that the wealthy, rather than the informed, may "make the market." This is a short-run problem since in the long run resources transfer from those mistaken to those correct. A journal, concerned about initial disparities in wealth among its subscribers and harassed by government officials who generally frown on lotteries, could invent its own currency, say "smarts", and endow initially each subscriber with a thousand smarts. I suppose the subscriber with the most smarts at the end of each year could be awarded a free subscription, though statisticians might wish to test whether the distribution of smarts reveals underlying ability differences or could as well have resulted from flips of a coin. The great benefit of a scheme like this is it allows clear determination of professional progress as the probability intervals get narrower and move toward one or zero. Empirical work which led to great revisions in the upper and lower probabilities could be highly rewarded. Today we undervalue empirical enterprises, basically because we have no way of measuring their contributions. To start the ball rolling, I hereby announce my asking price P^** = 0.02 and my big price P_* - 0.00001 for the following lottery: "A journal listed in the 1980 Social Science Citation Index will adopt by 1990 the scheme just described". These prices are in effect until further notice.