On the Impossibility of Informationally Efficient Markets By SANFORD J.GROSSMAN AND JOSEPH E.STIGLITZ* If competitive equilibrium is defined as a Jectures concerning certain properties of the situation in which prices are such that all equilibrium.The remaining analytic sections arbitrage profits are eliminated,is it possible of the paper are devoted to analyzing in that a competitive economy always be in detail an important example of our general equilibrium?Clearly not,for then those who model,in which our conjectures concerning arbitrage make no (private)return from the nature of the equilibrium can be shown their (privately)costly activity.Hence the to be correct.We conclude with a discussion assumptions that all markets,including that of the implications of our approach and for information,are always in equilibrium results,with particular emphasis on the rela- and always perfectly arbitraged are incon- tionship of our results to the literature on sistent when arbitrage is costly. “efficient capital markets.” We propose here a model in which there is an equilibrium degree of disequilibrium: I.The Model prices reflect the information of informed individuals(arbitrageurs)but only partially, Our model can be viewed as an extension so that those who expend resources to ob- of the noisy rational expectations model in- tain information do receive compensation. troduced by Robert Lucas and applied to How informative the price system is de- the study of information flows between pends on the number of individuals who are traders by Jerry Green (1973);Grossman informed;but the number of individuals (1975,1976,1978);and Richard Kihlstrom who are informed is itself an endogenous and Leonard Mirman.There are two assets: variable in the model. a safe asset yielding a return R,and a risky The model is the simplest one in which asset,the return to which,u,varies ran- prices perform a well-articulated role in con- domly from period to period.The variable u veying information from the informed to the consists of two parts, uninformed.When informed individuals ob- serve information that the return to a secur- (1) u=0+e ity is going to be high,they bid its price up, and conversely when they observe informa- where 6 is observable at a cost c,and e is tion that the return is going to be low.Thus unobservable.Both 0 and e are random the price system makes publicly available variables.There are two types of individu- the information obtained by informed indi- als,those who observe 0(informed traders), viduals to the uniformed.In general,how- and those who observe only price (unin- ever,it does this imperfectly;this is perhaps formed traders).In our simple model,all lucky,for were it to do it perfectly,an individuals are,ex ante,identical;whether equilibrium would not exist. they are informed or uninformed just de- In the introduction,we shall discuss the pends on whether they have spent c to ob- general methodology and present some con- tain information.Informed traders'de- mands will depend on and the price of the .University of Pennsylvania and Princeton Univer- risky asset P.Uninformed traders'demands sity,respectively.Research support under National Sci- ence Foundation grants SOC76-18771 and SOC77- An alternative interpretation is that 0 is a "mea- 15980 is gratefully acknowledged.This is a revised surement"of u with error.The mathematics of this version of a paper presented at the Econometric alternative interpretation differ slightly,but the results Society meetings,Winter 1975,at Dallas,Texas. are identical. 393