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 hat 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 implicat pur app 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 L. The model prices reflect the information of informed ndividuals(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) ossman 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, serve information that the return to a secur- (1) ity is going to be high, they bid its price up, and conversely when they observe informa- where 0 is observable at a cost c, and e is ion that the return is going to be low. Thus unobservable. Both 0 and e are random the price system makes publicly available varables. 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 以0 y asset P. Uninformed traders'demands 'An alternative interpretation is that g is a"me This is a revised er presen he Econometric alternative interpretation differ slightly, but the Society inter 1975. at Dallas Texas are identical 393 I 1 Sep 2013 OR Terms and ConditionsOn the Impossibility of Informationally Efficient Markets By SANFORD J. GROSSMAN AND JOSEPH E. STIGLITZ* If competitive equilibrium is defined as a situation in which prices are such that all arbitrage profits are eliminated, is it possible that a competitive economy always be in equilibrium? Clearly not, for then those who arbitrage make no (private) return from their (privately) costly activity. Hence the assumptions that all markets, including that for information, are always in equilibrium and always perfectly arbitraged are incon￾sistent when arbitrage is costly. We propose here a model in which there is an equilibrium degree of disequilibrium: prices reflect the information of informed individuals (arbitrageurs) but only partially, so that those who expend resources to ob￾tain information do receive compensation. How informative the price system is de￾pends on the number of individuals who are informed; but the number of individuals who are informed is itself an endogenous variable in the model. The model is the simplest one in which prices perform a well-articulated role in con￾veying information from the informed to the uninformed. When informed individuals ob￾serve information that the return to a secur￾ity is going to be high, they bid its price up, and conversely when they observe informa￾tion that the return is going to be low. Thus the price system makes publicly available the information obtained by informed indi￾viduals to the uniformed. In general, how￾ever, it does this imperfectly; this is perhaps lucky, for were it to do it perfectly, an equilibrium would not exist. In the introduction, we shall discuss the general methodology and present some con￾jectures concerning certain properties of the equilibrium. The remaining analytic sections of the paper are devoted to analyzing in detail an important example of our general model, in which our conjectures concerning the nature of the equilibrium can be shown to be correct. We conclude with a discussion of the implications of our approach and results, with particular emphasis on the rela￾tionship of our results to the literature on "efficient capital markets." I. The Model Our model can be viewed as an extension of the noisy rational expectations model in￾troduced by Robert Lucas and applied to the study of information flows between traders by Jerry Green (1973); Grossman (1975, 1976, 1978); and Richard Kihlstrom and Leonard Mirman. There are two assets: a safe asset yielding a return R, and a risky asset, the return to which, u, varies ran￾domly from period to period. The variable u consists of two parts, (1) = +e where 9 is observable at a cost c, and e is unobservable.' Both 9 and E are random variables. There are two types of individu￾als, those who observe 9 (informed traders), and those who observe only price (unin￾formed traders). In our simple model, all individuals are, ex ante, identical; whether they are informed or uninformed just de￾pends on whether they have spent c to ob￾tain information. Informed traders' de￾mands will depend on 9 and the price of the risky asset P. Uninformed traders' demands *University of Pennsylvania and Princeton Univer￾sity, respectively. Research support under National Sci￾ence Foundation grants SOC76-18771 and SOC77- 15980 is gratefully acknowledged. This is a revised version of a paper presented at the Econometric Society meetings, Winter 1975, at Dallas, Texas. 'An alternative interpretation is that 0 is a "mea￾surement" of u with error. The mathematics of this alternative interpretation differ slightly, but the results are identical. 393 This content downloaded from 202.115.118.13 on Wed, 11 Sep 2013 03:12:49 AM All use subject to JSTOR Terms and Conditions