TY - JOUR

T1 - Learning and Convergence to a Full-Information Equilibrium are not Equivalent

AU - Jun, Byoung

AU - Vives, Xavier

N1 - Funding Information:
Remark. The boundary case for which p = I + A/t/JIJ turns out to be more difficult to characterize. Nevertheless, it is possible to show that in that case both learning 9 and convergence to the FIE obtain. Convergence to the FIE happens at the usual rate n-1/2and learning 9 happens faster (at the rate of n-3/2 since the price precision fn is of the order of n3.) Acknowledgements. A preliminary version of the present paper was circulated under the title "Learning and Convergence in Rational Expectations Equilibria with Persistent Shocks". Support from the Spanish Ministry of Education through grants DGICYT PB90-Q132 and PB93-0619 is gratefully acknowledged. Further support for Jun from the CIRIT, Generalitat de Catalunya, is also acknowledged. We are grateful to Tilman Borgers, David Easley, Guy Laroque, two anonymous referees and participants at ESSET 94 at Studientzentrum Gerzensee for useful comments.

PY - 1996

Y1 - 1996

N2 - Convergence to a full-information equilibrium (FIE) in the presence of persistent shocks and asymmetric information about an unknown payoff-relevant parameter θ is established in a classical infinite-horizon partial equilibrium linear model. It is found that, under the usual stability assumptions on the autoregressive process of shocks, convergence occurs at the rate n-1/2, where n is the number of rounds of trade, and that the asymptotic variance of the discrepancy of the full-information price and the market price is independent of the degree of autocorrelation of the shocks. This is so even though the speed of learning θ from prices becomes arbitrarily slow as autocorrelation approaches a unit root level. It follows then that learning the unknown parameter θ and convergence of the equilibrium process to the FIE are not equivalent. Moreover, allowing for non-stationary processes of shocks, the distinction takes a more stark form. Learning θ is neither necessary nor sufficient for convergence to the FIE. When the process of shocks has a unit root, convergence to the FIE occurs but θ can not be learned. When the process is sufficiently explosive and there is a positive mass of perfectly informed agents, θ is learned quickly but convergence to the FIE does not occur.

AB - Convergence to a full-information equilibrium (FIE) in the presence of persistent shocks and asymmetric information about an unknown payoff-relevant parameter θ is established in a classical infinite-horizon partial equilibrium linear model. It is found that, under the usual stability assumptions on the autoregressive process of shocks, convergence occurs at the rate n-1/2, where n is the number of rounds of trade, and that the asymptotic variance of the discrepancy of the full-information price and the market price is independent of the degree of autocorrelation of the shocks. This is so even though the speed of learning θ from prices becomes arbitrarily slow as autocorrelation approaches a unit root level. It follows then that learning the unknown parameter θ and convergence of the equilibrium process to the FIE are not equivalent. Moreover, allowing for non-stationary processes of shocks, the distinction takes a more stark form. Learning θ is neither necessary nor sufficient for convergence to the FIE. When the process of shocks has a unit root, convergence to the FIE occurs but θ can not be learned. When the process is sufficiently explosive and there is a positive mass of perfectly informed agents, θ is learned quickly but convergence to the FIE does not occur.

UR - http://www.scopus.com/inward/record.url?scp=0344539246&partnerID=8YFLogxK

U2 - 10.2307/2297798

DO - 10.2307/2297798

M3 - Article

AN - SCOPUS:0344539246

VL - 63

SP - 653

EP - 674

JO - Review of Economic Studies

JF - Review of Economic Studies

SN - 0034-6527

IS - 4

ER -