### Abstract

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.

Original language | English |
---|---|

Pages (from-to) | 653-674 |

Number of pages | 22 |

Journal | Review of Economic Studies |

Volume | 63 |

Issue number | 4 |

Publication status | Published - 1996 Dec 1 |

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### ASJC Scopus subject areas

- Economics and Econometrics

### Cite this

*Review of Economic Studies*,

*63*(4), 653-674.

**Learning and Convergence to a Full-Information Equilibrium are not Equivalent.** / Jun, Byoung Heon; Vives, Xavier.

Research output: Contribution to journal › Article

*Review of Economic Studies*, vol. 63, no. 4, pp. 653-674.

}

TY - JOUR

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

AU - Jun, Byoung Heon

AU - Vives, Xavier

PY - 1996/12/1

Y1 - 1996/12/1

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.

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

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 -