The Speed of Rational Learning

Posted: 10 Aug 1999

See all articles by Alvaro Sandroni

Alvaro Sandroni

University of Pennsylvania - Department of Economics; Northwestern University - Kellogg School of Management

Rann Smorodinsky

Technion-Israel Institute of Technology - The William Davidson Faculty of Industrial Engineering & Management

Abstract

A central result in the rational learning literature is that if the true measure is absolutely continuous with respect to the beliefs then, given enough data, the updated beliefs merge with the true distribution. In this paper, we show that, under absolute continuity, weak merging occurs fast (at the rate "1 over square root of time") with density one. Moreover, if weak merging occurs fast enough (at the rate "1 over time")) then absolute continuity holds. These rates are sharp. We also show that, under some conditions, if weak merging occurs at the rate "1 over square root of time" then absolute continuity holds.

JEL Classification: D83

Suggested Citation

Sandroni, Alvaro and Smorodinsky, Rann, The Speed of Rational Learning. Available at SSRN: https://ssrn.com/abstract=165452

Alvaro Sandroni (Contact Author)

University of Pennsylvania - Department of Economics ( email )

Ronald O. Perelman Center for Political Science
133 South 36th Street
Philadelphia, PA 19104-6297
United States

Northwestern University - Kellogg School of Management ( email )

2001 Sheridan Road
Evanston, IL 60208
United States
847-491-5461 (Phone)
847-467-1220 (Fax)

Rann Smorodinsky

Technion-Israel Institute of Technology - The William Davidson Faculty of Industrial Engineering & Management ( email )

Haifa 32000
Israel

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