Pathological Outcomes of Observational Learning

MIT Dept of Economics Working Paper No. 96-19

Posted: 3 Sep 1997

See all articles by Lones Smith

Lones Smith

University of Wisconsin at Madison - Department of Economics

Peter Norman Sorensen

University of Copenhagen - Department of Economics

Date Written: June 1996

Abstract

This paper systematically analyzes and enriches the observational learning paradigm of Banerjee (1992) and Bikhchandani, Hirshleifer, and Welch (1992). Our contributions fall into three categories. First, we develop what we consider to be the right analytic framework for informational herding (convergence of actions and convergence of beliefs, using a Markov-martingale process). We demonstrate its power and simplicity in four major ways: (1) We decouple herds and cascades: Cascades might never arise, even though herds must. (2) We show that wrong herds can arise if and only if the private signals have uniformly bounded strength. (3) We determine when the mean time to start a herd is finite, and show that (absent revealing signals) it is infinite when a correct herd is inevitable. (4) We prove that long-run learning is unaffected by background noise from crazy/trembling decisions. Second, we explore a new and economically compelling model with multiple types, and discover that a twin observational pathology generically appears: Confounded learning. It may well be impossible to draw any further inference from history even while it continues to accumulate privately-informed decisions! Third, we show how the margingale property of likelihood ratios is neatly linked with the stochastic stability of the learning dynamics. This is not only allows us to analyze herding with noise, and convergence to our new confounding outcome, but also show promise for optimal experimentation.

JEL Classification: D83

Suggested Citation

Smith, Lones and Sorensen, Peter Norman, Pathological Outcomes of Observational Learning (June 1996). MIT Dept of Economics Working Paper No. 96-19, Available at SSRN: https://ssrn.com/abstract=10760

Lones Smith (Contact Author)

University of Wisconsin at Madison - Department of Economics ( email )

1180 Observatory Drive
Madison, WI 53706-1393
United States
608-263-3871 (Phone)
608-262-2033 (Fax)

HOME PAGE: http://www.lonessmith.com

Peter Norman Sorensen

University of Copenhagen - Department of Economics ( email )

Oster Farimagsgade 5
Building 26
Copenhagen K, 1353
Denmark
+45 35 32 3056 (Phone)

HOME PAGE: http://www.econ.ku.dk/sorensen

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