# Social learning and costly information acquisition

## Author

Listed:
• Roberto Burguet

() (Instituto de AnÂlisis EconÕmico, CSIC, Campus UAB, 08193 Bellaterra, Barcelona, SPAIN)

• Xavier Vives

() (Instituto de AnÂlisis EconÕmico, CSIC, Campus UAB, 08193 Bellaterra, Barcelona, SPAIN)

## Abstract

Short-lived agents want to predict a random variable $\theta$ and have to decide how much effort to devote to collect private information and consequently how much to rely on public information. The latter is just a noisy average of past predictions. It is shown that costly information acquisition prevents an unbounded accumulation of public information if (and only if) the marginal cost to acquire information is positive at zero $(C^\prime (0) > 0)$. When $C^\prime (0) = 0$ public precision at period n, $\tau_n$, tends to infinity with n but the rate of convergence of public information to $\theta$ is slowed down with respect to the exogenous information case. At the market outcome agents acquire too little private information. This happens either with respect to a (decentralized) first best benchmark or, for n large, with respect to a (decentralized) second best benchmark. For high discount factors the limit point of market public precision always falls short of the welfare benchmarks whenever $C^\prime (0) > 0$. In the extreme, as the discount factor tends to one public precision tends to infinity in the welfare-optimal programs while it remains bounded at the market solution. Otherwise, if $C^\prime (0) = 0$ public precision accumulates in an unbounded way both at the first and second best solutions. More public information may hurt at either the market or second best solutions.

## Suggested Citation

• Roberto Burguet & Xavier Vives, 2000. "Social learning and costly information acquisition," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 15(1), pages 185-205.
• Handle: RePEc:spr:joecth:v:15:y:2000:i:1:p:185-205
Note: Received: March 17, 1998; revised version: January 25, 1999
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## Citations

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Cited by:

1. Muendler, Marc-Andreas, 2005. "Rational Information Choice in Financial Market Equilibrium," University of California at San Diego, Economics Working Paper Series qt5q4764nj, Department of Economics, UC San Diego.
2. Marcello Miccoli, 2012. "Optimal dynamic public communication," Temi di discussione (Economic working papers) 856, Bank of Italy, Economic Research and International Relations Area.
3. Lars P. Feld & Benno Torgler & Bin Dong, 2008. "Coming Closer? Tax Morale, Deterrence and Social Learning after German Unification," CREMA Working Paper Series 2008-09, Center for Research in Economics, Management and the Arts (CREMA).
4. Celen, Bogachan & Hyndman, Kyle, 2006. "Endogenous Network Formation In the Laboratory," MPRA Paper 1440, University Library of Munich, Germany.
5. Xavier Vives, 2017. "Endogenous Public Information and Welfare in Market Games," Review of Economic Studies, Oxford University Press, vol. 84(2), pages 935-963.
6. Yang, Wan-Ru, 2011. "Herding with costly information and signal extraction," International Review of Economics & Finance, Elsevier, vol. 20(4), pages 624-632, October.
7. Hirshleifer, David & Teoh, Siew Hong, 2008. "Thought and Behavior Contagion in Capital Markets," MPRA Paper 9164, University Library of Munich, Germany.
8. Vives, Xavier, 1996. "Social learning and rational expectations," European Economic Review, Elsevier, vol. 40(3-5), pages 589-601, April.
9. David Hirshleifer & Siew Hong Teoh, 2003. "Herd Behaviour and Cascading in Capital Markets: a Review and Synthesis," European Financial Management, European Financial Management Association, vol. 9(1), pages 25-66.

### Keywords

Information externality; Costly information acquisition; Social learning; Learning from others.;

### JEL classification:

• D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
• D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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