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The Econometrics of Learning in Financial Markets

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  • Bossaerts, Peter

Abstract

The asymptotic behavior of the sample paths of two popular statistics that test market efficiency are investigated when markets learn to have rational expectations. Two cases are investigated, where, should markets start out at a rational expectations equilibrium, both statistics would asymptotically generate standard Brownian motions. In a first case, where agents are Bayesian and payoffs exogenous, the statistics have identical sample paths, but they are not standard Brownian motions. Whereas the finite-dimensional distributions are Gaussian, there may be a bias if agents' initial beliefs differ. A second case is considered, where payoffs are in part endogenous, yet agents consider them to be drawn from a stationary, exogenous distribution, which they attempt to learn in a frequentist way. In that case, one statistic behaves as if the economy were at a rational expectations equilibrium from the beginning on. The other statistic has sample paths with substantially non-Gaussian finite-dimensional distributions. Moreover, there is a negative bias. The behavior of the two statistics in the second case matches remarkably well the empirical results in an investigation of the prices of six foreign currency contracts over the period 1973–1990.

Suggested Citation

  • Bossaerts, Peter, 1995. "The Econometrics of Learning in Financial Markets," Econometric Theory, Cambridge University Press, vol. 11(01), pages 151-189, February.
  • Handle: RePEc:cup:etheor:v:11:y:1995:i:01:p:151-189_00
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    Cited by:

    1. Siddiqi, Hammad, 2015. "Anchoring and Adjustment Heuristic: A Unified Explanation for Equity Puzzles," MPRA Paper 68729, University Library of Munich, Germany.
    2. Guidolin, Massimo & Timmermann, Allan, 2003. "Option prices under Bayesian learning: implied volatility dynamics and predictive densities," Journal of Economic Dynamics and Control, Elsevier, vol. 27(5), pages 717-769, March.
    3. Angelos Kanas & Christos Ioannidis, 2012. "Revisiting the forward—spot relation: an application of the nonparametric long-run correlation coefficient," Journal of Economics and Finance, Springer;Academy of Economics and Finance, vol. 36(1), pages 148-161, January.
    4. Bruno Biais & Peter Bossaerts & Chester Spatt, "undated". "Equilibrium Asset Pricing Under Heterogeneous Information," GSIA Working Papers 2003-E42, Carnegie Mellon University, Tepper School of Business.
    5. Bondarenko, Oleg & Bossaerts, Peter, 2000. "Expectations and learning in Iowa," Journal of Banking & Finance, Elsevier, vol. 24(9), pages 1535-1555, September.
    6. Arthur, W.B. & Holland, J.H. & LeBaron, B. & Palmer, R. & Tayler, P., 1996. "Asset Pricing Under Endogenous Expectations in an Artificial Stock Market," Working papers 9625, Wisconsin Madison - Social Systems.

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