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On the Relation between Private Information and Non-Fundamental Volatility

  • Myungkyu Shim EMAIL logo and Doyoung Song
Published/Copyright: September 6, 2022
The B.E. Journal of Theoretical Economics
From the journal The B.E. Journal of Theoretical Economics Volume 23 Issue 2

Abstract

It is a well-established property that more precise private information leads to lower non-fundamental volatility in a coordination economy with dispersed information. In this note, we identify conditions under which such an argument holds or does not hold. In particular, we show that the opposite relationship holds when (1) there is a strong positive correlation between private information of different agents and (2) public information is endogenously generated.

Keywords: coordination game; financial prices; non-fundamental volatility; dispersed information
JEL Classification: D80; D83; G10
Corresponding author: Myungkyu Shim, School of Economics, Yonsei University, Seoul, South Korea, E-mail:

Funding source: Yonsei University and Yongwoon Scholarship Foundation

Award Identifier / Grant number: 2021-11-0410

Acknowledgements

We thank two anonymous referees for their helpful and insightful suggestions. Shim acknowledges the financial support from Yonsei University and Yongwoon Scholarship Foundation (Yonsei–Yongwoon Research Grant No. 2021-11-0410). Seoyoon Jeong and Seung Yong Yoo provided excellent research assistance.

Appendix A: Proof for Proposition 2

We first define g(x)≡f2(αx)αx. Then precision of the public signal is expressed as follows:

(A.1)αp*=1−2αξg(x)γ2(1−r)−1−4αξg(x)γ2(1−r)2αξg(x)γ2(1−r)2αx
(A.2)=(1−r)αx⋅γ2(1−r)2αξg(x)−1−γ2(1−r)2αξg(x)1−4αξg(x)γ2(1−r)

Define H≡2αξg(x)γ2(1−r). Then

(A.3)∂αp*∂αx=(1−r)⋅1H−1H1−2H−1+(1−r)αxg′(x)g(x)⋅−1H+1H1−2H+11−2H

Recall that it suffices to determine the sign of (1−r)−12∂αp*∂αx(1−r)αxαp*−1 to analyze the effect of precision of the private signal on the non-fundamental volatility. Define A≡1H1−1−2H and note that (1−r)αxαp*−1=2−AA−1.

If suffices to consider the following expression:

(A.4)−12(A−1)+2αxf′(x)f(x)−1⋅11−2H−A2−AA−1⪌−1

By rearranging the terms, we can obtain

(A.5)A1−αxf′(x)f(x)⪌0

As A > 0, we can get the following conditions stated in Proposition 2.

References

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Received: 2021-12-12
Accepted: 2022-07-10
Published Online: 2022-09-06

© 2022 Walter de Gruyter GmbH, Berlin/Boston

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https://doi.org/10.1515/bejte-2021-0166
Keywords for this article
coordination game; financial prices; non-fundamental volatility; dispersed information

Articles in the same Issue

  1. Frontmatter
  2. Research Articles
  3. Collusion, Shading, and Optimal Organization Design
  4. Software Cracking and Degrees of Software Protection
  5. The R&D Investment Decision Game with Product Differentiation
  6. An Urban Configuration with Online Competition
  7. Double Implementation in Dominant Strategy Equilibria and Ex-Post Equilibria with Private Values
  8. Risk Aversion and Uniqueness of Equilibrium in Economies with Two Goods and Arbitrary Endowments
  9. On Iterated Nash Bargaining Solutions
  10. Inter-league Competition and the Optimal Broadcasting Revenue-Sharing Rule
  11. The Weak Hybrid Equilibria of an Exchange Economy with a Continuum of Agents and Externalities
  12. Choosing Sides in a Two-Sided Matching Market
  13. Notes
  14. On the Relation between Private Information and Non-Fundamental Volatility
  15. Cost-Reducing Technologies and Labor Supply in a Krugman-type Model where Consumption is Time-Constrained: Some New Results
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