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Sources of entropy in representative agent models


  • Backus, David
  • Chernov, Mikhail
  • Zin, Stanley E.


We propose two metrics for asset pricing models and apply them to representative agent models with recursive preferences, habits, and jumps. The metrics describe the pricing kernel’s dispersion (the entropy of the title) and dynamics (time dependence, a measure of how entropy varies over different time horizons). We show how each model generates entropy and time dependence and compare their magnitudes to estimates derived from asset returns. This exercise--and transparent loglinear approximations--clarifies the mechanisms underlying these models. It also reveals, in some cases, tension between entropy, which should be large enough to account for observed excess returns, and time dependence, which should be small enough to account for mean yield spreads.

Suggested Citation

  • Backus, David & Chernov, Mikhail & Zin, Stanley E., 2011. "Sources of entropy in representative agent models," CEPR Discussion Papers 8488, C.E.P.R. Discussion Papers.
  • Handle: RePEc:cpr:ceprdp:8488

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    2. Hansen, Lars Peter, 2013. "Uncertainty Outside and Inside Economic Models," Nobel Prize in Economics documents 2013-7, Nobel Prize Committee.
    3. Timothy M. Christensen, 2014. "Nonparametric identification of positive eigenfunctions," CeMMAP working papers CWP37/14, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    4. repec:oup:rfinst:v:30:y:2017:i:2:p:442-504. is not listed on IDEAS
    5. Borovička, Jaroslav & Hansen, Lars Peter, 2014. "Examining macroeconomic models through the lens of asset pricing," Journal of Econometrics, Elsevier, vol. 183(1), pages 67-90.
    6. Hansen, Lars Peter, 2013. "Risk Pricing over Alternative Investment Horizons," Handbook of the Economics of Finance, Elsevier.
    7. Polanski, Arnold & Stoja, Evarist, 2015. "Extreme risk interdependence," Bank of England working papers 563, Bank of England.
    8. Schneider, Paul, 2015. "Generalized risk premia," Journal of Financial Economics, Elsevier, vol. 116(3), pages 487-504.
    9. Oh, Gabjin & Kim, Ho-yong & Ahn, Seok-Won & Kwak, Wooseop, 2015. "Analyzing the financial crisis using the entropy density function," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 464-469.
    10. David Backus & Nina Boyarchenko & Mikhail Chernov, 2016. "Term Structures of Asset Prices and Returns," NBER Working Papers 22162, National Bureau of Economic Research, Inc.
    11. Jaroslav Borovička & Lars Peter Hansen & José A. Scheinkman, 2016. "Misspecified Recovery," Journal of Finance, American Finance Association, vol. 71(6), pages 2493-2544, December.
    12. Irina Zviadadze, 2014. "Term-structure of consumption risk premia in the cross-section of currency returns," 2014 Meeting Papers 1075, Society for Economic Dynamics.
    13. Arnold Polanski & Evarist Stoja, 2016. "Extreme risk interdependence," ESRB Working Paper Series 12, European Systemic Risk Board.
    14. Anisha Ghosh & Christian Julliard & Alex P. Taylor, 2017. "What Is the Consumption-CAPM Missing? An Information-Theoretic Framework for the Analysis of Asset Pricing Models," Review of Financial Studies, Society for Financial Studies, vol. 30(2), pages 442-504.
    15. Hengjie Ai & Ravi Bansal, 2016. "Risk Preferences and The Macro Announcement Premium," NBER Working Papers 22527, National Bureau of Economic Research, Inc.
    16. Backus, David & Ferriere, Axelle & Zin, Stanley, 2015. "Risk and ambiguity in models of business cycles," Journal of Monetary Economics, Elsevier, vol. 69(C), pages 42-63.
    17. Jeremy Graveline & Irina Zviadadze & Mikhail Chernov, 2012. "Crash Risk in Currency Returns," 2012 Meeting Papers 753, Society for Economic Dynamics.
    18. Xiao Xiao & Chen Zhou, 2017. "Entropy-based implied moments," DNB Working Papers 581, Netherlands Central Bank, Research Department.
    19. Pierlauro Lopez, 2016. "Welfare Implications of the Term Structure of Returns: Should Central Banks Fill Gaps or Remove Volatility?," 2016 Meeting Papers 742, Society for Economic Dynamics.
    20. Caio Almeida & Kym Ardison & René Garcia & Jose Vicente, 2017. "Nonparametric Tail Risk, Stock Returns, and the Macroeconomy," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 15(3), pages 333-376.
    21. P. Lopez, 2014. "The Term Structure of the Welfare Cost of Uncertainty," Working papers 521, Banque de France.
    22. Chabakauri, Georgy, 2015. "Dynamic equilibrium with rare events and heterogeneous Epstein-Zin investors," LSE Research Online Documents on Economics 60737, London School of Economics and Political Science, LSE Library.
    23. Chernov, Mikhail & Graveline, Jeremy & Zviadadze, Irina, 2012. "Sources of Risk in Currency Returns," CEPR Discussion Papers 8745, C.E.P.R. Discussion Papers.
    24. Gospodinov, Nikolay & Maasoumi, Esfandiar, 2017. "General Aggregation of Misspecified Asset Pricing Models," FRB Atlanta Working Paper 2017-10, Federal Reserve Bank of Atlanta.
    25. Favero, Carlo A. & Ortu, Fulvio & Tamoni, Andrea & Yang, Haoxi, 2016. "Implications of Return Predictability across Horizons for Asset Pricing Models," CEPR Discussion Papers 11645, C.E.P.R. Discussion Papers.

    More about this item


    asset returns; bond yields; disasters; habits; jumps; pricing kernel; recursive preferences;

    JEL classification:

    • E44 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Financial Markets and the Macroeconomy
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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