IDEAS home Printed from
   My bibliography  Save this paper

Measuring “Dark Matter” in Asset Pricing Models


  • Hui Chen
  • Winston Wei Dou
  • Leonid Kogan


We formalize the concept of “dark matter” in asset pricing models by quantifying the additional informativeness of cross-equation restrictions about fundamental dynamics. The dark matter measure captures the degree of fragility for models that are potentially misspecified and unstable: a large dark matter measure signifies that the model lacks internal refutability (weak power of optimal specification tests) and external validity (high overfitting tendency and poor out-of-sample fit). The measure can be computed at low cost even for complex dynamic structural models. To illustrate its applications, we provide quantitative examples applying the measure to (time-varying) rare-disaster risk and long-run risk models.

Suggested Citation

  • Hui Chen & Winston Wei Dou & Leonid Kogan, 2019. "Measuring “Dark Matter” in Asset Pricing Models," NBER Working Papers 26418, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:26418
    Note: AP

    Download full text from publisher

    File URL:
    Download Restriction: no

    References listed on IDEAS

    1. Ivo Welch & Amit Goyal, 2008. "A Comprehensive Look at The Empirical Performance of Equity Premium Prediction," Review of Financial Studies, Society for Financial Studies, vol. 21(4), pages 1455-1508, July.
    2. Rhys Bidder & Ian Dew-Becker, 2016. "Long-Run Risk Is the Worst-Case Scenario," American Economic Review, American Economic Association, vol. 106(9), pages 2494-2527, September.
    3. Lars Ljungqvist & Thomas J. Sargent, 2004. "Recursive Macroeconomic Theory, 2nd Edition," MIT Press Books, The MIT Press, edition 2, volume 1, number 026212274x, December.
    4. Larry G. Epstein & Stanley E. Zin, 2013. "Substitution, risk aversion and the temporal behavior of consumption and asset returns: A theoretical framework," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 12, pages 207-239, World Scientific Publishing Co. Pte. Ltd..
    5. Jushan Bai & Pierre Perron, 1998. "Estimating and Testing Linear Models with Multiple Structural Changes," Econometrica, Econometric Society, vol. 66(1), pages 47-78, January.
    6. Lee, Lung-fei, 2007. "The method of elimination and substitution in the GMM estimation of mixed regressive, spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 140(1), pages 155-189, September.
    7. Pierre Collin-Dufresne & Michael Johannes & Lars A. Lochstoer, 2016. "Parameter Learning in General Equilibrium: The Asset Pricing Implications," American Economic Review, American Economic Association, vol. 106(3), pages 664-698, March.
    8. Timothy Cogley & Thomas J. Sargent, 2005. "Drift and Volatilities: Monetary Policies and Outcomes in the Post WWII U.S," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 8(2), pages 262-302, April.
    9. Andrews, Donald W K & Monahan, J Christopher, 1992. "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," Econometrica, Econometric Society, vol. 60(4), pages 953-966, July.
    10. Hansen, Lars Peter, 1985. "A method for calculating bounds on the asymptotic covariance matrices of generalized method of moments estimators," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 203-238.
    11. Chamberlain, Gary, 1987. "Asymptotic efficiency in estimation with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 34(3), pages 305-334, March.
    12. Saikkonen, Pentti, 1989. "Asymptotic relative efficiency of the classical test statistics under misspecification," Journal of Econometrics, Elsevier, vol. 42(3), pages 351-369, November.
    13. Newey, Whitney K, 1985. "Maximum Likelihood Specification Testing and Conditional Moment Tests," Econometrica, Econometric Society, vol. 53(5), pages 1047-1070, September.
    Full references (including those not matched with items on IDEAS)


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. Robert Barro & Tao Jin, 2021. "Rare Events and Long-Run Risks," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 39, pages 1-25, January.
    2. Matthew Baron & Wei Xiong, 2017. "Credit Expansion and Neglected Crash Risk," The Quarterly Journal of Economics, Oxford University Press, vol. 132(2), pages 713-764.
    3. Christian Schlag & Michael Semenischev & Julian Thimme, 2021. "Predictability and the Cross-Section of Expected Returns: A Challenge for Asset Pricing Models," Management Science, INFORMS, vol. 67(12), pages 7932-7950, December.
    4. Augustin, P. & Chernov, M. & Schmid, L. & Song, D., 2021. "Benchmark interest rates when the government is risky," Journal of Financial Economics, Elsevier, vol. 140(1), pages 74-100.
    5. Jerry Tsai & Jessica A. Wachter, 2014. "Rare Booms and Disasters in a Multi-sector Endowment Economy," NBER Working Papers 20062, National Bureau of Economic Research, Inc.
    6. Hansen, Lars Peter & Sargent, Thomas J., 2021. "Macroeconomic uncertainty prices when beliefs are tenuous," Journal of Econometrics, Elsevier, vol. 223(1), pages 222-250.
    7. John H. Cochrane, 2017. "Macro-Finance," Review of Finance, European Finance Association, vol. 21(3), pages 945-985.
    8. Hassan Afrouzi & Laura Veldkamp, 2019. "Biased Inflation Forecasts," 2019 Meeting Papers 894, Society for Economic Dynamics.
    9. Lars P. Hansen & Thomas J. Sargent, 2016. "Sets of Models and Prices of Uncertainty," NBER Working Papers 22000, National Bureau of Economic Research, Inc.
    10. Robert Barro & Tao Jin, 2021. "Rare Events and Long-Run Risks," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 39, pages 1-25, January.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Patrick Gagliardini & Diego Ronchetti, 2020. "Comparing Asset Pricing Models by the Conditional Hansen-Jagannathan Distance," The Journal of Financial Econometrics, Society for Financial Econometrics, vol. 18(2), pages 333-394.
    2. Tetiana Davydiuk & Scott Richard & Ivan Shaliastovich & Amir Yaron, 2023. "How Risky Are U.S. Corporate Assets?," Journal of Finance, American Finance Association, vol. 78(1), pages 141-208, February.
    3. Stefan Nagel, 2013. "Empirical Cross-Sectional Asset Pricing," Annual Review of Financial Economics, Annual Reviews, vol. 5(1), pages 167-199, November.
    4. Rossi, Barbara, 2013. "Advances in Forecasting under Instability," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 1203-1324, Elsevier.
    5. Fabrice Collard & Sujoy Mukerji & Kevin Sheppard & Jean‐Marc Tallon, 2018. "Ambiguity and the historical equity premium," Quantitative Economics, Econometric Society, vol. 9(2), pages 945-993, July.
    6. Bekaert, Geert & Engstrom, Eric & Xing, Yuhang, 2009. "Risk, uncertainty, and asset prices," Journal of Financial Economics, Elsevier, vol. 91(1), pages 59-82, January.
    7. Hui Hong & Zhicun Bian & Chien-Chiang Lee, 2021. "COVID-19 and instability of stock market performance: evidence from the U.S," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 7(1), pages 1-18, December.
    8. Stefan Nagel & Zhengyang Xu, 2022. "Asset Pricing with Fading Memory," Review of Financial Studies, Society for Financial Studies, vol. 35(5), pages 2190-2245.
    9. Jiawen Xu & Pierre Perron, 2023. "Forecasting in the presence of in-sample and out-of-sample breaks," Empirical Economics, Springer, vol. 64(6), pages 3001-3035, June.
    10. Mardi Dungey & Vitali Alexeev & Jing Tian & Alastair R. Hall, 2015. "Econometricians Have Their Moments: GMM at 32," The Economic Record, The Economic Society of Australia, vol. 91, pages 1-24, June.
    11. Alastair R. Hall, 2015. "Econometricians Have Their Moments: GMM at 32," The Economic Record, The Economic Society of Australia, vol. 91(S1), pages 1-24, June.
    12. Pohl, Walter & Schmedders, Karl & Wilms, Ole, 2021. "Asset pricing with heterogeneous agents and long-run risk," Journal of Financial Economics, Elsevier, vol. 140(3), pages 941-964.
    13. Roel van Elk & Marc van der Steeg & Dinand Webbink, 2013. "The effects of a special program for multi-problem school dropouts on educational enrolment, employment and criminal behaviour; Evidence from a field experiment," CPB Discussion Paper 241.rdf, CPB Netherlands Bureau for Economic Policy Analysis.
    14. Fu, Zhonghao & Hong, Yongmiao & Su, Liangjun & Wang, Xia, 2023. "Specification tests for time-varying coefficient models," Journal of Econometrics, Elsevier, vol. 235(2), pages 720-744.
    15. Timo Dimitriadis & Tobias Fissler & Johanna Ziegel, 2020. "The Efficiency Gap," Papers 2010.14146,, revised Sep 2022.
    16. Helmut Herwartz & Malte Rengel & Fang Xu, 2016. "Local Trends in Price‐to‐Dividend Ratios—Assessment, Predictive Value, and Determinants," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 48(8), pages 1655-1690, December.
    17. Matteo Mogliani, 2010. "Residual-based tests for cointegration and multiple deterministic structural breaks: A Monte Carlo study," Working Papers halshs-00564897, HAL.
    18. Hansen, Lars Peter, 2013. "Uncertainty Outside and Inside Economic Models," Nobel Prize in Economics documents 2013-7, Nobel Prize Committee.
    19. Karantounias, Anastasios G., 2023. "Doubts about the model and optimal policy," Journal of Economic Theory, Elsevier, vol. 210(C).
    20. Angelica Gianfreda & Francesco Ravazzolo & Luca Rossini, 2023. "Large Time‐Varying Volatility Models for Hourly Electricity Prices," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 85(3), pages 545-573, June.

    More about this item

    JEL classification:

    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

    NEP fields

    This paper has been announced in the following NEP Reports:


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:nbr:nberwo:26418. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: the person in charge (email available below). General contact details of provider: .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.