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Model comparison using the Hansen-Jagannathan distance

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  • Raymond Kan
  • Cesare Robotti

Abstract

Although it is of interest to empirical researchers to test whether or not a particular asset-pricing model is true, a more useful task is to determine how wrong a model is and to compare the performance of competing asset-pricing models. In this paper, we propose a new methodology to test whether two competing linear asset-pricing models have the same Hansen-Jagannathan distance. We show that the asymptotic distribution of the test statistic depends on whether the competing models are correctly specified or misspecified and are nested or nonnested. In addition, given the increasing interest in misspecified models, we propose a simple methodology for computing the standard errors of the estimated stochastic discount factor parameters that are robust to model misspecification. Using the same data as in Hodrick and Zhang (2001), we show that the commonly used returns and factors are, for the most part, too noisy to conclude that one model is superior to the other models in terms of Hansen-Jagannathan distance. In addition, we show that many of the macroeconomic factors commonly used in the literature are no longer priced once potential model misspecification is taken into account.

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Bibliographic Info

Paper provided by Federal Reserve Bank of Atlanta in its series Working Paper with number 2007-04.

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Date of creation: 2007
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Handle: RePEc:fip:fedawp:2007-04

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  1. Douglas Rivers & Quang Vuong, 2002. "Model selection tests for nonlinear dynamic models," Econometrics Journal, Royal Economic Society, vol. 5(1), pages 1-39, June.
  2. Campbell, John, 1996. "Understanding Risk and Return," Scholarly Articles 3153293, Harvard University Department of Economics.
  3. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
  4. Jagannathan, Ravi & Wang, Zhenyu, 1996. " The Conditional CAPM and the Cross-Section of Expected Returns," Journal of Finance, American Finance Association, vol. 51(1), pages 3-53, March.
  5. Robert J. Hodrick & Xiaoyan Zhang, 2000. "Evaluating the Specification Errors of Asset Pricing Models," NBER Working Papers 7661, National Bureau of Economic Research, Inc.
  6. Lars Peter Hansen & John Heaton & Erzo Luttmer, 1993. "Econometric Evaluation of Asset Pricing Models," NBER Technical Working Papers 0145, National Bureau of Economic Research, Inc.
  7. Ravi Jagannathan & Keiichi Kubota & Hitoshi Takehara, 1997. "Relationship between labor-income risk and average return: empirical evidence from the Japanese stock market," Discussion Paper / Institute for Empirical Macroeconomics 117, Federal Reserve Bank of Minneapolis.
  8. Cochrane, John H, 1996. "A Cross-Sectional Test of an Investment-Based Asset Pricing Model," Journal of Political Economy, University of Chicago Press, vol. 104(3), pages 572-621, June.
  9. Sydney Ludvigson & Martin Lettau, 1999. "Consumption, aggregate wealth and expected stock returns," Staff Reports 77, Federal Reserve Bank of New York.
  10. Newey, Whitney K & West, Kenneth D, 1987. "A Simple, Positive Semi-definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix," Econometrica, Econometric Society, vol. 55(3), pages 703-08, May.
  11. Wayne E. Ferson & Campbell R. Harvey, 1999. "Conditioning Variables and the Cross-Section of Stock Returns," NBER Working Papers 7009, National Bureau of Economic Research, Inc.
  12. Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-33, March.
  13. Robert F. Dittmar, 2002. "Nonlinear Pricing Kernels, Kurtosis Preference, and Evidence from the Cross Section of Equity Returns," Journal of Finance, American Finance Association, vol. 57(1), pages 369-403, 02.
  14. Kan, Raymond & Robotti, Cesare, 2008. "Specification tests of asset pricing models using excess returns," Journal of Empirical Finance, Elsevier, vol. 15(5), pages 816-838, December.
  15. Ferson, Wayne E & Harvey, Campbell R, 1991. "The Variation of Economic Risk Premiums," Journal of Political Economy, University of Chicago Press, vol. 99(2), pages 385-415, April.
  16. Alastair R. Hall & Atsushi Inoue, 2005. "The Large Sample Behaviour of the Generalized Method of Moments Estimator in Misspecified Models," Econometrics 0505002, EconWPA.
  17. Wayne E. Ferson & Ravi Jagannathan, 1996. "Econometric evaluation of asset pricing models," Staff Report 206, Federal Reserve Bank of Minneapolis.
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