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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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References

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  1. 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.
  2. 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.
  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. Campbell, John, 1996. "Understanding Risk and Return," Scholarly Articles 3153293, Harvard University Department of Economics.
  6. Sydney Ludvigson & Martin Lettau, 1999. "Consumption, aggregate wealth and expected stock returns," Staff Reports 77, Federal Reserve Bank of New York.
  7. 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.
  8. Hall, Alastair R. & Inoue, Atsushi, 2003. "The large sample behaviour of the generalized method of moments estimator in misspecified models," Journal of Econometrics, Elsevier, vol. 114(2), pages 361-394, June.
  9. Hodrick, Robert J. & Zhang, Xiaoyan, 2001. "Evaluating the specification errors of asset pricing models," Journal of Financial Economics, Elsevier, vol. 62(2), pages 327-376, November.
  10. Raymond Kan & Cesare Robotti, 2006. "Specification tests of asset pricing models using excess returns," Working Paper 2006-10, Federal Reserve Bank of Atlanta.
  11. Jagannathan, Ravi & Kubota, Keiichi & Takehara, Hitoshi, 1998. "Relationship between Labor-Income Risk and Average Return: Empirical Evidence from the Japanese Stock Market," The Journal of Business, University of Chicago Press, vol. 71(3), pages 319-47, July.
  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. Douglas Rivers & Quang Vuong, 2002. "Model selection tests for nonlinear dynamic models," Econometrics Journal, Royal Economic Society, vol. 5(1), pages 1-39, June.
  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. 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.
  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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Citations

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Cited by:
  1. Raymond Kan & Cesare Robotti & Jay Shanken, 2009. "Pricing Model Performance and the Two-Pass Cross-Sectional Regression Methodology," NBER Working Papers 15047, National Bureau of Economic Research, Inc.
  2. Sydney Ludvigson & Xiaohong Chen, 2004. "Land of Addicts? An Empirical Investigation of Habit-Based Asset Pricing Models," 2004 Meeting Papers 692, Society for Economic Dynamics.
  3. Barclay, Richard & Fletcher, Jonathan & Marshall, Andrew, 2010. "Pricing emerging market stock returns: An update," Emerging Markets Review, Elsevier, vol. 11(1), pages 49-61, March.
  4. Dovonon, Prosper, 2008. "Large sample properties of the three-step euclidean likelihood estimators under model misspecification," MPRA Paper 40025, University Library of Munich, Germany, revised 16 May 2010.
  5. Craig Burnside, 2010. "Identification and Inference in Linear Stochastic Discount Factor Models," NBER Working Papers 16634, National Bureau of Economic Research, Inc.
  6. Marmer, Vadim & Otsu, Taisuke, 2012. "Optimal comparison of misspecified moment restriction models under a chosen measure of fit," Journal of Econometrics, Elsevier, vol. 170(2), pages 538-550.
  7. Carlos Enrique Carrasco Gutierrez & Wagner Piazza Gaglianone, 2008. "Evaluating Asset Pricing Models in a Fama-French Framework," Working Papers Series 175, Central Bank of Brazil, Research Department.
  8. Pierluigi Balduzzi & Cesare Robotti, 2005. "Asset-pricing models and economic risk premia: a decomposition," Working Paper 2005-13, Federal Reserve Bank of Atlanta.
  9. Nikolay Gospodinov & Raymond Kan & Cesare Robotti, 2012. "Analytical solution for the constrained Hansen-Jagannathan distance under multivariate ellipticity," Working Paper 2012-18, Federal Reserve Bank of Atlanta.

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