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Nonparametric Euler Equation Identification and Estimation


  • Arthur Lewbel

    () (Boston College)

  • Oliver Linton

    () (London School of Economics)

  • Sorawoot Srisuma

    () (London School of Economics)


We consider nonparametric identification and estimation of consumption based asset pricing Euler equations. This entails estimation of pricing kernels or equivalently marginal utility functions up to scale. The standard way of writing these Euler pricing equations yields Fredholm integral equations of the first kind, resulting in the ill posed inverse problem. We show that these equations can be written in a form that equals, (or with habits, resembles) Fredholm integral equations of the second kind, having well posed rather than ill posed inverses. We allow durables, habits, or both to affect utility. We show how to extend the usual method of solving Fredholm integral equations of the second kind to allow for the presence of habits. Using these results, we show with few low level assumptions that marginal utility functions and pricing kernels are locally nonparametrically identified, and we give conditions for finite set and point identification of these functions. Unlike the case of ill posed inverse problems, the limiting distribution theory for our nonparametric estimators should be relatively standard.

Suggested Citation

  • Arthur Lewbel & Oliver Linton & Sorawoot Srisuma, 2010. "Nonparametric Euler Equation Identification and Estimation," Boston College Working Papers in Economics 757, Boston College Department of Economics, revised 23 Feb 2011.
  • Handle: RePEc:boc:bocoec:757

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    References listed on IDEAS

    1. Lawrance, Emily C, 1991. "Poverty and the Rate of Time Preference: Evidence from Panel Data," Journal of Political Economy, University of Chicago Press, vol. 99(1), pages 54-77, February.
    2. Hall, Robert E, 1978. "Stochastic Implications of the Life Cycle-Permanent Income Hypothesis: Theory and Evidence," Journal of Political Economy, University of Chicago Press, vol. 86(6), pages 971-987, December.
    3. An, Yonghong & Hu, Yingyao, 2012. "Well-posedness of measurement error models for self-reported data," Journal of Econometrics, Elsevier, vol. 168(2), pages 259-269.
    4. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    5. Chen, Xiaohong & Reiss, Markus, 2011. "On Rate Optimality For Ill-Posed Inverse Problems In Econometrics," Econometric Theory, Cambridge University Press, vol. 27(03), pages 497-521, June.
    6. Felix Kubler & Karl Schmedders, 2010. "Non-parametric counterfactual analysis in dynamic general equilibrium," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 45(1), pages 181-200, October.
    7. Gallant, Ronald & Tauchen, George, 1989. "Seminonparametric Estimation of Conditionally Constrained Heterogeneous Processes: Asset Pricing Applications," Econometrica, Econometric Society, vol. 57(5), pages 1091-1120, September.
    8. Hoderlein, Stefan & Nesheim, Lars & Simoni, Anna, 2017. "Semiparametric Estimation Of Random Coefficients In Structural Economic Models," Econometric Theory, Cambridge University Press, vol. 33(06), pages 1265-1305, December.
    9. Darolles, Serge & Florens, Jean-Pierre & Gourieroux, Christian, 2004. "Kernel-based nonlinear canonical analysis and time reversibility," Journal of Econometrics, Elsevier, vol. 119(2), pages 323-353, April.
    10. Carrasco, Marine & Florens, Jean-Pierre & Renault, Eric, 2007. "Linear Inverse Problems in Structural Econometrics Estimation Based on Spectral Decomposition and Regularization," Handbook of Econometrics,in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 77 Elsevier.
    11. Dunn, Kenneth B. & Singleton, Kenneth J., 1986. "Modeling the term structure of interest rates under non-separable utility and durability of goods," Journal of Financial Economics, Elsevier, vol. 17(1), pages 27-55, September.
    12. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-1445, November.
    13. Erich Battistin & Richard Blundell & Arthur Lewbel, 2009. "Why Is Consumption More Log Normal than Income? Gibrat's Law Revisited," Journal of Political Economy, University of Chicago Press, vol. 117(6), pages 1140-1154, December.
    14. Escanciano, Juan Carlos & Jacho-Chávez, David T. & Lewbel, Arthur, 2014. "Uniform convergence of weighted sums of non and semiparametric residuals for estimation and testing," Journal of Econometrics, Elsevier, vol. 178(P3), pages 426-443.
    15. Elie Tamer, 2010. "Partial Identification in Econometrics," Annual Review of Economics, Annual Reviews, vol. 2(1), pages 167-195, September.
    16. Sargan, J D, 1983. "Identification and Lack of Identification," Econometrica, Econometric Society, vol. 51(6), pages 1605-1633, November.
    17. Steve Ross, 2015. "The Recovery Theorem," Journal of Finance, American Finance Association, vol. 70(2), pages 615-648, April.
    18. Chapman, David A, 1997. " Approximating the Asset Pricing Kernel," Journal of Finance, American Finance Association, vol. 52(4), pages 1383-1410, September.
    19. Mankiw, N. Gregory, 1982. "Hall's consumption hypothesis and durable goods," Journal of Monetary Economics, Elsevier, vol. 10(3), pages 417-425.
    20. Timothy Christensen, 2014. "Nonparametric Stochastic Discount Factor Decomposition," Papers 1412.4428,, revised May 2017.
    21. Xiaohong Chen & Lars Peter Hansen & Jose Scheinkman, 2009. "Principal Components and Long Run Implications of Multivariate Diffusions," Cowles Foundation Discussion Papers 1694, Cowles Foundation for Research in Economics, Yale University.
    22. Cai, Zongwu & Ren, Yu & Sun, Linman, 2015. "Pricing Kernel Estimation: A Local Estimating Equation Approach," Econometric Theory, Cambridge University Press, vol. 31(03), pages 560-580, June.
    23. Andrews, Donald W.K., 1995. "Nonparametric Kernel Estimation for Semiparametric Models," Econometric Theory, Cambridge University Press, vol. 11(03), pages 560-586, June.
    24. Rothenberg, Thomas J, 1971. "Identification in Parametric Models," Econometrica, Econometric Society, vol. 39(3), pages 577-591, May.
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    Cited by:

    1. Timothy M. Christensen, 2014. "Nonparametric identification of positive eigenfunctions," CeMMAP working papers CWP37/14, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    2. Xiaohong Chen & Victor Chernozhukov & Sokbae Lee & Whitney K. Newey, 2014. "Local Identification of Nonparametric and Semiparametric Models," Econometrica, Econometric Society, vol. 82(2), pages 785-809, March.

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    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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