Hostname: page-component-8448b6f56d-gtxcr Total loading time: 0 Render date: 2024-04-17T17:32:52.371Z Has data issue: false hasContentIssue false
  • English
  • Français

NONPARAMETRIC EULER EQUATION IDENTIFICATION AND ESTIMATION

Published online by Cambridge University Press:  28 September 2020

Juan Carlos Escanciano ,
Stefan Hoderlein ,
Arthur Lewbel ,
Oliver Linton  and
Sorawoot Srisuma
Juan Carlos Escanciano*
Affiliation:
Universidad Carlos III de Madrid
Stefan Hoderlein
Affiliation:
Emory University
Arthur Lewbel
Affiliation:
Boston College
Oliver Linton
Affiliation:
University of Cambridge
Sorawoot Srisuma
Affiliation:
University of Surrey
*
Address correspondence to Juan Carlos Escanciano, Universidad Carlos III de Madrid, Getafe, Spain; e-mail: jescanci@eco.uc3m.es.
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider nonparametric identification and estimation of pricing kernels, or equivalently of marginal utility functions up to scale, in consumption-based asset pricing Euler equations. Ours is the first paper to prove nonparametric identification of Euler equations under low level conditions (without imposing functional restrictions or just assuming completeness). We also propose a novel nonparametric estimator based on our identification analysis, which combines standard kernel estimation with the computation of a matrix eigenvector problem. Our estimator avoids the ill-posed inverse issues associated with nonparametric instrumental variables estimators. We derive limiting distributions for our estimator and for relevant associated functionals. A Monte Carlo experiment shows a satisfactory finite sample performance for our estimators.

Type
ARTICLES
Information
Econometric Theory , Volume 37 , Issue 5 , October 2021 , pp. 851 - 891
Copyright
© The Author(s), 2020. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

We thank Don Andrews, Bob Becker, Xiaohong Chen, anonymous referees, and seminar participants at University of Miami, UC San Diego, joint MIT-Harvard, Semiparametric Methods in Economics and Finance Workshop (London, 2010), Cowles workshop (2010), AMES (Seoul, 2011), CFE (London, 2013), and the conference in honor of Don Andrews (Konstanz, 2015) for helpful comments. All errors are our own. This paper replaces “Nonparametric Euler Equation Identification and Estimation,” by Lewbel and Linton (2010), and by Lewbel, Linton, and Srisuma (2012), and replaces “Nonparametric Identification of Euler Equations,” by Escanciano and Hoderlein (2010, 2012).

References

REFERENCES

Abbott, B. & Gallipoli, G. (2018) Permanent-Income Inequality. Technical Report, University of British Columbia.Google Scholar
Abramovich, Y.A. & Aliprantis, C.D. (2002) An Invitation to Operator Theory. Graduate Studies in Mathematics 50. American Mathematical Society.CrossRefGoogle Scholar
Ai, C. & Chen, X. (2003) Efficient estimation of models with conditional moment restrictions containing unknown functions. Econometrica 71, 1795–1844.CrossRefGoogle Scholar
Alan, S., Attanasio, O., & Browning, M. (2009) Estimating euler equations with noisy data: Two exact GMM estimators. Journal of Applied Econometrics 24, 309–324.CrossRefGoogle Scholar
An, Y. & Hu, Y. (2012) Well-posedness of measurement error models for self-reported data. Journal of Econometrics 168, 259–269.CrossRefGoogle Scholar
Anatolyev, S. (1999) Nonparametric estimation of nonlinear rational expectation models. Economics Letters 62, 1–6.CrossRefGoogle Scholar
Blundell, R., Chen, X., and Kristensen, D. (2007) Semi-nonparametric IV Estimation of Shape-invariant Engel Curves, Econometrica, 75, 1613–1670.CrossRefGoogle Scholar
Cai, Z., Ren, Y., & Sun, L. (2015) Pricing kernel estimation: A local estimating equation approach. Econometric Theory 31, 560–580.CrossRefGoogle Scholar
Campbell, J.Y. & Cochrane, J. (1999) Force of habit: A consumption-based explanation of aggregate stock market behavior. Journal of Political Economy 107, 205–251.CrossRefGoogle Scholar
Carrasco, M. & Florens, J.P. (2000) Generalization of GMM to a continuum of moment conditions. Econometric Theory 16, 797–834.CrossRefGoogle Scholar
Carrasco, M., Florens, J.P., & Renault, E. (2007) Linear inverse problems and structural econometrics estimation based on spectral decomposition and regularization. In Heckman, J. & Leamer, E. (eds.), Handbook of Econometrics, vol. 6. North-Holland.Google Scholar
Chanchana, P. (2007) An Algorithm for Computing the Perron Root of a Nonnegative Irreducible Matrix. Ph.D. dissertation, North Carolina State University, Raleigh.Google Scholar
Chapman, D.A. (1997) Approximating the asset pricing kernel. The Journal of Finance 52, 1383–1410.CrossRefGoogle Scholar
Chen, X., Chernozhukov, V., Lee, S., & Newey, W. (2014) Identification in semiparametric and nonparametric conditional moment models. Econometrica 82, 785–809.Google Scholar
Chen, X., Linton, O. and Van Keilegom, I. (2003) Estimation of semiparametric models when the criterion function is not smooth, Econometrica, 71, 1591–1608. CrossRefGoogle Scholar
Chen, X., Hansen, L.P., & Scheinkman, J. (2000) Nonlinear Principal Components and Long-Run Implications of Multivariate Diffusions. Unpublished manuscript.Google Scholar
Chen, X., Hansen, L.P., & Scheinkman, J. (2009) Nonlinear principal components and long-run implications of multivariate diffusions. Annals of Statistics 37, 4279–4312.CrossRefGoogle Scholar
Chen, X., Jacho-Chavez, D.T., & Linton, O.B. (2016) Averaging of an Increasing number of moment condition estimators. Econometric Theory 32, 30–70.CrossRefGoogle Scholar
Chen, X. & Ludvigson, S.C. (2009) Land of addicts? An empirical investigation of habit-based asset pricing models. Journal of Applied Econometrics 24, 1057–1093.CrossRefGoogle Scholar
Chen, X. & Pouzo, D. (2009) Efficient estimation of semiparametric conditional moment models with possibly nonsmooth residuals. Journal of Econometrics 152, 46–60.CrossRefGoogle Scholar
Chen, X. & Reiss, M. (2010) On rate optimality for ill-posed inverse problems in econometrics. Econometric Theory 27, 497–521.CrossRefGoogle Scholar
Christensen, T.M. (2015) Nonparametric identification of positive eigenfunctions. Econometric Theory 31, 1310–1330.CrossRefGoogle Scholar
Christensen, T.M. (2017) Nonparametric stochastic discount factor decomposition. Econometrica 85, 1501–1536.CrossRefGoogle Scholar
Cochrane, J. (2001) Asset Pricing. Princeton University Press.Google Scholar
Connor, G. & Korajczyk, R.A. (1993) A test for the number of factors in an approximate factor model. The Journal of Finance 48, 1263–1291.CrossRefGoogle Scholar
Darolles, S., Fan, Y., Florens, J.-P., & Renault, E. (2011) Nonparametric instrumental regression. Econometrica 79, 1541–1565.Google Scholar
Darolles, S., Florens, J.P., & Gouriéroux, C. (2004) Kernel-based nonlinear canonical analysis and time reversibility. Journal of Econometrics 119, 323–353.CrossRefGoogle Scholar
Doukhan, P. (1994) Mixing. Properties and Examples. Lecture Notes in Statistics. Springer.Google Scholar
Doukhan, P., Massart, P., & Rio, E. (1995) Invariance principles for absolutely regular empirical processes. Annales de l’I.H.P. Probabilités et Statistiques 31(2), 393–427.Google Scholar
Dunn, K.B. & Singleton, K.J. (1986) Modeling the term structure of interest rates under non-separable utility and durability of goods. Journal of Financial Economics 17, 27–55.CrossRefGoogle Scholar
Einmahl, J.H.J. & Mason, D.M. (2005) Uniform in bandwidth consistency of kernel-type function estimators. Annals of Statistics 33, 1380–1403.CrossRefGoogle Scholar
Engl, H.W., Hanke, M., & Neubauer, A. (1996) Regularization of Inverse Problems. Kluwer Academic Publishers.CrossRefGoogle Scholar
Escanciano, J.C. (2019) Semiparametric Identification and Fisher Information. https://arxiv.org/abs/1609.06421.Google Scholar
Escanciano, J.C., Jacho-Chávez, D.T., & Lewbel, A. (2014) Uniform convergence of weighted sums of non and semiparametric residuals for estimation and testing. Journal of Econometrics 178, 426–443.CrossRefGoogle Scholar
Fisher, F. (1966) The Identification Problem in Econometrics. McGraw-Hill.Google Scholar
Gallant, A.R. & Tauchen, G. (1989) Seminonparametric estimation of conditionally constrained heterogeneous processes: Asset pricing applications. Econometrica 57, 1091–1120.CrossRefGoogle Scholar
Gayle, Wayne-Roy & Khorunzhina, Natalia (2018) Micro-Level Estimation of Optimal Consumption Choice With I ntertemporal Nonseparability in Preferences and Measurement Errors, Journal of Business & Economic Statistics, 36:2, 227–238.CrossRefGoogle Scholar
Gobet, E., Hoffmann, M., & Reiss, M. (2004) Nonparametric estimation of scalar diffusions based on low frequency data. Annals of Statistics 26, 2223–2253.Google Scholar
Hall, P. & Horowitz, J.L. (2005) Nonparametric methods for inference in the presence of instrumental variables. Annals of Statistics 33, 2904–2929.CrossRefGoogle Scholar
Hall, R.E. (1978) Stochastic implications of the life cycle-permanent income hypothesis: Theory and evidence. Journal of Political Economy 86, 971–987.CrossRefGoogle Scholar
Hansen, B. (2008) Uniform convergence rates for kernel estimation with dependent data. Econometric Theory 24, 726–748.CrossRefGoogle Scholar
Hansen, L.P. & Scheinkman, J.A. (2009) Long-term risk: An operator approach. Econometrica 77, 177–234.Google Scholar
Hansen, L.P. & Scheinkman, J.A. (2012) Recursive utility in a Markov environment with stochastic growth. Proceedings of the National Academy of Sciences 109, 11967–11972.CrossRefGoogle Scholar
Hansen, L.P. & Scheinkman, J.A. (2013) Stochastic Compounding and Uncertain Valuation. Working Paper. University of Chicago.CrossRefGoogle Scholar
Hansen, L.P. & Singleton, K.J. (1982) Generalized instrumental variables estimation of nonlinear rational expectations models. Econometrica 50, 1269–1286.CrossRefGoogle Scholar
Härdle, W. & Mammen, E. (1993) Comparing nonparametric versus parametric regression fits. Annals of Statistics 21, 1926–1947.CrossRefGoogle Scholar
Hoderlein, S., Nesheim, L., & Simoni, A. (2017) Semiparametric Estimation of Random Coefficients in Structural Economic Models. Econometric Theory, 33(6), 1265–1305.CrossRefGoogle Scholar
Kreĭn, M.G. & Rutman, M.A. (1950) Linear Operators Leaving Invariant a Cone in a Banach Space. American Mathematical Society.Google Scholar
Kress, R. (1999) Linear Integral Equations. Springer.CrossRefGoogle Scholar
Lewbel, A. (1987) Bliss levels that aren’t. Journal of Political Economy 95, 211–215.CrossRefGoogle Scholar
Lucas, R.E. (1978) Asset prices in an exchange economy. Econometrica 46, 1429–1445.CrossRefGoogle Scholar
Luenberger, D.G. (1997) Optimization by Vector Space Methods. Wiley.Google Scholar
Mankiw, N.G. (1982) Hall’s consumption hypothesis and durable goods. Journal of Monetary Economics 10, 417–425.CrossRefGoogle Scholar
Newey, W. & Powell, J. (2003) Instrumental variables estimation of nonparametric models. Econometrica 71, 1557–1569.CrossRefGoogle Scholar
Newey, W.K. & West, K.D. (1987) A simple, positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix. Econometrica 55, 703–708.CrossRefGoogle Scholar
Osborn, J.E. (1975) Spectral approximation for compact operators. Mathematics of Computation 29, 712–725.CrossRefGoogle Scholar
Pollard, D. (1984) Convergence of Stochastic Processes. Springer.CrossRefGoogle Scholar
Powell, J.L., Stock, J.H., and Stoker, T.M. (1989) Semiparametric Estimation of Index Coefficients, Econometrica, 57, 1403–1430. CrossRefGoogle Scholar
Radulović, D. (1996) The bootstrap for empirical processes based on stationary observations. Stochastic Processes and their Applications 65, 259–279.CrossRefGoogle Scholar
Ross, S.A. (2015) The recovery theorem. Journal of Finance 70, 615–648.CrossRefGoogle Scholar
Rothenberg, T.J. (1971) Identification in parametric models. Econometrica 39, 577–591.CrossRefGoogle Scholar
Sargan, J.D. (1983) Identification and lack of identification. Econometrica 51, 1605–1633.CrossRefGoogle Scholar
Schaefer, H.H. (1974) Banach Lattices and Positive Operators. Springer-Verlag.CrossRefGoogle Scholar
Tamer, E. (2010) Partial identification in econometrics. Annual Review of Economics 2(1), 167–195.CrossRefGoogle Scholar
van der Vaart, A.W. & Wellner, J.A. (1996) Weak convergence and empirical processes with applications to statistics. Springer Series in Statistics , 1st Edition. Springer-Verlag.Google Scholar
Zeidler, E. (1986) Nonlinear Functional Analysis and its Applications-Fixed Point Theorems. Springer-Verlag.CrossRefGoogle Scholar