Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-09T22:27:22.595Z Has data issue: false hasContentIssue false
  • English
  • Français

NONPARAMETRIC IDENTIFICATION OF POSITIVE EIGENFUNCTIONS

Published online by Cambridge University Press:  09 October 2014

Timothy M. Christensen
Timothy M. Christensen*
Affiliation:
New York University
*
*Address correspondence to Timothy Christensen, Department of Economics, New York University, 19 W. 4th Street, 6th Floor, New York, NY 10012, USA; e-mail: [email protected].
Get access Rights & Permissions [Opens in a new window]

Abstract

Important features of certain economic models may be revealed by studying positive eigenfunctions of appropriately chosen linear operators. Examples include long-run risk–return relationships in dynamic asset pricing models and components of marginal utility in external habit formation models. This paper provides identification conditions for positive eigenfunctions in nonparametric models. Identification is achieved if the operator satisfies two mild positivity conditions and a power compactness condition. Both existence and identification are achieved under a further nondegeneracy condition. The general results are applied to obtain new identification conditions for external habit formation models and for positive eigenfunctions of pricing operators in dynamic asset pricing models.

Type
ARTICLES
Information
Econometric Theory , Volume 31 , Issue 6 , December 2015 , pp. 1310 - 1330
Copyright
Copyright © Cambridge University Press 2014 

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.)

References

REFERENCES

Alvarez, F. & Jermann, U.J. (2005) Using asset prices to measure the persistence of the marginal utility of wealth. Econometrica 73(6), 1977–2016.CrossRefGoogle Scholar
Backus, D., Chernov, M., & Zin, S. (2014) Sources of entropy in representative agent models. Journal of Finance 69(1), 51–99.CrossRefGoogle Scholar
Bertholon, H., Monfort, A., & Pegoraro, F. (2008) Econometric asset pricing modelling. Journal of Financial Econometrics 6(4), 407–458.CrossRefGoogle Scholar
Chan, K.S. & Tong, H. (1985) On the use of the deterministic Lyapunov function for the ergodicity of stochastic difference equations. Advances in Applied Probability 17(3), 666–678.CrossRefGoogle Scholar
Chen, X., Chernozhukov, V., Lee, S., & Newey, W.K. (2014) Local identification of nonparametric and semiparametric models. Econometrica 82(2), 785–809.Google Scholar
Chen, X. & Ludvigson, S.C. (2009) Land of addicts? An empirical investigation of habit-based asset pricing models. Journal of Applied Econometrics 24(7), 1057–1093.CrossRefGoogle Scholar
Christensen, T.M. (2013) Nonparametric Stochastic Discount Factor Decomposition. Working paper, Yale University.Google Scholar
Darolles, S., Gourieroux, C., & Jasiak, J. (2006) Structural Laplace transform and compound autoregressive models. Journal of Time Series Analysis 27(4), 477–503.CrossRefGoogle Scholar
D’Haultfoeuille, X. (2011) On the completeness condition in nonparametric instrumental problems. Econometric Theory 27, 460–471.CrossRefGoogle Scholar
Dunford, N. & Schwartz, J.T. (1958) Linear Operators, Part I: General Theory. Interscience Publishers.Google Scholar
Eraker, B. (2008) Affine general equilibrium models. Management Science 54(12), 2068–2080.CrossRefGoogle Scholar
Escanciano, J.C. & Hoderlein, S. (2012) Nonparametric Identification of Euler Equations. Working paper, Indiana University.Google Scholar
Fan, J. & Yao, Q. (2003) Nonlinear Time Series: Nonparametric and Parametric Methods. Springer-Verlag.Google Scholar
Gallant, A.R. & Tauchen, G. (1989) Seminonparametric estimation of conditionally constrained heterogeneous processes: Asset pricing applications. Econometrica 57, 1091–1120.CrossRefGoogle Scholar
Gourieroux, C. & Jasiak, J. (2006) Autoregressive gamma processes. Journal of Forecasting 25(2), 129–152.CrossRefGoogle Scholar
Hansen, L.P. (2012) Dynamic valuation decomposition within stochastic economies. Econometrica 80(3), 911–967.Google Scholar
Hansen, L.P. & Renault, E. (2010) Encyclopedia of Quantitative Finance, Chapter Pricing Kernels. Wiley.Google Scholar
Hansen, L.P. & Scheinkman, J.A. (2009) Long-term risk: An operator approach. Econometrica 77(1), 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(5), 1269–1286.CrossRefGoogle Scholar
Härdle, W., Tsybakov, A., & Yang, L. (1998) Nonparametric vector autoregression. Journal of Statistical Planning and Inference 68(2), 221–245.CrossRefGoogle Scholar
Kato, T. (1980) Perturbation Theory for Linear Operators. Springer-Verlag.Google Scholar
Kreĭn, M.G. & Rutman, M.A. (1950) Linear Operators Leaving Invariant a Cone in a Banach Space. American Mathematical Society.Google Scholar
Lewbel, A., Linton, O.B., & Srisuma, S. (2011) Nonparametric Euler Equation Identification and Estimation. Working paper, Boston College and London School of Economics.Google Scholar
Monfort, A. & Pegoraro, F. (2007) Switching VARMA term structure models. Journal of Financial Econometrics 5(1), 105–153.CrossRefGoogle Scholar
Ross, S.A. (2013) The recovery theorem. Journal of Finance, forthcoming.Google Scholar
Schaefer, H.H. (1960) Some spectral properties of positive linear operators. Pacific Journal of Mathematics 10, 1009–1019.CrossRefGoogle Scholar
Schaefer, H.H. (1974) Banach Lattices and Positive Operators. Springer-Verlag.Google Scholar
Schaefer, H.H. (1999) Topological Vector Spaces. Springer-Verlag.CrossRefGoogle Scholar
Severini, T.A. & Tripathi, G. (2006) Some identification issues in nonparametric linear models with endogenous regressors. Econometric Theory 22, 258–278.CrossRefGoogle Scholar