Econometrica: Sep 2017, Volume 85, Issue 5

Nonparametric Stochastic Discount Factor Decomposition

DOI: 10.3982/ECTA11600
p. 1501-1536

Timothy M. Christensen

Stochastic discount factor (SDF) processes in dynamic economies admit a permanent‐transitory decomposition in which the permanent component characterizes pricing over long investment horizons. This paper introduces an empirical framework to analyze the permanent‐transitory decomposition of SDF processes. Specifically, we show how to estimate nonparametrically the solution to the Perron–Frobenius eigenfunction problem of Hansen and Scheinkman, 2009. Our empirical framework allows researchers to (i) construct time series of the estimated permanent and transitory components and (ii) estimate the yield and the change of measure which characterize pricing over long investment horizons. We also introduce nonparametric estimators of the continuation value function in a class of models with recursive preferences by reinterpreting the value function recursion as a nonlinear Perron–Frobenius problem. We establish consistency and convergence rates of the eigenfunction estimators and asymptotic normality of the eigenvalue estimator and estimators of related functionals. As an application, we study an economy where the representative agent is endowed with recursive preferences, allowing for general (nonlinear) consumption and earnings growth dynamics.

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Supplemental Material

Supplement to "Nonparametric Stochastic Discount Factor Decomposition"

This supplementary material contains sufficient conditions for several assumptions in Sections 3 and 4 and proofs of all results in the main text.

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Supplement to "Nonparametric Stochastic Discount Factor Decomposition"

This zip file contains the replication files for the manuscript and additional appendices E, F, and G.  Appendix F provides further details on the relation between the identification and existence conditions in Section 2.3 and the identification and existence conditions in Hansen and Scheinkman (2009) and Borovička et al. (2016). Appendix G presents proofs of results in Appendix C of the supplementary material and this online appendix.

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