We introduce econometric methods to perform estimation and inference on the permanent and transitory components of the stochastic discount factor (SDF ) in dynamic Markov environments. The approach is nonparametric in that it does not impose parametric restrictions on the law of motion of the state process. We propose sieve estimators of the eigenvalue-eigenfunction pair which are used to decompose the SDF into its permanent and transitory components , as well as estimators of the long-run yield and the entropy of the permanent component of the SDF, allowing for a wide variety of empirically relevant setups.Consistency and convergence rates are established.The estimators of the eigenvalue, yield and entropy are shown to be asymptotically normal and semiparametrically efficient when the SDF is observable. We also introduce nonparametric estimators of the continuation value under Epstein-Zin preferences, thereby extending the scope of our estimators to an important class of recursive preferences. The estimators are simple to implement, perform favorably in simulations, and may be used to numerically compute the eigenfunction and its eigenvalue in fully specified models when analytical solutions are not available .
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 econometric methods to extract the permanent and transitory components of the SDF process. We show how to estimate the solution to the Perron-Frobenius eigenfunction problem of Hansen and Scheinkman (2009) using data on the Markov state and the SDF process. Estimating directly the eigenvalue and eigenfunction allows one to (1) construct empirically the time series of the permanent and transitory components of the SDF process and (2) estimate the yield and the change of measure which characterize pricing over long investment horizons. The methodology is nonparametric, i.e., it does not impose any tight parametric restrictions on the dynamics of the state variables and the SDF process. We derive the large-sample properties of the estimators and illustrate favorable performance in simulations. The methodology is applied to 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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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
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perform estimation and inference on
extract
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stochastic discount factor (SDF ) in dynamic Markov environments. The approach is nonparametric in that it does not impose parametric restrictions on the law of motion of the state process. We propose sieve estimators of the eigenvalue-eigenfunction pair which are used to decompose the SDF into its
SDF process. We show how to estimate the solution to the Perron-Frobenius eigenfunction problem of Hansen and Scheinkman (2009) using data on the Markov state and the SDF process. Estimating directly the eigenvalue and eigenfunction allows one to (1) construct empirically the time series of the
R
, as well as estimators of the long-run
of the SDF process and (2) estimate the
R
entropy of the permanent component of the SDF, allowing for a wide variety of empirically relevant setups.Consistency and convergence rates are established.The estimators of the eigenvalue, yield and entropy are shown to be asymptotically normal and semiparametrically efficient when the SDF is observable. We also introduce nonparametric estimators of the continuation value under Epstein-Zin preferences, thereby extending the scope of our estimators to an important class of recursive preferences. The estimators are simple to implement, perform favorably in simulations, and may be used to numerically compute the eigenfunction and its eigenvalue in fully specified models when analytical solutions are not available
change of measure which characterize pricing over long investment horizons. The methodology is nonparametric, i.e., it does not impose any tight parametric restrictions on the dynamics of the state variables and the SDF process. We derive the large-sample properties of the estimators and illustrate favorable performance in simulations. The methodology is applied to study an economy where the representative agent is endowed with recursive preferences, allowing for general (nonlinear) consumption and earnings growth dynamics