Before revision: 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.
After revision: We introduce econometric methods to perform estimation and inference on 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 , 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.