Give me strong moments and time - Combining GMM and SMM to estimate long-run risk asset pricing models

The long-run consumption risk (LRR) model is a convincing approach towards resolving prominent asset pricing puzzles. Whilst the simulated method of moments (SMM) provides a natural framework to estimate its deep parameters, caveats concern model solubility and weak identification. We propose a two-step estimation strategy that combines GMM and SMM, and for which we elicit informative moment matches from the LRR model structure. In particular, we exploit the persistent serial correlation of consumption and the equilibrium conditions for market return and risk-free rate, as well as the model-implied predictability of the risk-free rate. We match analytical moments when possible and simulated moments when necessary and determine the crucial factors that are required for identification and reasonable estimation precision. By means of a simulation study---the first in the context of long-run risk modeling---we delineate the pitfalls associated with SMM estimation of LRR models, and we present a blueprint for successful estimation.