Give Me Strong Moments and Time - Combining GMM and SMM to Estimate Long-Run Risk Asset Pricing Models

Abstract

The long-run consumption risk (LRR) model is a promising approach to resolve prominent asset pricing puzzles. The simulated method of moments (SMM) provides a natural framework to estimate its deep parameters, but caveats concern model solubility and weak identification. We propose a twostep estimation strategy that combines GMM and SMM, and for which we elicit informative macroeconomic and financial moment matches from the LRR model structure. In particular, we exploit the persistent serial correlation of consumption and dividend growth 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 required for both identification and reasonable estimation precision. A simulation study-the first in the context of long-run risk modeling-delineates the pitfalls associated with SMM estimation of a non-linear dynamic asset pricing model. Our study provides a blueprint for successful estimation of the LRR model. Key words:asset pricing, long-run risk, simulated method of moments JEL: C58, G10, G12 * We are grateful to H. Hasseltoft for sharing his Matlab code for the computation of the endogenous LRR parameters and to J. Krause for providing a Matlab implementation of the CMAES algorithm. We retain the responsibility for all remaining errors.

A two-step indirect inference approach to estimate the long-run risk asset pricing model

“…Whether the model is solvable or not, and thus whether LRR model-implied data can be simulated in the first place, depends on the values of ξ M and ξ P . As pointed out by Grammig and Küchlin (2015), the LRR model is solvable for the parameter values calibrated by BY, whereas changes in the parameters within a plausible range can yield an insolvable model.…”