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Can consumption-based mechanisms generate positive and time-varying real term premia as we see in the data? I show that only models with time-varying risk aversion or models with high consumption risk can independently produce these patterns. The latter explanation has not been analysed before with respect to real term premia, and it relies on a small group of investors exposed to high consumption risk. Additionally, it can give rise to a “consumption-based arbitrageur” story of term premia. In relation to preferences, I consider models with both time-separable and recursive utility functions. Specifically for recursive utility, I introduce a novel perturbation solution method in terms of the intertemporal elasticity of substitution. This approach has not been used before in such models, it is easy to implement, and it allows a wide range of values for the parameter of intertemporal elasticity of substitution.
The long-run consumption risk model provides a theoretically appealing explanation for prominent asset pricing puzzles, but its intricate structure presents a challenge for econometric analysis. This paper proposes a two-step indirect inference approach that disentangles the estimation of the model's macro-economic dynamics and the investor's preference parameters. A Monte Carlo study explores the feasibility and efficiency of the estimation strategy. We apply the method to recent U.S.\data and provide a critical re-assessment of the long-run risk model's ability to reconcile the real economy and financial markets. This two-step indirect inference approach is potentially useful for the econometric analysis of other prominent consumption-based asset pricing models that are equally difficult to estimate.
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 two-step 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.