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Consumption-based asset pricing with rare disaster risk : a simulated method of moments approach
(2014)
The rare disaster hypothesis suggests that the extraordinarily high postwar U.S. equity premium resulted because investors ex ante demanded compensation for unlikely but calamitous risks that they happened not to incur. Although convincing in theory, empirical tests of the rare disaster explanation are scarce. We estimate a disaster-including consumption-based asset pricing model (CBM) using a combination of the simulated method of moments and bootstrapping. We consider several methodological alternatives that differ in the moment matches and the way to account for disasters in the simulated consumption growth and return series. Whichever specification is used, the estimated preference parameters are of an economically plausible size, and the estimation precision is much higher than in previous studies that use the canonical CBM. Our results thus provide empirical support for the rare disaster hypothesis, and help reconcile the nexus between real economy and financial markets implied by the consumption-based asset pricing paradigm.
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.
We study consumption-portfolio and asset pricing frameworks with recursive preferences and unspanned risk. We show that in both cases, portfolio choice and asset pricing, the value function of the investor/ representative agent can be characterized by a specific semilinear partial differential equation. To date, the solution to this equation has mostly been approximated by Campbell-Shiller techniques, without addressing general issues of existence and uniqueness. We develop a novel approach that rigorously constructs the solution by a fixed point argument. We prove that under regularity conditions a solution exists and establish a fast and accurate numerical method to solve consumption-portfolio and asset pricing problems with recursive preferences and unspanned risk. Our setting is not restricted to affine asset price dynamics. Numerical examples illustrate our approach.
We study consumption-portfolio and asset pricing frameworks with recursive preferences and unspanned risk. We show that in both cases, portfolio choice and asset pricing, the value function of the investor/representative agent can be characterized by a specific semilinear partial differential equation. To date, the solution to this equation has mostly been approximated by Campbell-Shiller techniques, without addressing general issues of existence and uniqueness. We develop a novel approach that rigorously constructs the solution by a fixed point argument. We prove that under regularity conditions a solution exists and establish a fast and accurate numerical method to solve consumption-portfolio and asset pricing problems with recursive preferences and unspanned risk. Our setting is not restricted to affine asset price dynamics. Numerical examples illustrate our approach.