Econometric Analysis of Long-Run Risk in Empirical Asset Pricing

Abstract

Research in financial economics has endeavored to explain asset pricing puzzles for decades. A popular theoretical approach that promises to resolve several asset pricing puzzles is the long-run risk (LRR) asset pricing model proposed by Bansal and Yaron (2004), a model that is intricate in nature and thus challenging to analyze with econometric techniques. This study is concerned with the econometric analysis of the LRR model, encompassing obstacles to the estimation, identification issues, and an empirical evaluation. For that purpose, different econometric methods are applied to the theoretical model, including the generalized method of moments (GMM), the simulated method of moments (SMM), indirect inference estimation, and maximum likelihood (ML) estimation that relies on filtering techniques. The recurring theme of all estimation strategies is that the estimation strategy must be consistent with the inherently recursive structure of the LRR model. The analysis of previous moment-based econometric approaches reveals identification issues. By means of a Monte Carlo study, a two-step GMM/SMM estimation strategy that exploits analytical moments where possible and simulated moments where necessary is shown to overcome the drawbacks of earlier methods. However, the precise estimation of the LRR model parameters requires the inclusion of a large number of auto-moments in the estimation. Subsequently, a more parsimonious estimation approach is developed: in a two-step indirect inference estimation strategy, tailor-made auxiliary models are used in each step to consecutively estimate the parameters that determine the macroeconomy and the financial market. In contrast to the two-step GMM/SMM estimation strategy, the indirect inference approach is entirely simulation-based and thus allows for different frequencies of the model and the data, making the method more useful for empirical applications. Finally, to enhance estimation precision and to estimate the stochastic variance parameters, which could not be identified by the previous methods, a maximum likelihood estimation strategy is developed. The use of filtering methods permits the application of maximum likelihood despite the presence of latent variables. The proposed three-step method allows for the estimation of the full set of LRR model parameters and thus overcomes the lack of identification of the parameters that characterize the fluctuating economic uncertainty. A Monte Carlo study demonstrates the efficiency gains and establishes the viability of the suggested method. Subsequently, an empirical application is conducted on monthly U.S. data, which provides evidence for a rather risk-averse investor, even though long-run risk is accounted for.