Asset Returns and Macro Risks in the Long-Run : A Low-Frequency Econometrics Analysis

In this paper, I identify the long-run risks (LRR) in the frequency domain, and further estimate the macro (consumption) risk premia in different frequency ranges. To achieve the identification, I employ the long-run projections and the associated inference procedure for I(0) process developed in Müller and Watson (2018, 2020). Build in their low-frequency regression framework in time series, I further propose a Bayesian implementation of two-pass regression to estimate the consumption risk premia in different frequency bands. I then perform the method on the US data across different asset classes. My empirical findings show that there is a low-frequency component (LRR) in consumption, which drives the long-run comovement of its with different financial variables. Importantly, the identified relevant cycles of LRR span around from 3 to 35 years. The resulting estimates are close to the choices of calibration parameters or estimated parameters based on other methods in the existing literature. My empirical results show that the low-frequency variations in consumption growth are not significantly priced in equity market, which is consistent with the implication of LRR models