Identifying Long-Run Risks: A Bayesian Mixed-Frequency Approach
发现消费增长率存在高度持久成分，通过贝叶斯混合频率模型估计现金流和资产价格，识别出三个波动过程，其中可预测现金流成分的波动对资产定价至关重要。
We document that consumption growth rates are far from i.i.d. and have a highly persistent component. First, we estimate univariate and multivariate models of cash‐flow (consumption, output, dividends) growth that feature measurement errors, time‐varying volatilities, and mixed‐frequency observations. Monthly consumption data are important for identifying the stochastic volatility process; yet the data are contaminated, which makes the inclusion of measurement errors essential for identifying the predictable component. Second, we develop a novel state‐space model for cash flows and asset prices that imposes the pricing restrictions of a representative‐agent endowment economy with recursive preferences. To estimate this model, we use a particle MCMC approach that exploits the conditional linear structure of the approximate equilibrium. Once asset return data are included in the estimation, we find even stronger evidence for the persistent component and are able to identify three volatility processes: the one for the predictable cash‐flow component is crucial for asset pricing, whereas the other two are important for tracking the data. Our model generates asset prices that are largely consistent with the data in terms of sample moments and predictability features. The state‐space approach allows us to track over time the evolution of the predictable component, the volatility processes, the decomposition of the equity premium into risk factors, and the variance decomposition of asset prices.