Identifying Long-Run Risks: A Bayesian Mixed-Frequency Approach

Abstract

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.

Valuation Risk Revalued

“…We examine in-depth the role of valuation risk by estimating a sequence of increasingly rich models. A notable difference from our results is that Schorfheide et al (2018) find a limited role for the general equilibrium demand channel. Creal and Wu (2017) focus on bond premia.…”

“…In standard asset pricing models, uncertainty enters through the supply side of the economy, either through endowment shocks in a Lucas (1978) tree model or productivity shocks in a production economy model. Recently, several papers introduced demand side uncertainty or "valuation risk" as a potential explanation of key asset pricing puzzles (Albuquerque et al, 2016(Albuquerque et al, , 2015Creal and Wu, 2017;Maurer, 2012;Nakata and Tanaka, 2016;Schorfheide et al, 2018). In macroeconomic parlance, valuation risk is typically referred to as a discount factor or time preference shock.…”

“…Albuquerque et al (2016) also focus on resolving the correlation puzzle (Campbell and Cochrane, 1999). Schorfheide et al (2018) use a Bayesian mixedfrequency approach that allows them to target entire time series, rather than specific moments. They focus on one model with three SV processes.…”

Informality and bank stability

“…In standard asset pricing models, uncertainty enters through the supply side of the economy, either through endowment shocks in a Lucas (1978) tree model or productivity shocks in a production economy model. Recently, several papers introduced demand side uncertainty or "valuation risk" as a potential explanation of key asset pricing puzzles (Albuquerque et al, 2016(Albuquerque et al, , 2015Creal and Wu, 2017;Maurer, 2012;Nakata and Tanaka, 2016;Schorfheide et al, 2018). In macroeconomic parlance, valuation risk is typically referred to as a discount factor or time preference shock.…”

Two Essays on Weak Identification in Macroeconomic Models

“…results in Schorfheide, Song, and Yaron (2018). Finally, the same rule for σ ν applies, which establishes that the long-run standard deviation of unfiltered consumption is not higher than 1.2 times that of its reported analogue.…”