Ebook Macroeconomic Uncertainty and Asset Prices: A Stochastic Volatility Model
Time-varying macroeconomic uncertainty is an important ingredient for asset valuation. When there is a great deal of uncertainty about how an economy will evolve overtime, this state is likely to be reflected in asset prices because financial markets demand premiums for bearing such non-diversifiable risk. The recent episode of financial crisis in 2008 shows that this is indeed a key link between macro variables and asset markets. However, the previous studies using macroeconomic models to explain asset prices did not pay much attention to this channel of generating risk premiums.
Specifically, the most popular macroeconomic asset pricing models identify consumption growth as the link between macroeconomic variables and asset returns via a simple yet elegant Euler equation. Alas, the aggregate consumption behaves like a random walk and the size of unconditional variance of the consumption growth is fairly modest, which makes difficult measuring the macroeconomic uncertainty via the consumption growth.
Moreover, even if the measurement issue is settled, the standard consumption-based models fail to justify high average equity premium with low and stable interest rates because of the small consumption volatility. Consequently, the role of the stochastic macroeconomic uncertainty is minimal in this setting.
In this paper, we tackle this issue by introducing a novel stochastic volatility component in the consumption-based asset pricing model with a recursive preference function. Regarding the measurement of time-varying macroeconomic uncertainty, we set the volatility processes for consumption and dividend growths to be driven by non-linear functions of latent factors consisting of the common and idiosyncratic components. The common stochastic component is regarded as representing the "macroeconomic uncertainty". We specify the common volatility factor to be persistent and let the actual volatilities be generated by a parametric logistic function. This setup yields volatility processes having two asymptotic levels (high and low uncertainty regimes) with smooth transitions between them.
The existence of transition periods across the high and low regimes of volatilities implies that there is uncertainty about which regimes an economy will end up within the next period and introduces uncertainty about uncertainty. Epsteinand Zin (1989) show that economic agents prefer early resolution of uncertainty if the risk aversion parameter is larger than the reciprocal of the elasticity of intertemporal substitution for the Kreps Porteusutility function. Equipped with this utility function, our volatility setup can create high risk premiums even with a modest level of consumption volatility since economic agents dislike uncertainty about regimes to which they may belong, especially if the perceived macroeconomic uncertainty unravels slowly.
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