The empirical finance literature has provided substantial evidence that risk premia are time(varying (see for instance Campbell and Shiller (1988), Fama and French (1989), Ferson and Harvey (1991), Cochrane (2005)). Yet, standard business cycle models such as the real business cycle model, or the DSGE models used for monetary policy analysis, largely fail to replicate the level, the volatility, and the cyclicality of risk premia.
This seems an important neglect, since empirical work suggests a tight connection between risk premia and economic activity. For instance, Philippon (2008) and Gilchrist and Zakrajsek (2007) show that corporate bonds spreads are highly correlated with real physical investment, both in the time series and in the cross(section. A large research, summarized in Backus, Routledge and Zin (2008), shows that the stock market, the term premium, and (negatively) the short rate all lead the business cycle.
I introduce time(varying risk premia in a standard real business cycle model, through a small, sto(chastically time(varying risk of economic sdisastert, following the work of Rietz (1988), Barro (2006), and Gabaix (2007). Existing work has so far been confined to endowment economies, and hence does not consider the feedback from time(varying risk premia to macroeconomic activity. I prove two theoretical results, which hold under the assumption that a disaster reduces total factor productivity (TFP) and the capital stock by the same amount.
First, when the risk of disaster is constant, the path for macro(economic quantities implied by the model is the same as that implied by a model with no disasters, but a different discount factor !. This sobservational equivalencet(in a sample without disasters) is similar to Tallarini (2000): macroeconomic dynamics are essentially unaffected by the amount of risk or the degree of risk aversion. Second, when the risk of disaster is time(varying, an increase in probability of disaster is observationally equivalent to a preference shock.
This is interesting since these shocks appear to be important in accounting for the data, according to estimation of DSGE models with multiple shocks such as Smets and Wouters (2003). An increase in the perceived probability of disaster can create a collapse of investment and a recession, as risk premia rise, increasing the cost of capital. Demand for precautionary savings increase, leading the yield on less risky assets to fall, while spreads on risky securities increase. These business cycle dynamics occur with no change in current or future total factor productivity.
Quantitatively, I find that this parsimonious model can match many asset pricing facts ( the mean, volatility, and predictability of returns ( while maintaining the basic success of the RBC model in accounting for quantities. This is important since many asset pricing models which are successful in endowment economies do not generalize well to production economies (as explained in Jermann (1998), Lettau and Uhlig (2001), Kaltenbrunner and Lochstoer (2008)). This second shock also substantially increases the correlation between asset prices (or risk premia) and economic activity, making it closer to the data.
One obvious limitation of the paper is that the probability of disaster is hard to observe. As an empirical exercise, I infer the probability of disaster from asset prices. I then feed into the model this estimated probability of disaster. The variation over time in this probability appears to account for a significant fraction of business cycle dynamics, and it especially helps matching sharp downturns.
This risk of an economic disaster could be a strictly rational expectation, or more generally it could reflect a time(varying belief, which may differ from the objective probability ( i.e., waves of optimism or pessimism (see e.g. Jouini and Napp (2008)). For instance, during the recent financial crisis, many commentators, including well(known macroeconomists, have highlighted the possibility that the U.S. economy could fall into another Great Depression. My model studies the macroeconomic effect of such time(varying beliefs.
This simple modeling device captures the idea that aggregate uncertainty is sometimes high, i.e. people sometimes worry about the possibility of a deep recession. It also captures the idea that there are some asset price changes which are not obviously related to current or future TFP, i.e. sbubblest, sanimal spiritst, and which in turn affect the macroeconomy.
Introducing time(varying risk premia requires solving a model using nonlinear methods, i.e. going beyond the first(order approximation and considering shigher order termst. Researchers disagree on the importance of these higher order terms, and a fairly common view is that they are irrelevant for macroeconomic quantities. Lucas (2003) summarizes: sTallarini uses preferences of the Epstein$Zin type, with an intertemporal substitution elasticity of one, to construct a real business cycle model of the U.S. economy.
He finds an astonishing separation of quantity and asset price determination: The behavior of aggregate quantities depends hardly at all on attitudes toward risk, so the coeffi cient of risk aversion is left free to account for the equity premium perfectly. My results show, however, that these higher(order terms can have a significant effect on macroeconomic dynamics, when we consider shocks to the probability of disaster.
The paper is organized as follows: the rest of the introduction reviews the literature. Section 2 studies a simple analytical example in an AK model which can be solved in closed form and yields the central intuition for the results. Section 3 gives the setup of the full model and presents some analytical results. Section 4 studies the quantitative implications of the model numerically. Section 5 considers some extensions of the baseline model. Section 6 presents the empirical evaluation of the model, backing out the probability of disaster from asset prices.
