Time-Varying Risk of Disaster, Time-varying Risk Premia, and Macroeconomic Dynamics

Trustees Of Boston University, Boston

Investigators

Abstract

Intellectual Merit The empirical finance literature has provided substantial evidence that risk premia are time-varying. 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 and cyclicality of risk premia. This seems an important neglect, since empirical work suggests a tight connection between risk premia and economic activity: the default premium is correlated with investment, and the stock market, the term premium and (negatively) the short rate lead GDP. Introducing time-varying risk premia requires solving a business cycle model using nonlinear methods, i.e. going beyond the first-order approximation and considering ?higher order terms?. Researchers disagree on the importance of these higher order terms, and the standard view is that they are irrelevant for macroeconomic quantities. The PI's results show, however, that this is not always the case. The proposal introduces time-varying risk premia in a standard business cycle model, through a small, time-varying risk of a ?disaster?. The possibility of disasters, such as wars or economic depressions, can generate large risk premia. Existing work has so far confined itself to endowment economies however, and hence does not consider the feedback from time-varying risk premia to macroeconomic activity. This risk of an economic disaster could be a purely rational expectation, or more generally it could reflect a time-varying belief which is not equal to the objective probability. There are two important channels through which time-varying risk premia (here caused by an increase in the probability of disaster) can affect macroeconomic aggregates. First, discount rates increase, spreads widen, and asset values fall, which tends to reduce aggregate investment, directly through a cost-of-capital effect and indirectly by affecting collateral values. Aggregate employment and output also fall, leading to a recession. These business cycle dynamics occur with no change in total factor productivity. Under some conditions the increase in probability of disaster is observationally equivalent to a preference shock, which is interesting since these shocks appear to be important in accounting for the data (e.g. Smets and Wouters (2003)). Finally, this simple model is at least qualitatively, and potentially quantitatively, consistent with the lead-lag relationships between asset prices and the macroeconomy mentioned above. This would be a first paper. The second channel (which would be another paper) is that changes in risk-premia affect the willingness to engage in risky investments. Economic activity turns to lower risk, lower expected return projects, which has the effect of lowering aggregate productivity and output. This reallocation effect has interesting micro-implications, for which the PI provides some support in the proposal. There are several other interesting extensions which are discussed in the proposal. Broader Impact of the Proposed Activity DSGE models are becoming the workhorse for macroeconomic policy analysis and even forecasting, yet most of them abstract from risk premia and the financial side of the economy. The proposal would lead to progress in this direction, which is important for positive as well as normative analysis. This model is especially helpful in thinking about periods of ?turbulence? in asset markets, such as the recent financial crisis: many commentators have highlighted the possibility that the U.S. economy could fall into another Great Depression. This model studies the macroeconomic effects of such time-varying beliefs. This is also a model of ?asset pricing bubbles? in that it gives a coherent framework where asset prices can move for reasons unrelated to current or future productivity. In terms of research cooperation, the project touches on many areas, including business cycle, asset pricing, and investment theory, and hence would hopefully lead to more interaction between these fields