We present a production economy with nominal price rigidities that explains several asset pricing facts, including a downward-sloping term structure of the equity premium, upward sloping term structures of nominal and real interest rates, and the cyclical variation of the term structures. In the model, after a productivity shock a countercyclical labor share exacerbates the procyclicality of dividends, and hence their riskiness, and generates countercyclical inflation. The dividend share gradually increases after a negative productivity shock as the price level increases sluggishly, so the payoffs of short-duration dividend claims (bonds) are more (less) procyclical than the payoffs of long-duration claims (bonds). A slow-moving external habit then produces large and countercyclical prices for these risks as well as high risk premia at very long horizons. In bad times, the slope of equity (bond) yields for the observable maturities becomes more negative (more positive), but risk premia also increase at longer horizons, and market equity premia end up increasing by more than short-run equity premia. The simultaneous presence of market and home consumption habits allows for uniting habits and a production economy without compromising the model’s ability to fit macroeconomic variables. The central bank’s anti-inflationary stance plays a key role in shaping equity and bond prices.
We propose a novel approximation of the risky steady state and construct first-order perturbations around it for a general class of dynamic equilibrium models with time-varying and non-Gaussian risk. We offer analytical formulas and conditions for their local existence and uniqueness. We apply this approximation technique to models featuring Campbell-Cochrane habits, recursive preferences, and time-varying disaster risk, and show how the proposed approximation represents the implications of the model similarly to global solution methods. We show that our approximation of the risky steady state cannot be generically replicated by higher-order perturbations around the deterministic steady state, which cannot account well for the effects of risk in our applications even up to third order. Finally, we argue that our perturbation can be viewed as a generalized version of the heuristic loglinear-lognormal approximations commonly used in the macro-finance literature.
