Continuous-Time Macro-Finance

I characterize asset prices in general equilibrium with risky production. I develop a macroeconomic model that generalizes the framework of Cox, Ingersoll and Ross (1985a) to include elastic labor supply and production with multiple constant elasticity of substitution technologies. I solve for the time- and state-dependent equilibrium of the model using a novel deep neural network technique to approximate optimal policy rules. The calibrated model produces empirically-plausible risk-free rates, equity risk premia, and volatility surfaces from deep microfoundations and reasonable parameter values for uncertainty in production. The numerical solution procedure is far more flexible than standard methods and reveals previously-unknown features of equilibrium behavior and asset prices. My model leads to a novel understanding of aggregate fluctuations. I find that technological shocks are not sufficient to generate aggregate fluctuations. Instead, I locate their origin in shocks to the yield of productive factors within individual production processes. Recovery from an adverse shock involves complex adjustments to the quantity and allocation of productive factors which bring the economy to a different equilibrium state than the one prevailing prior to the shock. We explain why such behaviors cannot be observed in standard macroeconomic models, and discuss their consequences for economic policy.