Asset Pricing for Dynamic Economies

In the economies that we have studied up to this point, output has been taken as exogenous and no explicit consideration has been given to optimal investment decisions. Yet asset-pricing models such as the APT seek to model asset returns as a function of economy-wide sources of uncertainty, one of which may be technological uncertainty. There is also a large literature that seeks to link firms' investment decisions with their optimal financial structure. To address these issues, we now study investment and production decisions in an uncertain environment.

The one-sector optimal growth model has become the mainstay of dynamic macroeconomic modeling. Cass [99] and Koopmans [285] studied the long-run behavior of the deterministic one-sector optimal growth model, and showed the existence of a steady-state solution. This model was extended to the uncertainty case by Brock and Mirman [78], [79] and Mirman and Zilcha [344], who derived the optimal policy functions and the invariant distribution for capital stocks characterizing the stochastic steady state.

In Section 10.1, we provide a competitive equilibrium interpretation of the one-sector optimal growth model under uncertainty by considering first a setup where households own the capital stocks and make all investment decisions and second where they rent capital to firms on a period-by-period basis. This is similar to the approach in Brock [76], [77], who integrated the asset-pricing model with production, and Mehra and Prescott [340], who describe how to analyze dynamic competitive equilibrium models under uncertainty using a recursive approach.