Equity, Bonds, Growth and Inflation in a Quadratic Infinite Horizon Economy

This paper exhibits a class of infinite-horizon economies with incomplete markets (GEI) for which the equilibrium can be explicitly derived. We show that if agents have preference orderings represented by expected discounted quadratic utilities and if their endowments are tradable, then the equilibrium consumption and welfare of agents can be expressed as a function of the least variable income stream (LVI) obtainable by trading on the financial markets. If in addition the economy has a Markov structure, then the LVI can be calculated. The model is used to study the behavior of agents on the equity and bond markets in an economy in which the growth and inflation processes are calibrated to fit U.S. data. Two related findings emerge: first, the proportion of bonds in the portfolios of even the most risk-averse agents is small (less than 2%); second, since equity dominates the portfolios of agents, the welfare loss due to variable inflation is small