A heterogenous-agent new Keynesian model for the evolution of the distribution of wealth

New Keynesian models, designed to explore the role of active monetary policy in market economies, have found some other applications, including models of capital accumulation. Most such models however are based on representative agent assumptions that conflict with some important facts regarding the distribution of wealth and income, as they assume that all agents are alike in these regards, or indeed that there is only one aggregate agent. They are also based on life cycle models of consumption and saving, which (as Piketty observes) imply that each agent would accumulate wealth roughly in proportion to the agent’s annual income. However, in fact many consumers even in advanced countries have essentially no wealth, and their economic action is constrained by lack of liquidity. A modest recent literature of heterogenous-agent new Keynesian (HANK) models extends the discussion of the role of monetary policy by allowing policy changes to relax the liquidity constraints of some consumers. Extending work in a recent book by McCain, this paper constructs a version of a HANK model in which, given a markup of borrowing over lending rates, no interior solution is possible. Agents differ both in initial-period wealth and an idiosyncratic parameter of the productivity of human capital. Agents characterized either by low initial-period wealth or high productivity of human capital may find that the rate of return to formation of illiquid human capital exceeds that of saving in liquid assets. Their rational decisions correspond to a corner solution at zero financial assets. Implications for the evolution of the distribution of wealth are discussed.