The Dynamics of Capital Accumulation in the US: Simulations after Piketty

We develop a dynamic model where a competitive firm produces a single good from labor and capital, with market clearing rates of return. Individuals are heterogeneous in skills, with an endowment in capital/wealth increasing in skill. Individuals aspire to a standard consumption level, with a constant marginal propensity to consume out of income above this level. We define a steady state of this model as an equilibrium where factor returns and wealth shares remain constant. We calibrate the model to the US economy and obtain that a steady state exists. We then study three variants of the model: one with a higher rate of return for large capitals than for smaller ones, one with social mobility, and one with a capital levy financing a lump sum transfer. In all variants, a steady state exists. We also run the model starting from the 2012 US wealth distribution and obtain convergence to the steady state in the basic model as well as in all variants. Convergence takes a long time and is non monotone, with factor returns and wealth shares moving away from their steady state values for long periods.