Solving Ramsey Problems with Nonlinear Projection Methods

This paper applies nonlinear projection methods to solve Ramsey problems in a stochastic monetary economy. The presence of nonlinear distortions in the Ramsey problem requires the use of a solution procedure which captures these effects. The nonlinear projection method, even with low-order Chebyshev polynomials as employed in this paper, is able to capture a significant portion of the Jensen's inequality effects. As an example of the usefulness of nonlinear projection methods, we examine Barro's (1987, 1979) conjecture that welfare gains are available from policy smoothing with debt. Increases in the volatility of distortionary monetary policy are more than offset by declines in the volatility of distortionary labor taxes so that introduction of debt is welfare enhancing.