Reconsidering the Welfare Cost of Inflation in the US: A Nonparametric Estimation of the Nonlinear Long-Run Money Demand Equation using Projection Pursuit Regressions

This paper, first, estimates the appropriate, log-log or semi-log, linear long-run money demand relationship capturing the behavior US money demand over the period of 1980:Q1 to 2010:Q4, using the standard linear cointegration procedures found in the literature, and the corresponding nonparametric version of the same based on Projection Pursuit Regression (PPR) methods. We then, compare the resulting welfare costs of inflation obtained from the linear and nonlinear money demand cointegrating equations. We make the following observations: (i) The appropriate money demand relationship for the period of 1980:Q1 to 2010:Q4 is captured by a semi-log function, since no cointegrating relationship could be obtained for the log-log model; (ii) The semi-elasticity of interest rate obtained from the PPR method is found to be more than double the corresponding estimate obtained under the linear case; (iii) Based on the estimation of semi-log cointegrating equations, the welfare cost of inflation was found to at the most lie between 0.0131 percent of GDP to 0.2186 percent of GDP for inflation rates between 0 percent and 10 percent, and; (iv) In comparison, the welfare cost of inflation obtained from the semi-log non-linear long-run money demand function, obtained using the PPR method, for 0 to 10 percent of inflation ranges between 0.4929 to 1.9468 percent of GDP. These results suggest that the Federal Reserve’s current policy, which generates low but still positive rates of inflation, might not be an adequate approximation in terms of the welfare cost of inflation. Perhaps, moving all the way to a Friedman-type deflationary rule for a zero nominal interest is a more desired policy given the size of welfare loss.