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:Q1–2010: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:Q1–2010:Q4 is captured by a semi-log function; (ii) based on the estimation of semi-log cointegrating equations, the welfare cost of inflation was found to at the most lie between 0.0131 % of GDP and 0.2186 % of GDP for inflation rates between 0 and 10 %, and; (iii) in comparison, the welfare cost of inflation obtained from the semi-log non-linear long-run money-demand function, derived using the PPR method, for 0–10 % of inflation ranges between 0.4930 and 1.9468 % of GDP. However, the standard errors associated with the welfare cost estimates obtained from PPR relative to the linear models tend to indicate that the nonlinear money demand provides more precise estimates of the welfare costs primarily for higher rates of inflation.