A Time-Varying Approach of the Us Welfare Cost of Inflation

Abstract

Money-demand specifications exhibit instability, especially for long spans of data. This paper reconsiders the welfare cost of inflation for the US economy using a flexible time-varying (TV) cointegration methodology to estimate the money-demand function. We find evidence that the TV cointegration estimation provides a better fit of the actual data than a time-invariant estimation and that the throughout unitary income elasticity only exists for the log–log form over the entire sample period. Our estimate of the welfare cost of inflation for a 10% inflation rate lies in the range of 0.025–0.75% of gross domestic product (GDP) and averages 0.27%. In sum, our findings fall well within the ranges of existing studies of the welfare cost of inflation. We find that the welfare cost averages 7.4% higher during expansions than recessions for 10% inflation rate. Finally, the interest elasticity of money demand shows substantial variability over our sample period.

Time-Varying Money Demand and Real Balance Effects

“…It provides a microfounded interpretation of the interest semi-elasticity of money demand and the welfare cost of in ‡ation. This extends the work of many scholars (Cagan, 1956;Lucas, 1981;Meltzer, 1963;Sidrauski, 1967;Fischer, 1981;Cooley and Hansen, 1989;Dotsey and Ireland, 1996;Lucas, 2000;Ireland, 2009;Miller et al, 2019). The identi…cation of the changes in the semi-elasticity and the welfare cost can explain the contrasting welfare estimates presented in the existing literature (Broaddus and Goodfriend, 1984;Reynard, 2004;Ireland, 2009;Lucas and Nicolini, 2015).…”

“…A large variation in these numbers between the two time periods is also observed. There are signi…cant changes in the elasticity of money demand, a result which is consistent with the …ndings of Ireland (2009), but di¤erent from those found in Miller et al (2019). 12 First, the elasticity of substitution between consumption and real balances between the two periods is said to have fallen.…”

“…The …ndings also explain the shifts in the welfare cost of in ‡ation and connect both the household behavior and changes in the U.S. macroeconomic dynamics through the money demand function. The time-varying aspect of the semi-elasticity contributes to the money demand instability (Khan, 1974;Judd and Scadding, 1982;Tesfatsion and Veitch, 1990;Hafer and Jansen, 1991;Miller, 1991;Lütkepohl, 1993;Chen, 2006;Ireland, 2009;Hall et al, 2009;Inagaki, 2009;Jawadi and Sousa, 2013;Lucas and Nicolini, 2015;Miller et al, 2019). These results indicate that the singlevalued approach to approximating the welfare cost of in ‡ation presented in previous literature captures only the sample average at each point in time.…”

“…Following Ireland (2009) and Miller et al (2019), the money-income ratio is measured by dividing the Cynamon et al (2006) sweep-adjusted M1 money stock (M1RS aggregate) by nominal GDP, the three-month U.S. Treasury bill rate, which serves as the measure of i and matches the risk-free rate, nominally-denominated bonds that serve as an alternative store of value in theoretical models of money demand. 6 We utilize both static ordinary least squares (SOLS) and dynamic ordinary least squares (DOLS) estimates of the parameters of the money demand, linking ln (m) and i.…”

“…For example,Ireland (2009) found a welfare cost for a 10% in ‡ation rate of less than 0.25% of income;Lucas (2000) found a welfare cost for 10% in ‡ation of just over 1.8% income; Fischer (1981) found a welfare cost for 10% in ‡ation between 0.2% and 0.3% income;Cooley and Hansen (1989) found that a welfare cost of 10% in ‡ation is about 0.4% of GDP using a cash-in-advance version of the business cycle model Miller et al (2019). found a welfare cost for 10% in ‡ation of just over average 0.27% income.…”