Seigniorage-maximizing inflation

What is the seigniorage-maximizing level of inflation? Four models formulae for the seigniorage maximizing inflation rate (SMIR) are compared. Two sticky-price models arrive at very different quantitative recommendations although both predict somewhat lower SMIRs than Cagan’s formula and a variant of a .ex-price model due to Kimbrough (2006). The models differ markedly in how inflation distorts the labour market: The Calvo model implies that inflation and output are negatively related and that output is falling in price stickiness whilst the Rotemberg cost-of-price-adjustment model implies exactly the opposite. Interestingly, if our version of the Calvo model is to be believed, the level of inflation experienced recently in advanced economies such as the USA and the UK may be quite close to the SMIR. JEL Classification: E4; E52; E61; E63. Keywords: Price stickiness; Revenue maximizing inflation; Inflation tax; Seigniorage; price dispersion. 1. Introduction What is the seigniorage-maximizing level of in‡ation? The answer provided by Cagan (1956) was to set the in‡ation tax rate equal to the inverse of the interest semi-elasticity of the demand for money. Modern general equilibrium treatments of the issue allow that question to be posed in richer theoretical environments. For example, Easterly et al. (1995), endogenized the money demand function via a cash-in-advance constraint resulting in a variable semi-interest elasticity of money demand. They argued that this quali…es in important ways the conclusions of the ‘Cagan rule’. Recently, Kimbrough (2006) has argued that, in addition to modelling money demand, it is important to model the labour-leisure choice. Failing to do so ignores the real e¤ects of in‡ation and hence its impact on the in‡ation-tax base. He develops a ‡exible-price, general equilibrium model with an endogenous labour-leisure choice and with a role for money in reducing transactions costs associated with consumption. He argues that in‡ation reduces the e¤ectiveness of money and causes a substitution toward leisure. The combined e¤ect (on money demand and labour supply) implies a maximizing level of seigniorage lower than prescribed by the Cagan rule. This paper incorporates the potential for price stickiness to impact the seigniorage maximizing in‡ation rate (SMIR). Two versions of popular models of price stickiness are developed, the Calvo (1983) model and the Rotemberg (1982) quadraticcosts-of-price-adjustment model (see also Schmitt-Grohe and Uribe, 2004). Similar along some obvious dimensions, these models nevertheless di¤er in important ways on how in‡ation distorts the real economy. Consequently, they arrive at quantitatively di¤erent conclusions regarding the SMIR. The quantitative conclusions of the sticky-price models are compared with a close variant of the ‡ex-price model developed by Kimbrough (2006) and with the Cagan rule. The key issue that is highlighted is how in‡ation distorts equilibrium in the labour market and so a careful decomposition is provided of the impact of in‡ation on the labour markets in the general equilibrium environments developed. Interestingly, the sticky-price models generally suggest a relatively low SMIR; in particular the Calvo model often recommends an in‡ation rate quite close to that seen recently in many advanced economies, such as the US and the UK. The rest of the paper has the following structure. Section 2 sets up a model similar to Kimbrough (2006) but extended to incorporate monopolistically competitive producers. The section brie‡y derives the Cagan rule before modelling …rms’ price setting behavior following Calvo (1983). Section 3 introduces the