a b s t r a c tMost estimates of the welfare costs of inflation are devised considering only noninterest-bearing assets, ignoring that since the 1980s technological innovations and new regulations have increased the liquidity of interest-bearing deposits. We investigate the resulting bias. Sufficient and necessary conditions on its sign are presented, along with closed-form expressions for its magnitude. Two examples dealing with bidimensional bilogarithmic money demands show that disregarding interestbearing monies may lead to a non-negligible overestimation of the welfare costs of inflation. An intuitive explanation is that such assets may partially make up for the decreased demand of noninterest-bearing assets due to higher inflation.
This paper builds on Lucas (2000) and on Cysne (2003) to derive and order six alternative measures of the welfare costs of inflation (five of which already existing in the literature) for any vector of opportunity costs. The ordering of the functions is carried out for economies with or without interestbearing deposits. We provide examples and closed-form solutions for the log-log money demand both in the unidimensional and in the multidimensional setting (when interest-bearing monies are present). An estimate of the maximum relative error a researcher can incur when using any particular measure is also provided.
The authors dedicate this work to the memory of Renato Zanforlin.JEL classification: C0 E40 D50 D60
Keywords:Money demand Integrability Sidrauski Shopping time Interest-bearing assets a b s t r a c t This paper investigates which properties money-demand functions must satisfy so that they are consistent with Lucas's [Lucas Jr., R.E., 2000. Inflation and welfare. Econometrica 68, 247-274] versions of the Sidrauski and the shopping-time models. We conclude that shopping-time-integrable money-demand functions are necessarily also Sidrauski-integrable, but that the converse is not necessarily true, unless a boundedness assumption on the nominal interest rate is made. Both the log-log with an interest-rate elasticity greater than or equal to one and the semi-log money demands may serve as counterexamples. All the models and results are also extended to the case in which there are several assets in the economy performing monetary functions.
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