An ordering of measures of the welfare cost of inflation in economies with interest-bearing deposits

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.

Measures of the welfare cost of inflation: a complete ordering

This paper presents three contributions to the literature on the welfare cost of ináation. First, it introduces a new sensible way of measuring this cost - that of a compensating variation in consumption or income, instead of the equivalent variation notion that has been extensively used in empirical and theoretical research during the past fiftt years. We Önd this new measure to be interestingly related to the proxy measure of the shopping-time welfare cost of ináation introduced by Simonsen and Cysne (2001). Secondly, it discusses for which money-demand functions this and the shopping-time measure can be evaluated in an economically meaningful way. And, last but not least, it completely orders a comprehensive set of measures of the welfare cost of ináation for these money-demand specification. All of our results are extended to an economy in which there are many types of monies present, and are illustrated with the log-log money-demand specification.

Welfare cost of inflation considering adoption decisions and interest-bearing deposits

Attanasio et al. (JPE, 2002) have used microeconomic data on households to provide new estimates of the welfare costs of infiation using Bailey's unidimensional welfare measure as a basis for their calculations. Such a measure does not properly take into consideration lhe fact that the majority of households in their sample (58.7 percent) holds not only bank deposits and currency, but also a second type of interest-bearing assct. This work devises alternative formulas which account for the existence of bank deposits and a sccond interest-bearing asset in the economy, as well as for adoption decisions regarding alternative financiai technologies.

Welfare costs of inflation: the case for interest-bearing money and empirical estimates for Brazil

We provide in this paper a closed fonn for the Welfare Cost of Inflation which we prove to be closer than Bailey's expression to the correct solution of the corresponding non-separable differential equation. Next. we extend this approach to ao economy with interest-bearing money, once again presenting a better appoximation than the one given by Bailey's approach. Fmally, empirical estimates for Brazil are presented.

The welfare cost of macroeconomic uncertainty in the post-war period

Lucas (1987) has shown the surprising result that the welfare cost of business cycles is quite small. Using standard assumptions on preferences and a fully-áedged econometric model we computed the welfare costs of macroeconomic uncertainty for the post-WWII era using the multivariate Beveridge-Nelson decomposition for trends and cycles, which considers not only business-cycle uncertainty but also uncertainty from the stochastic trend in consumption. The post-WWII period is relatively quiet, with the welfare costs of uncertainty being about 0:9% of per-capita consumption. Although changing the decomposition method changed substantially initial results, the welfare cost of uncertainty is qualitatively small in the post-WWII era - about $175.00 a year per-capita in the U.S. We also computed the marginal welfare cost of macroeconomic uncertainty using this same technique. It is about twice as large as the welfare cost ñ$350.00 a year per-capita.

A general-equilibrium closed-form solution to the welfare costs of inflation (Forthcoming, Revista Brasileira de Economia)

This work presents closed-form solutions to Lucasís (2000) generalequilibrium expression for the welfare costs of ináation, as well as to the di§erence between the general-equlibrium measure and Baileyís (1956) partial-equilibrium measure. In Lucasís original work only numerical solutions are provided.

The welfare cost of macroeconomic uncertainty in the post-war period

With standard assumptions on preferences and a fully-fledged econometric model we computed the welfare costs of macroeconomic uncertainty for post-war U.S. using the BeveridgeNelson decomposition. Welfare costs are about 0.9% per-capita consumption ($175.00) and marginal welfare costs are about twice as large.

An intra-household approach to the welfare costs of inflation

The literature on the welfare costs of in‡ation universally assumes that the many-person household can be treated as a single economic agent. This paper explores what the heterogeneity of the agents in a household might imply for such welfare analyses. First, we show that allowing for a single-unity or for a multi-unity transacting technology impacts the money demand function and, therefore, the welfare costs of in‡ation. Second, we derive su¢cient conditions that make the welfare assessments which depart directly from the knowledge of the money demand function (as in Lucas (2000)) robust under this alternative setting. Third, we compare our general-equilibrium measure with Bailey’s (1956) partial-equilibrium one.

An intra-household approach to the welfare costs of inflation (Revised Version, Forthcoming 2006, Estudos Econômicos)

The literature on the welfare costs of ináation universally assumes that the many-person household can be treated as a single economic agent. This paper explores what the heterogeneity of the agents in a household might imply for such welfare analyses. First, we show that allowing for a one-person or for a many-person transacting technology impacts the money demand function and, therefore, the welfare costs of ináation. Second, more importantly, we derive su¢ cient conditions under which welfare assessments which depart directly from the knowledge of the money demand function (as in Lucas (2000)) are robust (invariant) under the number of persons considered in the household. Third, we show that Baileyís (1956) partial-equilibrium measure of the welfare costs of ináation can be obtained as a Örst-order approximation of the general-equilibrium welfare measure derived in this paper using a many-person transacting technology.

Welfare costs of inflation when interest-bearing deposits are disregarded: a calculation of the bias

Most estimates of the welfare costs of in ation are devised considering only noninterest- bearing assets, ignoring that since the 80s technological innovations and new regulations have increased the liquidity of interest-bearing deposits. We investigate the resulting bias. Suscient 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 interest-bearing monies may lead to a non-negligible overestimation of the welfare costs of in ation. An intuitive explanation is that such assets may partially make up for the decreased demand of noninterest-bearing assets due to higher in ation.

Welfare characterization of monetary-applied models and three implications

This paper demonstrates that the applied monetary models - the Sidrauski-type models and the cash-in-advance models, augmented with a banking sector that supplies money substitutes services - imply trajectories which are Pareto-Optimum restricted to a given path of the real quantity of money. As a consequence, three results follow: First, Bailey’s formula to evaluate the welfare cost of inflation is indeed accurate, if the longrun capital stock does not depend on the inflation rate and if the compensate demand is considered. Second, the relevant money demand concept for this issue - the impact of inflation on welfare - is the monetary base. Third, if the long-run capital stock depends on the inflation rate, this dependence has a second-order impact on welfare, and, conceptually, it is not a distortion from the social point of view. These three implications moderate some evaluations of the welfare cost of the perfect predicted inflation.

The n-dimensional bailey-divisia measure as a general-equilibrium measure of the welfare costs of inflation

This paper shows that in economies with several monies the Bailey-Divisia multidimensional consumers surplus formula may emerge as an exact general-equilibrium measure of the welfare costs of in ation, provided that preferences are quasilinear.

WeIfare costs of inflation the case for interest-bearing money and empiricaI Estimates for Brazil

We provide in this paper a closed fonn for the Welfare Cost of Inflation which we prove to be closer than Bailey's expression to the correct solution of the corresponding non-separable differential equation. Next, we extend this approach to an economy with interest-bearing money, once again presenting a better appoximation than the one given by Bailey's approach. Finally, empirical estimates for Brazil are presented.