On measuring the welfare cost of inflation
What this paper finds — and why it matters
Measuring the welfare cost of inflation requires specifying a money demand function, a definition of money, and an approach to consumer surplus; existing estimates vary widely because these choices are not standardized. This paper advances the literature by applying neoclassical monetary demand theory that integrates the demand for money with the demands for consumption and leisure, using the Normalized Quadratic (NQ) flexible functional form that avoids imposing specific elasticity assumptions. The main contribution is to extend the Serletis and Xu (2021, 2023) framework to derive Hicksian (compensating variation) money demand functions from the NQ model and compare welfare cost estimates based on these against estimates from the Marshallian (consumer surplus) approach—a comparison not previously made within this integrated demand-system framework. The paper uses U.S. CFS Divisia monetary aggregates across multiple levels of monetary aggregation and finds that the two approaches yield internally consistent but quantitatively different welfare cost estimates, with the Hicksian compensating variation approach providing theoretically preferred measures that are robust across specifications.
Summary of a forthcoming paper, AI-assisted and human-reviewed. See the linked original for the authoritative claims and full conditions.
Q1. What is the neoclassical demand system approach and how does it differ from earlier methods?
The Serletis-Xu framework integrates the demand for money with the demands for consumption goods and leisure in a joint utility maximization problem, estimating a flexible NQ functional form in a systems context rather than fitting a single-equation money demand specification. Earlier approaches—such as the log-log specification (Lucas 2000) or semi-log specification (Ireland 2009)—estimate a single money demand equation under a maintained functional form assumption and a fixed interest elasticity (often −0.5 as in the Baumol-Tobin model). The NQ approach, derived from the dual demand system of Diewert (1974), makes no assumption about the functional form of money demand and allows demand interactions among consumption goods, leisure, and money (as recommended by Abbott and Ashenfelter 1976 and Barnett 1979), which is necessary for correct welfare measurement when money is consumed jointly with other goods.
Q2. What is the distinction between the Marshallian and Hicksian approaches to measuring welfare cost?
The Marshallian (Bailey 1956) approach measures the area under the inverse money demand curve between the zero-inflation and positive-inflation nominal interest rates, which corresponds to consumer surplus but does not hold utility constant. The Hicksian (compensating variation) approach measures the income that must be given to the consumer to restore the same utility after the inflation increase as before—holding utility constant rather than income. The Hicksian approach is theoretically preferred because it measures the true welfare loss from inflation under standard consumer theory; the Marshallian approach can under- or over-estimate the true cost depending on income effects. The paper’s main contribution is to derive the Hicksian demands from the NQ model and compute the compensating variation, previously not done within this flexible-functional-form demand system framework.
Q3. What role do Divisia monetary aggregates play?
The paper uses CFS (Center for Financial Stability) Divisia monetary aggregates—which aggregate monetary assets using economic quantity indices that weight components by their monetary service flows—rather than simple-sum aggregates such as M1 or M2. Simple-sum aggregates treat all monetary assets as perfect substitutes regardless of yield differentials, introducing a substitution bias that misrepresents the quantity of monetary services; Divisia aggregates are theoretically consistent with the neoclassical demand system approach used here. The paper reports welfare cost estimates across multiple levels of monetary aggregation to assess sensitivity to the definition of money.
Q4. How do the results compare with the prior literature?
The paper’s estimates, while internally consistent with the NQ flexible form and Divisia aggregates, are in the range of prior estimates in the literature; the Hicksian compensating variation estimates differ from Marshallian consumer surplus estimates in ways consistent with theory, providing a more theoretically grounded benchmark. The wide range of estimates in the existing literature (discussed in the paper’s Table 1)—from the Lucas (2000) log-log model to the Ireland (2009) semi-log model—reflects sensitivity to functional form, money definition, data frequency, and methodology; the paper’s NQ framework addresses functional-form sensitivity while comparing the two surplus measures.
Key concepts
compensating variation (Hicksian welfare cost of inflation) : the income required to restore a consumer’s utility to its pre-inflation level after an inflation increase, holding utility constant; the paper’s main new estimate, derived from Hicksian money demand functions.
Normalized Quadratic (NQ) flexible functional form : a globally flexible functional form (Diewert and Wales 1988) used to approximate the consumer’s cost function without imposing restrictions on substitution elasticities; allows derivation of both Marshallian and Hicksian demand functions.
Divisia monetary aggregates : theoretically consistent monetary aggregates that weight monetary assets by their monetary service flows (user costs) rather than summing them with equal weights; CFS Divisia aggregates are used here as the measure of money.