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For Americans with fading memories of the 1970s, the past few years have been a reminder: Inflation hurts. Exactly how much it hurts is a question that some of the best minds in economics have tried to answer. Advancing our understanding has implications for monetary policymakers balancing a dual mandate of price stability and maximum employment.
One possible cost of inflation is the opportunity cost of holding cash when the price level is rising. Two significant findings stake out the boundaries of this debate. In a 2000 paper, Robert Lucas found a relatively high cost of moderate inflation through this channel: the equivalent of 1.1 percent of lifetime consumption, expressed in welfare terms. Peter Ireland, however, revisited Lucas’ data in 2009 and determined that these welfare costs of inflation are negligible, just 0.04 percent of consumption.
The stakes are real and practical. Many modern economic models are “moneyless,” implicitly assuming these costs are negligible. Ireland’s computations could justify this assumption. But is the assumption a reasonable one?
In recently updated research, Minneapolis Fed Principal Research Economist Juan Pablo Nicolini and Luca Benati of the University of Bern take a fresh run at measuring the cost of inflation, arriving at a higher result much closer to Lucas’ estimate than Ireland’s (Minneapolis Fed Staff Report 675, “The Welfare Costs of Inflation Reconsidered”). Benati and Nicolini integrate more recent data, including, crucially, the prolonged period of low inflation in the U.S. between 2009 and 2019. They also analyze data from other developed countries, including three where nominal interest rates fell below zero.
Benati and Nicolini interrogate various assumptions and functional forms for money demand to arrive at lower and upper bounds for the welfare cost of 5 percent annual inflation. For the U.S. they estimate the cost lies between 0.35 percent and 0.8 percent of lifetime consumption—much closer to Lucas’ estimate of 1.1 percent. This suggests a quantitatively significant opportunity cost of holding money, reflecting a mounting cost to the efficiency of transactions even when inflation is relatively low.
The economists follow the approach first proposed by Martin Bailey in 1956—adopted by Milton Friedman, Lucas, and many others, and theoretically validated in 2019 by Alvarez, Lippi, and Robatto—of equating this cost of inflation to the area under the demand curve for money. This curve plots how the quantity of liquid money in a nation’s economy varies with the prevailing short-term nominal interest rate. All else equal, nominal interest rates rise 1-for-1 with expected inflation. People will hold less money at higher interest rates, which represent the opportunity cost of holding cash that could be earning higher returns.
While the shape of the relationship varies from country to country, this “theory of real money demand” is generally borne out by the data, as in the U.S. through the 20th century (see figure).
In a zero-interest-rate world, businesses and consumers would hold some optimal amount of non-interest-bearing money. Inflation and higher interest rates lead them to hold less than this optimal amount. As in other areas of welfare economics, this loss to society can be mathematically captured by the integral (that is, the area) bounded by the horizontal axis, the money demand curve, and a vertical line at the level of the interest rate. This per-period loss is then translated into welfare terms, as a percentage of average lifetime consumption.
From this widely agreed premise, Benati and Nicolini work through the specific questions that determine whether this area of welfare loss is economically meaningful—or small enough to be practically ignored.
Foremost among those questions: What functional form (the equation relating money to rates) best fits the data? The answer varies across countries, eras, and different ranges of interest rates. For the U.S., the economists find the best overall fit from a form originating in the 1950s with Richard Selden and Henry Latané, which implies that money demand is satiated (fully met) as rates approach a lower bound (typically zero). However, a logarithmic (“log-log”) functional form—while it unrealistically implies infinite money demand at very low rates—fits the data better when rates are below 2 percent and when they enter negative territory. The economists use Selden-Latané as their conservative baseline but apply the log-log form to pin down their upper bound for the welfare loss. (They also assess Ireland’s preferred “semi-log” specification but find the similar-looking Selden-Latané form is generally a better fit.)
Evaluating these functional forms depends on the authors’ updated estimation of each form’s elasticity of money demand (the rate at which demand rises or falls with the interest rate). With the new data through 2019, their finding of an elasticity for the U.S. of about 0.17 percent in the log-log context is lower than that used by Lucas (that is, money holdings appear to be less sensitive to rate changes). However, their estimate of the semi-elasticity (approximately 9 percent for each percentage point change in the rate) and its analogous Selden-Latané parameter (a value of 37) are high. This is a pivotal finding given that Selden-Latané is the superior fit for the data at all but the lowest rates.
Benati and Nicolini also address the important matter of what counts as “money” in this context. Money demand should reflect money in its most liquid forms. Until 1982 in the U.S., this meant cash and checking accounts (the aggregate known as “M1”). A regulatory change that year unleashed an explosion of money market demand accounts (MMDAs), which paid interest but could be drawn upon, much like checking. Ireland included only a subset of these, known as “sweep” accounts. But Benati and Nicolini follow Nicolini’s earlier work with Robert Lucas, arguing that all MMDA funds are essentially as liquid as any checking account. This larger measure, which they call “NewM1,” produces a steeper curve and thus greater welfare effects of inflation, especially at low levels. The authors find further support for their approach in the demand curves of other countries, which had no such regulatory break.
The international results are mixed, but all closer to the Lucas result than to Ireland’s. Some countries, such as Australia and Japan, generate higher welfare costs than the U.S. For countries including Denmark and Sweden, they adapt their approach to accommodate interest rates that dropped below zero in recent years. Taken together, the results underscore the importance of assessing the form and parameters of each country’s money demand on its own terms. Even similarly developed economies treat money differently.
The full costs of inflation are likely varied and diffuse. Benati and Nicolini are seeking the baseline conveyed by the money demand curve: the efficiency loss from holding liquid money when inflation is sapping its value and it might be earning better returns. This does not reflect additional potential costs of inflation, such as distorted price and wage contracts or the difficulty of planning investments and purchases.
Benati and Nicolini find this underlying cost of inflation is likely much larger than the negligible effect embedded in much of today’s practical economic analysis. The finding, they write, “questions the validity of performing monetary policy evaluation in cashless models.”
Read the Minneapolis Fed staff report: “The Welfare Costs of Inflation Reconsidered”
Jeff Horwich is the senior economics writer for the Minneapolis Fed. He has been an economic journalist with public radio, commissioned examiner for the Consumer Financial Protection Bureau, and director of policy and communications for the Minneapolis Public Housing Authority. He received his master’s degree in applied economics from the University of Minnesota.
