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Third Quarter 2021, 
Vol. 103, No. 3
Posted 2021-07-01

Is It Time for Some Unpleasant Monetarist Arithmetic?

Posted 2021-05-26


Sargent and Wallace (1981) published "Some Unpleasant Monetarist Arithmetic" 40 years ago. Their central message was that a central bank may not have the power to determine the long-run rate of inflation without fiscal support. In a policy regime where the fiscal authority is non-Ricardian, an attempt on the part of the central bank to lower inflation may end up backfiring. I develop a structural model to illustrate this result through the use of a diagram. In addition, I use the model to explain how low inflation, low interest rates, and high primary budget deficits can coexist. I also use the model to explain why it is easier for a central bank to lower inflation than to raise it. I conclude with some recommendations for state-contingent monetary policy.

I thank, without implicating, Marco Bassetto and Miguel Faria e Castro for their comments on an earlier draft. David Andolfatto is senior vice president and economist at the Federal Reserve Bank of St. Louis.


Forty years ago, Sargent and Wallace (1981) suggested that an attempt on the part of a central bank to tighten monetary policy for the purpose of reducing the long-run rate of inflation could conceivably backfire in the absence of fiscal support. This idea seems contrary to the common belief that an "independent" central bank can determine the long-run rate of inflation. For example, the Federal Open Market Committee's (FOMC's) "Statement on Longer-Run Goals and Monetary Policy Strategy"—the FOMC's Nicene Creed, so to speak—states, among other things, that

"The inflation rate over the longer run is primarily determined by monetary policy, and hence the Committee has the ability to specify a longer-run goal for inflation."1

According to conventional theory, however, the extent to which the Federal Reserve can fulfil its price-stability mandate without any reference to fiscal policy depends on what Leeper (1991) has labeled a passive fiscal policy regime. In such a regime, the central bank recommends a target and uses interest rate policy to stabilize aggregate demand, thereby stabilizing inflation around that target. The fiscal authority, in turn, accommodates central bank policy by absorbing the fiscal consequences of monetary policy in a manner consistent with stabilizing the long-run debt-to-GDP (gross domestic product) ratio. This conventional division of responsibilities is what Kirsanova, Leith, and Wren-Lewis (2009) label the consensus assignment.

In the scenario considered by Sargent and Wallace (1981), however, the consensus assignment is reversed. In particular, the fiscal authority is assumed not to accommodate the central bank in the manner just described. Instead, it is the central bank that accommodates the budgetary consequences of fiscal policy by generating the necessary seigniorage revenue. It is in this context that attempting to monetize a smaller fraction of outstanding Treasury securities has the effect of increasing the rate of inflation. A tighter monetary policy ends up increasing the interest expense of debt issuance. And if the fiscal authority is unwilling to curtail the rate of debt issuance, the added interest expense must be monetized—at least if outright default is to be avoided.

Sargent and Wallace (1981) examine monetary-fiscal coordination in the context of a standard monetarist model. There is an assumed demand for central bank liabilities. The fiscal authority issues indexed debt. Monetary policy transforms interest-bearing debt into zero-­interest reserves, and inflation is the byproduct of debt monetization.2 The idea, however, is more general than this. Sims (2011), for example, examines the same question using a "fiscal theory of the price level" and arrives at the same answer for essentially the same reason. Future primary budget deficits and surpluses correspond to increases and decreases in the future supply of outside assets, respectively. The inflationary consequences of an increase in the interest rate depends on whether the resulting interest expense is financed with an increase in the primary surplus or an acceleration of nominal debt issuance. The distinction between central bank and Treasury liabilities made by Sargent and Wallace (1981) is not critical in understanding the logic of unpleasant monetarist arithmetic.

Ascertaining the relative dominance of a monetary authority vis-à-vis the fiscal authority at a point in time, or even with the benefit of hindsight, is not always a straightforward exercise.3 Such analysis presents an added challenge for monetary policymakers because theory suggests that the qualitative properties of a stabilizing interest rate policy depends critically on the nature of the prevailing fiscal regime; see Davig and Leeper (2007).

It seems fair to say there is considerable uncertainty over the nature of the fiscal policy regime prevailing in the United States today. Deficit and debt levels are elevated relative to their historical norms, and the current administration seems poised to embark on an ambitious public spending program. While bond yields remain low relative to historical norms, longer-dated bond yields are beginning to rise. In the event that inflation rises and then remains intolerably above target, the Federal Reserve is expected to raise its policy rate. In theory, this is the conventional policy response necessary to stabilize inflation under a passive fiscal policy regime. But if the fiscal authority is determined to pursue its deficit policy into the indefinite future, raising the policy rate may only keep a lid on inflation temporarily and possibly only at the expense of a recession.4 In the longer run, an aggressive interest rate policy may contribute to inflationary pressure—at least until the fiscal regime changes.5 Needless to say, getting the sign wrong on its next policy rate move is something the FOMC will want to avoid.

The goal of my article here is twofold. First, I want to develop a structural model to address the issue of monetary-fisal policy coordination at a level suitable for, say, advanced undergraduates. A simple model is desirable because the economic mechanisms are readily understandable and are therefore more likely to be taken seriously in policy discussions, assuming they make sense, of course. Structural models are also useful because "first-pass economic intuition" does not always survive the logic test of general equilibrium. To this end, I study a version of the Sargent and Wallace (1981) overlapping generations model and focus mainly on stationary equilibria.6 The non-stationary examples studied by Sargent and Wallace (1981) and Sims (2011) constitute interesting (and important) examples of what I think is a more general point that can be illustrated much more simply. Although one could model monetary policy as open market operations in the way Sargent and Wallace (1981) do, I instead employ the cleaner "fiscalist" approach of Sims (2011). And because I use an overlapping generations model, monetary policy can have real effects without having to appeal to assumptions relating to the stickiness of nominal prices. These real effects are potentially important for understanding how a lack of monetary-fiscal coordination can result in recession and how the threat of such an outcome can be used by the monetary authority to potentially discipline fiscal policy.

Second, I use the model to offer what I think is a compelling (or, at least, provocative) reason for why inflation has remained so low in the United States (and in other jurisdictions) despite historically low interest rates and growing primary deficits. The model can also be used to explain why central banks can be expected to be more successful in lowering the long-run rate of inflation than they would be in attempting to raise it.

The model has three key policy parameters: a nominal interest rate; a real primary budget deficit; and a "money" growth rate, where "money" is interpreted broadly to comprise the total supply of outside securities. I assume that the monetary authority determines the nominal interest rate and that the fiscal authority determines the budget deficit and the pace at which the supply of its nominal securities grows over time. The demand for real money balances is influenced by these policy parameters, as well as other factors. All of these variables are linked via a consolidated government budget constraint.

The first thing I demonstrate is that in the long run—which is to say, in a stationary state—inflation is determined by the money growth rate. This may not sound surprising, but since the supply of money is determined by the fiscal authority, the long-run rate of inflation is ultimately a fiscal phenomenon.7 It follows that the only way for monetary policy to influence the long-run rate of inflation (as opposed to the price level) is by influencing the money growth rate. This is only possible if the fiscal authority permits the primary budget deficit to absorb some or all of the budgetary consequences of interest rate policy. And if it does, then a high-­interest-rate policy leads to higher inflation (and vice versa). While this causal relationship seems consistent with the so-called neo-Fisherian proposition (Williamson, 2016), the economic mechanism is very different. In particular, the result I report holds even if rational expectations is not assumed.

Next, I examine the effect of interest rate policy in Ricardian and non-Ricardian fiscal regimes. The analysis here essentially restates known results, albeit in the context of a very tractable analytical setting. I also consider the effect of shocks that impinge directly on the demand for Treasury securities. U.S. Treasury securities are used extensively as collateral in wholesale banking arrangements and as a safe store of value for domestic and foreign agencies. There is evidence suggesting that the demand for U.S. Treasury securities has increased significantly over the past 25 years. The analysis here is novel, I think. The model suggests that an increase in the level demand for (real) Treasury balances contributes to persistently high primary budget deficits (in the Ricardian case) and persistently low inflation (in the non-­Ricardian case).

Finally, I use the model to study what happens when monetary and fiscal authorities have different preferences regarding inflation. The exercise here is in the spirit of the conflict scenarios studied by Bianchi and Melosi (2019). I consider two thought experiments. In the first experiment, the central bank attempts to keep the rate of inflation lower than the long-run rate implied by the stance of fiscal policy. This is a Volcker scenario. In the second experiment, the central bank attempts to keep the rate of inflation higher that the long-run rate implied by the stance of fiscal policy. This is a Yellen/Powell scenario. The analysis provides a simple reason for why Volcker was successful in bringing inflation down, while Yellen/Powell were not successful in moving inflation higher.

Read the full article.