In honor of Tom Sargent's prize, I extract the last section of (forgive the self-promotion) my forthcoming book The Clash of Economic Ideas (due out in April from Cambridge University Press).

Unpleasant monetarist arithmetic

During the early 1980s a group of economists then at the University of Minnesota and the Federal Reserve Bank of Minneapolis, Thomas J. Sargent, Neil Wallace, and Preston Miller, spelled out a worrisome potential connection between the growth of government debt and the resort to inflationary finance. Their basic message was that the ability to finance government spending with borrowing will eventually hit a ceiling, leaving money-creation the only method left for covering continued budget deficits. The resulting inflation cannot then be stopped, because money-creation cannot be stopped, unless there is a fiscal reform: “the monetary authority is forced to create money” to satisfy a need for seigniorage revenue.

In a much-discussed 1981 article entitled “Some Unpleasant Monetarist Arithmetic,” Sargent and Wallace asked their readers to consider a fiscal and monetary regime in which the fiscal authority (say, the Congress) first announces the path of future budget deficits. By rearranging the budget constraint, we see that the size of a budget deficit (G – T) must be matched by the sum of new borrowing and monetary expansion:

G – T = ΔD + ΔM.

In other words, a budget deficit implies some combination of bond finance and inflationary finance.

To explain the limit on bond finance, Miller and Sargent defined G as spending on things other than debt service, and defined ΔD as the proceeds from borrowing net of debt service (i.e. net of interest and principal payments on the public debt). From an ordinary upward-sloping supply curve for loanable funds it follows that the real interest yield required by bond-buyers (lenders) rises with the volume of a government’s debt, other things equal. The size of ΔD then eventually hits a ceiling for “Laffer Curve”-type reasons. At some high ratio of debt to GDP, issuing new debt is a wash (nothing is gained for government spending) because the rising bond yield demanded by the market raises the cost of debt service on the entire debt (as it is rolled over) by as much as the new amount borrowed. Only inflationary finance then remains to meet ongoing deficits.

To avoid this “unpleasant” fate, Sargent and Wallace advised, the path of deficits must be kept in check. They suggested that the monetary authority should announce its plans for future money growth first, thus limiting the feasible path of deficits. Alternatively, a switch from fiat money regime to a commodity money regime could effectively restrict the path of M. As Sargent commented elsewhere:

Remember that under the gold standard, there was no law that restricted your debt-GDP ratio or deficit-GDP ratio. Feasibility and credit markets did the job. If a country wanted to be on the gold standard, it had to balance its budget in a present-value sense. If you didn’t run a balanced budget in the present value sense, you were going to have a run on your currency sooner or later, and probably sooner. So, what induced one major Western country after another to run a more-or-less balanced budget in the 19th century and early 20th century before World War I was their decision to adhere to the gold standard.

Sargent here seemed to assume that a government central bank issues the country’s gold-redeemable currency, and bears the brunt of a speculative attack. Many countries under the classical gold standard before World War I, like the United States, Canada, and Australia, had in fact no central bank, but instead decentralized private note-issue. A more general statement of the disciplinary mechanism would be: If a country didn’t run a balanced budget in the present value sense (spending balanced by present taxes or a credible commitment to future taxes), the international bond market would put a high default premium on its bonds, eventually making further bond finance impossible.

Some critics regarded Sargent and Wallace’s scenario as far-fetched. In a 1984 comment, Michael Darby argued that their model was “seriously wrong as a guide to understanding monetary policy in the United States.” An economy reaches the “unpleasant” zone in their model when the real yield on government bonds exceeds the economy’s growth rate. The real yields on US Treasury bonds and bills from 1926-81, Darby pointed out, had averaged close to 1 percent per annum, while the economy grew at around 3 percent per annum. Deficits were financed by new debt without the real yield appreciably rising or the revenue from bond finance coming close to a ceiling. The monetary authority’s hands were therefore never tied by fiscal policy, and it could choose the rate of money creation independent of the size of the deficit. The United States, one might say, remained in Pleasantville.

In a reply, Miller and Sargent emphasized that the real yield on government bonds isn’t given, but rises with the real debt or debt-to-GDP ratio. Darby’s evidence about United States’ past does not rule out the real yield on US government bonds someday rising above the economy’s growth rate if the debt-to-GDP continues to rise (a point Darby had already conceded in theory, but thought far from currently relevant). They noted two other effects working toward unpleasantness as the debt-to-GDP ratio rises: (1) Private capital and real income decline as government debt crowds out capital formation, therefore T falls and the deficit grows relative to GDP; and (2) The real demand to hold money falls as bond yields rise, therefore the tax base for real seigniorage falls. As if anticipating the events in Greece and Ireland twenty-five years later, they warned that a large jump in the size of government budget deficits can push a previously pleasant economy it into the unpleasant zone where real government bond yields rise above the economy’s growth rate and the debt-to-GDP ratio begins to grow without limit.

Sargent would go on to explain the Greek and Irish fiscal crises by applying the unpleasant-arithmetic argument. Despite the European Central Bank’s rules against any member country running a large deficit or accumulating a high debt-to-GDP ratio, a number of countries at the European Union economic periphery—Greece, in particular—violated the rules convincingly enough to unleash the threat of unpleasant arithmetic in those countries. The telltale signs were persistently rising debt-GDP ratios in those countries. Of course, the unpleasant arithmetic allows them to go up for a while, but if that goes on too long, eventually you’re going to get a sovereign debt crisis.

Time will tell whether—or how soon—the governments of Japan, the United States, the United Kingdom, or other countries will get a debt crisis. But seeing government debt sharply rising in those countries, and having observed events in Greece and Ireland, one can no longer dismiss the unpleasant scenario of a sovereign debt crisis as far-fetched.