Some Unpleasant Monetarist Arithmetic

“In his presidential address to the American Economic Association (AEA), Milton Friedman (1968) warned not to expect too much from monetary policy… [but] did assert that a monetary authority could exert substantial control over the inflation rate, especially in the long run.” The paper’s purpose is “to argue that, even in an economy that satisfies monetarist assumptions, if monetary policy is interpreted as open market operations, then Friedman’s list of the things that monetary policy cannot permanently control may have to be expanded to include inflation” (Introduction, p. 1). The authors are explicit that this qualification depends on how monetary and fiscal policy are coordinated and on the form of the public’s demand for government bonds.

Under “monetary policy dominates fiscal policy,” the monetary authority independently announces the path of base money, which determines the seignorage available to the fiscal authority, which “must set its budgets so that any deficits can be financed by a combination of the seignorage chosen by the monetary authority and bond sales” – and “the monetary authority can permanently control inflation…because it is completely free to choose any path for base money” (Introduction, pp. 1-2). Under the opposite scheme, “fiscal policy dominates monetary policy”: the fiscal authority independently announces its deficits and surpluses, and “the monetary authority is forced to create money and tolerate additional inflation” whenever those deficits “cannot be financed solely by new bond sales.” The paper’s entire analysis proceeds under this second scheme.

“Suppose that the demand for government bonds implies an interest rate on bonds greater than the economy’s rate of growth. Then, if the fiscal authority runs deficits, the monetary authority is unable to control either the growth rate of the monetary base or inflation forever” (Introduction, p. 2). The mechanism: fighting inflation by holding down base-money growth forces the government to finance deficits (and eventually the interest on previously issued bonds) via more bond sales; if the bond rate exceeds the growth rate, “the real stock of bonds will grow faster than the size of the economy,” which cannot continue once “the demand for bonds places an upper limit on the stock of bonds relative to the size of the economy.” Once that limit binds, the principal and interest on the bonds sold to fight inflation “must be financed, at least in part, by seignorage,” and “sooner or later…the result is additional inflation.”

"(a) A common constant growth rate of n for real income and population. (b) A constant real return on government securities that exceeds n. (c) A quantity theory demand schedule for base or high-powered money, one that exhibits constant income velocity" (Section “Tighter money now can mean higher inflation eventually,” p. 2). The authors stress the deliberate choice of assumptions: this model “embraces as unqualified a set of monetarist assumptions as we can imagine,” precisely so that the paper’s conclusion about the limits of monetary policy cannot be attributed to weakening any premise that monetarists themselves rely on – “the argument hinges entirely on taking into account the future budgetary consequences of alternative current monetary policies” once the real bond return exceeds the growth rate.

Policy is described by a constant base-money growth rate theta for periods 2 through T, after which monetary policy is set to hold constant the real per-capita stock of interest-bearing government debt attained at T, denoted b^e(T). The authors show in two steps: first, that the inflation rate for all periods after T is an increasing function of b^e(T), given that the real bond rate exceeds n (equation 6); second, using the government’s per-capita budget-constraint recursion (equations 8-9), that “b^e(T) is larger the smaller theta is.” Chaining these together: “less inflation now achieved through monetary policy on its own implies more inflation in the future” (Section “Tighter money now can mean higher inflation eventually,” pp. 3-4). A footnote stresses the result “does not depend on the magnitude of the D(t) sequence” – it holds for any given fiscal deficit path, however large or small.

The first model’s simple quantity-theory demand for money “ignor[es] any dependence of the demand for base money on the expected rate of inflation,” a dependence for which “Bresciani-Turroni (1937) and Cagan (1956) found substantial evidence…by studying countries that had undergone rapid inflation” (Section “Tighter money now can mean higher inflation now,” pp. 4-5). Once money demand depends on expected future inflation, the current price level depends “on the current level and all anticipated future levels of the money supply” (citing Sargent and Wallace 1973) – so anticipated future money creation, forced by the debt dynamics of the first model, “can limit the power of tighter monetary policy to deliver even a temporarily lower inflation rate” today.

Using parameters gamma_1 = 3.0, gamma_2 = 2.5, R = .05, n = .02, and a fixed per-capita deficit sequence of .05 for ten periods, the authors compare a “tight” policy (theta = .106) to a “loose” policy (theta = .120): the price level at t = 1 is 1.04 percent higher under the tighter policy, and the tight-policy inflation rate stays above the loose-policy inflation rate at every date shown (Section “Tighter money now can mean higher inflation now,” pp. 5-6). The authors call the result “spectacular in that the easier, or looser, monetary policy is uniformly better than the tighter policy” – indeed, Pareto superior in the underlying overlapping-generations welfare comparison (Appendix A) – concluding that “in this example, the tighter current monetary policy fails to even temporarily reduce inflation below the level it would be under the looser policy.”

First, “that the real rate of interest exceeds the growth rate of the economy,” which the authors say they adopt because it “seems to be maintained by many of those who argue for a low rate of growth of money no matter how big the current deficit is”; they note that even relaxing this to allow bond demand to be an increasing function of the real return, the qualitative conclusion survives as long as bond demand has an upper bound (Concluding Remarks, p. 6). Second, “that the path of fiscal policy D(t) is given and does not depend on current or future monetary policies” – a claim not about private behavior but “about the behavior of the monetary and fiscal authorities and the game that they are playing,” specifically the assumption “that the fiscal authority moves first.”

No – the authors explicitly note an alternative interpretation of monetary-restraint proposals: “as calls to let the monetary authority move first and thereby impose discipline on the fiscal authority.” Under this alternative game, the monetary authority commits permanently and bindingly to a fixed theta rule “not just for t = 2, 3,…, T, but for all t >= 1,” forcing “the fiscal authority to choose a D(t) sequence consistent with the announced monetary policy” (Concluding Remarks, pp. 6-7). The authors list fixed exchange rates and a commodity standard (such as the gold standard) as other mechanisms that can impose this kind of fiscal discipline, and state plainly: “nothing in our analysis denies the possibility that monetary policy can permanently affect the inflation rate under a monetary regime that effectively disciplines the fiscal authority.” The paper’s target is specifically the case where fiscal policy is taken as independently given and not subject to such discipline.

Appendix A presents “a simple formal model that implies the assumptions used in the preceding paper,” a version of Samuelson’s (1958) overlapping-generations model with poor agents (who hold currency) and rich agents (who hold bonds, issued in denominations too large for the poor to afford, with a legal restriction on intermediation preventing pooling) (Appendix A). Because individual agents are explicitly identified in this microfounded setting, the authors note it “has the virtue that…policies can be compared in terms of the welfare of the individuals in the model” – which is what allows the paper’s numerical example to be described not just as producing a higher price level under tight money, but as an equilibrium that is Pareto-dominated by the looser-money alternative.