Monetary vs Fiscal Theories of the Price Level
A Reconciliation
The University of Miami Economics Department recently hosted a conference on “New Challenges for Fiscal and Monetary Policy (program available here). The conference was interesting and fun (read John Cochrane’s impressions here). I especially appreciated the discussion by Marco Bassetto, who explained the connection between the fiscal theory of the price level (FTPL), unpleasant monetarist arithmetic (UMA), and the Monetarist view of inflation. I want to do something similar here using a simple version of a model I describe in more detail here. The main takeaway is that Monetarist and Fiscalist theories of the price level are much more closely related than first meets the eye.
The Model
Let’s start off by considering an economy with a fixed level of output and zero inflation. There is a fixed stock of nominal government debt, D. The central bank holds a share 0 < x < 1 of the debt, which it purchases by creating money, M. The remaining debt B (for bonds) is held by the private sector; i.e., D = M + B with,
Notice that the fiscal authority determines the total amount of government paper in the economy D, while the monetary authority determines its composition M + B. An increase in x can be thought of as quantitative easing (QE), while a decrease in x can be thought of as quantitative tightening (QT).1
Monetarists insist that there is an important difference between M and B. Money is the stuff we use to buy things. Bonds cannot be used to buy things—they are instead used primarily as a saving vehicle.2 But because money is also a store of value, relatively illiquid bonds must earn a relatively higher rate of return if they are to be willingly held in private wealth portfolios. Let q denote the interest rate on money. Let r denote the interest rate on bonds. Because there is no inflation, q and r represent both the nominal and real interest rates. The traditional assumption is that money is dominated in rate of return; i.e., q < r. Since 2008, however, the Fed is legally permitted to pay interest on reserve balances (IORB) so that q = r (a flat yield curve across reserves and treasury securities) is a scenario that needs to be considered.
A central component of the Monetarist view is the so-called money demand function, commonly denoted by L (for liquidity). Here, L is measured in units of output; i.e., the demand for real (price level adjusted) money balances firms and households are willing to carry from one period to the next. Assume that the demand for real money balances for transaction purposes is proportional to the level of economic activity as measured by the real GDP. Since RGDP is fixed here, so is the demand for real money balances—that is, as long as money is dominated in rate of return by bonds. The supply of nominal money balances M is determined by the central bank. For a given price level P, this implies a supply of real money balances M/P.
If q < r, then individuals and agencies will want to economize on their real money balances as much as possible. Equilibrium, in this case, implies M/P = L. If q = r, then individuals and agencies are willing to hold money beyond what is needed for transaction purposes—money and bonds are equally good saving vehicles. In this latter case, M/P > L. To summarize:
where, recall, M = xD.
Next, assume that the real (price level adjusted) demand for bonds S (for saving) is increasing in r.3 The supply of nominal bonds in the hands of the public B is determined by the central bank. For a given price level P, this implies a supply of real bond balances B/P. Equating supply and demand implies
where, recall, B = (1-x)D. The second equation above recognizes that money and bonds are perfect substitutes in wealth portfolios when q = r.
Finally, there is the government budget constraint. Let z denote the real (price level adjusted) primary budget surplus. The primary surplus is used to service the debt,
Note that if q = r, then z = r(D/P) or z = rS(r).
Monetarist Theory (q < r)
Let me begin with the traditional scenario, q < r. In this case, the price level is determined by P = M/L. The central bank is in full control of the price level. Who is in ultimate control of central bank policy is a question I’ll return to later. For now, let me describe a standard monetary policy operation: a reduction in the quantity of government securities held on the Fed’s balance sheet (i.e., a decrease in x).
Quantitative tightening (lower x) changes the composition of the debt D = M + B. The money supply goes down and the supply of bonds offered to the private sector goes up. Because the demand for real money balances is fixed, the price level P = M/L goes down. Equilibrium in the bond market requires S(r) = B/P. As B goes up and P goes down, bonds become more plentiful both in a nominal and real sense. The price of bonds must fall—i.e., bond yields must rise—to clear the market.
Oh, you might say, that’s nice. But central banks control interest rates, not the money supply. Fine. Instead of assuming an exogenous x and an endogenous r, we can assume an exogenous r and an endogenous x. In this latter case, the central bank determines the interest rate and then passively accommodates the relative demands for money and bonds.4
Implicit in this textbook description of monetary policy is the assumption that fiscal policy passively accommodates monetary policy. Consider the government budget constraint written in a slightly different form,
By changing the composition of the debt, the Fed changes the interest expense on the outstanding debt. Less low-interest money and more high-interest bonds means an increase in debt service cost. At the same time, the real supply of debt (D/P) has increased (because of the decline in P). The implicit assumption is that the primary surplus z increases relative to GDP (fiscal austerity) to finance the higher interest expense.
But what if the fiscal authority is not in the mood for fiscal austerity? Then one would then expect an expansion in D to finance the added interest expense. For a given x, this implies an increase in M and therefore an increase in P, thwarting the Fed’s disinflationary desire.5
If conventional theory already ascribes an important (albeit downplayed) role for fiscal policy in determining the price level and inflation, what is the FTPL all about? According to John Cochrane (see my interview with him here), FTPL differs from standard Monetarism in that the former theory ascribes no special role to that component of the national debt labeled money. What matters for the price level is the total amount of government and not its composition between money and bonds. FTPL also emphasizes fiscal support for determining the price level, but as we just saw above, the same is true of standard theory.
Fiscal Theory of the Price Level (q = r)
In the model described above, the size of the Fed’s balance sheet becomes irrelevant when money (reserves) earn the same rate of return as bonds. Banks, for example, can hardly tell the difference in holding 4% bills or 4% reserves. While the Fed can still control the composition of the debt, when q = r, the effect is like changing the composition of $10 and $5 bills in the economy. Nobody cares.
Let’s take a look at the math when q = r. First, we have M/P > L. That is, individuals and agencies are satiated with liquidity. Banks do not have to worry about scrambling for scarce reserves in the Federal Funds market. Corporate treasurers don’t have to worry about managing cash balances. This is the idea behind the so-called Friedman rule. In this “abundant reserves” regime, the demand for money accommodates itself to the supply of money.
Next, we have the condition S(r) = D/P. While there is no distinct demand for money vs. bonds, there is still a demand for government paper (people just don’t care about the composition of that paper). Next, combine this latter expression with the government budget constraint to form z = rS(r). We now have two equations,
Now, if we hold D fixed and assume that z passively adjusts to satisfy the government budget constraint, we see how monetary policy (r) can determine the price level. If the Fed wants a lower P, it raises r (with z accommodating the implied higher interest expense).
What about the FTPL idea that the price level is determined by a valuation equation, similar to the way finance types price stocks? To see things from this perspective, just rearrange the equations above as follows,
The right-hand-side of the equation above represents the present value of an infinite stream of primary budget surpluses discounted at the constant interest rate, r. With D determined by fiscal policy, the price level adjusts to satisfy the valuation equation above.
Conclusion
The FTPL shares more with standard Monetarism than meets the eye. The valuation equation for debt seems like a radical way to think about price level determination. It implies that an unfunded expenditure shock (an increase in D not matched by an increase in the z/r leads to an increase in the price level). But standard Monetarist thinking leads to the same conclusion if: (i) we take a broader definition of the money supply to include the national debt; and (ii) we explicitly take into account the way monetary policy interacts with the government budget constraint.
In models that include commercial banks, an increase in x might also correspond to the purchase of government securities by commercial banks financed with deposit liabilities.
All U.S. persons are permitted to open an account with the U.S. Treasury at TreasuryDirect. These interest-bearing money accounts cannot be used to make payments because they are not connected to a payment rail. A rationale for this policy choice is provided in Kocherlakota (2003) and Andolfatto and Martin (2023).
In the model I cited earlier, a higher bond yield induces a portfolio substitution effect as investors move out of physical capital investment into government bonds.
So, even in the traditional Monetarist model, one can think of monetary policy as interest rate targeting by a central bank willing to abandon control of the size of its balance sheet.
The original Sargent-Wallace exercise in UMA considered a dynamic version of this model in which lower inflation today implied higher inflation tomorrow. But the basic idea is the same: long run inflation targeting requires fiscal support.