# Some Unpleasant Monetarist Arithmetic

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This is an intuitive summary, please see the actual paper for the mathematical derivations (the notes from class are actually easier to follow).

The purpose of the paper is to argue that even if monetarist assumptions hold, Friedman’s list of what monetary policy cannot control must be expanded to include inflation. An economy that satisfies monetarist assumptions is one that has a monetary base closely connected to its price level and one in which the monetary policy can raise seignorage.

1. The public’s demand for interest bearing bonds constrains the government in two ways. A. It sets a constrains the government by setting an upper limit to the amount of bonds relative to the size of the economy. B. It affects the interest rate at which government must borrow.

2. Two polar coordination strategies. A. If monetary policy dominates fiscal policy, then the fiscal budget is constrained by the amount of seignorage and bonds and thus monetary policy has the power to control inflation. B. If fiscal policy dominates monetary policy, then the fiscal budget is set, and monetary policy must adjust bonds and the amount of seignorage to finance the budget and thus monetary policy has less power over inflation. Under this policy, the only way monetary policy can hold down inflation is by holding down the base level of money and increasing bonds. Eventually the bond limit will be reached, requiring inflation to pay off the debt and interest coming due (so fighting inflation with tight monetary policy will eventually result in more inflation).

The Model:

A tighter monetary policy (ϴ) now implies a greater amount of bonds (b(T))required when the debt limit is reached (T). This ignores the fact that the demand for base money is dependent upon the expected future inflation rate. If the demand for money depends upon the expected inflation rate then the current price level depends on the current and all future anticipated money supply levels. Thus a high rate of inflation expected in the future, will lead to a high rate of inflation in the current period (this lowers monetary policy’s ability. This makes the Pareto superior option a looser monetary policy.

Government’s Budget Constraint:

Government Expenditures= New Bonds + Seingorage G(t) + R(t-1)B(t-1) =T(t) + B(t) –B(t-1) + [H(t) – H (t-1)]/P(t)

H(t)=High powered money (currency + reserves). If P(t) is higher, you have to print more to make the same amount.

Primary Deficit:

D(t) = B(t) – B(t-1) (1+R(t-1)) + [H(t) – H (t-1)]/P(t)

P(t)=(1/h)*H(t)

To learn P(t) we need to follow the money. We assume money grows at a fixed rate (ϴ) from time t to T.

H(t+1) = (1+ ϴ)Ht

At time T the Fed hits the debt ceiling as determined by bond buyers. So B(T) becomes fixed forever and all new expenditures above receipts must be paid for with seignorage. From T on, fiscal policy determines monetary policy. So:

D(T+1)= 0 – B(T)R(T) + [H(t) – H (t-1)]/P(t)

B(T)R(T) + D(T=1) = [H(T+1)-H(T)]/P(T+1) Total Deficit = Seignorage

B(T)R(T) + D(T+1)= [H(T+1)-H(T)]/(1/h)*H(T+1)

- [B(T)R(T) + D(T+1)]/h = Growth rate of nominal money (inflation) *******

Result: Slower month growth in past = more inflation later.

Results with some Cagan: Tighter money now means higher inflation in the future, higher inflation in the future equals higher inflation now. (Result is rigged a bit with assumptions). Indicates that monetary and fiscal policy must be coordinated.

Two Crucial Assumptions for results to hold: A. The real rate of interest exceeds the growth rate of the economy B. The path of fiscal policy (D(t)) is given and does not depend upon monetary policy (assumes fiscal policy moves first and dominates monetary policy).