Sargent and Wallace have one goal in their paper: to show that, under fiscal dominance, the Central Bank cannot control inflation, even with a pure monetarist theoretical framework. Not in the short run, not in the long run.
The setup is as follows. The public’s demand for interest-bearing government debt constrains the government of a monetarist economy in a least two ways: 1) By setting an upper limit on the real stock of government bonds relative to the size of the economy. 2) By affecting the interest rate the government must pay on bonds.
The extent to which these constraints bind depends on the way the fiscal and monetary policies are coordinated.
Consider two polar forms of coordination: on the one hand, imagine that monetary policy dominates fiscal policy. Under this coordination scheme, the monetary authority can permanently control inflation in a monetarist economy, because it is completely free to choose any path for base money.
On the other hand, imagine that fiscal policy dominates monetary policy. If the fiscal authority’s deficits cannot be financed solely by new bond sales, then the monetary authority is forced to create money and tolerate additional inflation.
Under the second coordination scheme, where the monetary authority faces the constraints imposed by the demand for government bonds, the form of this demand is important. In particular, suppose that the demand for government bonds implies an interest rate on bonds greater than the economy’s rate of growth. Then, Sargent and Wallace show that the monetary authority is unable to control either the growth rate of the monetary base or inflation forever. (We will see why below).
Being limited simply to dividing government debt between bonds and base money, a monetary authority trying to fight current inflation can only do so by holding down the growth of base money and letting the real stock of bonds held by the public grow. If the principal and interest due on these additional bonds are raised by selling still more bonds, so as to continue to hold down the growth in base money, then, because the interest rate on bonds is greater than the economy’s growth rate, the real stock of bonds will grow faster than the size of the economy. This cannot go on forever, since the demand for bonds places an upper limit. Once that limit is reached, the principal and interest due on the bonds already sold to fight inflation must be financed by seigniorage. Sooner or later, the result is additional inflation.
The first section of the paper establishes a model that is extremely monetarist. The model implies that, although fighting current inflation with tight monetary policy works temporarily, it eventually leads to higher inflation.
In the second section, the paper includes a more realistic demand for base money, one that depends on the expected rate of inflation (a Cagan-like money demand). In a particular example of that second monetarist model, tighter money today leads to higher inflation today.
First model: Tighter money now can lead to higher inflation later
Three key assumptions:
- A common constant growth rate for real income and population, “n”.
- A constant real return on government securities that exceeds “n”. So that “r”>”n”.
- A quantity theory demand schedule for base or high-powered money, one that exhibits constant income velocity. (M*V=P*Y, with V constant).
The argument hinges entirely on taking into account the future budgetary consequences of alternative current monetary policies when the real rate of return on government bonds exceeds “n”, the growth rate of the economy.
The (primary) deficit must be financed by issuing some combination of currency and interest-bearing debt. We let alternative monetary policies be alternative constant growth rates of the stock of base money, for a certain period of time. Then, at a specific time T, the path of base money is determined by the condition that the stock of interest-bearing real government debt per capita be held constant at whatever level it attains at t=T (which is consistent with there being a limit on real debt per capita).
Note that assumptions 1) and 3) imply that the price level, at any given time, is proportional to the stock of base money per capita. So that both variables are always growing at the same rate. Thus when we specify monetary policy (a given growth rate of base money from today until period T), we are simultaneously choosing the inflation rate.
We are interested in determining how the inflation rate for the periods after T depends on the inflation rate chosen for the periods before T. The inflation rate after T depends on the stock of interest-bearing real government debt per capita attained at T, and to be held constant thereafter (denoting that per capita stock b^theta_t).
How is it that the inflation rate after T depends on the stock of debt? Consider that A) after T, we want the stock of debt per capita to remain constant, and B) The price level is always some factor of the available money supply in the economy. Therefore, because the interest rate is higher than the growth rate, every period we would have a larger stock of debt that we need to somehow bring down. This leaves only two choices: primary surpluses or monetization. Assuming that we cannot reduce the primary deficit, the only available option for the government is to print money to pay off the existing debt.
So we know that a higher debt stock at time T implies a higher need for monetization and hence higher inflation. But how does the chosen monetary policy before T impact the debt stock? Easy: the tighter is monetary policy in earlier periods (for a given primary deficit), the higher will be the stock of bonds required to finance government expenses. Hence, tighter monetary policy from times 0 to T implies a higher stock of debt at T, and a higher inflation rate from T onwards.
Conclusion: tight money gives us low inflation for a while, but eventually leads to sustained higher inflation in the future.
Second model: Tigher money now can mean higher inflation now
Things get even more interesting if we augment the demand demand function to make it more realistic: specifically, once we incorporate a Cagan-like functional form in which people’s expectation of future inflation plays a role in the price level today.
Following insights by Sargent and Wallace, the price level today depends on the current level of the money supply, as well as all anticipated future levels of the money supply. Thus, if people expect higher levels of money creation in the future, it will feed into the price level today. You can see where this is going: if people know that a tight monetary policy will lead to a high level of government debt and, thus, to a very rapid expansion of the money supply after time T, they will incorporate these beliefs into their demand for money today, and the current price level will be affected. This stunts the ability of the Central Bank to control inflation even today.
Crucial assumptions:
There are two critical assumptions here. First, r > g. That is, the real rate of interest on government debt is higher than the economy’s growth rate. Second, we assume away the fact that primary surpluses can be ran in order to offset the mounting stock of debt. This second issue is very interesting, because it basically depends on which institution dominates the other: do fiscal authorities set the path of spending and force the Central Bank to choose how that spending is composed (ie. allocate the deficit financing between debt and extra money)? Or does the Central Bank “move first”, and set a fixed growth of the money supply, effectively setting fiscal authorities’ budgetary restriction? We are assuming the former, which is why these situations are called fiscal dominance.
Source: Sargent and Wallace, “Some Unpleasant Monetarist Arithmetic“.
Econ Notes 