The conventional Market Monetarist view of monetary policy can be summarized by two points:
1. Target the forecast.
2. Target the level.
David Beckworth articulates the latter point as follows:
What these inflation critics miss is that the Fed could actually raise the level of aggregate nominal spending by a meaningful amount without jeopardizing long-run inflation expectations. This is possible if one uses a price level or a NGDP level target that provides a credible nominal anchor.
If this is indeed correct, then perhaps it is a conundrum as to why the FOMC doesn’t adopt a level target. However, it is not necessarily clear that this statement is true. If the Fed were to adopt a target of the price level or the level of nominal GDP, could they keep inflation expectations stable? It is likely that this depends on the aggressiveness of monetary policy. In fact, if the Fed were to adopt the type of policy described by points 1 and 2 above, it would actually be the case that more aggressive monetary policy would lead to the potential for self-fulfilling expectations. As a result, there is reason to be skeptical of level targeting.
To illustrate this point, consider a simple model. First suppose that the price level is governed by a Wicksellian process:
where is the price level, is the natural rate of interest, is the market rate of interest, and are parameters, is the expectations operator, is a stochastic shocks, and all variables are expressed as logarithms.
In addition, suppose that monetary policy is governed by points 1 and 2 above such that:
where is the target for the price level, is a monetary policy disturbance, and the variables are expressed as logarithms. This rule captures the market monetarist objectives of a level target and a forecast target.
To simplify the analysis, it is assumed above that the price level target and the natural rate of interest are constant over time. To simplify this even further, let’s re-write the equations above without these constant terms:
Now, substituting the second equation into the first, we can get a rational expectations difference equation for the price level:
where . A necessary condition for a unique rational expectations solution is that . Thus, the more aggressive the response of monetary policy to deviations of the expected price level from its target, the less likely this condition is to hold. In addition, if this condition is not satisfied, then the price level will be subject to self-fulfilling expectations. In other words, if the Fed responds too aggressively to the deviation of the expected price level from target, it is possible that price level expectations could become unanchored thereby generating self-fulfilling fluctuations.
It is important to note that the conclusion above is not unique to an interest rate rule. We can re-write this as a modified Cagan model with rational expectations. Thus re-write the first equation:
where is the money supply. Now describe a rule for the money supply that is consistent with points 1 and 2 above (agains, suppressing constants for simplicity):
Substituting the monetary policy rule into the first equation yields:
where the variables are as defined above. Notice that the greater the responsiveness of monetary policy, the less likely there is a unique, rational expectations equilibrium.
So what is the source of this instability? Why is it that price level expectations can become unanchored? The reason is that an aggressive monetary policy is designed to rapidly converge to the desired price level. For example, if inflation expectations have been 2% for some time and the inflation rate rises to say 7%, the public might lose confidence in the central bank to maintain price level stability.
The idea that rapid convergence is behind the results above can be illustrated by modifying our basic framework. Suppose that rather than focusing exclusively on the price level, the Fed were to also place emphasis in the expected rate of inflation in their monetary policy rule. Thus, the rule could modified such that:
Again, ignoring constants and substituting this rule into our equation for the price level, we arrive at:
Now the condition for a unique equilibrium is that . Thus, for a given responsiveness of monetary policy to the expected price level, a greater responsiveness of the central bank to the expected rate of inflation can ensure a unique, rational expectations equilibrium.
What this very simple model illustrates is that a monetary policy that is consistent with points 1 and 2 above does not necessarily keep price level expectations anchored. If monetary policy is too aggressive, price level expectations can become unanchored thereby resulting in the potential for self-fulfilling price level fluctuations. The lesson then is that a policy consistent with points 1 and 2 above must also be mindful of the rate of change in the variable for which the Fed is targeting the forecast. A policy consistent with points 1 and 2 alone might not be sufficient to keep the price level anchored.