The Taylor Rule Without Interest Rate Smoothing Is Very Good at Keeping the Economy Close to its Potential
One of the difficulties with studying monetary policy with economic models is that simple economic models tend to make good monetary policy too easy. Consider the following illustration involving a simplified version of the Taylor rule. Let the nominal interest rate determined by the central bank be a function of current output, inflation and the capital stock, where the capital stock is an easily observed and tracked indicator of potential output. Note that we have focused on an operational definition of monetary policy, based on currently observed variables. To the extent that monetary policy at a deeper level is based on predictions of the future, we are interested in the projection of those predictions on observed variables. We also are not assuming that the central bank can directly observe the potential or "natural" level of output. The other nonstandard feature of this specification in comparison with the standard Taylor rule for monetary policy is leaving out interest rate smoothing. We do this for two reasons. First, from the standpoint of optimal monetary policy, interest rate smoothing seems mostly unmotivated. Even if there is an argument for some interest rate smoothing, why should it be as strong as it is? Why should there be a reluctance to move the short-term rate by more than a quarter of a point or at most a half point in a six week period? Second, to the extent that effects come solely from the interest-rate-smoothing aspect of monetary policy, this fact is itself very important.
We also take as the baseline case Calvo price setting, partly to argue for the move toward models of price setting that yield more inflation inertia. We claim that, away from the zero bound on the nominal interest rate, a simplified Taylor rule of the form
,(1.1)
where is the nominal interest rate, will put the economy very close to the flexible-price equilibrium even when real shocks hit the economy, as long as the effect of the real shocks on full employment ("natural") output and the full employment ("natural") real interest rate occurs immediately and is long-lived compared to the length of time nominal things can matter to the real economy. The reason is straightforward. Given the level of full employment output yf and the full employment real interest rate , there is a level of inflation that is consistent with both (1.1) and the Fisher equation:
,(1.2)
which can be solved to yield
(1.3)
Graphically, a value of inflation equal to puts the monetary policy line directly on top of the (yf,) point. The equations of Calvo price setting are equivalent to inflation smoothing in the same sense that the standard Permanent Income Hypothesis gives consumption smoothing or Hayashi's version of Q-theory gives investment smoothing:
(1.4)
where h is the length of a period. Since with Calvo pricing, there is nothing to prevent inflation from immediately adjusting to a value close to . A wise choice of bkin the nominal interest rate rule can avoid the need for any subsequent change in inflation to keep the monetary policy line on top of the (yf,) point. The direct conditioning of the nominal interest rate rule on the capital stock can cancel out the effect on of the evolution of yfand due to the capital accumulation induced by the real shock. In accordance with (1.4), the constancy of after the initial jump makes this monetary policy rule consistent with output staying at the full employment level.
Obviously, to the extent the monetary policy rule relies on lagged data on output and inflation, it will take that length of time in the model before the economy can get to full-employment output. (The capital stock is probably slow-moving enough that a lag in its measurement should not be too important.) Also obviously, interest-rate smoothing can delay the achievment of full-employment until after the nominal interest rate adjusts to the target level. But since the inflation rate is forward-looking in Calvo price setting, it should jump to approximately the level that will yield full-employment after the nominal interest rate adjusts.
Note how easy this monetary policy is to implement. Although the monetary authority could do something fancier, this is good enough to keep the economy at full employment.
Given the model of the behavior of the private agents in the economy, it is hard to argue that the implementation of such a rule is too hard for the central bank if done based on lagged data. Issues like multiple different sticky prices can probably be dealt with by choosing the appropriately weighted aggregate of different prices and outputs for the inputs to monetary policy rule.
Although we find the existing degree of interest rate smoothing undermotivated by genuine economic concerns, it would be very strange to claim that departures from full employment were mostly due to interest rate smoothing, and that is not what we are claiming. Instead, we think at least part of the difficult with this story is that inflation does not instantly jump to the right level. The model implies that the subset of firms that are actually in the midst of changing prices will fully process all available information and perceive entire expected future path of the economy and act accordingly. This is what we think fails in the real world, motivating our interest in models of sticky inflation.