###### CERF Blog

**The Taylor Rule**

The Taylor Rule relates the target federal funds rate with the gap between actual and target inflation and between actual and capacity output. The higher is inflation or the lower is the output gap, the higher is the target funds rate. The rule is both descriptive and prescriptive. It was originally proposed by John Taylor in 1993 to describe or explain observed Fed behavior over the period 1986-1993. For the most part, this was a period in which the Fed was targeting the funds rates. Subsequently, the rule has sometimes been used to suggest what the Fed should do, and deviations between the funds rate and the target rate implied by the rule have been taken to indicate excessive Fed accommodation or lack thereof. In particular, John Taylor himself has used this approach to argue that Fed policy was too easy in the 2002-2005 timeframe thus leading to the housing bubble. Similarly, according to the Taylor Rule the Fed was too stimulative during the 1970s, thus leading to the “Great Inflation” of that era.

If you apply the Taylor Rule today, you are likely (subject to some equivocation due to difficulties of precisely measuring the inputs to the rule, thus enabling varying estimates of the target funds rate) to find a target rate below zero. The original Taylor Rule is

FFR = RR + PT + 1.5*(P-PT) + 0.5*Output Gap

FFR = Target federal funds rate

RR = Real rate of interest

PT = Target inflation

P = Actual inflation

Output Gap = Percent deviation of actual output from potential output

Assuming a real rate of 1%, target inflation of 2%, an inflation gap of zero and an output gap of negative 9%, we obtain a target funds rate of negative 1.5%. It is obviously difficult to target a funds rate below zero so, to the extent Fed policy attempted to target the funds rate, there would be a problem (this problem is known as the Zero Lower Bound (“ZLB”)). The Fed believes that monetary policy can still be effective at the ZLB, even though the funds rate cannot be pushed lower.

The fed funds target rate today is the range 0-.25%. Since the observed rate is higher than the Taylor Rule, Fed policy could be viewed as “tight” today. At least, it could be if it weren’t for Quantitative Easing (QE). The Fed has been aggressively conducting QE. In the past three years the monetary base has just about tripled. Has the Fed done enough or too much?

**The McCallum Rule**

To answer this question, we need a rule which is not constrained by the ZLB. A good choice for this is the McCallum Rule named after, appropriately enough, economist Ben McCallum. The McCallum Rule describes a path for growth in the monetary base that is consistent with achieving a target path for nominal GDP. Suppose we target 5% growth in nominal GDP and attempt to define the path of base growth that would achieve this rate of nominal growth. The linkage between nominal GDP and the monetary base is the velocity of the monetary base, that is, the ratio of nominal GDP to the base. While the Fed can control the monetary base fairly closely, in order to achieve a nominal GDP target the Fed would have to adjust for changes in the monetary base.

Since 2007, base velocity has declined almost two-thirds (from 16 to 6). Base velocity began to fall sharply in late 2008, coincident with the collapse in real and nominal GDP growth. The Fed did react in real time, with monetary base growing by more than $700 billion in Q4 2008. Is this consistent with the McCallum Rule?

The McCallum Rule^{1} can be expressed as follows:

Base growth = 5.0% – Estimated Velocity Growth – k*(GDP Gap)

Base growth = Growth rate of monetary base

GDP Gap = Percent difference of nominal GDP from target GDP

Here we are assuming that 5% is a reasonable target growth rate for nominal GDP based on target inflation of 2% and a long-term trend real growth rate of 3%. The GAP Gap is currently approximately minus 9%, similar to the Output Gap mentioned above. The parameter k determines the speed at which the GDP Gap is closed.

Implementation of the McCallum Rule depends on the choice of the parameter k and the method used to adjust for changes in base velocity. In our simulations, we have used a three-month moving average (that is, assume base growth next period is equal to the average growth over the prior three months). We find that a value of k=.25 (for a quarterly simulation) describes a path for the monetary base over the past four years that is consistent with observed base growth (that is, the Bernanke Fed has effectively been operating according to a McCallum Rule with k=.25). Values of k greater than .25 would have been more expansive that has occurred and values less than .25 would have been more restrictive than has been observed.

**Nominal GDP Targeting**

Even if base velocity stabilizes, the NGDP Rule will continue to call for base growth in excess of 5 percent so long as the GDP gap remains negative. That is, more QE should be in the works.

Should the Fed move to explicit nominal GDP targeting?

Proponents of nominal GDP targeting assert that it has several advantages over interest rate or inflation targeting. First, compared to inflation, nominal GDP is relatively easy to measure. There are numerous measures of inflation, but just one nominal GDP. Second, it automatically addresses the Fed’s dual mandate of seeking price stability and full employment. Third, it imposes an explicit anchor on monetary policy.

A disadvantage is the need to adjust for changes in velocity and the need to pick the appropriate correction factor (value of k). Also, because inflation is not explicitly targeted in the MR, opponents argue that inflation is more likely to be unleashed with an NGDP rule. However, if nominal growth is credibly targeted at 5 percent, then inflation expectations are likely to remain subdued. After all, with long-term real growth of 3 percent, nominal growth of 5 percent means long-term inflation is constrained to 2.0 percent.

More QE is probably in our future. By tying monetary policy to a nominal income target the Fed can at the same time provide a rationale for further monetary stimulus now and provide confidence that excess monetary stimulus will be extracted later. Once velocity begins rising and nominal income reaches its target, under the rule monetary base growth will slow and eventually turn negative.

^{1}There is more than one version of the McCallum Rule. The one stated here targets the level of nominal GDP. Other versions target the growth rate of nominal GDP.