The Taylor Rule offers clues to upcoming Fed policy

William Hester, CFA
January 2005
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The topic of inflation is gaining attention. Even though there were plenty of signs in 2004 - including a rising Consumer Price Index - it was the Fed who put it on investors' radar screens this week. In the minutes released last week from their December meeting Fed members cited "developments that could pose upside inflation risks."

The hawks on the committee listed the culprits as a weaker dollar, slowing productivity improvements and an economy growing close to its potential.

This left investors thinking that the Fed may be more aggressive in setting interest rates this year, which pressured short-term interest rates higher. But questions remain. How aggressive will the Fed be? Over what length of time will they raise rates?

Since June the Fed has increased overnight interest rates five times in as many meetings. In December, the Federal Open Market Committee (FOMC) said that future changes in interest rates will likely be 'measured'. But they've been tight-lipped about the duration of these moves.

That's partly because even they don't know yet. As the FOMC sets interest rate policy this year, they will aim for a policy they believe will allow the economy to grow at its potential while keeping inflation low and stable. They'll be seeking the 'neutral' Fed Funds rate.

The difficulty for investors (and the Fed's voting members) is that this rate isn't static. As the performance of the economy changes, so does the interest rate that the Fed targets to keep growth and inflation in balance.

Some help can come from the Taylor Rule, a model that infers a Federal Funds rate by taking into account measures of recent economic growth and inflation. John Taylor, the U.S. undersecretary of the Treasury for international affairs and a professor of economics at Stanford University, proposed the model in 1992.

The model, widely respected by economists, is beginning to make a revival in Fed speeches and interviews. Early last month Fed governor Ben Bernanke said the Fed looks at both "feedback" models, such as the Taylor Rule, and forecast-based models to make monetary policy decisions.

The model may get a whole lot more popular. Taylor is routinely mentioned as a successor to Federal Reserve Chairman Alan Greenspan, whose term ends in January 2006.

Taylor's Rule

Taylor views monetary policy as an ongoing effort to keep both inflation and growth in economic output close to acceptable rates. He starts by adding the current inflation rate to a real funds rate of 2 percent, representing a historically neutral monetary policy.

The rule then adjusts this sum by factoring in the difference between (1) the actual inflation rate and acceptable inflation (assumed to be 2 percent) and (2) the GDP gap - the difference between the real and the "potential" gross domestic product. Potential GDP is often defined as the maximum GDP that can be attained while still keeping inflation low and stable.

r = 2 + p + .5 (p - 2) + .5 (y)

r - target federal funds rate (average for the quarter)

p - rate of inflation

y - GDP gap

So, according to Taylor's rule, in an ideal economy - operating at full potential and with price rises holding at 2 percent - the Fed would set the funds rate at 4 percent: the base rate of 2 percent adjusted for 2 percent inflation. The Fed would tighten policy if either inflation rises above its target or the economy heats up above potential. The Fed would loosen policy if inflation falls below its target or the economy becomes slack.

Using the most recent economic figures, third quarter inflation - measured by the GDP deflator - was 2.2 percent, while GDP fell 1.8 percent below its potential level, according to estimates by the Congressional Budget Office. Therefore, the Taylor Rule estimates the Fed's target rate should be 3.4 percent.

That Taylor Rule-suggested rate sits above the current Fed Funds target rate of 2.25 percent. This spread helps explain why many economists expect the Fed to continue to raise rates this year as they move from an accommodative policy to a more neutral one.

3.4 Percent and Done?

Does that mean the Fed will rest when its overnight rate reaches 3.4 percent? Not necessarily. Rates may eventually rise above this level, or stop long before it. That's because as the growth rate of the economy and the trend in prices change this year, so will the estimated neutral Fed Funds rate.

The analysis can be extended by taking into consideration the possibility of changing variables, like faster economic growth or a spike in inflation. To do this, we can put forecasts for growth and inflation for the coming year into the Taylor Rule to estimate a funds rate based on these assumptions.

Economists polled by Bloomberg News expect the economy to expand 3.5 percent in the fourth quarter of 2005, slowing from its current rate. The average forecast for inflation is 1.7 percent, compared with the current 2.2 percent. (The Taylor Model traditionally uses the GDP deflator. In these examples I've adjusted the survey's CPI forecasts for the long-term trends between the CPI and the GDP deflator. The calculations below also use both GDP growth forecasts and CBO estimates of potential GDP for the fourth quarter of 2005 to estimate the output gap).

Using these forecasts, the rule suggests an average Fed Funds rate of 2.8 percent in the fourth quarter of this year. Assuming rates rise by 25 basis points at each meeting, the Fed would be finished after the second or third meeting.

Forecasting the economy perfectly is a rare event. So it's a good idea to run a number of projections through the model, to better understand the variation the Fed Funds rate may take. One way to do that is to use forecasts furthest from the mean.

Plugging in a forecast for strong growth (4.8 percent in the fourth quarter, according to Bloomberg's survey) with rapid inflation (3.2 percent), the Taylor Rule implies an average Funds rate of 5.7 percent in the fourth quarter. In that case the Fed would need to raise overnight rates by 50 basis points in each of the first seven meetings. It's difficult to imagine that the bond and stock markets have this much tightening priced into them.

Assuming the economy slows (2.5 percent) and price increases slow considerably (.6 percent) the Taylor Rule suggests a rate of less than one percent. In this case the Fed would need to lower rates from current levels.

Assuming fast growth and rapid inflation - and its opposite combination - shows a wide distribution between the levels of possible interest rates. Nearly 5 percentage points separate the two. Keep in mind though that historical data show that strong economic growth generally coincides with low inflation, not strongly rising prices (see Breaking Monetary Policy into Pieces).

The large spread between these two estimates is also being driven by a lack of agreement on expected inflation. While the Fed - and therefore the markets - becomes more focused on the rate of price increases, economists have widely differing views on what to expect. The range around economists' forecasts for inflation this year is the largest it's been in the nine years of the survey's history.

The Real Rate

If forecasting economic growth and inflation weren't difficult enough, there's another unknown. It's the neutral real rate, the first term in Taylor's equation. Though a 2 percent neutral real rate is assumed in the model, most economists agree that this number changes through time, based on productivity trends and exogenous shocks to the economy.

In a November Wall Street Journal article, a number of Fed members said the range for the neutral real rate is likely between 2 percent and 4 percent. If so, this would boost the rates we estimated.

But Fed Vice Chairman Roger Ferguson Jr. and Janet Yellen, president of the San Francisco Federal Reserve Bank, both suggested that currently the rate is closer to the low end of the range. Ms. Yellen was quoted as saying that the problems in the economy - such as the U.S. trade deficit and tepid business investment - "may be holding the intermediate-term equilibrium real rate down".

That argument would leave the above calculations above mostly unchanged. Using the average forecasts for economic growth and inflation, the Taylor implied Fed Funds rate for the fourth quarter is 2.8 percent, with much variability around the estimate because of the disagreement on inflation forecasts.

For the CBO's quarterly estimates of potential GDP, see http://research.stlouisfed.org/fred2/series/GDPPOT .

Thanks to Ken Kim of Stone & McCarthy Research Associates and Ethan Harris of Lehman Brothers for helpful conversations.