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Mutable Economic Laws and Calculating Unemployment and Output Gaps—An Application to Taylor Rules

The Taylor rule, which expresses the federal funds rate as a function of how far inflation is from its long-run target and how far output is from its potential, is often thought to be a useful guide to monetary policy. Economist John Taylor proposed that the weight on the inflation gap be 1.5 and the weight on the output gap be 1. Given that the dual mandate of the Federal Reserve includes inflation and employment, many people write the Taylor rule in terms of an employment gap instead of an output gap. With an unemployment Taylor rule, the funds rate responds to deviations of unemployment from its “natural rate,” sometimes called the nonaccelerating inflation rate of unemployment or NAIRU. The coefficient on the unemployment gap is usually taken to be 2. Many economists typically include the lagged funds rate as well. We also include this “inertial” term (which is estimated to be 0.8) because while the funds rate typically moves in the direction suggested by the Taylor’s original rule, these movements are typically only partial; thus, it takes a series of policy moves to reach the level a simple Taylor rule suggests.

The Taylor rule is garnering more attention lately as many think that the fed funds rate may be raised soon (“liftoff”). Some believe that the Fed is already behind the curve and should have raised rates a while ago. The chart below shows that if the Fed would have followed an unemployment Taylor rule, the funds rate today would be 1.85 percent, and if it had followed the output Taylor rule, the rate would be 0.69 percent. Notice that there is over a percentage point difference in these two rules. Both of these estimates suggest that the Fed may have been slow to increase rates. But such conclusions depend critically on how accurately potential output or the natural rate of unemployment is measured (such conclusions also depend in part on the particular form of the Taylor rule used; for simplicity, this analysis focuses on the simple rule described above). Both concepts are hard to estimate with any precision, and this lack of precision should be recognized when policy recommendations are made using a Taylor-type rule.

Where the Fed Funds Rate Would Be Using a Taylor Rule

Potential output and the natural rate of unemployment are useful economic concepts, but they are measured with considerable error. Estimates are extremely difficult to make, and large revisions are made periodically. This is particularly true in the aftermath of the Great Recession. For example, the Congressional Budget Office’s (CBO) 2007 estimate of what output would be in 2015 differs from its current estimate by approximately a trillion dollars. This difference is similar to the decline in the gap at the trough of the recession. It is as if the CBO now sees the recession as a permanent shock to GDP. Put another way, after the large fall in GDP, output increased at roughly the same rate as potential (as projected in 2007).

Estimates of Potential GDP

The revision translates into nearly a 7 percentage-point difference in the output gap. In terms of Taylor rules, this difference suggests that if potential output today were at the 2007 estimate, the Taylor rule would call for a federal funds rate of about -5 percent (if interest rates were not constrained by the zero lower bound).  This is not meant to say that people currently believe that output is over 9 percent below potential. But estimates of potential GDP are very fluid, and it suggests there is considerable error in our current measure.

Estimates of the Output Gap

The CBO’s estimate of the natural rate of unemployment is also fluid, though the revisions are much smaller. In 2007 the CBO estimated that the natural rate of unemployment was, and would remain, at 5 percent. But today the estimate is 5.4 percent. A Taylor rule with the 5 percent natural rate would predict a federal funds rate of 0.59 percent in 2015:Q1, while the funds rate predicted would be 1.85 percent with a 5.4 percent natural rate.

Estimates of the Natural Unemployment Rate
Estimates of the Unemployment Gap

This difference is especially dramatic because a Taylor rule with our current estimate of the natural rate suggests that liftoff would have been about a year ago, in 2013:Q4 (the old natural rate estimate suggests liftoff in 2014:Q4). Contributing to this difference is that the CBO now thinks the natural rate peaked at about 6 percent in 2012:Q1. This is compared to the 5 percent that in 2007 they had projected it would be in 2012.

Estimates of the Federal Funds Rate Using Taylor Rule with the Unemployment Gap

One problem in calculating the natural rate and potential output is that they both rely on statistical regularities that do not hold independent of policy and expectations. Both NAIRU and potential output are basically theoretical constructs that are fundamentally unobservable.  For example, to calculate the natural rate of unemployment the CBO and others use an empirical relationship called the Phillips curve. The Phillips curve stipulates that when unemployment is above the NAIRU, inflation will decrease one year later. During the recession inflation did not decline nearly as much as some estimates of the Phillips curve would predict, and this discrepancy has continued to this day. The issue is sometimes referred to as the missing inflation puzzle. The Phillips curve is a statistical relationship and is not necessarily stable over time, the CBO revises its NAIRU series so that it better aligns with an estimated Phillips curve. This is seen in the chart below, where the orange dots have been revised up to the blue dots. While other input such as demographic data is used to determine the NAIRU, the CBO still relies on an empirical relationship to help inform it about what NAIRU is.

Phillips Curve, 1985-2014

It should not be surprising that this empirical relationship missed substantially after a big crisis like the Great Recession, especially given all the unconventional monetary policies during the period. But a problem arises when this simple statistical relationship is taken to always hold. Today most researchers believe the Phillips curve is not backward looking but forward looking. But because expectations are hard to measure, many forecasters use a backward-looking curve. Arguably during normal times this may not be too far off, but currently it is much less clear. The version of the Phillips curve researchers use states that changes in inflation depend on expectations of the gap going forward and not just today’s gap. One reason inflation did not collapse during the Great Recession is because the Fed promised low interest rates going forward as well. How much this mattered quantitatively is not clear, making it extremely difficult to know how much missing inflation there should have been during the Great Recession.

Potential output is calculated from the natural rate series. Thus, potential output will incorporate all the errors involved in calculating the NAIRU. To arrive at potential, researchers make some adjustments to the natural rate of unemployment and use Okun’s law to transform unemployment into output. Okun’s law is a historical correlation stating that when unemployment decreases by 1 percent, GDP increases by 2 percent. Just like the Phillips curve, this is actually not a law, but is instead a rough empirical relationship that has been observed over time. Unfortunately, this relationship, too, has fared particularly poorly during the recovery. Now instead of a missing inflation puzzle, there is a puzzle over missing output. Unemployment has declined from a high of 10 percent in October 2009 to 5.5 percent today, but GDP has not had nearly such a robust recovery.

Okun's Law 1985-2014

These misses are quite large and accumulate. Because of the failure of Okun’s law, GDP is about 2 percent below potential, while unemployment is only 0.3 percentage points above its natural rate. Potential will likely be revised down in the future if these misses continue.

But even here the policy implications are not obvious. One reason why Okun’s law may have fared so poorly is because of the increased use of part-time employment. Part-time workers are not unemployed, but they do not produce the same output as full-time workers.

Full-Time or Part-Time Employment

Because of the relatively large share of employment that is part-time, some think that the output gap may be closer than the unemployment rate gap in terms of measuring the amount of slack in the economy. These are important issues for the stance of policy, but unfortunately there is no clear right or wrong answer. It does suggest that perhaps we should pay relatively more attention to inflation in setting policy than our slack estimates.

While the prevailing methodologies to estimate NAIRU and potential output are imperfect, they are still useful. However, everyone needs to be mindful of the imprecision that results from the methodologies, and take care in predicting policy actions like liftoff.

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