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Implied Taylor Rules among Forecasters

It has become commonplace to think of the Fed in normal times (when the federal funds rate is above zero) as operating in terms of a Taylor-type rule. The Taylor rule postulates that the Fed chooses deviations of the funds rate from its long-run target level based on the “inflation gap” (deviation of inflation from its long-term target of 2 percent), the unemployment (or output) gap, and the past funds rate. While such a rule necessarily abstracts from the many complexities that factor into the Fed’s actual setting of the federal funds rate target, it can effectively capture the historical evolution of monetary policy.

We explore whether professional forecasters appear to use a Taylor rule when they forecast the future funds rate, and if so, how similar their regression coefficients are to each other and to those in a Taylor rule that fits the historical data. We start by assuming that all forecasters follow a Taylor rule with an unemployment gap, and then we back out the implied Taylor rule coefficients from their forecasts of inflation, unemployment, and the funds rate. If the coefficients for each forecaster differ a great deal, it suggests that they use different versions of the Taylor rule or they don’t use such a rule at all.

To estimate forecasters’ Taylor rule coefficients, we use the projections that come from the Federal Reserve Bank of Philadelphia's Survey of Professional Forecasters. Among the questions asked in the survey are “What do you anticipate the inflation rate to be over the next four quarters?” and “What will the unemployment rate be four quarters from now?” While forecasters are not asked about what they expect the funds rate to be, they are asked what they think the 90-day T-bill rate will be three quarters from now, and since the T-bill rate is roughly the average of the funds rate over the next 90 days, we use this as a proxy for their funds rate forecast four quarters hence. We use these forecasts as inputs to estimate the implied coefficients of their Taylor rules.

We have continuous data for 18 forecasters since 1995. The chart below plots the Taylor rule coefficients that are implied by each of their inputs for inflation and unemployment.

Figure 1: Regression Coefficients of Individual Forecasters, Aggregate

If a data point appears in the upper right area of the graph, it implies that a given forecaster’s Taylor rule responds more aggressively to both inflation and unemployment than does the typical forecaster. If a point is in the lower left area, it implies that a forecaster’s Taylor rule does not respond strongly to current data. Instead, forecasts of future funds rates are driven mostly by where the funds rate will move in the long run and today’s funds rate. (Because an aggressive stance for unemployment is a large negative number, we plot the negative of the unemployment rate coefficient.)

There is a tremendous amount of variability in the coefficients. They range from a forecaster who sees basically no relationship between his funds rate forecast and his inflation and unemployment forecasts, to the 18th forecaster, who responds strongly to both inflation and unemployment (coefficients of 1.0 and 0.6, respectively). Perhaps even more interesting is that none of the forecasters has Taylor rule coefficients that resemble the fit of a Taylor rule to actual data on inflation and unemployment, rather than forecasts. The point labeled “aggregate data” corresponds to the coefficients of the Taylor rule implied by using actual realized data for unemployment, inflation, and the funds rate. That is, these are the coefficients in a Taylor Rule implied by the historical behavior of monetary policy as it relates to actual inflation and unemployment. Interestingly, the unemployment responses, in particular, are much larger than those of any of the individual forecasters.

The median forecast is frequently taken to be the “consensus” forecast. If we compare the median forecast to the aggregate, we find that the median’s inflation coefficient is roughly the same as the aggregate’s, but the unemployment coefficient is substantially higher. In fact, the implied Taylor rule of the median forecaster bears little resemblance to the one describing the Fed’s behavior. The chart below shows what the median and aggregate Taylor rules would suggest for the funds rate over time given the realized values of inflation, unemployment, and past interest rates. While the two estimated funds rate series necessarily track each other, there are huge discrepancies. It is not uncommon for them to differ by over 100 basis points. In the policy space, such a gap is extremely large.

Figure 2: Taylor Rules the Median Forecaster, Aggregate

To help illustrate the variability of the Taylor rules, we graphed the federal funds rates that would be produced by the implied Taylor rules of the forecasters with the strongest and weakest responses to inflation and unemployment—those in the top tercile of the first chart above and those in the bottom tercile. (To group the forecasters, we separated them into three groups of six in terms of their combined inflation and unemployment response. This requires aggregating inflation and unemployment into a single number. While there is necessarily some arbitrariness to combine them we weight the two by the tradeoff between the two exhibited in the version of the Taylor Rule estimated with actual aggregate data.) The group with the strongest response to inflation and output tracks the behavior of past monetary policy marginally best. In fact, the forecaster that tracks the aggregate Taylor rule the best is the most extreme forecaster in terms of his or her inflation and unemployment responses. But even then the differences between the two can be large.

Figure 3: Taylor Rules for the Lower and Upper Terciles, Aggregate
Figure 4: Taylor Rules for the 18th Forecaster, Aggregate

We concentrated on forecasters’ inflation and unemployment responses because these would be the current data determining the funds rate in a Taylor rule. The past funds rate is included to capture the fact that the actual funds rate moves very slowly. (Because we obtained the SPF estimated Taylor rules from forecasts, it is the current funds rate for them.) To see whether there is a relationship between how much a forecaster depends on the past fed funds rate and on the inflation-unemployment response, we plot the coefficients of both.

Figure 5: Regression Coefficients of Individual Forecasters

There is an inverse relationship between how strongly forecasters rely on today’s funds rate in determining where the funds rate will be in the future and how strongly they rely on their forecasts of inflation and unemployment. Those that do not rely on inflation and unemployment tend to rely more on the current funds rate. This suggests that some forecasters assume the funds rate will be essentially what it is today without following any Taylor rule, while others appear to believe that a Taylor rule is important in determining the funds rate. Our estimates of forecasters’ Taylor rules show that, if we assume they follow an unemployment Taylor rule, their coefficients are very different. Similarly, none of the forecasters’ implicit Taylor rules is similar to estimates of the historical reaction of the funds rate to inflation, unemployment, and last year’s funds rate, and this is especially true of the median or “consensus” forecaster.

Our estimates of forecasters’ Taylor rules show that, if we assume they follow an unemployment Taylor rule, their coefficients are very different. Similarly, none of the forecasters’ implicit Taylor rules is similar to estimates of the historical reaction of the funds rate to inflation, unemployment, and last year’s funds rate, and this is especially true of the median or “consensus” forecaster.

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