# Reverse Engineering the FOMC’s Policy Rule

In the last two expansions, the unemployment rate fell well below the NAIRU and inflation rose to nearly 2%  or modestly above. In both cases, the FOMC raised the fund’s rate well above the estimated neutral rate.  Recessions quickly followed. Today, the unemployment rate is already ½ percentage point below FOMC  participants’ median estimate of the NAIRU, and the unemployment rate is likely to be revised lower in the  December projections. The inflation rate is expected to reach the 2% objective by 2019, if not sooner. Does the experience in the last two expansions presage a similar policy response in this expansion, a substantial overshoot of the neutral fund’s rate? Based on the policy rules Yellen wrote down in 2012 and 2015, the answer would be yes. On the other hand, participants’ median rate projections have the fund’s rate just converging to their median estimate of the neutral rate in 2019, rather than overshooting it. Here, we search for a rule whose prescriptions are in line with participants’ rate projections.

Simple Policy Rules

We start with a simple, generalized form of a Taylor-like policy rule, a specification consistent with each of the rules we consider: a rule for normal times.

We then proceed to a rule adapted to the presence of headwinds and another rule more consistent with participants’ rate projections today.

All three rules are in the form of equation (1):

where r is the prescribed fund’s rate, r* is the real equilibrium or neutral funds rate, π is the inflation rate, and UGAP and IGAP are the deviations of the unemployment rate and inflation, respectively, from their mandate consistent levels. α and β are “response parameters” that indicate the intensity of the response of the prescribed fund’s rate to changes in UGAP and IGAP, respectively. In all the rules we discuss, the response parameter on IGAP is the same, 0.5.

Yellen’s Policy Rules

We first identify two rules that Yellen has set out: one she says is appropriate in normal times and the other  adapted to the presence of headwinds in the post-Great Recession period, including now.1

1 Policy Rules According to Yellen, Macroeconomic Advisers, July 10, 2015.

Yellen’s rule for normal times (Yellen 2012)

Yellen set out a rule in 2012 that she saw as appropriate in normal times.2 That rule had a long history and was conventional by then.3In that rule, the real neutral rate, r* in (1), is assumed to be participants’ median estimate of the “funds rate in the long run”, translated into real terms, and referred to as the “longer run” or  “normal” r-star. The response parameter on UGAP, of special importance in our story, is 2.3.4

In 2015, Yellen changed the 2012 rule to be consistent with the experience of headwinds in the post-Great Recession period which warranted a more accommodative monetary policy than otherwise.5In this case,  there are now two r-stars: one prevailing in normal times, referred to as the “longer run” or “normal” r-star,  and one in the presence of headwinds, which we refer to as the “current” r-star.6(Policy Rules According to  Yellen, Macroeconomic Advisers, July 10, 2015). The current r-star is expected to converge to its longer

run, or normal, level as headwinds disappear. In participants’ median rate projections, that is anticipated to occur by the end of 2019.

Yellen’s estimate of the current neutral rate is based on estimates of r-star from a model developed by Laubach and Williams (LW).7 At the time she introduced the Yellen 2015 rule, she said her estimate of r-star was “near  zero,” and it was zero when she reported the prescription from this rule.8

The Laubach-Williams model was later updated in a 2016 paper by Holston, Laubach, and Williams (HLW) and participants began to cite that model when discussing their estimates of the current r-star.9 So we use estimates based on that model beginning in 2016. The HLW estimate has fallen in the last two quarters to below its 0.5% average since 2012. Such dips gave occurred before over this sample, so we chose to use a steady  0.5% for the HLW estimate of r-star, which converted to nominal terms would be 2½%. This is consistent with the level Williams now assumes for his estimate of nominal r-star, which, in his case, is viewed as the  “new normal,” both the current and longer-run r-star.10

2 Vice Chair Janet L. Yellen, “The Economic Outlook and Monetary Policy,” At the Money Marketeers of New York University, New York,  New York, April 11, 2012.

3 This is the specification of a Taylor-like policy rule that I was using at the Board in the late 1990s, with the staff’s input. It has been our go-to rule ever since I left the Board and has been one of the favored specifications used by the staff for prescriptions from a suite of rules presented to FOMC participants before each meeting. In any case, this rule has gone through several name changes in  Yellen’s use of it. First, she called it Taylor 1999, based on a rule Taylor wrote down in 1999. But he disavowed that rule. So, Yellen now calls her rule a “balanced approach rule”, identifying it with the “balanced approach strategy” first set out in 2012 in the FOMC’s  Statement on Longer-run Objectives and Monetary Policy Strategy. But, in my view, this rule has nothing to do with that strategy, so I  call it simply “Yellen 2012.”

4 Yellen says that the defining feature of this rule is the aggressive response to deviations from the NAIRU; that is, in (1), the large response parameter on UGAP. Specifically, it was large relative to the implied coefficient Taylor 1993. See John B. Taylor (1993),  “Discretion versus Policy Rules in Practice,” Carnegie-Rochester Conference Series on Public Policy, vol. 39 (December), pp. 195-214. 5 Janet L. Yellen, “Normalizing Monetary Policy: Prospects and Perspectives”, “The New Normal and Monetary Policy”, a research conference sponsored by the Federal; Reserve Bank of San Francisco, March 27, 2015.

6 What is viewed as “normal” for r-star itself has evolved over time—specifically declined, especially since 2012—due (at least in part)  to declining potential output growth, seen as the principal determinant of the normal r-star. So, we are really in a period of new normals since then.

7 Laubach, Thomas, and John C. Williams. 2003. “Measuring the Natural Rate of Interest,” Review of Economics and Statistics, 85(4),  November 1063–1070.

8 See footnote 5 in Janet L. Yellen, “Normalizing Monetary Policy: Prospects and Perspectives”, “The New Normal and Monetary Policy”,  a research conference sponsored by the Federal; Reserve Bank of San Francisco, March 27, 2015. In 2015, the Laubach-Williams estimate was virtually zero.

9 Holston, Kathryn, Thomas Laubach, and John C. Williams, “Measuring the Natural Rate of Interest: International Trends and  Determinants. Economics,” “Federal Reserve Board, August 19, 2016.

10 John C. Williams, “Interest Rates and the ‘New Normal,’” October 5, 2017.

Participants’ Policy Projections and Prescriptions from the Yellen Rules

We noted in our earlier commentary that Yellen 2012 prescribes a path of the fund’s rate very consistent with the FOMC’s response to the undershoots of the NAIRU in the last two expansions, 1991-2002 and 2002- 2007: (Undershooting and Overshooting). An increase in the fund’s rate of 100 points and 200 basis points,  respectively, above the estimate of the neutral rate in response to undershoots of the NAIRU by ½ and 1  percentage point, respectively. However, as we see in Figure 1, participants’ median projections of the fund’s rate, reported in the September SEP, move to their median estimate of their longer-run or normal neutral r star only for 2019 at its earliest (2.8%), even though the unemployment rate is ½ percentage point below the NAIRU and stabilizes there and inflation reaches 2% and stabilizes there. For 2020, participants’ median fund’s rate projection is 2.9%, just a tenth higher. Same story. That’s inconsistent with prescriptions from either Yellen 2012 or Yellen 2015, 3½%.

Reverse Engineering the Policy Rule

Our task is to uncover the implied policy rule that is consistent with participants’ macro projections and rat projections today. We use the latest median macro projections and rate projections by participants, reported in the September SEP. Then we reverse engineer the policy rule. That is, we look for a set of parameters in a rule in the form of (1) that will prescribe a path of the fund’s rate consistent with participants’ rate projections. Here are two assumptions about the parameters in (1) that do so.

First, if α = 0. In this case, the FOMC would not raise the fund’s rate above its neutral level when the unemployment rate falls below its estimate of the NAIRU, unless and until inflation rises above the 2%  objective. This might be consistent, for example, with participants viewing the Phillips curve as very flat,  inflation expectations as stable, and seeing lasting benefits from an unemployment rate below the NAIRU.  This is the “don’t shoot until you see the color of their eyes” strategy. This is exemplified by President Evans:

“I also think a reasonable case can be made for holding off increasing the fund’s rate until inflation actually  gets to 2 percent on a sustainable basis.”11

Second, UGAP = 0. In this case, the unemployment rate is taken as equal to the NAIRU even when the unemployment rate is below the median estimate of the NAIRU. That might be consistent with uncertainty about how low the NAIRU is or with an assumption that the NAIRU is best measured as a range rather than a point. This would presumably continue until inflation moved above 2%.

Prescriptions under the two assumptions are of course the same, so in the figures below-showing prescriptions from our implied policy rule there is only one line, labeled α = 0.

Prescriptions from Yellen 2012 and Yellen 2015 assuming α = 0

In Figure 2, we see that prescriptions from Yellen 2012 (based on participants’ median estimates of r-star)  and Yellen 2015 (based on the HLW estimates), even with α = 0, are both initially well above the actual fund’s rate through 2016, and above participants’ median fund’s rate projections through 2017. This reflects that the FOMC has intentionally been maintaining a modestly accommodative policy stance, and intends to continue doing so until 2019, even though the unemployment rate is already below the NAIRU and inflation is expected to move to 2% in 2019.

In addition, we also can see in Figure 2 that the prescriptions from Yellen 2012 were earlier much higher than for Yellen 2015, reflecting the initially much larger gap between the participants’ median estimate of the longer-run r-star (used in Yellen 2012) and the HLW estimate of the current r-star (used in Yellen 2015). For

11 Charles L. Evans, “Reflections on the Current Monetary Policy Environment”, Global Independence Center, London, England, June 3,  2016.

For example, the median estimate of r-star was 4¼% in 2012, while the Laubach-Williams estimate was near  2% (in nominal terms), a gap of 250 basis points. By 2016, the gap had narrowed to 50 basis points; and today it is just 25 basis points. By 2019, the implied rule using participants’ median estimate of r-star just equals r-star when α is zero. That rule meets our test: Participants’ prescribed fund’s rate should equal the participants’ median estimate of r-star in 2019.

Convergence of the Current and Longer-run r-stars

Participants expect the current r-star to have converged to its longer-run level in 2019. In Figure 3, we assume that convergence begins in 2018 and that the current and long-run r-stars are both 2¾% in 2019. So, in  Figure 3, we see that the implied rule with α = 0, now with a single line for the prescribed funds’ rate by  2019, prescribes a path of the fund’s rate that just reaches the median estimate of r-star in 2019.12 Mission accomplished!

We again show a point for Yellen 2012 and Yellen 2015 in 2020:Q4, both assuming a neutral funds rate of  2¾% in nominal terms, and α = 2.3, the level in both those rules. These prescriptions are, of course, the

12 We have been assuming that the convergence occurs through a rise in the current r-star to participants’ median estimate of the longer-run r-star. That’s consistent with the expectation that the headwinds which have been holding down the current rate will have dissipated by the end of 2019, in line with what is anticipated by participants. But a convergence of the two rates has been underway for some time, and is now almost completed, but with the median estimate of the longer-term rate converging to the relatively unchanged HLW  estimate of the current rate. That is consistent with the HLW view that their estimate is the new normal. It is just as likely, therefore, perhaps more likely, that participants’ median estimate of the r-star will converge to today’s HLW estimate. See Learning About the New Normal,  November 3, 2017. The basic conclusion would remain the same—that the rule with α = 0 would prescribe a funds rate consistent with participants’ rate projections in 2019, except that rate would be 2½%, the HLW estimate, rather than 2¾%, the current median estimate of participants.

same now, and well above participants’ median estimate of r-star, by well more than 100 basis points, at  3½%.13

The Balanced Approach in Action

I admit that a policy rule with α = 0 seems inconsistent with the very concept of a Taylor-like policy rule:  that the FOMC responds by adjusting the fund’s rate in response to deviations from both the NAIRU and the inflation objective. On the other hand, it is the case that prescriptions of a policy rule with α = 0 are consistent with the participants’ median projections of the fund’s rate in 2019! That, after all, was our task.14

And as we emphasized in our recent commentary, there are good reasons why the Committee may acting as if the parameter on UGAP was much lower than 2.3, closer indeed to zero: a flatter Phillips curve; perhaps more stable inflation expectations than in the last two expansions; and inclination to allow the unemployment rate to fall modestly below the NAIRU for a while, given the more favorable tradeoff and lasting benefits of a  “hot” labor market; the uncertainty about how to measure slack and low the NAIRU is; and the logic of asymmetric inflation objective. (Undershooting and Overshooting

Still, α = 0 would be a very special case for a policy rule, holding only under very unusual circumstances,  perhaps like those recently faced by the FOMC, and, at this extreme perhaps only once the unemployment rate got to the estimated NAIRU and began to fall below. Such a special case is consistent with the FOMC’s  “balanced approach strategy”, first set out in 2012 and reaffirmed every year since.15 (“The Balanced  Approach: An Exploration”, Macroeconomic Advisers, November 17, 2015) Under the balanced approach strategy, a rule in the form of (1) can, in effect, have different parameters on UGAP, and perhaps IGAP,  depending on the circumstances, specifically depending on whether the objectives are complementary or not.

Objectives are not complementary when moving the fund’s rate in a given direction pushes one objective toward its mandate-consistent level and the other away. That’s the case today. In this case, the FOMC must set a priority in terms of which deviation the Committee responds to at the expense of the other. The priority,  according to the balanced approach strategy, depends on which deviation is greater, and on how long it is expected to take for each objective to reach its mandate consistent level.16 The question today is, of course,  not what direction to move the fund’s rate, but whether to move it in December or wait and see between the  December and March meetings, as well as the projected pace of rate hikes in 2018 and beyond.

There seems to be an emerging recognition that the balanced approach strategy provides guidance today with respect to how participants should balance the deviations from the employment and inflation objectives in their near-term policy decisions. Rosengren and Kaplan have recently used the balanced approach strategy to explain why they support a hike in December.

“Inflation remains below the Federal Reserve’s target, which might suggest added patience in removing accommodation, given that the economy is below the equilibrium rate of interest. At the same time, the unemployment rate is currently below the level most FOMC participants think will be sustainable, which would suggest the additional removal of accommodation. How should the FOMC  balance these somewhat conflicting factors? The Statement on Longer-Run Goals and Monetary Policy  Strategy provides guidance for following a balanced approach. While these so-called “misses” in the

13 We focus on 2019 because that is when prescriptions from our implied rule with α = 0 coincide precisely with participants’ median projection of the longer-run neutral rate, despite the unemployment rate being below the NAIRU and inflation at 2%. In 2020, participants’ median projection of the fund’s rate rises, but only a tenth above the neutral rate. Virtually, the same story. 14 I guess this might reflect, at the margin, participants’ reluctance to show in their rate projections moving above the neutral rate, or,  for that matter, and overshooting of the 2% objective.

15 Statement on Longer-Run Goals and Monetary Policy Strategy, January 2017.

16 Language from the Statement on Longer-Run Goals and Monetary Policy Strategy, January 2017.

mandate are of relatively similar magnitudes currently, most forecasts expect the inflation “miss” to  be temporary, but the unemployment “miss” to be more persistent.”17

“We are committed to following a ‘balanced approach to policy. This approach involves assessing  ‘other’ factors, such as the magnitude of deviations from our longer-run inflation goal and deviations of employment from the Committee’s assessment of its maximum level, as well as the timing of expected return to mandated and/or sustainable levels. Put more plainly, even though we are not  meeting our inflation objective, the size of the expected full employment overshoot is growing and  should be taken into account in assessing appropriate monetary policy actions.”18

Both Rosengren and Kaplan’s application of this strategy calls for setting a priority on preventing the unemployment rate from falling further below the NAIRU, even at the expense of a slower movement of inflation to 2%.  This is the basis for their support of a hike in December. Their views are therefore consistent with a policy rule in the form of (1) with α > 0. But their remarks do confirm that the balanced approach strategy, in some circumstances, calls for different priorities concerning responding to deviations from the two objectives.

On the other hand, the balanced approach strategy calls for patience for those participants who are concerned that underlying inflation has declined quite sharply recently, and believe the priority of the FOMC should be to raising inflation to 2%, even at the expense of a decline in the unemployment rate to further below the  NAIRU. That’s consistent with a pause in December, a wait-and-see posture.

Looking Forward

The policy rule that the Committee, in effect, follows is likely to evolve, for example, if the unemployment rate falls further below the NAIRU, the incoming inflation data firms (as it may already be doing), and inflation is projected, as it the case today, to get to at least 2% by 2019. Still, would the median dot for 2018 move higher in December if, as we expect, participants’ median forecast for the unemployment rate is revised down,  below 4%, with no change in the median inflation forecast? Not likely, we expect, in December, but this logic is raising the probability of four hikes in 2018, and, indeed, we have just changed our call from three hikes in  2018 to four. Nevertheless, if and when the implied policy rule does evolve, in effect, to imply that α is above zero, all the developments since the last two expansions suggest that it may remain smaller than the 2.3 level in Yellen 2012 and Yellen 2015.