The FOMC’s New Individual Economic Projections andMacroeconomic Theories∗
Natsuki Arai†
September 20, 2022∗

I am grateful to Larry Ball, Ippei Fujiwara, Yasuo Hirose, Hibiki Ichiue, Sophocles Mavroeidis, Yoshiyuki Nakazono, Rodrigo Sekkel, Tara Sinclair, Jonathan Wright, Yohei Yamamoto, and the participants of the seminars at
George Washington University, Johns Hopkins University, Keio University, National Chengchi University, and Yokohama City University, and the participants at Hitotsubashi Institute for Advanced Study, Macroeconometric Modeling Workshop 2020, CEF 2021 for their helpful comments. I thank Shian Chang for excellent research assistance. I
gratefully acknowledge the financial support of the Taiwanese Ministry of Science and Technology’s grants 108-2410H-004-009 and 110-2410-H-004-183. All errors are the sole responsibility of the author.
†
Department of International Business, National Chengchi University. Address: No. 64, Sec. 2, Tz-nan Rd.,
Wenshan, Taipei 11605, Taiwan. E-mail: narai@nccu.edu.tw.

1Abstract
This paper examines whether the economic projections made by individual policymakers of
the Federal Open Market Committee (FOMC) are consistent with macroeconomic facts andtheories. By analyzing the projections between 2007 and 2016, this paper finds that they are
consistent with Okun’s law, revealing a significantly negative relationship between unemployment and output growth projections. The relationship between inflation and unemployment
projections associated with the Phillips curve is much weaker and more dispersed. The FOMC’sreaction function is estimated to be consistent with a conventional Taylor rule, with a sufficiently
aggressive response to the inflation gap satisfying the Taylor principle and a negative responseto the unemployment gap.

Keywords: FOMC, Individual Economic Projections, Okun’s Law, Phillips Curve,
Taylor Rule

J.E.L. codes: C53, E43, E47, E58

2

1

Introduction

Recently, central banks’ communications have become increasingly important in the conduct ofmonetary policy. This was particularly the case when many advanced economies experienced theeffective lower bound (ELB) following the financial crisis of 2008–2009 and the COVID-19 crisis
in 2020. Since 2007, the Federal Open Market Committee (FOMC) has published a Summary of
Economic Projections (SEP) made by individual policymakers, which has become one of the mostimportant communication tools for the Federal Reserve (Fed). According to a survey conductedby Olson and Wessel (2016), nearly half of Fed watchers from both academia and the private
sector regard the SEP as useful. However, there is one caveat to this: As only a summary of the
projections, such as the range and central tendency, is available at the time of FOMC meetings, only
variable-by-variable summaries of the projections are observed.1 As a result, it is impossible forthe public to associate the projections of different macroeconomic variables or the macroeconomic
projections with the appropriate paths of monetary policy.
In this paper, I overcome this shortcoming by using a new data set of the FOMC participants’ anonymous individual economic projections between 2007 and 2016 to examine two researchquestions. First, I investigate the empirical properties of the FOMC’s individual economic projections and assess whether they are consistent with standard macroeconomic facts and theories,
such as Okun’s law and the Phillips curve. As FOMC policymakers are highly experienced macroeconomists, with access to a vast array of staff and resources to direct economic research at the Fed,
it is crucial to evaluate whether their individual projections are consistent with textbook macroeconomic relationships. Second, this paper investigates the reaction function of the FOMC, whichcharacterizes its monetary policy decisions in response to changing economic conditions, as discussed in Bernanke (2016). More specifically, I estimate the Taylor rule based on the inflation andunemployment gaps—deviations of inflation and unemployment rates from their natural levels—
using the FOMC’s individual economic projections. There are several advantages to using these
individual projections. The FOMC publishes all the relevant projections to estimate the reaction
function, including projections of the federal funds rate and long-run macroeconomic projections.
1

For an assessment based on the aggregate summary of economic projections, see Arai (2016) and Kalfa andMarquez (2019).

3

These projections enable us to compute the inflation and unemployment gaps with which we candirectly estimate the FOMC’s reaction function. In addition, there are substantial variations in
the FOMC’s individual projections for longer horizons, even though the actual federal funds rate
remained at the ELB for most of the sample period.2
To answer these questions, this paper employs regressions based on repeated cross-sectional
data. I assume that FOMC policymakers have the same coefficients in each regression to capture
their collective macroeconomic principles. This is because estimating the collective principles isuseful as a benchmark, given that the FOMC’s decisions are based on consensus, and the principles
tested in this paper are widely accepted in macroeconomics. By exploiting the cross-sectionalvariation of individual projections, this paper provides more efficient estimates than those using
the time-series variation of aggregate projections.
I first run the regressions at each forecast horizon, from one to fourteen quarters ahead, toaccount for the different nature of forecasting across horizons. Then, I provide the pooled regression combining all horizons with the horizon- and meeting-fixed effects. For the estimation of
the FOMC’s reaction function, I apply the censored regression (Tobit) model to account for the
nonlinearity associated with the ELB.
The results indicate that the FOMC’s individual projections are consistent with Okun’s law—theassociation between output growth and the unemployment rate is strongly negative and statisticallysignificant. Although the relationship between unemployment and inflation (i.e., the Phillips curve)
is negative and statistically significant, the relationship is weak and dispersed. The estimates of thereaction function indicate that the FOMC’s individual economic projections are consistent with aconventional Taylor rule. The equilibrium real interest rate and the response to the inflation gap are
estimated to be positive and statistically significant. In particular, the magnitude of the responseto the inflation gap is larger than one in most cases, consistent with the Taylor principle that acentral bank should be sufficiently aggressive against inflation to maintain stability. The responseto the unemployment gap is significantly negative in all specifications, consistent with the dual
mandate of the Fed.
This paper offers four extensions to the main results. First, I analyze the consistency of the2

Bundick (2015), Pierdzioch et al. (2016), and Kim and Pruitt (2017) also exploited this advantage of survey
forecasts to estimate the reaction function.

4

Survey of Professional Forecasters (SPF) with Okun’s law and the Phillips curve during the same
sample period using the SPF’s individual forecasts. Similar to the FOMC’s forecasts, I find a robust
Okun’s law relationship and a weak Phillips curve relationship, which suggests that these tendencies
are likely driven by the sample period rather than by the factors specific to the forecasters. Second,
I conduct the same analysis using the aggregate SEP using the sample between 2007 and 2022,
finding largely similar results. Third, I offer estimates based on the quantile regression to shedsome light on the dispersion of estimates across quantiles. Last, I use the FOMC’s output gaps
instead of the unemployment gaps to estimate the FOMC’s reaction function. The evidence ismixed when output gaps are used for the estimation, but this is likely due to downward revisionsof the longer-run projections for output growth during the sample period.
These results are largely consistent with the existing literature. Several papers find that Okun’s
law serves as a useful guide for forecasters.3 Given the significance of Okun’s law for forecasting, it isnatural to find this robust relationship between output growth and unemployment rate projections.
Conversely, several papers have documented that the forecasting performance of the models basedon the Phillips curve has deteriorated over the years, as discussed in Stock and Watson (2008) andFaust and Wright (2013). In particular, many papers claim that the Phillips curve has flattened inrecent decades.4 Therefore, it is not surprising that the observed correlation between inflation andunemployment projections made by FOMC policymakers and private forecasters is weak. Casey(2020) reached the same conclusion by studying professional survey forecasts in the US, UK, andEurope. Finally, the estimates of the FOMC’s reaction function are consistent with the estimatesin earlier papers by Kahn and Palmer (2016) and Morris (2017), which were based on the FOMC’s
aggregate SEP, and by Belongia and Ireland (2019), which was based on the Fed’s Greenbook
forecasts.
The contribution of this paper is twofold. First, it is one of the first attempts to investigate
the empirical properties of the FOMC’s new individual economic projections, which have attracted
3

For example, see Ball et al. (2015), Guisinger and Sinclair (2015), Mitchell and Pearce (2010), and Pierdzioch etal. (2011). In fact, Jordà et al. (2020) show that a simple model incorporating Okun’s law can help refine the advancedata release of real GDP, even during the COVID-19 pandemic.
4
For example, see Del Negro et al. (2020), Gagnon and Collins (2019), Hooper et al. (2020), Jorgensen and Lansing(2019), Kuttner and Robinson (2010), Matheson and Stavrev (2013), and Simon et al. (2013).

5

renewed interest since 2007.5 Since the FOMC began to publish them as one of its primary communication tools, the analysis of these new projections is particularly relevant for monetary policy.
Similar to the papers by Carvalho and Nechio (2014), Dräger et al. (2016), and Tillmann (2010),
which studied the consistency of survey expectations with macroeconomic facts and theories, thispaper confirms that the FOMC’s individual economic projections are broadly consistent with thesefacts and theories. Second, this paper provides quantitative estimates of the FOMC’s reaction
function at the ELB, exploiting the variation at longer-horizon forecasts. Given that investors pay
substantial attention to the FOMC’s communication, which has significant impacts on various asset
prices,6 providing quantitative estimates of the FOMC’s reaction function could be useful. Even
though the Fed engaged in unconventional monetary policy at the ELB rather than the conventional policy characterized by the reaction function, the quantitative estimates will be particularly
valuable when the liftoff of interest rates is expected near the end of the ELB.
The remainder of this paper is organized as follows: Section 2 describes the data and methods
used. Section 3 presents the main empirical results, and Section 4 provides extensions to the main
results. Section 5 offers concluding remarks.

2

Methodology

In this section, I first explain the details of the FOMC’s individual economic projections. Second, I
explain the calculation of the annual changes in the unemployment projections used in the analysis.
Third, I describe the test to determine whether the FOMC’s individual economic projections are
consistent with Okun’s law. Fourth, I set out a similar test for the Phillips curve. Finally, I describe
the estimation of the FOMC’s reaction function.
5
For the analysis of the FOMC’s individual economic projections prior to 2007, see Meade and Sheets (2005),
Nakazono (2013), Romer (2010), Sheng (2015), and Tillmann (2011). According to Powell and Wessel (2020), morethan 60% of survey respondents answered that SEP is useful, while only 20% of them answered so for monetary
policy reports to Congress that published the projections prior to 2007.
6
For recent discussions, see Bodilsen et al. (2021), Couture (2021), Du et al. (2018), and Indriawan et al. (2021).

6

2.1

Data

The FOMC’s economic projections are the numerical projections of several macroeconomic series
over the next two to three years and over the longer run:7 real GDP growth, the unemployment rate,
PCE inflation, and core PCE inflation. Since 2012, the FOMC has started publishing the projected
path of the future federal funds rate (FFR) associated with these macroeconomic projections.
The FOMC’s economic projections are the annual projections that target the level or growth ratein the fourth quarter of a given year. Although all the participants of the FOMC meetings submit
their projections, only a set of summary statistics are released immediately after the meeting, suchas the ranges, central tendency, and median.8 The FOMC releases these projections four times a
year, typically in March, June, September, and December.
Recently, individual FOMC policymakers’ economic projections have been made available tothe public with a five-year lag, and projections from 2007 to 2016 are currently available. These
individual projections are anonymous, and policymakers are identified by randomly assigned numbers, which are reshuffled at every meeting. Therefore, researchers can analyze the variations in
the projections made at each meeting across different macroeconomic variables. The participants’
keys that map these numbers and the identities of policymakers are released 5 or 10 years after ameeting.9 As a result, individual projections with policymakers’ identities are partially available
from 2007 to 2011 and for 2016 at the time of writing.10

2.2

Calculation of Annual Changes

The FOMC’s economic projections are in the form of growth rates for real GDP growth, PCE
inflation, and core PCE inflation, whereas they are based on the levels for the unemployment rate.
For a regression analysis, it is convenient to compute the annual changes in the unemployment rate.
First, I denote the forecast of the unemployment rate made by forecaster i at the qth quartersiof year t forecasting h years ahead (h = 0, . . . , 3) as Ût+h|t,q. Then, I compute the forecasts of the7

The projections over the longer run were added in 2009.
The FOMC began to release median projections in September 2015.
9
The embargo period was initially 10 years and the FOMC changed it to 5 years in 2016.
10
Appendix Table A1 provides the summary statistics of the projections with identities, listing the mean of projections across all forecast horizons and the corresponding standard deviation. These statistics suggest that variations
between policymakers are substantial, especially for projections of the federal funds rate.
87

annual change relative to the previous year as follows:i≡∆Ût+h|t,qÛ i − Ut−1|t,qt|t,qfor h = 0


Û i
i
t+h|t,q − Ût+h−1|t,q

for h = 1, 2, 3,(1)

where Ut−1|t,q is the real-time realized value of year t − 1 observed at the qth quarters of year t. In
other words, I calculate the annual changes by taking the difference between the real-time realized
value and the projections for the nowcasts (h = 0) and computing the incremental changes in the
projections for the subsequent forecasts (h = 1, 2, 3).
Figure 1 depicts the calculation of the annual changes. For illustration, suppose that theforecasts are made at the second quarter of year t. Then, the forecasts for the fourth quarterof year (h = 0) and for the fourth quarter of the next year (h = 1) by forecaster i are denotedii
as Ût|t,2
and Ût+1|t,2, respectively. By taking the difference between them, I effectively computethe forecast of the annual changes between year t and year t + 1 made at the second quarter,iii . For the forecast of the fourth quarter of the same year, the annual∆Ût+1|t,2= Ût+1|t,2− Ût|t,2change is computed by taking the difference between the forecast and the real-time realized valueiiof the previous year, ∆Ût|t,2= Ût|t,2− Ut−1|t,2 .

2.3

Test for Okun’s Law

Okun’s law shows a negative relationship between changes in the unemployment rate and output
growth, which characterizes a short-run fluctuation of the economy:∆Ut = α − β∆Yt ,(2)

where ∆Ut is the change in the level of the unemployment rate and ∆Yt is the growth rate ofoutput. Typically, we assume the coefficient, α, to be 1.5% and the magnitude of the slope, β, tobe 0.5 for the US economy.11
It is straightforward to test whether the FOMC individual policymaker’s projections are con11

For example, see Mankiw (2018).

8

sistent with Okun’s law using the following regression:ii+ εit+h|t,q ,= αh,q − βh,q ∆Ŷt+h|t,q∆Ût+h|t,q(3)iwhere ∆Ût+h|t,q
is the forecast of the changes in the unemployment rate made by forecaster i atithe qth quarters of year t forecasting h years ahead, and ∆Ŷt+h|t,q
is the corresponding forecast for

GDP growth.
To investigate the collective principle of the FOMC, I assume that the policymakers share thesame parameters in the regression. Even though this is arguably a strong assumption, given that asubstantial degree of heterogeneity is observed among FOMC policymakers,12 I maintain it for two
reasons. First, since the FOMC collectively makes monetary policy decisions based on consensus,
estimating the FOMC’s collective principle is useful as a benchmark for the public. Second, themacroeconomic facts and theories tested in this paper are widely accepted in macroeconomics
and FOMC policymakers largely agree with these facts and theories.13 In other words, FOMC
policymakers’ dispersions are likely driven by their views on the state and the future course of theeconomy, rather than by their views on macroeconomic facts and theories.
Using this specification, I first run separate regressions for each combination of the forecasthorizons and the quarters, which range from nowcast (h = 0 and q = 4: forecasting the fourth
quarter of the year at the same quarter) to fourteen quarters ahead (h = 3 and q = 3: forecasting
the fourth quarter three years ahead at the third quarter of a year). It is natural to separate
the sample according to the forecast horizons, since the nature of forecasting practice likely differs
depending on the length of the forecast horizons.
Second, I pool the forecasts across all horizons to estimate the coefficients by controlling for the12

For a critical review of the FOMC’s communications and their dispersion among policymakers, see Faust (2016).
Vissing-Jorgensen (2019) propose several reforms to the FOMC’s communications because FOMC policymakers strategically use their communications to influence the consensus, which eventually confuses investors.
13
For example, Tillmann (2010) finds that the slope of the Phillips curve is not materially different between thegovernors of the Federal Reserve and regional Reserve Bank Presidents. Fendel and Rülke (2012) and Jung andLatsos (2015) reach similar conclusion for the FOMC’s reaction function.

9effects at specific meetings:ii+= α − β∆Ŷt+h|t,q∆Ût+h|t,q

Q
T
X
X

δt,q Dt,q + εit+h|t,q ,(4)t=2007 q=1

where Dt,q is the dummy variable for a specific FOMC meeting, and T and Q denote the last yearof the sample and the maximum number of quarters, respectively. The dummy variable aims tocontrol for the effects of news at each FOMC meeting, which could affect all the forecasts acrossdifferent horizons made at the same meeting. Alternatively, the dummy variable for individual
forecast horizons, Dh,q , could be included to control for the horizon fixed effects.

2.4

Test for the Phillips Curve

The test for the Phillips curve, which describes a trade-off between inflation and unemployment, isconstructed in a similar manner. A typical Phillips curve is defined in gap form as follows:n) + vt ,πt+h = Et [πt+h ] − θ(Ut+h − Ut+h(5)where π, U n , and v denote the rate of inflation, the natural rate of unemployment, and the supply
shock, respectively.14 To describe the test for the Phillips curve, I introduce new notations. I denote
R i
i [π
Et,q
f (πt+h |Ωt,q )πt+h dπt+h as the expected inflation rate h years ahead by policymakert+h ] =
i, where f i (πt+h |Ωt,q ) is the probability density assigned by policymaker i to inflation h years ahead
conditional on the information set Ωt,q .
This specification of the Philips curve could be tested by taking the first-order differences ofthe projections as follows:iii∆π̂t+h|t,q= γh,q − θh,q ∆Ût+h|t,q+ νt+h|t,q
,

(6)


i
i [π
i
where ∆π̂t+h|t,q
is defined in the same way as in Equation (1). Note that γh,q ≡ Et,qt+h ] − Et,q [πt+h−1 ] +


n,i
n,i
θh,q Ût+h|t,q− Ût+h−1|t,q, which combines the annual changes of inflation expectations and thenatural rate of unemployment at the same meeting. For simplicity, I assume that γh,q is constant,
14

For example, see Mankiw (2018).

10which implies that policymaker i does not change the paths of their inflation expectations and theforecasts of the natural rate of unemployment across horizon h and h − 1 at each FOMC meeting.
Similar to the test of Okun’s law, I assume that both the constant and coefficients are the sameacross individual policymakers.
Following the same method outlined in the regression that tests Okun’s law, I pool the forecasts
across all horizons by adding the fixed effects for each FOMC meeting,
Q
T
X
X

i
i
+
= γ − θ∆Ût+h|t,q∆π̂t+h|t,qi,
δt,q Dt,q + νt+h|t,q(7)t=2007 q=1

where Dt,q is the dummy variable for a specific FOMC meeting, and T and Q denote the last yearof the sample and the maximum number of quarters, respectively.

2.5

Estimating the FOMC’s Reaction Function

The reaction function of FOMC policymakers characterizes their monetary policy decisions in response to changing economic conditions by taking the trade-offs in their policy objectives into
account. The FOMC’s new individual economic projections offer several advantages for estimating
the reaction function. First, since FOMC policymakers publish their inflation and unemployment
rate projections in the longer run, along with their fixed-target forecasts, researchers can directly
measure the inflation and unemployment gaps as the difference between them. Second, the estimation will not be constrained by the ELB because forecasts of future interest rates could be positiveat sufficiently long forecast horizons, even though the short-term federal funds rate was stuck at
the ELB between 2012 and 2015. Therefore, individual FOMC policymakers’ projections will offer
researchers substantial variation in their estimations.
Typically, the FOMC’s reaction function is described by the Taylor rule, in which the optimal interest rate depends on the inflation and output gaps, the latter of which can be measured
by the unemployment gap using Okun’s law. In this paper, I use the Taylor rule based on the11unemployment gap as the main specification:15
nit+h = ρ + φπ (πt+h − π ∗ ) − φU (Ut+h − Ut+h
),

(8)

n
where it is the nominal interest rate, π ∗ is the target inflation rate, and Ut+his the natural rateof unemployment. The constant, ρ, could be interpreted as the equilibrium real interest rate thatwould prevail when both the inflation and unemployment gaps are closed. This specification does
not include the past interest rate, although it is a common term to include in the Taylor rule torepresent inertia in the interest rate. This is because I cannot track the individual participants’projections across meetings.
Using FOMC policymakers’ inflation and unemployment rate projections in the longer run, I
characterize the forecasts of a hypothetical interest rate implied by the Taylor rule as ĩit+h|t,q , which
would not be constrained by the ELB:

i
i
i
i
i
− π̂LR|t,q) − φUĩit+h|t,q = ρh,q + φπh,q (π̂t+h|t,qh,q (Ût+h|t,q − ÛLR|t,q ) + εt+h|t,q ,(9)where the subscript LR denotes the projections over the longer run. Similar to the tests of Okun’s
law and the Phillips curve, I assume that both the constant and coefficients are the same acrossindividual policymakers. To account for the nonlinearity of the federal funds rate associated with
the ELB, I assume that the published forecasts of the federal funds rate, îit+h|t,q , are censored atzero as follows:îit+h|t,q =



ĩi
t+h|t,qif ĩit+h|t,q > 0,0if ĩit+h|t,q ≤ 0.

(10)

In other words, we only observe the forecasts of the Taylor-rule implied policy rate ĩit+h|t,q when it
is positive. To estimate this model, I apply the Tobit model following Kim and Pruitt (2017).16
The likelihood for a given forecast horizon h and quarter q is written as follows:15

For example, see Chapter 3 of Galı́ (2015). The results based on the output gap are discussed in Section 4.4.
The methodology is based on Amemiya (1984), the details of which are explained in Section 7.4. of Verbeek(2017). Mavroeidis (2021) proposes a methodology to exploit the nonlinearity associated with the ELB to test theefficacy of unconventional monetary policy.
16

12

N Y
Y

Lh,q =

"
1−Φ

i
i
i
i
ρh,q + φπh,q (π̂t+h|t,q− π̂LR|t,q) − φUh,q (Ût+h|t,q − ÛLR|t,q )#!

σ

i=1 t∈T i,0

h,q

×

N Y
Y
i=1 t∈T
/ i,0

" i
#!
i
i
i
i
ît+h|t,q − ρh,q + φπh,q (π̂t+h|t,q− π̂LR|t,q) − φU
1h,q (Ût+h|t,q − ÛLR|t,q )ϕ, (11)σσh,qwhere Φ and ϕ denote the cumulative distribution function and probability density function ofi,0
the normal distribution, and N denotes the number of policymakers. Th,qis defined as the set
i,0≡ {t = 1, . . . , T : îit+h|t,q = 0}. Theof samples where the ELB becomes binding, namely, Th,qparameters are estimated by maximizing the likelihood.
Following the same method outlined in the tests for Okun’s law and the Phillips curve, thisregression could be estimated by pooling the forecasts across all horizons and adding the fixed
effects for each FOMC meeting as follows:iiiiĩit+h|t,q = ρ + φπ (π̂t+h|t,q− π̂LR|t,q) − φU (Ût+h|t,q− ÛLR|t,q
)+

Q
T
X
X

δt,q Dt,q + εit+h|t,q ,(12)t=2007 q=1

where Dt,q is the dummy variable for a specific FOMC meeting. By following the same procedure,
I obtain the estimates by the maximum likelihood based on the Tobit model.

3

Results

3.1

Okun’s Law

Figure 2 shows the scatter plot of the changes in the unemployment rate and GDP growth with thecorresponding fitted line. It is evident from the figure that there is a strong negative correlation
between the forecasts of output growth and changes in the unemployment rate, which implies that
the FOMC’s economic projections are consistent with Okun’s law. The estimates of the regression
analysis, summarized in Table 1, confirm this observation. The estimates of the constant andcoefficient are 1.12 and −0.56 for the pooled regression, 1.41 and −0.55 for the regression with thefixed effects for the FOMC meetings, as described in Equation (4), and 1.03 and −0.63 for the13regression with the fixed effects for the forecast horizons, all of which are statistically significant.
These estimates suggest that the FOMC’s economic projections closely follow conventional Okun’slaw, with a constant of 1.5 and a slope of −0.5. The Wald test strongly rejects the null hypothesisthat the values of the coefficients are all zero. The adjusted R2 are quite high, and approximately
70% of the variation is explained by the Okun’s law regression.
Figure 3 shows the estimated slope coefficients of Okun’s law at each quarterly horizon, as
described in Equation (3), with the corresponding standard errors. Although the magnitudes ofthe estimates at the horizons within a year tend to be significantly larger than the conventional
value of 0.5, they converge around 0.5 at the longer horizons.
To interpret this difference in the estimated coefficients across forecast horizons, Figure 4 shows
the output growth and the changes in unemployment projections at different forecast horizons.
The figure suggests that the projections made during the Great Recession between 2008 and 2009
contribute to the steeper estimated slopes at the shorter horizons.17 This result likely reflects theinformation advantage on short-term forecasts and policymakers’ views on the persistence of acurrent economic shock, as documented in the literature.18 On the one hand, FOMC policymakers
primarily use information about a current economic shock, which is partially available in real time,
to formulate their nowcasts and short-run forecasts. On the other hand, they rely on macroeconomic
principles in the medium to long term once the effects of a current economic shock starts to fade
away.

3.2

The Phillips Curve

Figure 5 shows the scatter plot of the changes in inflation and the unemployment rate with thecorresponding fitted line in which inflation is measured by PCE or core PCE. Unlike the test for
Okun’s law, the association between inflation and unemployment projections is much weaker, withmany observations deviating substantially from the fitted line for both measures of inflation. Table
2 summarizes the results of the regression analysis, and they are consistent with this observation.
The estimated slopes of the Phillips curve are between −0.21 and −0.20 for PCE inflation and17

Appendix Table A2 shows the pooled estimates excluding the Great Recession (from December 2007 to June2009 following NBER). The results are generally similar to the results obtained using the whole sample.
18
For details, see Faust and Wright (2013) and Wright (2019).

14

between −0.17 and −0.16 for core PCE inflation, both of which are statistically significant. The
estimates of the constant are very close to zero—between −0.07 and −0.02 for PCE inflation andbetween −0.12 and −0.01 for core PCE inflation—and statistically insignificant in most cases,
which does not reject the implication that γ is zero. Although the Wald test significantly rejects
the null hypothesis that the values of the coefficients are all zero, the adjusted R2 are much lower
than in the Okun’s law regression, and only 6 to 30% of the variation is explained by the Phillips
curve regression.
Figure 6 shows the estimated slopes of the Phillips curve at each quarterly horizon, as describedin Equation (6), with the corresponding standard errors. Similar to the results of Okun’s law, thefigure displays substantial variation in the estimates across horizons. The slope of the Phillips curveis approximately −0.1 at most horizons, whereas the magnitude of the estimates between three andseven quarters ahead is substantially larger than the other horizons and with substantially larger
standard errors. Although the magnitude of the estimates depends on the measure of inflation, thegeneral pattern of the results is similar.
To interpret this result, Figure 7 depicts the changes in inflation and unemployment rates acrossdifferent forecast horizons. The figure suggests that the large estimated coefficients in the medium
term likely reflect the fact that inflation was subdued during the Great Recession and the following
period of recovery.19 At the onset of the Great Recession, FOMC policymakers expected inflation
to fall dramatically—perhaps reaching close to zero—given the severity of the macroeconomic
shock, and they thus predicted a large magnitude of increases in the unemployment rate andreductions in inflation. Similarly, FOMC policymakers predicted that inflation would increase as
the unemployment rate gradually declined during the recovery. Although these predictions are likely
to have steepened the slope of the Phillips curve over medium-term horizons, a sharp fall or risein inflation did not occur as anticipated.20 As the target period approaches, FOMC policymakers
modify their inflation projections accordingly, which makes the slope suggested by the short-term
projections smaller.
19

Appendix Table A3 shows the pooled estimates excluding the Great Recession, which leads to results similar to
those using the whole sample.
20
In particular, the fact that inflation did not fall much during the Great Recession is called “missing disinflation.”
For a detailed discussion, see Ball and Mazumder (2011), Christiano et al. (2015), Coibion and Gorodnichenko (2015),
and Gilchrist et al. (2017).

15

3.3

Reaction Function

Figure 8 shows the scatter plot of the federal funds rate, unemployment gap, and inflation gap
measured by PCE. As the figure shows, FOMC policymakers expect the federal funds rate to riseat longer horizons, although it has been stuck at zero in the short term. Table 3 presents the average
partial effect of the Tobit regression.21 The results show that the estimated effect of the constant,which may be interpreted as the equilibrium real interest rate, are positive, and their magnitude is
between 1.86 and 2.91. The estimated responses to the unemployment gap are significantly negativein all cases, ranging from −0.67 to −0.40, while the estimated responses to the inflation gap are
significantly positive at between 0.80 and 2.63. These results suggest that the FOMC’s economic
projections are broadly consistent with a conventional Taylor rule to achieve the dual mandate of
maximizing employment and stabilizing inflation. In particular, the magnitudes of the responses
to the inflation gap are larger than one in most cases, which is consistent with the Taylor principlethat central banks should be sufficiently aggressive against inflation to maintain stability.22
Figure 9 shows the estimated responses to the unemployment and inflation gaps at each quarterly horizon, as described in Equation (9), with the corresponding standard errors. The responseto the unemployment gap is close to zero at the short horizons within a year and becomes significantly negative at the longer horizons. The response to the inflation gap is close to zero at the shorthorizons within a year, and they reach above one at most long-term horizons, although the corresponding standard errors become larger. Given that the short-term interest rate was stuck nearzero during most of the sample period, from 2012 to 2015, it is not surprising that the responses
to both the inflation and unemployment gaps are estimated to be zero at the short horizons.
21
Corresponding estimates based on the linear model are listed in Appendix Table A4, which shows that theestimated effects are broadly similar to those of the Tobit model. This is likely because expectations are less subject
to the ELB.
22
For details, see Galı́ (2015).

16

4

Extensions

4.1

Comparison with the SPF forecasts

As an extension, I conduct the same analysis using the individual forecasts of the SPF during thesame period between 2007 and 2016. One thing to note is that the FOMC’s projections and the
SPF are not fully comparable due to their designs, and there are several minor differences. First,
the SPF’s unemployment forecasts target the annual average of the unemployment rate, instead of
the value at the fourth quarter targeted by the FOMC. Therefore, the calculation of the annualchanges in the unemployment rate is based on the annual average of the real-time data observedat the time of the forecasts. Second, the maximum horizon of the SPF for real economic variables
is four years, whereas the maximum horizon for price levels is three years. Third, the timing of
the survey is in the middle of the quarters for the SPF forecasts, while it is typically in the lastmonth of the quarters for the FOMC’s projections. Finally, the economic models that the FOMC’s
policymakers and the SPF forecasters use may differ, as discussed in Binder (2021).
Tables 4 and 5 present the empirical results of Okun’s law and the Phillips curve based on the
SPF forecasts. The results are generally similar to those obtained using the FOMC’s individual
projections. For Okun’s law, both the constant and slope are significant, with magnitudes close
to the conventional values. The estimates of the constants are between 0.91 and 1.17, and theestimated slopes are between −0.61 and −0.45. Adjusted R2 are relatively high, and approximately
60% of the variations are explained by the regression. On the other hand, the Phillips curves
found in the SPF forecasts are much weaker and more dispersed. The estimated slopes range
from −0.35 to −0.23, and most of the constants are estimated to be insignificant. Although thenull hypothesis that all the coefficients are zero is strongly rejected, the explanatory power of theregression is relatively low, with R2 between 0.13 and 0.25 for PCE inflation and 0.25 and 0.35 forcore PCE inflation. These results suggest that empirical patterns found in the FOMC’s individual
projections—a robust Okun’s law relationship and a weak Phillips curve relationship—are likely
driven by the sample period rather than factors specific to the forecasters.23
To shed light on how individual forecasters act differently in following these macroeconomics
23

For a more detailed comparison of FOMC and other private forecasts, see Bespalova (2020), Ellison and Sargent(2012), Gamber and Smith (2009), Hubert (2014), and Romer and Romer (2000).

17

principles, the tables also list the results after controlling for the individual fixed effects and theirinteraction terms with the slope. The estimated coefficients for both Okun’s law and the Phillips
curve are largely similar, suggesting that individual differences across forecasters would not materially affect the main results. In addition, the table lists the proportion of forecasters whose
controls are significantly rejected at the 5% level. The results suggest that only a moderate fraction of forecasters have a significantly different tendency from the common principles. The only
exception is the slope of the Phillips curve using core PCE, in which nearly 70% of the forecasters
have significantly different slopes from the common principle. However, this is likely due to thepositive estimate of the slope of the Phillips curve. Overall, these results confirm that heterogeneity
across forecasters has only a modest quantitative effect on the pooled estimates, and cross-sectionalvariation is useful to identify the common coefficients.

4.2

Comparison with the Aggregate SEP

I also conduct the same analysis using the FOMC’s aggregate SEP. Since the SEP is released
immediately after meetings, we have a longer sample available from 2007 to 2022, although thesample size is substantially smaller without cross-sectional variation. The SEP is released in theform of ranges, and I use the midpoint of the central tendency for the analysis, which excludes thethree lowest and highest values of the projections from the ranges.24
Tables 6 and 7 show the estimates of Okun’s law and the Phillips curve.25 The results are
generally similar to those obtained using the FOMC’s individual projections. For Okun’s law, theestimates of the constants are between 1.17 and 1.30, and the estimated slopes are between −0.65
and −0.63, which is consistent with the conventional values. Adjusted R2 are high, and nearly 90%of the variations are explained by the regression. On the other hand, the Phillips curve relationshipis much weaker, with the estimated slopes between −0.28 and −0.18 with insignificant constants.
Although the null hypothesis that all the coefficients are zero is strongly rejected, the adjusted R2
is extremely low.
24

The analysis using other summary statistics, such as lowest or highest values or those for ranges, leads toquantitatively similar results.
25
Due to the small sample size, I only report the pooled estimates with horizon and meeting fixed effects.

18

4.3

Quantile Regression

To shed light on the heterogeneity across quantiles, I conduct the estimation based on a quantile
regression, which estimates the τ th quantile of the dependent variable conditional on the independent variables, instead of a conventional regression that estimates the average effects.26 Figure 10
shows a summary of quantile regression estimates based on the linear model of Okun’s law, thePhillips curve, and the reaction function. Due to a relatively small sample, I use the linear models
without fixed effects as a benchmark and present the estimates for τ , ranging from 0.2 to 0.8.
The figure suggests that a substantial degree of heterogeneity across quantiles exists, althoughnone of them significantly change the signs. For example, the estimated slope of Okun’s law ranges
between -0.35 and -0.6, while its corresponding OLS estimate is -0.56. For the Phillips curve, there
is not much heterogeneity in the slope, perhaps because the explanatory power of regression issmall. For the reaction function, the disparity in the constant is substantial, ranging between 1.2
and 3.0. However, the disparity in the responses of the unemployment and inflation gaps is notas large as those of the constant. The estimated response to inflation is less than one for lower
quantiles, which contradicts the Taylor principle.
Although the results display a substantial degree of heterogeneity across quantiles, we should
be careful about interpretation. Since the model does not control for any fixed effects, observed
heterogeneity could be caused by various factors, including news at a specific FOMC meeting,a tendency in forecasting for certain horizons, and the different attitudes of policymakers. The
estimates provide the combined effects of these various factors.

4.4

Estimation of the Reaction Function Based on the Output Gap

Table 8 presents the average partial effect of the Tobit regression using the output gap. The results
are different from the results based on the unemployment gap in two ways. First, the estimatedeffect of the output gap turn out to be significantly negative in many cases, which is not consistent
with a conventional Taylor rule. More specifically, the results imply that a negative output gap
is associated with a hike in the federal funds rate. Second, the estimates of the constant and the
response to the inflation gap are much more volatile depending on the specification—the estimated26

For details, see Koenker and Hallock (2001).

19

constant ranges from 1.81 to 3.08, and the estimated response to the inflation gap ranges from 0.32
to 3.31.
These different estimates likely reflect the changes in output growth projections in the longer
run. As indicated in Figure 11, many FOMC policymakers substantially revised down their projections for output growth in the longer run after 2012, when they started to release the projections
for the federal funds rate. As the output gap is measured as the difference between the projections
targeting a specific year and the projections in the longer run, these revisions in the longer-run
projections likely changed the signs of the output gaps. As a result, the estimates of the reaction
function became volatile, and the signs of the responses to the output gaps flipped. By studying
several survey forecasts from official institutions, Coibion et al. (2018) point out that the estimatesof potential output often exhibit cyclical sensitivity in practice, contradicting the prediction fromtheory. The fluctuation due to such sensitivity had a particularly large impact on the estimationof the FOMC’s reaction function because of the short sample period.

5

Conclusion

By analyzing the individual projections made by FOMC policymakers between 2007 and 2016, thispaper finds that they are largely consistent with macroeconomic facts and theories. The relationshipbetween output growth and unemployment projections is significantly negative, consistent with
Okun’s law, and the relationship between inflation and unemployment projections associated with
the Phillips curve is weak and more dispersed. This paper also provides estimates of the FOMC’sreaction function, which are consistent with a conventional Taylor rule.
Overall, the results set out in this paper indicate that textbook macroeconomic principles
served as a useful forecasting guide for FOMC policymakers during the Great Recession and its
aftermath. Understanding the FOMC’s forecasting principle is crucial for the efficacy of monetary
policy, especially at the ELB, where communication on future monetary policy plays an importantrole.
This paper offers two innovations by exploiting the cross-sectional variations of the FOMC’s
individual projections. First, it provides more efficient estimates of the FOMC’s macroeconomic

20

principles, especially for the reaction function, even when the sample period is relatively short.
Second, this paper highlights that FOMC policymakers’ forecasting behaviors differ across theforecast horizons—they tend to follow macroeconomic principles for relatively longer horizons,
while there are some deviations in the short run. None of these innovations is feasible withoutcross-sectional variations.
This paper demonstrates that the FOMC’s individual projections provide researchers with substantially richer variations. Once the FOMC policymakers’ identities become public, researchers
will be able to analyze the relationship between their individual projections, individual characteristics, and voting behaviors.27 Further research on the FOMC’s collective decision making would
enhance the understanding of their conduct of US monetary policy, which I will leave for a future
exercise.

27

Recent studies provide an interpretation of observed heterogeneity among FOMC participants in terms of theirprojections and votes. For example, Schultefrankenfeld (2020) analyzed how dissenting views on appropriate monetary
policy result in forecast disagreement, and Malmendier et al. (2021) claimed that FOMC participants’ own inflation
experiences affect their attitude toward inflation.

21

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27

i
Ût+1|t,2i
Ût|t,2

Ut−1|t,2

Year t − 1
Q4

Year tQ2

Year tQ4i∆Ût|t,2

Year t + 1
Q4

i∆Ût+1|t,2

Note: This figure illustrates the calculation of annual changes in the unemployment rate based on the projections released at Q2
by policymaker i. The blue lines describe the projections published at Q2 of the year, the blue dotted line shows the real-timedata of the level at the previous year, and the red lines describe the computed annual changes.

Figure 1: Illustration of Computing Annual Changes

28

4
1Q ahead
2Q
3Q
4Q
5Q
6Q
7Q
8Q
9Q
10Q
11Q
12Q
13Q
14Q
Fitted line

Changes in the Unemployment Rate

3

2

1

0

-1

-2

-3
-3

-2

-1

0

1

2

3

4

5

6

Output Growth

Figure 2: The FOMC’s Output Growth and Unemployment Projections

29

0

Estimated Coefficients of Okun's Law

-0.25

-0.5

-0.75

-1

-1.25

-1.5
1

2

3

4

5

6

7

8

9

10

11

12

13

14

Horizons

Note: This figure shows the estimated slope of Okun’s law using the samples of individual horizons. The estimates are shownin the circle with the bands of standard deviation based on HAC standard errors.

Figure 3: Estimated Slope of Okun’s Law at Individual Horizons30Horizon=1Q

4

2

1

0

-1

-2

-3
-2

4

2

1

0

-1

2

Output Growth

4

-3
-2

20071031
20081029
20091104
20101103
20111102
20120913
20121212
20131218
20141217
20151216
20161214

2

1

0

-1

-2

-2

0

Horizon=9Q

3

3

Changes in the Unemployment Rate

Changes in the Unemployment Rate

3

Horizon=5Q

Changes in the Unemployment Rate

4

0

2

4

Output Growth

-3
-2

0

2

4

Output GrowthNote: This figure shows the plot of output growth and the changes in the unemployment rate at different forecast horizons,
with different colors depicting the different meeting days.

Figure 4: The FOMC’s Output Growth and Unemployment Projections at Different Forecast Horizons

31Changes in Inflation (PCE)

2
1
0
-1
-2
-3

-2

-1

0

1

2

3

4

2

3

4

Changes in Inflation (Core PCE)

Changes in Unemployment

2
1

1Q ahead
2Q
3Q
4Q
5Q
6Q
7Q
8Q
9Q
10Q
11Q
12Q
13Q
14Q
Fitted line

0
-1
-2
-3

-2

-1

0

1

Changes in Unemployment

Figure 5: The FOMC’s Inflation and Unemployment Projections (PCE and Core PCE)

32

Estimated Slope (PCE)

0.5

0

-0.5

-1

1

2

3

4

5

6

7

8

9

10

11

12

13

14

9

10

11

12

13

14

Estimated Slope (Core PCE)

Horizons

0.5

0

-0.5

-1

1

2

3

4

5

6

7

8

Horizons

Note: This figure shows the estimated slope of the Phillips curve based on PCE and Core PCE using the samples of individualhorizons. The estimates are shown in the circle with the bands of standard deviation based on HAC standard errors.

Figure 6: Estimated Coefficients of the Phillips Curve at Quarterly Horizons

33Horizon=1Q
2.5

Horizon=5Q

2.5

2

2

1.5

1.5

1.5

1

0.5

0

-0.5

-1

Changes in Inflation (PCE)

2

Changes in Inflation (PCE)

Changes in Inflation (PCE)

2.5

1

0.5

0

-0.5

-1

0.5

0

-0.5

-1

-1.5

-1.5

-2

-2

-2

0

2

4

Changes in Unemployment

-2.5
-2

0

2

4

Changes in Unemployment

20071031
20081029
20091104
20101103
20111102
20120913
20121212
20131218
20141217
20151216
20161214

1

-1.5

-2.5
-2

Horizon=9Q

-2.5
-2

0

2

4

Changes in Unemployment

Note: This figure shows the plot of the changes in PCE inflation and the unemployment rate at different forecast horizons, withdifferent colors depicting the different meeting days.

Figure 7: The FOMC’s Inflation and Unemployment Projections at Different Forecast Horizons

34

Figure 8: The FOMC’s Projections for the Unemployment Gap, Inflation Gap (PCE), and Federal
Funds Rates

35

4

3

3

2

2

1

1

0

0

-1

-1

-2

-2

-3

-3
1

2

3

4

5

6

7

8

9

10

11

12

13

14

Reaction to the Unemployment Gap

Reaction to the Inflation Gap (PCE)

4

4

4

3

3

2

2

1

1

0

0

-1

-1

-2

-2

-3

-3
1

2

3

4

5

6

7

8

9

10

11

12

13

Reaction to Unemployment Gap

Reaction to Inflation Gap (Core PCE)

Horizons

14

Horizons

Note: This figure shows the estimated responses to the inflation gap (blue solid line) and the unemployment gap (red dottedline) using the samples of individual horizons. The estimates are shown in the circle with the bands of standard deviation basedon HAC standard errors.

Figure 9: Reactions to the Inflation and Unemployment Gaps at Individual Horizons

36

(a) Okun's Law
-0.3

Slope

Constant

1.5

1

-0.4

-0.5
0.5
0.2

0.3

0.4

0.5

0.6

0.7

-0.6
0.2

0.8

0.3

0.4

Quantile

0.5

0.6

0.7

0.8

0.6

0.7

0.8

Quantile(b) Phillips Curve
-0.15

0.4

Slope

Constant

0.2
0
-0.2

-0.2

-0.25

-0.4
-0.6
0.2

0.3

0.4

0.5

0.6

0.7

-0.3
0.2

0.8

0.3

0.4

Quantile

0.5

Quantile(c) Reaction Function (Linear Model)
-0.5

2.5
2
1.5
1
0.2

0.4

0.6

Quantile

0.8

1.6

Coef. on Inf. Gap

Coef. on Un. Gap

Constant

3

-0.6

-0.7

-0.8
0.2

0.4

0.6

Quantile

0.8

1.4
1.2
1
0.8
0.6
0.2

0.4

0.6

0.8

Quantile

Note: This figure shows the estimates based on a quantile regression. The corresponding OLS estimates are depicted by thedotted line.

Figure 10: Quantile Regression Estimates of Okun’s Law

37

7
Output Growth
Unemployment
Start of FFR projections

Long-Run Projections (percent)

6

5

4

3

2

1

0
2010

2011

2012

2013

2014

2015

2016

Meeting Dates

Note: This figure shows the individual projections of FOMC policymakers for output growth and unemployment over the longer
run. The starting date of the projections for the federal funds rate (FFR) is denoted by the dotted line.

Figure 11: The FOMC’s Individual Projections over the Longer Run

38

Constant
Slope
Fixed effects:
Meetings
Horizons
Wald statistics
Adjusted R2
Observations

(1)

(2)

(3)

1.12∗∗∗−0.56∗∗∗

1.41∗∗∗−0.55∗∗∗

1.03∗∗∗−0.63∗∗∗

Yes
1124.53∗∗∗
0.68
2225

4550.56∗∗∗
0.73
2225

Yes
1826.86∗∗∗
0.72
2225

a.

This table shows the results of regressions testing Okun’s law withdifferent specifications.
b.
Inference is based on heteroscedasticity and autocorrelation robust(HAC) standard errors. ∗∗∗ denotes the significance level at 1%.

Table 1: Estimates of Okun’s Law (FOMC’s Individual Projections)

39

(1)
Constant
Slope
Fixed effects
Meetings
Horizons
Wald statistics
Adjusted R2
Observations−0.03−0.21∗∗∗

PCE
(2)
−0.02
−0.21∗∗∗(3)−0.07−0.20∗∗∗(1)−0.01−0.17∗∗∗

Yes
21.80∗∗∗
0.06
2225

442.33∗∗∗
0.22
2225

Core PCE(2)−0.12∗∗−0.16∗∗∗(3)−0.06−0.17∗∗∗

Yes
Yes
52.94∗∗∗
0.07
2225

68.93∗∗∗
0.18
2225

1251.01∗∗∗
0.30
2225

a.

Yes
111.94∗∗∗
0.17
2225

This table shows the results of regressions testing the Phillips curve with two measures of inflation (PCE andCore PCE) and different specifications.
b.
Inference is based on HAC standard errors. ∗∗ and ∗∗∗ denote the significance level at 5% and 1%, respectively.

Table 2: Estimates of the Phillips Curve (FOMC’s Individual Projections)

40

(1)
Constant
Responses to:
Unemployment Gap
Inflation Gap
Fixed effects
Meetings
Horizons
Log Likelihood
Observations

PCE
(2)

(3)

(1)

Core PCE(2)(3)

2.09∗∗∗

1.86∗∗∗

2.90∗∗∗

2.14∗∗∗

1.96∗∗∗

2.91∗∗∗−0.67∗∗∗
1.29∗∗∗−0.61∗∗∗
1.46∗∗∗−0.57∗∗∗
0.80∗∗∗−0.67∗∗∗
2.15∗∗∗−0.40∗∗∗
2.63∗∗∗−0.52∗∗∗
1.27∗∗∗

Yes−274.871258

Yes−204.92
1258

Yes−93.571258−266.221258−197.721258

Yes−89.121258

a.

This table shows the average partial effect of the Tobit regression estimating the reaction function with two measures of
the inflation gap (PCE and Core PCE) and different specifications.
b.
Inference is based on HAC standard errors. ∗∗∗ denotes the significance level at 1%.

Table 3: Estimated Partial Effect of the Reaction Function (FOMC’s Individual Projections)41

Constant
SlopeControls
Meetings
Horizons
Individual

(1)

(2)

(3)

(4)

(5)

1.08∗∗∗−0.56∗∗∗

1.17∗∗∗−0.45∗∗∗

0.95∗∗∗−0.61∗∗∗

1.01∗∗∗−0.57∗∗∗

0.91∗∗∗−0.47∗∗∗

Yes
Yes
Yes
(15.2%)

Individual ∗ slope
Wald statistics
Adjusted R2
Observations

368.26∗∗∗
0.58
3084

4990.09∗∗∗
0.70
3084

370.54∗∗∗
0.61
3084

1910.04∗∗∗
0.63
3084

a.

Yes
(42.2%)
Yes(18.2%)
7273.35∗∗∗
0.65
3084

This table shows the results of regressions testing Okun’s law with different specifications.
Inference is based on HAC standard errors. ∗∗∗ denotes the significance level at 1%.
c.
The proportion of forecasters, whose fixed effects are significantly different from zero with the significance level of 5%, is listed in the parenthesis.
b.

Table 4: Estimates of Okun’s Law (SPF’s Individual Forecasts)

42

(1)

(2)

(3)

(4)

(5)

0.07
−0.31∗∗∗

0.03−0.30∗∗∗

−0.05
−0.12

Panel A: PCE
Constant
Slope
Controls
Meetings
Horizons
Individual

0.08∗∗−0.32∗∗∗

0.16−0.35∗∗∗
Yes

Yes
Yes
(2.0%)

352.66∗∗∗
0.15
3084

Yes
(9.1%)
Yes(13.6%)
2705.61∗∗∗
0.16
3084

0.11
−0.23∗∗∗

−0.03
0.12

Individual ∗ slope
Wald statistics
Adjusted R2
Observations

79.22∗∗∗
0.13
3084

654.65∗∗∗
0.25
3084

303.04∗∗∗
0.14
3084

Panel B: Core PCEConstant
Slope
Controls
Meetings
Horizons
Individual

0.07∗∗∗−0.24∗∗∗−0.14−0.26∗∗∗−0.04−0.23∗∗∗

Yes
Yes
Yes
(2.0%)

Individual ∗ slope
Wald statistics
Adjusted R2
Observations

392.35∗∗∗
0.25
3084

936.18∗∗∗
0.30
3084

684.48∗∗∗
0.26
3084

1008.25∗∗∗
0.33
3084

Yes
(3.0%)
Yes(68.2%)
3203.77∗∗∗
0.35
3084

a.

This table shows the results of regressions testing the Phillips curve with different specifications.
Inference is based on HAC standard errors. ∗ and ∗∗∗ denote the significance level at 10% and 1%,
respectively.
c.
The proportion of forecasters, whose fixed effects are significantly different from zero with the significance level of 5%, is listed in the parenthesis.
b.

Table 5: Estimates of the Phillips Curve (SPF’s Individual Forecasts)

43

Constant
Slope
Fixed effects:
Meetings
Horizons
Wald statistics
Adjusted R2
Observations

(1)

(2)

(3)

1.30∗∗∗−0.63∗∗∗

1.68∗∗∗−0.66∗∗∗

1.17∗∗∗−0.65∗∗∗

Yes
706.39∗∗∗3630.69∗∗∗

0.87
202

0.87
202

Yes
1319.39∗∗∗
0.88
202

a.

This table shows the results of regressions testing Okun’s law withdifferent specifications, using the midpoints of the central tendencyof the FOMC’s aggregate projections.
b.
Inference is based on heteroscedasticity and autocorrelation robust(HAC) standard errors. ∗∗∗ denotes the significance level at 1%.

Table 6: Estimates of Okun’s Law (FOMC’s Aggregate Projections)44Constant
Slope
Fixed effects
Meetings
Horizons
Wald statistics
Adjusted R2
Observations

(1)

PCE
(2)

(3)

(1)

−0.04
−0.25∗∗∗−0.02−0.27∗∗∗

0.24−0.28∗∗∗

0.00−0.18∗∗∗

Yes
14.03∗∗∗
0.10
202

672.11∗∗∗
−0.04
202

Core PCE(2)−0.12−0.18∗∗∗(3)
0.12−0.19∗∗∗

Yes
Yes
37.62∗∗∗
0.09
202

16.12∗∗∗
0.13
202

1634.82∗∗∗
0.00
202

a.

Yes
39.58∗∗∗
0.10
202This table shows the results of regressions testing the Phillips curve with different specifications, using the
midpoints of the central tendency of the FOMC’s aggregate projections.
b.
Inference is based on HAC standard errors. ∗ and ∗∗∗ denote the significance level at 10% and 1%, respectively.

Table 7: Estimates of the Phillips Curve (FOMC’s Aggregate Projections)

45

(1)
Constant
Responses to
Output Gap
Inflation Gap
Fixed effects
Meetings
Horizons
Log Likelihood
Observations

PCE
(2)

(3)

(1)

Core PCE(2)(3)

1.81∗∗∗

2.06∗∗∗

3.05∗∗∗

2.00∗∗∗

2.15∗∗∗

3.08∗∗∗−0.41∗∗∗
1.53∗∗∗−0.19∗∗
1.90∗∗∗−0.96∗∗∗
0.32∗∗−0.45∗∗∗
2.81∗∗∗−0.29∗∗∗
3.31∗∗∗−0.92∗∗∗
1.09∗∗∗

Yes−622.891258−288.61
1258

Yes
Yes
−256.751258−539.421258−211.251258

Yes−215.861258a.

This table shows the results of regressions estimating the reaction function with two measures of the inflation gap(PCE and Core PCE) and different specifications.
b.
Inference is based on HAC standard errors. ∗∗ and ∗∗∗ denote the significance level at 5% and 1%, respectively.

Table 8: Estimated Partial Effect of the Reaction Function Based on the Output Gap

46

Online Appendix for “The FOMC’s New Individual Economic Projections andMacroeconomic Theories” by Natsuki Arai

47

Affiliations

GDP

Unemp.

PCE

Core PCE

FFR

Num. of Obs.

Atlanta
Philadelphia
DallasCleveland
Minneapolis
Richmond
Governors
Kansas CitySan Francisco
New York
BostonSt. Louis
Chicago

2.18
2.50
2.51
2.53
2.54
2.57
2.62
2.64
2.72
2.80
2.80
2.80
2.86

7.02
6.47
7.04
7.00
6.99
7.10
6.95
7.01
6.89
6.87
6.92
6.82
6.88

1.78
2.04
1.87
1.78
1.82
1.76
1.66
1.69
1.55
1.80
1.44
1.95
1.73

1.70
1.92
1.61
1.60
1.75
1.61
1.51
1.59
1.46
1.64
1.29
1.80
1.61

1.70
1.97
1.75
2.20
1.48
2.46
1.57
2.09
2.18
1.52
2.06
1.06
1.71

70
70
70
70
70
70
357
67
70
70
70
70
70

Standard Dev.

1.38

1.83

0.61

0.43

0.90

1194

a.

This table shows the summary statistics of FOMC’s individual projections between 2007 and 2011 and 2016, according
to their affiliations. The table is sorted with the mean of GDP growth.
b.
The mean is calculated as the average of projections across all forecast horizons except the long run.

Table A1: Summary Statistics of FOMC’s Individual Projections with Identity

48

Constant
Slope
Fixed effects:
Meetings
Horizons
Wald statistics
Adjusted R2
Observations

(1)

(2)

(3)

0.77∗∗∗−0.45∗∗∗

1.12∗∗∗−0.43∗∗∗

0.78∗∗∗−0.53∗∗∗

Yes
1124.07∗∗∗4887.05∗∗∗

0.48
1854

0.54
1854

Yes
3342.39∗∗∗
0.58
1854

a.

This table shows the results of regressions testing Okun’s law withdifferent specifications, excluding the sample period of Great Recession from December 2007 to June 2009.
b.
Inference is based on heteroscedasticity and autocorrelation robust(HAC) standard errors. ∗∗∗ denotes the significance level at 1%.

Table A2: Estimates of Okun’s Law Excluding Great Recession (FOMC’s Individual Projections)49

Constant
Slope
Fixed effects
Meetings
Horizons
Wald statistics
Adjusted R2
Observations

(1)

PCE
(2)

(3)

(1)

0.11∗
−0.03

−0.02
−0.13∗∗∗

−0.02
0.00

0.04
−0.14∗∗∗

Yes
9.56∗∗∗
0.00
1854

368.21∗∗∗
0.13
1854

Core PCE(2)−0.12∗∗−0.18∗∗∗(3)−0.06−0.16∗∗∗

Yes
Yes
160.34∗∗∗
0.03
1854

45.30∗∗∗
0.06
1854

1354.95∗∗∗
0.22
1854

Yes
104.50∗∗∗
0.11
1854

a.

This table shows the results of regressions testing the Phillips curve with two measures of inflation (PCE andCore PCE) and different specifications.
b.
Inference is based on HAC standard errors. ∗∗ and ∗∗∗ denote the significance level at 5% and 1%, respectively.

Table A3: Estimates of the Phillips Curve Excluding Great Recession (FOMC’s Individual Projections)

50

(1)
Constant
Responses to:
Unemployment Gap
Inflation Gap
Fixed effects
Meetings
Horizons
Wald statistics
Adjusted R2
Observations

PCE
(2)

(3)

(1)

Core PCE(2)(3)

2.18∗∗∗

2.39∗∗∗

1.55∗∗∗

2.23∗∗∗

2.32∗∗∗

1.50∗∗∗−0.70∗∗∗
1.35∗∗∗−0.63∗∗∗
1.52∗∗∗−0.58∗∗∗
0.82∗∗∗−0.63∗∗∗
2.24∗∗∗−0.41∗∗∗
2.73∗∗∗−0.54∗∗∗
1.30∗∗∗

Yes

Yes

896.97∗∗∗1608.18∗∗∗

0.60
1258

0.64
1258

Yes
2091.53∗∗∗
0.70
1258

961.94∗∗∗1806.72∗∗∗

0.61
1258

0.64
1258

Yes
2459.05∗∗∗
0.70
1258

a.

This table shows the results of regressions testing the Taylor rule with two measures of inflation gap (PCE and Core PCE)
and difference specifications.
b.
Inference is based on heteroscedasticity and autocorrelation robust (HAC) standard errors. ∗∗∗ denotes the significancelevel at 1%.

Table A4: Estimates of the Response Function Based on the Linear Model (FOMC’s Individual Projections)51