Program: Johns Hopkins SAIS MIEF 2016

Candidate: Sebastian Herrador Date: June 13, 2016

MIEF 2016 ~ CAPSTONE PROJECT

FOMC SEP Target Rate Projections How are they determined and what do they tell us about the Fed's policy

decisions?

I. ABSTRACT Previous work has focused on understanding the extent to which the latest information

available, including other forecasts, is being used for revising the set of FOMC’s projections and

assessing their overall predictability. In this paper, I present an extension of this work by studying

the target rate lift-off projections. I evaluate how the public can quantify the extent to which

changes to expectations of future unemployment, headline inflation, and stability in both the

energy prices and financial markets will influence future monetary policy decisions. Can these

projections help us understand the timing and pace of the recent target rate lift-off? What about

the policy decision to keep near zero Fed Funds Rate Target for 7 years?

This is an important study because it evaluates the overall role of the Summary of Economic

Projections (SEP) in reassuring the credibility of monetary policy in the US. In particular, it has

been well documented that a deterioration in the credibility of a central bank has irreversible

implications for the functioning of the domestic economy and, in the case of the US, it also plays

a key role internationally by influencing exchange rates with the world’s largest reserve currency

and the direction of global capital flows. To this end, I find that the FED’s SEP projections are

consistent with standard macroeconomic relationships and, in particular, the extent to which the

rate lift-off was postponed can be attributed to the large influence of an unexpected decline in the

world price of crude oil in 2014-15. Regression estimates show that every 10% decrease in the

price of WTI led to a 0.10ppts downward revision of the SEP forecasts across all horizons.

Moreover, current SEP lift-off projections continue to suggest an annual 1 percentage point

increase in Fed Funds Rate until 3 percent is reached provided the price and unemployment levels

oscillate around current values.

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II. BODY

1. Overview of FOMC projections

Given the extent to which monetary policy depends on credibility and the degree to which the

public is able to anticipate policies, there is no doubt that both the communication strategy and the

signaling channel of a central bank play an essential role in today’s macroeconomic set of policy tools.

As a result, it is no surprise that over the years the FED has been increasingly inclined towards

transparency as a way for policies to be adequately internalized by the public. Arguably, a key

component of this communication strategy can be found explicitly in the shape of official forecasts.

This was stressed in 2007 when the FED began releasing its Summary of Economic Projections in

order to complement the FOMC post-meeting minutes.

" The Federal Open Market Committee (FOMC) announced on Wednesday that, as part of its ongoing commitment to improve the accountability and public understanding of monetary policy making, it will increase the frequency and expand the content of the economic projections that are made by Federal Reserve Board members and Reserve Bank presidents and released to the public. "1

Since then, the FOMC began making quarterly releases of forecasts with the projected level of

GDP growth, inflation and unemployment expected for the end of every year. Although multiple

forecasting horizons are presented –including one for the current year, the two following years, and,

sometimes, a fourth year–, these summaries are limited because the whole distribution of participants’

projections is not released. Only the range and central tendency (which excludes top and bottom 3

projections) of the projections are made available to the public. Appendix 1 and 2 show examples of

the SEP releases found after each FOMC meeting.

While an anonymized list of the entire distribution of the individual votes can be found for some

years, this is only made available to the public after a 5 year lag making it very difficult to conduct

robust statistical analyses of variables in question. As a result, these restrictions have made it

substantially cumbersome to use econometric methods to examine the extent to which such

projections can help map the trajectory of policy decisions. Nevertheless, starting in 2012 the set of

1 Press Release Nov. 14, 2007

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variables in the SEP was expanded so as to also incorporate forecasts for the target interest rates. Not

only do these projections complete the basic set of variables that represent the core of monetary policy

but they also come with more information themselves since the whole distribution (as opposed to

only the range and the central tendency) of individual projections is released.

While one would think that the release of such projections would immediately bring about a big

breakthrough in the study of monetary policy, research in this field remains limited and only a few

economists have assessed the extent to which the consistency and timing of monetary policy can be

understood using the information provided by these forecasts. However, predicting the timing of

monetary policy decisions continues to be very relevant today given that the Fed has proven to be

ready to increase interest rates by announcing its first rate hike decision at the end of 2015.

Since then, however, monetary policy has remained unchanged despite the great expectations that

the Federal Reserve would continue to tighten monetary policy lifting the federal funds target at least

two more times in 2016. While many have expressed their belief that FOMC projections have not

improved the public’s understanding of monetary policy, in this paper I will argue that the SEP may

actually provide a good roadmap for the future of monetary policy as it provides a neat illustration of

the Fed’s policy reaction function provided stability in the price and unemployment levels and specially

now that we are moving away from the Zero Lower Bound (ZLB).

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2. Target rate projections ~ in and out of the ZLB

Figure1(Rangeofprojectionsforeachyeargoinglefttorightfromoldesttonewest)

Given that monetary policy must remain credible for it to work, one would expect that on

average policy makers follow a policy path that is substantially similar to their projected path.

However, if we were to take the FOMC’s target rate projections made from 2012 through 2015

at face value, the recent rate hike seems to be long overdue. The mean of the SEP target rate

projections was mostly over 0.5 since 2013 for all forecasts made more than 2 quarters before

the end of the year being forecasted. (see Figure 1) Marquez and Herrador in 2016 note that since

2008 FOMC’s projections show errors that are large, one-sided, and persistent. They ask how

can decisions be understood if the FOMC doesn’t provide a mapping from projections to

decisions?

With regards to this question they highlight two points that need to be taken into

consideration. First, forecasts from alternative sources over this period of time were not any

better than those of the FOMC. Second and more importantly, the fact that FOMC participants

are not impartial observers of their own forecasts but rather must influence the economy so as

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to meet their dual mandate. However, unemployment and inflation projections were also

characterized by long periods of over-optimism followed by equally long periods of over-

pessimism. To the extent that the variables being forecasted are endogenous, a failure to correctly

assess future conditions of the labor market as well as the price level will influence the predictions

of the projected policy response. While some may consider this a weakness, this is why it remains

important to study the SEP because, in spite of these projections being systematically wrong,

consistency in their over persistence may actually offer important information about the FOMC’s

implicit reaction function.

This particular case is well illustrated by the recent work of Kahn and Palmer in 2016, who

used the SEP to estimate an approximation of the FOMC’s response function. They estimated

the relationship between the target rate forecast and the rest of the forecasts by regressing the

projected Federal Funds Rate on its fourth lag, a constant, the deviation of headline inflation

from 2 percent and the deviation of the unemployment rate from dynamic estimates of the natural

rate, they constructed coefficients that were then used to historically show the path of a counter

factual implied Fed Funds Rate. Surprisingly these fitted values resemble the actual policy

responses to inflation and unemployment from 2001 to December 2008, before policy became

constrained by the Zero Lower Bound (ZLB) (see Figure 2).

Figure 2: Fed Funds Rate Target –Actual vs Projections from the SEP- (Source: Kahn and Palmer)

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Two things are appreciated in Figure 2, which shows the counter-factual scenario that uses

the predicted values for pre-2008 using the regression results from the whole sample. First, there

seems to be evidence for a shadow target rate implicit function that doesn’t materialize because

policy makers are constrained by the ZLB. However, to the extent that SEP relationships are an

accurate measure of the non-ZLB reaction function, understanding the SEP forecast may actually

give the public a good mapping of policy going forward. This is important as we move closer to

the highly anticipated 1% level of the target rate by the end of the year.

The second and subtler point is that these projections tend to systematically under-predict

the actual target rate by on average 2 percentage points. This may be attributed to two things.

First of all, there was no quarterly SEP available prior to 2007 so it is difficult to estimate shifts

in the FED’s policy preferences in particular as the Board has changed its composition of central

bankers. One example of intra-mandate variations in preferences, is the difference in policy

between the Bernanke and Yellen mandate, which was estimated to be as large as 0.6 percentage

points by Marquez and Herrador in 2016.

Moreover, the second point worth noting is the presence of a large degree of endogeneity

and the small sample of SEP projections. Not surprisingly the point estimates are very sensitive

to different regression specifications, the inclusion of control variables, and using other

estimation methods other than OLS. The fitted values in Figure 2 come from a regression where

the coefficient on the inflation gap in the historical policy reaction function is 1.3, the coefficient

on inflation in the SEP reaction function is 1.7, and the constant term is roughly 4 percent.

Nevertheless, one needs to take caution when reviewing these results. In particular, when using

a FIML specification Marquez and Herrador find that there is upward bias of at least half a

percentage point in the OLS estimates of the implied reaction function to unemployment and

inflation. Figure 2.1 shows an alternative specification that excludes the fourth lag. Notice that

the variation in Fed Fund’s Rate target is much later in this case. Figure 2.2 shows the fitted values

of a different specification that assesses the levels as opposed to the gap between the independent

variables and their natural levels. In both cases, the predicted values make the case for a two to

three years earlier lift-off. This suggests that the Fed’s predictability may involve a further

understanding of its level of persistence and their views in the perceived natural rates of

unemployment.

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Figure 2.1 Fed Funds Rate Target –Actual vs Projections from the SEP- (no lag)

Figure 2.2 Fed Funds Rate Target –Actual vs Projections from the SEP- (no lag and using the levels rather than the inflation or the unemployment gaps as explanatory variables)

3. Other SEP projections In general, what remains true about the SEP is that there is a period of over-optimism

followed by a period of mixed expectations. Figure 3 shows the set of projections made for each of the 7 years after the crisis for the rate of unemployment and GDP growth. It depicts how the ranges of the SEP projections (left to right from the earliest to the latest set of forecasts made) converged to their actual value. These figures clearly illustrate the large extent to which every participant in the FOMC persistently failed to recognize the magnitude of the 2008 crisis but was

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overoptimistic about the extent to which monetary policy was going to boost growth and bring unemployment down. Forecasts improve starting by the set of projections made for 2013. However, while the unemployment forecasts were for the most part over-pessimistic, the GDP growth projections continued to be over optimistic. Altogether, as the economy moved out of the crisis, the sets of projections at every FOMC for these two indicators were less disperse suggesting an increase in the level of consensus about the direction of the economy.

Figure(s)3(Source:HerradorandMarquez2016)

0

2

4

6

8

10

12

2007 2008 2009 2010 2011 2012 2013 2014 2015

SEPProjectionsoftheUnemploymentRate(Range)

Actual

SEPProjections oftheUnemployment Rate(Range)

-4

-3

-2

-1

0

1

2

3

4

5

6

2007 2008 2009 2010 2011 2012 2013 2014 2015

SEPProjectionsoftheRealGDPGrowth(Range)

Actual

SEPProjections oftheRealGDPGrowth (Range)

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Things are much grimmer for inflation. Figure 3 shows the set of projections made for each

of the 7 years after the crisis for PCE headline inflation.

Although the extent to which there is persistence in the over-projecting of inflation is much

lower than for unemployment and GDP growth, the FOMC was not been able to provide either

accurate nor precise forecasts for such an indicator. Most of the discussion about this is centered

around the unexpected fluctuations in energy prices and the sudden changes in the valuation of

financial assets. In particular, during this period we saw two sharp declines in the price of a barrel

of oil from mid $90s down to mid $40s in 2008 and from $110 early in 2014 down to mid $40 in

2015 and further down to mid $20s at the start of in 2016.

Kahn and Palmer provide an interesting claim about the impact of missed inflation projection

on the FOMC’s ability to accurately forecast their target rate. They claim that “the FOMC’s

anticipated response to projected increases in inflation was the primary factor responsible for the

-1

0

1

2

3

4

5

2007 2008 2009 2010 2011 2012 2013 2014 2015

SEPProjectionsofthePCEInflation(Range)

Actual

SEPProjections ofthePCEInflation(Range)

Figure4(Source:MarquezandHerrador2016)

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missed [target fed funds rate] projections.” Although fluctuations in the price of financial assets,

as illustrated in Figure 4 by the S&P500 index, do have statistical influence on the interest rate

forecasts (to be elaborated over the following sections) there is no immediate trend that would

at first sight suggest it had an influence on the delay of the recent rate hike decision.

4. Projecting a Lift-Off

The sample of FOMC target interest rate projections is much more reduced than the

projections for the other macroeconomic indicators since they began being released on 2012.

They are consistently off from the actual effective funds rate because they mistakenly anticipated

an earlier realization of a projected rate hike, which was not experienced until the end of 2015.

Instead of being taken at face value the information provided by these projections could be read

as a roadmap or plan for the pace at which policy makers expect rates to return to their long run

equilibrium.

Figure 6 illustrates a number of curves that portray the schedule of interest rate projections

released for each meeting since June 2012. Notice that, while the projection schedule keeps being

pushed to the right, the slope of the schedule remains pretty much constant overtime. In other

words, although the FOMC’s projections are being revised to convey their decision to keep

postponing rate hike, their intention to increase interest rates anywhere between 100 to 75 basis

points per year remains constant. Perhaps the most interesting feature of Figure 6, which shows

the average of the rate hike schedule presented at every SEP since June 2012, is the considerable

rescheduling of the interest rate hike plans that occurred from 2014 throughout 2015 as

appreciated by the dotted lines to the right.

Figure5.0WTICrudeOilPricesandS&P500Index(Source:FRED) Figure5.1

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Figure6:SEPtargetrateforecasts

This highlights the point made earlier about the drop in energy prices allowing the Fed to

stretch its expansionary policy for about another year without having to worry too much about

inflation. Although another consideration, which is to a great extent related to the fall of energy

prices, is the strengthening of the dollar in particular relative to emerging market currencies, I will

not examine this issue in this study. If at all it would amplify the anticipated effect of a decline in

inflation due to a lowering in the cost of importing to the US. Figure 7, groups the average FOMC

projections made in any given year. We observe considerable overlap between the rate hike

projections in 2013 and 2014 but a clear difference between these and 2015.

0

0.5

1

1.5

2

2.5

3

3.5

4

2012 2013 2014 2015 2016 2017 2018

AverageRateHikePathfromSEPProjections(byMeetingwhereforecastismade)

19-Jun-12

12-Sep-12

11-Dec-12

19-Mar-13

18-Jun-13

17-Sep-13

17-Dec-13

18-Mar-14

17-Jun-14

16-Sep-14

16-Dec-14

17-Mar-15

16-Jun-15

16-Sep-15

15-Dec-15

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Figure7

The consistency in the pace (illustrated by the slope of the previous two charts) at which the

FOMC has conveyed its expectations to increase the target interest rate reflects important

considerations with regards to whether monetary policy decisions are being informed by standard

macroeconomic models. Is the FED’s decision to raise rates considering both objectives of its dual

mandate to attain full employment and price stability? The answer to this question will be at the core

of the econometric work presented in the following sections.

The road maps in Figures 6 and 7 should be seen as a base for future policy decisions, but may

change as new data comes in. What remains true for the years to come is that unexpected shocks to

inflation may be either temporary or permanent. The nature of these shocks will influence expectations

about future inflation and will hence determine whether the FOMC chooses to adjust by shifting the

policy schedule rather than changing the pace of the rate hike. On the other hand, it is remains difficult

to say anything about how the Fed’s reaction function will change to unexpected changes to

unemployment because since 2008 we have not experience any other substantial shocks to the labor

market.

However, we can already see from Figures 8 that the ranges of FOMC forecasts for headline

inflation, GDP growth, and unemployment are flat and tight around 2, 2.5, and 5 percent respectively,

which does suggest that the Fed may have an agenda to pursue macroeconomic stability around those

-1

0

1

2

3

4

5

2012 2013 2014 2015 2016 2017 2018

AverageRateHikePathfromSEPProjections(byyearwhereforecastismade)

2012

2013

2014

2015

Actual

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values. While this could be problematic because ideally we would want to have large enough variation

in our explanatory variables to explain changes in our dependent variables, there seems to be enough

variation in our sample to provide a robust statistical relationship across variables even when different

measures of the FOMC are chosen.

Figure8(SEPprojectionsfor2016-18)

-1

0

1

2

3

4

5

2015 2016 2017 2018

SEPProjectionsofthePCEInflation(Range)

SEPProjections ofthePCEInflation(Range)

-3

-2

-1

0

1

2

3

4

5

6

2015 2016 2017 2018

SEPProjectionsoftheRealGDPGrowth(Range)

SEPProjections oftheRealGDPGrowth (Range)

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2

4

6

8

10

12

2015 2016 2017 2018

SEPProjectionsoftheUnemploymentRate(Range)

SEPProjections oftheUnemployment Rate(Range)

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The rest of this paper goes into detail as it aims to understand the dynamics behind the patterns

that we have been discussing so far. It provides a statistical examination of the extent to which

macroeconomic indicators are exposed to exogenous shocks to energy prices and financial assets. In

particular, it examines the influence that these shocks have the on distribution and realizations of the

FOMC SEP interest rate projections. The regressions ahead study the consistency of interest rate

forecast to changes in expected inflation and unemployment when looking at a variety of

specifications, time periods and estimation methods. Section 5 examines the existing literature on the

SEP’s. Section 6 goes into detail about how the data was assembled for this study. Section 7 highlights

the different econometric specifications considered in this study. Section 8 shows the most important

results and compares them against different robustness checks. Section 9 through 12 look at the

conclusions that can draw from this analysis, the existing limitations and scope for future work.

5. Understanding the SEP in the literature

Previous evidence has mostly focused on the examination of the set of SEP projections as a good

forecasting tool. Romer (2010) documents that the SEP forecasts of concepts that are closely related

are strongly correlated in the expected directions, but that there is nonetheless substantial independent

variation. He finds that a higher 1 percentage point CPI inflation forecast is associated with the GDP

forecast also being higher by 0.75 percentage points and that a forecast of GDP growth being higher

by 1 percentage point is associated with a forecast of the unemployment rate being lower by 0.18

percentage points. Kahn and Palmer (2016) also highlight that one key feature of the FOMC’s protocol

is that participants release projections for several years ahead in each forecast meeting suggesting the

possibility of an intertemporal correlations of forecasts from each meeting. When evaluating the

strength of this correlation they find that for unemployment, the correlation of forecasts one year

ahead is important but it varies from meeting to meeting. However, for inflation, the calculations

reveal that the correlations vary in magnitude and sign.

Further work conducted by Rülke and Tillman (2011) and Nakazono (2013) show substantial

evidence for herd behavior in the forecasts. This is an important consideration given that most

econometric work requires the errors of each individual observation to be independently distributed.

Furthermore, they found instances where non-voting participants submitted “extreme” forecasts to

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register their disagreements and have some sort of influence over policy decisions by skewing the

perceived mean of the forecasts.

There has also been work by Tillman (2011) that differentiated the statistical properties and the

predictive power of shorter horizon forecasts relative to those with longer horizons depending. In

particular, it is documented that at long horizons the variation of members’ projections contains

information which is more relevant for explaining future inflation than information embodied in the

midpoint. On a more technical note about forecasting efficiency and the study of forecast revisions,

Arai (2014) tests whether the revisions to these projections are unpredictable and finds that FOMC’s

efficiency is generally accepted for inflation, but often rejected for real economic variables, notably

for the unemployment rate. He claims that the rejection is due to the relatively stronger autocorrelation

of unemployment revisions, which may reflect information rigidity of FOMC’s views about

unemployment. Nevertheless, it is found that the joint efficiency of the entire projection is accepted

in most cases.

Marquez and Herrador (2016) document that the FOMC forecast provides little additional

information than the Survey of Professional Forecasters (SPF) released a month before by the

Philadelphia FED. In particular, they find that the FOMC projections are much more influenced by

judgments from the values of the SPF for inflation (𝜋"#$) and unemployment (𝑢"#$) than the actual

present levels of inflation and unemployment. More importantly they note that given the interest-rate

forecast, the upward pressure on the forecast of the federal funds rate from a one percent increase in

the SPF headline inflation forecast needs to be offset by an increase in the SPF unemployment

forecast. They quantify this tradeoff to be 0.43 meaning that an interest-rate forecast remains

unchanged if an increase in πspf is accompanied by an increase in 𝑢spf of 0.43 percentage points. The

implied interest-rate forecast is about 2 percent; if one allows for uncertainty in the intercept of the

mapping equation, then the 66% confidence interval for the interest-rate forecast ranges from 1.4

percent to 2.6 percent. Kahn and Palmer (2016) also conclude that the Summary of Economic

Projections provides insights into FOMC participants’ views on how the federal funds rate target

should respond to inflation and unemployment. Although the projections in the SEP have proved to

be consistently wrong—as have most projections of the future—they do provide information about

the FOMC’s implicit reaction function.

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6. Statistical analysis: Data and key variables

As reviewed earlier, since October 2007, FOMC participants (voting and non-voting) submit

quarterly projections for inflation, unemployment, and the federal funds rate among other variables.

There are at most 19 participant submissions for each of these meetings: 12 from the Federal Reserve

Bank presidents and 7 from the Board of Governors of the Federal Reserve System; to maintain

confidentiality of FOMC participants are not identified in these projections. Rather, participants are

assigned a number randomly and the number may change from meeting to meeting. The projection

horizon includes the current year and two additional years. During the last two meetings of each year,

participants extend their projections by one year. The multi-year character of this protocol yields as

many as 14 forecasts for a given year.

Participants’ projections are revised in response to economic developments. Further, the revisions

use information available through the conclusion of the meeting, on each participants’ assumptions

regarding a range of factors likely to affect economic outcomes, and on his or her assessment of

appropriate monetary policy. Importantly, forecasts revisions cannot be unambiguously interpreted as

reactions to news. As indicated earlier, FOMC participant projections depend on their assessments of

the appropriate monetary policy. Thus as participants’ terms expire, new participants will bring their

own assessment which then means different forecasts, even in the absence of economic news.

Since 2012, the FOMC has been releasing participant’s projections for the federal funds rate. For

inflation and unemployment, the FOMC has been releasing since 2007 the Ranges and Central

Tendencies of these projections. The FOMC also releases with a five year delay the individual

participant’s projections for inflation and unemployment:

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Source: Marquez and Herrador (2016)

This peculiarity in FOMC data releases

means that the period with interest-rate

forecasts from individual participants does

not overlap with the period of inflation and

unemployment forecasts from individual

participants. Given the simultaneity of the

model, Marquez and Herrador (2016)

combine data from two types of releases

from the FOMC for meetings over the

period 2012-2015 (enclosed area): participant-specific projections for the federal funds rate and

bounds of projections for inflation and the unemployment rate. This database serves as the core for

this analysis.

For analytical purposes, denote 𝑖(,*,+ as the federal funds rate projection at time t (the date of the

FOMC meeting) by the 𝑗(- FOMC participant (𝑗 = 1…𝑛() for the 𝑦(- year (𝑦 = 2012…2018).

Note that the number of FOMC forecasts submitted at date𝑡, 𝑛(, might vary from meeting to meeting.

The mean of the participant’s projections for 𝑖 in year 𝑦 and meeting 𝑡 is:

𝑖(,+ =1𝑛(

𝑖(,*,+; 𝑛( ≤ 19=>

*?@

The following table shows how the data projections for the FFR are then assembled:

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The vector of projections of the average federal funds rate in 2014 is:

𝑖AB@C = [𝑖*E=FAB@A,AB@C; … ; 𝑖GFHAB@A,AB@C]′

This vector has 11 entries because there were 11 meetings from June 2012 to December 2014

that included a projection for 2014; these observations are enclosed in a rectangle. Stacking the

vector of forecasts of average fed funds rate across all FOMC meetings yields:

𝑖 = [𝑖AB@A; 𝑖AB@K; 𝑖AB@C]′

For analytical purposes, adopt the following notation with regards to unemployment and

inflation forecasts:

𝜋(,+- : upper bound of the range of inflation forecasts in year y made during FOMC date t

𝜋(,+L : lower bound of the range of inflation forecasts in year y made during FOMC date t

𝑢(,+- : upper bound of the range of unemployment forecasts in year y made during FOMC date t

𝑢(,+L : lower bound of the range of unemployment forecasts in year y made during FOMC date t

𝜋(M@N actual inflation one month prior to the FOMC meeting (t-1)

𝑢(M@N actual unemployment one month prior to the FOMC meeting (t-1)

𝜋(M@OPQ SPF inflation forecast in year y made at time t-1

𝑢(M@OPQ SPF unemployment forecast in year y made at time t-1

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The following table illustrates the alignment of forecasts and conditioning variables for 𝜋AB@A-

and 𝜋AB@K- . Note that when comparing FOMC forecasts with SPF forecast we always match the

latest available forecast for the same horizon prior to each meeting. The same goes for matching

actual information for unemployment and inflation (as obtained from the Fed’s FRED).

The observations enclosed by the rectangle emphasize the role of current information in

conditioning forecasts at different horizons. For example, the actual inflation rate as of October 2010

is being used in the November 2010 meeting as information to forecast the inflation for 2012 and

2013.

Previous work has been focused on a wide examination of multiple dependent variables including

individual SEP forecasts (where available), mean, median, central tendencies, and ranges. In this

particular, study I will focus primarily on the mean of the interest rate projections and the central

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tendency midpoint (denoted with 𝑚𝑝 in the equations ahead) for the unemployment and inflation.

Doing this when looking at the entire sample from 2008 onwards would be misleading given the large

degree of variation of the level of consensus from meeting to meeting. However, for the period after

2012 the central tendencies for unemployment and inflation have been significantly tight making it

reasonable to proceed in this manner. (see Appendix 3)

In this extension of the Marquez and Herrador (2016) database I match the latest available prices

of the WTI price of crude oil and S&P 500 index with every observation. As a robustness check, I

also constructed a variable to measure the volatility of such prices. This took the standard deviation

of the time frame period in between each FOMC meeting.

7. Identification and Econometric Specification

The first postulated estimation model is:

𝑖(,+ = c + βWπX,YZP + β[uX,Y

ZP + εX^ (1)

Equation (1) assumes that the interest-rate forecasts depends on the mid-point of the forecast central

tendency distributions of inflation and unemployment forecasts. Ideally, we would like to use the

means of the distributions of participant’s projections for inflation and unemployment but the FOMC

has not released participant specific projections.

Alternatively, and as a measure of robustness we modify the previous model and substitute the FOMC

forecast with the SPF forecast and the actuals:

𝑖(,+ = c + βWπX,Y"#$ + β[uX,Y"#$ + εX"#$ (2)

𝑖(,+ = c + βWπX,YN + β[uX,YN + εXN (3)

Having understood the relationship between the three concepts we proceed to control for the

influence of external shocks and other control variables as follows:

𝑖(,+ = c + βWπX,YZP + β[uX,Y

ZP + β_ζX + κX + βb𝑋d,(d^?@ + εX

ZPeO-fHdO (4)

Where ζY represents the log level of the latest price of oil observed before the meeting, κY is an

additional unobservable shock and 𝑋d,+ is a vector containing a number of control variables as

observed at y.

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Finally, another specification looks at the extent to which shocks to the price of oil interact with

inflation forecasts to affect the projection of future rates:

𝑖(,+ = c + βWπX,YZP + β[uX,Y

ZP + β_ζX + βW_πX,YZP · ζX + εX^=(FhNH(^f=O (5)

First we use simple OLS estimates (with robust standard errors) to run these specifications. Later we

control for concerns over the variance stationary nature of the variables in question by looking a the

first differenced equations and controlling for additional endogeneity by solving a simultaneous model

similar to FIML to serve as a robustness check.

In addition, we test for these specifications across different time periods. In particular and as expected,

we observe a big influence of ζY on 𝑖 for the period that only looks at projections made after 2014

when the oil price was movement were rather unexpected. Another robustness check is carried out by

including dummies that control for different forecast horizons.

8. Results Figure 9 (Full Sample 2012-present)

The table in figure 9 shows a variety of

regression specifications estimated over the entire

sample for which we have target rate forecasts.

Higher inflation projections are consistent

with an upward 1.4 ppt revision of the average

projection of the target rate for the same horizon.

This is point estimate is similar and significant

regardless if the forecast is made by the FOMC or

the SPF. Surprisingly, changes to today’s inflation

doesn’t seem to affect projections of future target

rates.

As expected, higher unemployment

projections are consistent with a downward 0.6

ppt revision of the average projection of the target rate for the same horizon. This is also true

regardless if the forecast is made by the FOMC or the SPF. Changes in today’s unemployment,

however, do seem to affect projections of future target rates.

22

The price of oil and changes to the S&P index have weak influence over target rate forecasts.

Now, lets look at the entire sample as we estimate

the coefficients of the first differenced equations. (Table

in Figure 10) In this case, these differences represent the

revisions for the projections and the changes to the price

of oil. The coefficients estimated in this model in

column 1, which only looks at inflation, unemployment,

and the target rate, are statistically insignificant.

However, in column 2, when also controlling for the

price of oil, both the log level of the price of oil and the

unemployment projection revision coefficient become

significant and have the expected sign and similar

magnitude to the previous result. This is remarkable because this specification includes the whole

period for which we have target rate projections.

Figure11(Recentsample2014-present)

The table in Figure 11 shows a variety of

regression specifications that were estimated on a

smaller but more recent sample which only looks at the

projections made starting in 2014.

Higher inflation projections are still consistent

with an upward revision of the average projection of

the target rate for the same horizon. This is true

regardless if the forecast is made by the FOMC or the

SPF. Changes to today’s inflation don’t seem to affect

projections of future target rates.

For this period not only are higher unemployment

projections consistent with a downward revision of the

average projection of the target rate but the participant’s assessment of future rates seems to be twice

as sensitive to changes in unemployment projections. This is also true regardless if the forecast is made

Figure10FirstDifferences

23

by the FOMC or the SPF. However, changes to today’s unemployment, continues not to affect

projections of future target rates.

More importantly, over this period changes to the price of an oil barrel have a strong influence

over target rate forecasts. A 10% decrease in the price of WTI has been associated with a 0.10ppts

downward revision for the Summary of Economic Projections (SEP) forecasts for all the horizons.

This is consistent with the narrative discussing the delay in the implied lift-off by the SEP.

In Appendix 4, I include further robustness checks both for the entire and recent samples. The

results are consistent even when controlling for multiple forecast horizons. Furthermore, the

relationship remains pretty much the same even when using at the central tendency low and high

bounds instead of the mid points as our explanatory variables. Finally, controlling for the 3-month

standard deviation of the price of oil does not change the results by much for either sample selection.

As a robustness check, Appendix 5 uses the PcGive statistical software to compute the coefficients

for the entire sample by solving for a simultaneous system of equations. The relationship between the

rates, unemployment and inflation remain similar to the first set of OLS results but the influence of

the price of oil is not captured in this model.

9. Understanding shifts in the distribution of SEP forecasts

Appendix 6 compares the distribution of the projections at the four different meetings that took

place in the years 2014 and 2015. The darker colors denote the projections that occurred in the most

recent meetings. What we see is that in 2014 the projections where evenly distributed around the mean

of the year forecasted. No one color is predominantly distributed either above or bellow the year’s

mean projections for each horizon. However, in 2015 we see that the darker colors are predominantly

bellow the lighter ones denoting that the projections shifted in a parallel manner across forecast

horizons as the year passed by. We clearly see the dark bars evenly concentrated bellow the mean for

all forecasts made in 2015.

24

Figure 12

Figure 12 summarizes this pattern by

showing how the ranges and mean of the

projections made in 2015 shifted down as

the price of WTI Oil continued to drop

throughout the year for every horizon level.

25

10. Concluding remarks

This study finds strong evidence for a consistent policy reaction function that can be derived

from the available information contained in the set of FOMC SEP forecasts. When looking at the

whole sample of target fund projections, a 1% upward revision in inflation projections tends to

increase target rate projections by about 0.6 to 1.5 ppts. Moreover, an upward revision in

unemployment projections is associated with a downward target rate revision of 0.6 to 1.5. The

unemployment coefficient estimate is higher when we restrict our analysis to a more recent sample

only considering the last 2 years of projections. This seems to suggest that the Fed may be more

sensitive to changes in unemployment over changes in inflation as the economy moves away from the

ZLB.

For the recent sample, the influence of inflation projection on target fund projections can be

mostly attributed to the large drop in the price of a barrel of crude oil. In particular, this explains the

observed rate lift-off delay of 2014-15 since 10% decrease in the price of WTI was found to be

associated with a 0.10 percentage point downward revision for the target rate forecasts for all the

horizons. This unexpected exogenous shock shifted the timing of the policy schedule but not did not

affect projections about the pace at which the rate hike would occur.

Should the SEP provide a clear roadmap of non-ZLB policy decisions, as documented by

previous work, the rate hike is expected to be of about 1 percentage point per year over the next 3

years provided that the price and the unemployment levels remain close to current values. Although

the recent energy price shock gives us useful information about how FOMC target rate forecasts are

determined, it remains difficult to say anything about how the Fed’s response function will change to

unexpected changes to unemployment because since 2008 we have not experience any other

substantial shocks to the labor market.

11. Challenges to current work The main challenge of this work relates to the extent to which our data can be treated as a

representative sample of all past and future FOMC projections. In particular, our data is considerably

small and mostly covers the historically unprecedented long period where the Fed Funds Rate was

26

near zero. Since the target rate projection sample was only available after June 2012, we have less than

53 observations which may be a source of potential endogeneity especially because unemployment

has done nothing but drop since that date. As a result, we also don’t have enough information about

how the FOMC's target rate expectations could react to large shocks to the labor market. Moreover,

inflation has not been above the 2 percent target so we have yet to see how the SEP react in periods

of high inflation expectations.

Maybe it is the case that there isn’t much variation yet in the data to allow us to have enough

power to estimate the effect of the regressors on target rate projections. Moreover, this study may be

further challenged because it is not able to distinguish for asymmetric preferences, which may include

the possibility that the FOMC may have different postures for positive and negative shocks to either

labor market or the price level (ex. different ways of fighting inflation and deflation).

Since the period of study was characterized by tight central tendency bounds, it would be

difficult to assess whether these results hold true even if the the central tendency ranges were to be

much wider as they were before 2012. In general, forecast bounds might remain unchanged, along

with their mid-point, even though forecasts are being revised. Thus, it would be interesting to see if

in the future the results still hold even when there is further dispersion.

12. Further work First of all, more research needs to be conducted as more SEPs keep being released especially

now that the median statistics are also being released for unemployment and inflation projections,

starting since September 2015. It is also important to allow for vintage variations in both quantitative

and qualitative information. In particular, one could investigate how shocks to unemployment, energy

prices, and financial assets have been perceived in the past by incorporating text analysis measures of

the financial press, mining over social media, and using “Big Data” resources.

It may also be a good idea to study whether different series related to unemployment and

inflation contain any predictive power. In particular, more work needs to be conducted using different

measures of labor force participation, differentiating between unemployment in exportable and non-

exportable sectors, or maybe across different regions. One may also account for more nuanced

measures of policy objectives by relating the target rate to the state of the credit markets by looking at

27

the yield curve and the futures rate markets. Finally, other multiple breakdowns of the price level could

be explored by including changes to core-inflation, housing prices, wages, among others.

III. References

Arai, N. (2015) “Evaluating the Efficiency of FOMC’s New Economic Projections,” accepted, Journal of Money, Credit and Banking.

Ericsson, N. R (2016) "Testing for and Estimating Structural Breaks and Other Nonlinearities in a Dynamic Monetary Sector," Federal Reserve Board, forthcoming.

Fendel, R. and J. Rülke (2012) "Are Heterogenous FOMC Forecasts Consistent with the Fed’s Monetary Policy?” Economic Letters, 116, 5-7.

Kahn, George A., and Andrew Palmer. (2016) “Monetary Policy at the Zero Lower Bound: Revelations from the FOMC’s Summary of Economic Projections.” Economic Review (01612387) 101.1

Marquez, J., and Herrador, S., (2016) “The Future of Illusions or the Illusions of the Future: FOMC Economic Projections 2008-15” available at SSRN and Research Gate

Nakazono, Y. (2013) "Strategic Behavior of Federal Open Market Committee board Members: Evidence from Member’s Forecasts," Journal of Economic Behavior & Organization, 93, 62-70.

Romer, D. (2010) "A New Data Set on Monetary Policy : The Economic Forecasts of Individual Members of the FOMC," Journal of Money, Credit, and Banking, 42, 951-957.

Rülke, J. and P. Tillman (2011), "Do FOMC Members Herd?" Economic Letters, 11, 176-179.

Tillman, P. (2011) "Strategic Forecasting of the FOMC," European Journal of Political Economy, 27, 547-553.

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IV. Appendix

Appendix 1 (Example of Unemployment, Inflation and GDP growth SEP projections)

29

Appendix 2 (Example of Fed Funds Rate SEP projections)

30

Appendix 3 (post 2012 selected SEP central tendencies)

0

2

4

6

8

10

12

2011 2012 2013 2014 2015

UnemploymentRate_CentralTendency

Actual

Unemployment Rate_Range

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

2011 2012 2013 2014 2015

PCEInflation_CentralTendency

Actual

PCEInflation_Range

31

Appendix 4 (Robustness Checks)

Entire Sample

32

Recent Sample

33

Appendix 5 (Solving for a simultaneous system equations)

Source: PcGive output

34

Appendix 6 (Distribution Overlaps)

byyearforcasted

byyearforcasted