GPIF Working Paper

The Dot Plot andDynamics of Financial Markets and Economy
December 28, 2022
SAITO Amane
MIYAZAKI Koichi
KIMURA Genzo
ABE Yuki

EXECUTIVE SUMMARY

In investment business, much emphasis is placed on analyzing US monetary policy, which has asignificant impact on global financial markets. Hence, the dot plot, which is the policy rate outlook
of FOMC participants, attracts a lot of attention.

While there have been numerous analyses of the relationship between FOMC and the markets, tothe best of the author's knowledge, there have been few analyses of the relationship between thedot plot and market/economic developments based on econometric models.

This paper takes Cochrane and Piazzesi [2002] as a starting point and analyzes the relationshipbetween the dot plot and market/economic developments from various angles. Specifically, we
analyze the causality of Granger [1969], the forecast accuracy of the median forecasts in the dot
plot, and the relationship between the median forecasts in the dot plot and yield curves using themodel by Nelson and Siegel [1987] and Svensson [1994].

1.Introduction
In investment business, the analysis of US monetary policy, which has a significant impact on global
financial markets, is of great importance. Therefore, market participants pay close attention to the policy
decisions of the Federal Open Market Committee (hereinafter referred to as “FOMC”), the decision-making
body of the Federal Reserve System (hereinafter referred to as "Fed"), the central bank of the United States,
and the discussions behind those decisions. In addition, they also pay great attention to the Summary of
Economic Projections (hereinafter referred to as "SEP") and the monetary policy rate outlook (hereinafterreferred to as "dot plot") by FOMC participants as a means of forecasting the future monetary policy.
There has been a great deal of analyses of FOMC’s monetary policy and market reactions. For example,
Lunsford [2020], using the forward guidance statements by FOMC from 2000 to 2006, analyzed the market
impact of the statement on the risk of the economic outlook and the statement on the direction of monetary

Note: This working paper is a compilation of research results by GPIF staff, and the contents and opinions expressed in the text do
not represent the official views of GPIF.

policy, and found that the statement regarding the direction of monetary policy had a stronger impact on
the market. Bauer and Swanson [2021] noted that FOMC statement had the opposite effect on market
expectations regarding GDP growth, unemployment rate, and inflation from the macroeconomic model.
Such an impact of FOMC statement on market expectations had been interpreted as a "Fed Information
Effect.” However, Bauer and Swanson [2021] show that there was no “Fed Information Effect” on market
expectations because FOMC also reacted to the same information as the market. In addition, Cochrane andPiazzesi [2002] used daily market data to analyze the relationship between the Federal Funds (hereinafterreferred to as "FF") rate (hereinafter referred to as "policy interest rate") target and market interest rates.
They pointed out that market reactions to changes in the policy interest rate, which are recognized asmonetary policy change shocks in monthly data, are not necessarily the shocks in daily data. They also
analyzed the impact of monetary policy change shocks extracted based on daily data on US Treasury rates
and showed that the impact of the shocks was larger than that of the analysis based on monthly data.
Furthermore, they conducted an analysis using a vector autoregression model (hereinafter referred to as"VAR model") and pointed out that there was no impact of monetary policy change shocks on nonfarm
employment and inflation. As used in Cochrane and Piazzesi [2002], the VAR model and causality test1 ofGranger [1969] are widely used in the analysis of spillover effects of price fluctuations among assets andcausality between markets and economic indicators. For example, Yang [2005] analyzed the government
bond markets of six European countries and showed that Granger causality was not confirmed acrossgovernment bond markets even when short-term correlations were clear. Nomura and Miyazaki [2013]
conducted Granger causality test analysis of the relationship between the volatility skew of foreignexchange options and the rate of return on the USD/JPY and confirmed the causality from the rate of returnon the USD/JPY to the volatility skew.
As described above, there have been many analyses of the relationship between FOMC and markets, thespillover effects of price fluctuations among assets, and the causality between markets and economic
indicators, but to the best of the author's knowledge, there has been few econometric analyses of therelationship between the dot plot and markets or economic indicators. Therefore, this paper analyzes theimpact of the dot plot on them from various angles, starting from Cochrane and Piazzesi [2002]. Specifically,
we use Granger causality test with a VAR model to confirm the relationship between the median forecasts
in the dot plot (hereinafter referred to as “median forecasts”) and market interest rates and economic
indicators, and to clarify to what extent the median forecasts can predict future policy interest rates.
Furthermore, we analyze the impact of the median forecasts on the term structure of US Treasury rates using
models by Nelson and Siegel [1987] and Svensson [1994] that explain the shape of the yield curve. This
paper makes an academic contribution by confirming the analysis by Cochrane and Piazzesi [2002] withrecent data and by analyzing the relationship between the median forecasts and market interest rates and1

A method for testing causality proposed by Granger [1969]. It is a test to statistically determine whether another time series
data is useful in predicting time series data. However, it is important to note that this test only analyzes the temporal relationshipbetween time series data, and does not determine the "causal relationship," which indicates the relationship between cause andeffect.

p. 2

economic indicators.
This paper is organized as follows. Section 2 describes the data used in the analysis, and Section 3 provides
an analysis using Granger causality with VAR model between the median forecasts and market interest rates
and economic indicators. Section 4 analyzes the predictive power of the median forecasts, and Section 5analyzes the impact of the median forecasts on the US yield curve. Section 6 is summary and implications.

2. The Dot Plot and Its Data Structure
2.1 What is the Dot Plot?
The FOMC releases SEP quarterly, which provides a forecast of near-term economic indicators and policy
interest rates by the seven members of the Federal Reserve Board (hereinafter referred to as "FRB") and
the Governors of the twelve regional Federal Reserve Banks. Of these forecasts, each participant's forecastof the policy interest rate is published and shown as a dot in graph and therefore referred to as the "dot plot"(see Section 2.2). The dot plot attracts a great deal of attention from market participants because it shows
the predicted values for all FOMC participants2, including those who have a vote on monetary policy andthose who don’t. However, it has also been criticized because of the large variation in the forecast values
for each FOMC participant and because anonymous forecasts do not tell us what economic outlook is being
assumed when the forecasts are changed. In fact, the former Fed Chair Janet Yellen and the current Fed
Chair Jerome Powell have indicated that it is not appropriate to look at the dot plot when forecasting themonetary policy (FOMC [2014], FOMC [2021], Fed [2019]).
The SEP was first published by the FRB on October 31st, 2007. The Fed Chair at that time, Ben Bernanke3,
is known for having served as Fed Chair from 2006 to 2014, which included the period of the global
financial crisis. He had been researching inflation targeting (hereinafter referred to as "inflation target")before he took office at the FRB, and the SEP was introduced as an indirect inflation target. Later, amid azero-interest-rate policy in the US in response to the global financial crisis, the FOMC decided on January
25th, 2012 to introduce PCE (Personal Consumption Expenditure, hereinafter referred to as "PCE") inflation
target of around 2%, and also the dot plot was added to the SEP. The dot plot was expected to indicate thatmonetary policy going forward would be accommodative under a zero-interest-rate policy, and to have aneasing effect by making monetary policy work against long-term interest rates. Thus, in interpreting the dot
plot, it is necessary to consider it based on the comments of the FOMC participants on the dot plot.

2

Initially, forming a consensus on the outlook among FOMC participants was considered, but since the maximum number of
FOMC participants is 19 and it is difficult to reach a consensus, a form was adopted in which the outlook and forecast range foreach participant is published.
3 According to Bernanke [2015], it is necessary to cut long-term interest rates during recessions, such as mortgage rates andcorporate bond yields, especially in a low interest rate environment where the room for rate cuts is limited due to the limited
impact from Federal Funds rate cut. Therefore, it is necessary to demonstrate to market participants the long-term policy
direction of monetary policy through an inflation target.

p. 3

(Source: FRB Website)

Figure 1 The Dot plot published in June 2022
2.2 The Dot Plot Data Structure and Schedule for Publication
Figure 1 shows the dot plot published on June 15th, 2022 (FOMC [2022]). In Figure 1, the dots represent
increments by 0.125% the policy interest rate forecasts of each of the 18 FOMC participants for the end of2022, 2023, 2024, and the Longer run. However, one participant did not submit a forecast for the Longer
run, leaving the number of dots at 17. The Longer run policy rate is referred to as the neutral interest rate.
This is because the Longer run interest rate represents the level at which policy rates would converge if
appropriate monetary policy were implemented and there were no additional financial or economic shocks.
At the press conference after the FOMC meeting on January 25th, 2012, when the dot plot was first published,
Fed Chair Ben Bernanke stated that in the dot plot they would focus on the median value for each year.
Hence, the median forecast is generally used in the dot plot analysis. Therefore, we also use the median
forecasts for analysis in this paper. In 2012, SEPs were released in January, April, June, September, andDecember, and except for March 2020, when they were not released due to the spread of the COVID-19,
they have been released quarterly in March, June, September, and December since 2013. For March andJune SEP, forecasts are given for "end of current year," "end of next year," "end of year after next," and"Longer run." For September and December SEP, when the end of the year approaches, forecasts are also
given for "end of 3 years later.” As shown in Figure 2, the outlook for the " end of current year " shows 9months later in March, 6 months later in June, 3 months later in September, and a few weeks later in
December, so it should be noted that the outlook period shortens every 3 months. As noted above, the dot
plot is released in the last month of each quarter, so the forecasts are based on market and economic
developments for that quarter.

p. 4

(Source: Authors' compilation from the FRB website)

Figure 2: Forecast Period for the Dot Plot by Quarter of Publication (for 2013)
When checking the specific pre FOMC schedule, two weeks before the FOMC meeting, the Beige Book,an analysis of economic developments in each region by the twelve regional Federal Reserve Banks isreleased. Beginning on the Saturday two weeks before the FOMC meeting, the so-called "blackout period,"
during which no external information is disseminated by FOMC participants, begins. Then, about one weekprior to the FOMC meeting, "Tealbook," the document containing an analysis of economic conditions andmonetary policy options by the FRB staff are distributed to FOMC participants. Based on such informationand others, FOMC participants are to submit the forecast value on the Friday immediately before the FOMC
meeting, but even after that, they can revise their forecasts on the first day of the FOMC meeting. On thefirst day of the FOMC meeting, it seems that the staff provides a summary of financial market developments
and an explanation of its analysis and forecasts of domestic and foreign economic conditions. Therefore,
the dot plot forecast values are determined based on market and economic developments over a quarter
period since the last dot plot, but given the above circumstances, in some cases the forecast values may
reflect the discussions on the first day of the FOMC meeting.

3. Causality Between the Median Forecast and the Markets/Economy
3.1 Related Literature and the Position of this Paper
This section analyzes the causality between the dot plot and the market/economy. Cochrane and Piazzesi[2002], a previous study that is highly relevant to this analysis, analyzed the relationship between the policy
interest rate and market interest rates. They used daily data on the one month Eurodollar interest rates and
1 to 10 year US Treasury rates as market interest rates against the policy interest rate to see how market
interest rates had reacted to the changes in the policy interest rate in 2001. As a result, market interest rates
generally moved in advance of the policy interest rate, and when market interest rates reached in advanceto the level to which the policy interest rate would change, they pointed out that this as no shock from thepolicy interest rate change. They also pointed out that the number of shocks caused by monetary policychange in the analysis using daily data is smaller than in the analysis using monthly data.

p. 5

Then, the regression analysis is conducted for the monetary policy change shocks identified in the daily
data, using the change in the market interest rate from two days before the policy interest rate change day
to one day after the policy interest rate change day as the dependent variable and the change in the policy
interest rate as the explanatory variable. The result of this analysis indicates that a monetary policy change
shock causes large changes in market interest rates (50-70 bps) and has a larger impact on long-term interest
rates than on short-term interest rates. They also pointed out that the impact of a monetary policy change
shock is not clear for nonfarm employment and inflation.
Cochrane and Piazzesi [2002] analyzed the relationship during 2001. The global economy after 2001 has
experienced the expansion of globalization, the global financial crisis, and the subsequent zero-interest-rate
policy, which may have changed the structure of financial markets and the relationship between interest
rates. Therefore, this paper will check whether market interest rates continue to precede policy interest rates
even after 2015, when the US first lifted its zero-interest rate policy. Furthermore, by newly adding the dot(Source: Generated by Authors from Factset data)(Source: Generated by Authors from Factset data)

Figure 3: Policy Interest Rate and Short-Term Interest
Rates

Figure 4: Policy Interest Rate and US Treasury Rate

(Source: Generated by Authors from Factset data)(Source: Generated by Authors from Factset data)

Figure 5 Median Forecasts and Short-term Interest
Rates

Figure 6 Median Forecasts and US Treasury Ratesp. 6

plot to the analysis, we will also analyze the relationship between market interest rates and the outlook of
FOMC participants.
The trend in the one month US dollar LIBOR rate4 and the policy interest rate in Figure 3 confirms thatduring the interest rate hike cycle from 2015 to 2019, short-term interest rates rose gradually ahead of thepolicy interest rate hike, with the one month US dollar LIBOR rates rising rapidly just before the FOMC
meeting to incorporate the rate hike. In the relationship between the US Treasury rate and the policy interest
rate shown in Figure 4, the US Treasury rate incorporates the policy interest rate change at an earlier stage
than the short-term rate, and the policy interest rate appears to follow the US Treasury rate. This relationshipis also observed in the interest rate cut cycle after 2019 and in the interest rate hike cycle after 2022,
confirming a similar trend to that of Cochrane and Piazzesi [2002]. In contrast, Figures 5 and 6 show the
relationship between the median forecasts (the end of current year) and market interest rates, which is the
new subject of analysis in this paper. For short-term interest rates in Figure 5, compared to Figure 3, market
interest rates appear to follow the median forecast, while the US Treasury rate in Figure 6 is ahead of themedian forecast as in Figure 4, suggesting that the FOMC is forecasting policy interest rates in response tomarket interest rates. Since the relationship between the median forecasts and market interest rates is notclear, we will analyze the causality between the median forecasts and market interest rates using the VAR
model.
3.2 Model and Analysis Setup
In this section, we perform Granger causality test using the VAR model. The first step is to consider thevariables 𝑥 and 𝑦 . These two variables are the time series data of 𝑡

1,2, … , 𝑛 , and assumed to bestationary. For these two variables, we construct the VAR model consisting of the following equations (1)and (2). In equation (1), the variable 𝑥 depends on the constant term, variables 𝑋
and 𝑌

𝑦

𝑥

,𝑥

,…,𝑥

, up to the past 𝑝 periods, and the error term 𝜀 , .

,𝑦

,…,𝑦

𝑥

𝜇,

𝛼 𝑥

⋯

𝛼 𝑥

𝛽𝑦

⋯

𝛽 𝑦

𝜀 ,

(1)

𝑦

𝜇 ,

𝛾 𝑥

⋯

𝛾 𝑥

𝛿 𝑦

⋯

𝛿 𝑦

𝜀 ,

(2)

In this case, testing if the variable 𝑌

is useful in predicting the variable 𝑥 is called Granger causality

test (Hamilton [1994]), and the causality for variable 𝑥 due to 𝑌
(3). Similarly, the causality for variable 𝑋

is tested for null hypothesis in equation

due to 𝑦 is tested for null hypothesis in equation (4).

4LIBOR (London Inter-Bank Overnight Rate) was discontinued at the end of December 2021 except for some indicators for the
dollar, and all indicators are scheduled to be discontinued by the end of June 2023. In this report, LIBOR is used because theperiod under analysis is mainly on the period prior to the end of December 2021 and because it refers to indicators for the dollar
that are calculated over the entire period under analysis.

p. 7

𝐻:𝛽

𝛽

⋯

𝛽

0

(3)

𝐻: 𝛾

𝛾

⋯

𝛾

0

(4)

The Granger causality test for the median forecasts analyzes the causality between the median forecast
and the change in the market interest rates, as shown in Figure 7. For example, when the median forecasts
for 3 periods are available from 𝐹𝑂𝑀𝐶 to 𝐹𝑂𝑀𝐶 , the analysis of the causality from the median forecast
to market interest rates and economic indicators tests the impact of (a) the change in the median forecast
from 𝐹𝑂𝑀𝐶 to 𝐹𝑂𝑀𝐶 , to (d) the change in the market interest rate from 𝐹𝑂𝑀𝐶 to 𝐹𝑂𝑀𝐶
and the economic indicator available at the time of 𝐹𝑂𝑀𝐶

1𝑑𝑎𝑦

1𝑑𝑎𝑦. Conversely, the analysis of thecausality from market interest rates and economic indicators to the median forecast tests the effect of (b)the change in market interest rates from 𝐹𝑂𝑀𝐶 to 𝐹𝑂𝑀𝐶
at the time of 𝐹𝑂𝑀𝐶

1𝑑𝑎𝑦 and the economic indicator available

1𝑑𝑎𝑦 to (a) the change in the median forecast. In other words, it confirms whether

the change in one value is affected by the change in the other values.
In selecting the lag 𝑝 of the explanatory variables for the VAR model, it is common to use information
criterion such as AIC (Akaike's Information Criterion, hereinafter referred to as "AIC"). However, as
pointed out in Section 2.2, the median forecast published from March to December forecasts the same point
in time, "end of current year," "end of next year," and "end of year after next." In particular, the "Longer
run" has a mechanism to be updated to the outlook for the same forecast period to the most recent value inall median forecasts. Therefore, when considering causality from the median forecasts to market interest
rates and economic indicators, it is appropriate to refer to the most recent median forecasts available at thatpoint in time. In addition, in considering causality from market interest rates and economic indicators to themedian forecasts, it is necessary to consider that median forecasts are published in the last month of therelevant quarters based on the quarterly market and economic developments. Therefore, in this analysis
using quarterly data, market interest rates and economic indicators are set as 𝑝

1, the most recent ones

that are considered most likely to be referenced when setting the median forecast. The VAR models used in
the estimation are equations (1') and (2') where 𝑥𝑡 represents the median forecast, 𝑦𝑡 represents market
interest rates and economic indicators, subscript 𝑖 is each of the median forecasts’ projected period, andsimilarly 𝑗 is each type of market interest rate and economic indicator.

𝑥,

𝜇,

𝛼, 𝑥,

𝛽, 𝑦,

𝜀 ,

(1’)

𝑦,

𝜇,

𝛾, 𝑥,

𝛿, 𝑦,

𝜀 ,

(2’)

The above analysis of the effect of (a) the change in the median forecasts on (d) the change in market
interest rates shows that 𝑥 ,is the change in the median forecasts from 𝐹𝑂𝑀𝐶 to 𝐹𝑂𝑀𝐶 . 𝑦 ,is thep. 8

change in market interest rates from 𝐹𝑂𝑀𝐶 to 𝐹𝑂𝑀𝐶
of 𝐹𝑂𝑀𝐶

1𝑑𝑎𝑦, or the economic indicators available as

1𝑑𝑎𝑦 in equation (2'). In addition, the analysis of the effect of (d) the change in market

interest rates on (c) the change in the median forecasts shows that 𝑦 ,rates from 𝐹𝑂𝑀𝐶 to 𝐹𝑂𝑀𝐶

is the change in market interest

1𝑑𝑎𝑦, or the economic indicator available as of 𝐹𝑂𝑀𝐶

1𝑑𝑎𝑦, and𝑥 , is the change in the median forecasts from 𝐹𝑂𝑀𝐶 to 𝐹𝑂𝑀𝐶 . Therefore, it should be noted that data𝑥,and 𝑦 ,

as of time 𝑡 are different between equations (1') and (2'). For the above VAR model, theimpact from the median forecasts to market interest rates and economic indicators is tested by 𝐻 : 𝛾 ,and the impact on the median forecasts is tested by 𝐻 : 𝛽 ,0,0.

(Source: Prepared by the authors)

Figure 7 Data Image of VAR model
Table 1 Descriptive Statistics of Variables Used in VAR Analysis
Variables

Unit

N

Mean

STD

Min

0.25%

Median0.75%

MaxEnd of Current Year

%pt Change

41

0.08

0.48

-1.50

0.00

0.00

0.00

1.75

2

End of Next Year

%pt Change

41

0.09

0.51

-1.50

-0.25

0.00

0.25

1.88

3

End of Year After Next

%pt Change

41

0.06

0.55

-1.75

-0.25

0.00

0.44

1.50

4

Longer Run%pt Change

41

-0.04

0.11

-0.25

-0.06

0.00

0.00

0.13

Median Forecastsi=1Market Rates / Economic Indicators
j =1

US Treasury 2 Year Rate

%pt Change

41

0.08

0.41

-1.43

-0.02

0.02

0.13

1.44

2

US Treasury 3 Year Rate

%pt Change

41

0.07

0.40

-1.40

-0.06

0.05

0.16

1.37

3

US Treasury 5 Year Rate

%pt Change

41

0.06

0.39

-1.28

-0.11

0.04

0.22

1.34

4

US Treasury 7 Year Rate

%pt Change

41

0.05

0.39

-1.14

-0.17

0.02

0.17

1.26

5

US Treasury 10 Year Rate

%pt Change

41

0.03

0.39

-1.02

-0.21

0.00

0.18

1.19

6

US Treasury 30 Year Rate

%pt Change

41

0.01

0.35

-0.67

-0.25

-0.01

0.18

0.88

7

FF Futures End of Current Year

%pt Change

41

0.01

0.36

-1.31

-0.04

0.00

0.04

1.41

8

FF Futures End of Next Year

%pt Change

41

0.01

0.38

-1.31

-0.15

0.01

0.09

1.20

9

FF Futures End of Year After Next

%pt Change

41

0.33

0.76

-0.56

-0.11

0.08

0.57

2.58

10

CPI

YoY, %

41

2.25

1.95

-0.10

1.40

1.70

2.30

8.60

11

Core CPI

YoY, %

41

2.34

1.18

1.20

1.70

2.00

2.20

6.50

12

PCE

YoY, %

41

1.91

1.46

0.10

1.25

1.60

1.95

6.60

13

Core PCE

YoY, %

41

1.98

0.96

1.13

1.50

1.69

1.97

5.22

14

Unemployment Rate

%

41

5.65

1.92

3.60

4.10

5.10

6.90

13.00

(Source: Generated by Authors from Factset data)p. 9

3.3 Data
The data used in the analysis are the change in the dot plots published quarterly5, the change in the US
Treasury rates and in the Federal Fund futures (hereinafter referred as “FF futures”), which are expected tointeract with the median forecasts. As for the economic indicators, we use the year-on-year change in themost recent monthly Consumer Price Index (hereinafter referred to as "CPI"), PCE and unemployment rateavailable at the time of each FOMC meeting. They are those related to the FRB dual mandate6. The data
sample 𝑡 is from April 2012 to June 2022. Table 1 shows their descriptive statistics.
Figures 8 through 11 show the trend in the median forecasts, FF futures, US Treasury rates, and economic
indicators, respectively. Since 2012, when the impacts of the global financial crisis remained, the median
forecasts for end of current year and end of next year forecasts have remained at 0.125%, indicating the(Source: Generated by Authors from Factset data)

Figure 8 Median Forecasts(Source: Generated by Authors from Factset data)

Figure 10: US Treasury Rates(Source: Generated by Authors from Factset data)

Figure 9: FF Futures(Source: Generated by Authors from Factset data)

Figure 11: Economic Indicators

5

For April 2012 to June 2012, the change is at 2-months intervals.
While central banks generally have a mandate for "price stability," the FRB has a similar mandate also for "maximizing employment," which
is why it is called a dual mandate.
6

p. 10

continuation of the zero-interest rate policy. However, the end of year after next forecast have been risingsince the second half of 2012 and end of next year forecast have been rising since the second half of 2013,
suggesting a rate hike ahead. Meanwhile, the Longer run, which indicates the destination of convergence,has been gradually declining along with the decline in the potential growth rate. Thereafter, the median
forecasts have declined due to the interest rate cut cycle in 2019 and the spread of COVID-19 and rose
again after 2021. FF futures in Figure 9 are moving in line with such monetary policy changes, and the US
Treasury rates in Figure 10 are moving ahead of FF futures.
In addition to this, the economic indicators in Figure 11 show that the headline CPI and PCE have gradually
increased, and the unemployment rate has declined since 2015, when the actual rate hike took place.
Furthermore, since 2019, inflation rate has been declining and unemployment rate has been rising alongwith interest rate cuts. Therefore, it is difficult to say that there was the impact of FOMC's tightening(easing) by raising (lowering) policy interest rates and the median forecasts on economic indicators. As
noted by Bauer and Swanson [2021], this suggests that the FOMC is making decisions in line with previous
market interest rates and economic conditions.
3.4 Results and Discussion
Table 2 represents the results of Granger causality test. Each row shows the values of the end of current
year, end of next year, end of year after next and Longer run median forecasts and each column shows themarket interest rates and economic indicators. The top row of each column is the F value and the bottom
row is the p value, with blue shadows for those statistically significant at 1% level, green shadows for
those significant at 5% level, and gray shadows for those significant at 10% level.
First, regarding the impact of market interest rates and economic indicators on the median forecasts, we
confirmed that all variables have a statistically significant impact on the end of current year to the end ofyear after next forecasts, while the 5 to 10 year US Treasury rates and FF futures for the 2 year ahead
contract have a statistically significant on the Longer run median forecast. In terms of the magnitude of
the impact of each variables, the F value of the FF futures for the end of current year contract is 68.5,
which is the greatest compared to other variables, indicating that it has a large impact.
The next most influential variables are the US Treasury 2 year interest rate (55.71), the US Treasury 3
year interest rate (40.45), and the FF futures for the 1 year ahead contract (38.62). On the other hand, theUS Treasury 30 year interest rate (8.25), the US Treasury 10 year interest rate (13.32), and the FF futures
for the 2 year ahead contract (8.09) are found to be statistically significant, although their effects are
relatively small. In other findings on inflation rate and employment, a greater emphasis is observed oncore CPI (7.88) and core PCE (9.84) compared to headline inflation rate of CPI (4.41) and PCE (4.35).
These trends are similar for the end of next year forecast in the dot plot, indicating that FOMC
participants' predictions for policy interest rates in the near future are set according to market interest
rates (especially for shorter terms), inflation rates and labor market conditions.
For the end of year after next forecast, the US Treasury 2 year interest rate (23.61) and the FF futures forp. 11

Table 2 Results of Granger Causality Test
Impact of the Median Forecast in the Dot Plot on Market / Economy
UST2Y

UST3Y

UST5Y

UST7Y

UST10Y

UST30YEnd ofCurrent Year
FF Futures

End of Next
Year FF
FuturesYear After
Next FF
FuturesCPI

Core CPI

PCE

Core PCEUNEMP Rate

End of Current
Year

0.71

0.68

0.35

0.14

0.13

0.01

0.02

0.83

0.36

0.93

0.03

0.40

0.97

0.14

(0.40)(0.41)(0.56)(0.71)(0.72)(0.92)(0.88)(0.37)(0.55)(0.34)(0.87)(0.53)(0.33)(0.71)End of Next
Year

0.06

0.01

0.01

0.01

0.00

0.01

2.21

0.03

0.35

0.01

0.52

0.01

0.06

0.06

(0.80)(0.94)(0.92)(0.93)(0.99)(0.94)(0.14)(0.86)(0.56)(0.92)(0.47)(0.94)(0.81)(0.81)End of Year
After Next

0.03

0.03

0.04

0.01

0.02

0.06

1.23

0.03

0.05

0.00

0.51

0.02

0.08

0.02

(0.86)(0.87)(0.85)(0.94)(0.88)(0.81)(0.27)(0.86)(0.82)(0.97)(0.48)(0.89)(0.78)(0.90)

Longer Run

0.56

0.88

0.50

0.15

0.00

0.21

0.00

0.71

1.05

0.35

0.17

0.10

0.04

0.05

(0.46)(0.35)(0.48)(0.70)(0.98)(0.65)(0.99)(0.40)(0.31)(0.55)(0.68)(0.76)(0.83)(0.82)***, ** and * indicate that the respective coefficients are statistically significant at the 1%, 5% and 10% level. Figures indicate F-values and those in parentheses indicate p-values.

Impact of Market / Economy on the Median Forecast in the Dot Plot
UST2Y

UST3Y

UST5Y

UST7Y

UST10Y

UST30YEnd ofCurrent Year
FF Futures

End of Next
Year FF
FuturesYear After
Next FF
FuturesCPI

Core CPI

PCE

Core PCEUNEMP Rate

End of Current
Year

55.71***

40.45***

25.28***

17.12***

13.32***

8.25***

68.5***

38.62***

8.09***

4.41**

7.88***

4.35**

9.84***

10.84***(0.00)(0.00)(0.00)(0.00)(0.00)(0.01)(0.00)(0.00)(0.01)(0.04)(0.01)(0.04)(0.00)(0.00)End of Next
Year

60.45***

51.14***

29.12***

17.79***

12.32***

6.39**

54.26***

50.25***

14.33***

4.35**

7.3***

5.93**

11.23***

5.01**(0.00)(0.00)(0.00)(0.00)(0.00)(0.01)(0.00)(0.00)(0.00)(0.04)(0.01)(0.02)(0.00)(0.03)End of Year
After Next

23.61***

23.4***

15.62***

9.31***

6.37**

3*

22.32***

22.73***

15.19***

7.42***

7.82***

10.43***

10.62***

3.11*(0.00)(0.00)(0.00)(0.00)(0.01)(0.09)(0.00)(0.00)(0.00)(0.01)(0.01)(0.00)(0.00)(0.08)

0.70

1.58

2.82*

3.17*

3.13*

2.71

0.15

2.43

4.7**

0.00

0.00

0.21

0.34

0.31

(0.40)(0.21)(0.10)(0.08)(0.08)(0.10)(0.70)(0.12)(0.03)(0.96)(0.96)(0.65)(0.56)(0.58)

Longer Run***, ** and * indicate that the respective coefficients are statistically significant at the 1%, 5% and 10% level. Figures indicate F-values and those in parentheses indicate p-values.

(Source: Generated by Authors from Factset data)p. 12the 1 year ahead contract (22.73) are statistically significant, which is similar to the dot plot forecast for
the end of current year and next year, but the F values for market interest rates are generally lower. On theother hand, the F values for CPI (7.42), PCE (10.43), core CPI (7.82), and core PCE (10.62) are larger
than those in the end of current year and next year dot plot results, indicating that FOMC participants arepaying more attention to economic indicators with respect to the end of year after next policy interest rate
forecast.
For the Longer run that is the neutral interest rate, the significant variables are the US Treasury 5, 7, and10 year interest rates and the FF futures for the 2 year ahead contract, all of which have smaller F values
than the results for the end of current year to year after next the median forecasts in the dot plot.
Therefore, in forecasting the Longer run, we believe that the forecast values are based on different
variables. It can be said that this is because the Longer run indicates where the policy interest rate would
converge in the absence of additional policy changes or shocks, and the level of the interest rate being set
based on the long-term equilibrium level, such as the potential growth rate of the economy, rather than on
recent market and economic developments.
On the other hand, the causality from the dot plot to market interest rates and economic indicators has
little impact among any of the variables. This is because, as we have already seen in Figures 5 and 6,
trends in the median forecasts are incorporated into market interest rates in advance.
As above, it can be said that in the relationship between the median forecasts and market interest rates
and economic indicators, the market does not incorporate in the FOMC participants' median forecasts offuture policy interest rates. However, the FOMC participants consider future monetary policy based onmarket and economic developments. Therefore, the relationship between market interest rates and policy
interest rates shown by Cochrane and Piazzesi [2002] is confirmed in the relationship between market
interest rates and the median forecasts.

4. Predictive Power of the Median Forecast for Policy Interest Rates
4.1 Data and Analysis Setup
In the analysis in Section 3, Granger causality test was conducted on the quarterly changes in the median
forecasts, market interest rates, and economic indicators, and it was confirmed that no influence from themedian forecasts was found. In this section, we use two methods to analyze how accurately the quarterly
median forecasts forecasted future policy interest rates.
In the first method of analysis (hereinafter referred to as "Method 1"), the difference between the forecast
values at the end of current year, next year, and year after next in the quarterly the median forecasts and therealized values of the policy interest rate at the end of the subsequent time period (current year, next year,
and year after next) is calculated. Specifically, the forecast for 1 month (or less) ahead can be obtained fromthe end of current year forecast value of the December FOMC, the forecast of 3 months ahead can beobtained from the end of current year forecast value of the September FOMC, and the forecast for 6 months

p. 13

ahead can be obtained from the end of current year forecast value of June FOMC. Furthermore, when using
the end of next year forecast value, the December FOMC forecast is 12 months ahead, the September FOMC
forecast is 15 months ahead, and when using the end of year after next forecast value, forecasts up to 33
months ahead can be calculated (see Appendix A for the actual calculation formula). For FF futures, thevalues of the end of current year, next year, and year after next contracts as of the publication date of thedot plot are used to calculate forecasts from 1 month (or less) to 33 months in the future. The difference
between those median forecasts, FF futures forecasts, and the subsequently realized policy interest rate arecalculated, and the difference is defined as the "quarterly forecast accuracy”. Since the dot plots are
published for approximately 10 years starting in 2012, a forecast accuracy of 8 to 10 samples can becalculated for each forecast period.
In the second analysis method (hereinafter referred to as " Method 2"), to increase the number of samples
analyzed regarding the forecast values at the same period compared to Method 1, the median forecasts
suggesting the policy interest rate 1 year ahead and 2 year ahead estimated based on certain assumptions.
By using assumptions, the median forecasts themselves cannot be used, but more values for the same future
point in time can be obtained than in Method 1. For example, the median forecasts that implies the policy
interest rate 1 year ahead, as of March of each year, would be the sum of the value of the median forecasts
at the end of current year(the forecast for 9 months going ahead) and the difference between the forecast at
the end of next year and the forecast at the end of current year multiplied by 0.25 (by calculating the forecast
for 3 months going ahead, starting at the end of current year). The difference between the median forecaststhat suggests the policy interest rate 1 year ahead as of March and the policy interest rate realized as ofMarch of the following year is defined as the "1 year ahead forecast accuracy." By performing similarcalculation for dot plots published as of June, September, and December, "1 year ahead forecast accuracy"
can be calculated for 37 samples (See Appendix B for the actual formula).
The same calculation is also performed for the 2 year ahead forecast accuracy. In other words, the median
forecasts for the 2 year ahead forecast is calculated by the sum of the median forecasts for the end of thenext year forecast (or the forecast for 21 months ahead in the case of the dot plot at the March FOMC
meeting), and the difference between the median forecasts for the end of year after next forecast and theend of next year forecast multiplied by 0.25 (by calculating the forecast value for 3 months ahead, startingat the 1 year end ahead). In addition, the difference between the median forecasts suggesting the forecast
policy interest rate for 2 year ahead, and the policy interest rate realized at the end of the 2 year later isdefined as the "2 year ahead forecast accuracy." By performing similar calculation for median forecasts
published as of June, September, and December, "2 year ahead forecast accuracy" is calculated for 33
samples. For FF futures, the "1 year ahead forecast accuracy" and "2 year ahead forecast accuracy" arecalculated using the values of the end of current year, next year and year after next contracts on the date thedot plot is published. The number of samples is the same as that for the dot plot. The "quarterly forecast
accuracy," "1 year ahead forecast accuracy," and "2 year ahead forecast accuracy" for the median forecasts
and FF futures, calculated using the above two analysis methods, are discussed in the next section.

p. 14

4.2 Results and Discussion
Figure 12 and 13 show the results of Method 1. Histograms are created for the "quarterly forecast
accuracy" of the median forecasts and the FF futures and kernel density estimations7 are performed. The
estimation results show that the distribution is generally similar in shape between the median forecasts andthe FF futures for all forecast periods, and the shorter the forecast period, the thinner the tails of the
distribution, the smaller the difference between the forecast value and the realized value, and the better theforecast accuracy. The average forecast accuracy for the 3 months ahead is 0.08% pt for the median forecast
and 0.19% pt for the FF futures, indicating that the median forecast in the dot plot has better forecast
accuracy. This trend is confirmed over relatively short forecast periods, with forecast accuracy 6 months
ahead (median forecasts: -0.04% pt; FF futures: 0.19% pt) and 9 months ahead (median forecasts: -0.03%
pt; FF futures: 0.12% pt). On the other hand, the forecast accuracy for 12 months ahead (median forecasts:-0.35% pt; FF futures: -0.08% pt) confirms that the FF futures have better forecast accuracy for longer
forecast periods, except for the 18 months forecast accuracy.
Figure 14 shows the kernel density estimation for the histogram created for the median forecasts and the
FF futures calculated in Method 2, and the "1 year ahead forecast accuracy" and "2 year ahead forecast
accuracy." The distribution for the shorter "1 year ahead forecast accuracy" has thinner tails, while the
distribution for the "2 year ahead forecast accuracy" has fatter tails with larger variance. The average of theforecast accuracy for 1 year ahead is 0.27% pt for the median forecasts and -0.01% pt for FF futures, whilefor 2 year ahead, it is 0.78% pt for the median forecasts and -0.22% pt for the FF futures, confirming thatthe forecast accuracy for the FF futures is better, as in Method 1 in longer forecast periods.
As indicated by the above two analysis methods, the median forecasts for the near future (less than 1 year
ahead) has a good forecasting accuracy. This is because FOMC participants' opinions on the policy interest
rate are more likely to converge for the near term, and the actual policy interest rate will be changed
accordingly. For longer horizons, on the other hand, policy interest rates follow market rates, and FF futures,
which reflect forecasts by a broader range of participants than the FOMC, will have better forecasting
accuracy. While it is not confirmed that the median forecasts have impact on the market with respect tochanges in quarterly data for which Granger causality tests were conducted, it is thought to have predictive
power in the near term for forward-looking policy interest rate forecasts.

7

A method for estimating the distribution (density function) of the entire original data from sample data. The commonly usedmethod of estimation and testing by assuming a distribution in econometric analysis is called the parametric method. In contrast,
the method in which the distribution itself is considered unknown and inferring statistical parameters such as mean and varianceis called the nonparametric method. In the approximation of the density function by the nonparametric method, given 𝑛observed variables 𝑥 , 𝑖 1,2, … , 𝑛 from the same distribution, the density function estimate 𝑓 𝑥 can be estimated by thefollowing formula when the density function of 𝑥 is 𝑓 𝑥 . ℎ is a parameter called bandwidth.
𝑓 𝑥

1
𝑛ℎ

𝐾

𝑥

𝑥
ℎ

𝐾 ∙ is a function called kernel, so the method of estimating the density function of the original data from the data using
nonparametric methods, is called kernel density estimation. Tanizaki [2005] provides more details on the nature of kernel
functions and bandwidths.

p. 15

(Source: Generated by Authors from Factset data)

Figure 12: "Quarterly Forecast Accuracy"
for Median Forecasts(Source: Generated by Authors from Factset data)

Figure 13: "Quarterly Forecast Accuracy" for FF
Futures(Source: Generated by Authors from Factset data)

Figure 14: "1 Year Ahead Forecast Accuracy" and "2 Year Ahead Forecast Accuracy" for Median
Forecasts and FF Futures

p. 16

5. The Term Structure of US Treasury Rates, Which Incorporates theDot Plot Information
5.1 Models and Methods
As revealed by Granger causality test, market interest rates have been moving ahead of the median
forecasts, and no market impact was identified from changes in the median forecasts on a quarterly basis.
Therefore, the median forecasts appear to follow market interest rates, meanwhile as Lunsford [2020] points
out, the market is influenced by the wording of the FOMC's forward guidance.
The FOMC normally meets eight times a year, including meetings at which the dot plot is not released,
and it is possible that the next dot plot is incorporated in advance as the market reacts to the wording of theforward guidance and statements there. In such a case, at the time the dot plot is released, the shape of theyield curve, which represents the term structure of interest rates, would reflect the path of the policy interest
rate indicated by the dot plot. Nelson and Siegel [1987] developed the model that explain the yield curve
shape by level, slope, and curvature (hereinafter referred to as "NS model"). It was extended to a modelwith respect to curvature by Svensson [1994] (Nelson Siegel Svensson, hereinafter referred to as “NSS
model.”) We utilize the NSS model to analyze whether the US Treasury yield curve incorporates the pathof the policy interest rate indicated by the median forecasts in the dot plot.
Equation (5) represents the NSS model. 𝛽 is the parameter of level of the yield curve, 𝛽 is the that ofslope, and 𝛽 and 𝛽 are parameters representing the curvature. λ and κ are called the decay factor andmainly regarding at which term the peak of the curvature is located. 𝜏 denotes the term.

𝑦 𝜏

𝛽

𝛽

1

𝑒
𝜆𝜏

𝛽

1

𝑒
𝜆𝜏

𝑒

𝛽

1

𝑒
𝜅𝜏

𝑒

(5)

To estimate the NSS model, there is a non-linear method where all parameters are estimated at once,
including λ and κ, and a linear regression method where λ and κ are fixed. For example, Gürkaynak et
al. [2007] estimated all six parameters of the NSS model at once by the maximum likelihood method, butalso reported that the trend in parameters were unstable. On the other hand, Diebold and Li [2006] estimated
𝛽 ,𝛽 ,𝛽by linear regression with λ as a constant value 8 . We defined λ0.60 and κ

0.18 toestimate the NSS model parameters 𝛽 , 𝛽 , 𝛽 , 𝛽 using the method of Diebold and Li [2006]. Note that
this analysis does not regress on the yield itself, but rather on the present value basis (see Appendix C for
details on the estimation method). The estimation covers 41 periods from April 2012 to June 2022, and thezero-coupon rates of US Treasuries by maturity as of the publication date of the dot plot are used for all
periods. The target maturity (𝜏) used in the estimation is between 1 and 30 years, out of a range of 1 month8

Other methods have also been conducted by Wahlstrøm et al. [2022] in estimate of the NSS model, first estimating the fourparameters in the NS model and based on those values, estimating the remaining two parameters in the NSS model.

p. 17

to 50 years for which data are available, and illiquid maturities are excluded9.
Figures 15 through 19 show the estimated results for the parameters of the NSS model. As reference indicesfor the estimated results, US Treasury 10 year rate for the level (𝛽 ), the US Treasury 1-10 year spread forthe slope (𝛽 ), the “curvature = US Treasury 3 year rate * 2 - (US Treasury 1 year rate + US Treasury 30
year rate)” for the curvature 1 (𝛽 ), and “curvature = US Treasury 10 year interest rate*2 – (US Treasury 1
year rate + US Treasury 30 year rate)” for the curvature 2 (𝛽 ) are utilized. The level (𝛽 ) rose through mid2013 due to the market's growing view of a lifting of the zero-interest rate policy, followed by a decline ininterest rates due to the emerging market shocks in early 2016 and the global spread of the COVID-19 inearly 2020, and the rise in interest rates is captured in preparation for a rate hike in 2022. The slope (𝛽 )shows a divergence from the reference indicator in the 2017-2019 period and around 2022, but the trend ofslope contraction and subsequent slope expansion from 2012 to 2014 is replicated. Furthermore, thecurvature 1 (𝛽 ) and curvature 2 (𝛽 ) also generally follow the reference indicator when the market(Source: Generated by Authors from Factset data)

Figure 16: Level (𝛽 )(Source: Generated by Authors from Factset data)

Figure 18 Curvature 1 (𝛽 )9(Source: Generated by Authors from Factset data)

Figure 17: Slope (𝛽 )(Source: Generated by Authors from Factset data)

Figure 19 Curvature 2 (𝛽 )Each year from 1 to 5 years and 7, 9, 10, 15, and 30 years.

p. 18

fluctuates significantly, which is thought to reproduce the characteristics of the yield curve when it
fluctuates10.
Using the parameters estimated in this way (𝛽 , 𝛽 , 𝛽 , 𝛽 ) as explained variables, we conduct a regression
analysis using the end of current year forecast median forecasts (explanatory level) and the difference
between the end of year after next and next year forecasts (explanatory slope) as explanatory variables todetermine to what extent the median forecasts are incorporated into the yield curve. The level and slope
using FF futures are also calculated in the same manner as the median forecasts, and by using them as
explanatory variables, the results of these regression analyses are compared.
5.2 Results and Discussion
Table 3 represents the result of the regression. First, regarding the coefficient value for the level (𝛽 ), theslope of the median forecasts is 0.26 at the 1% significance level. For FF futures, both the level and theslope are shown to be significantly positive impact, with a level of 0.14 at the 5% significance level and aslope of 0.60 at the 1% significance level. Therefore, when the difference between the end of next year andyear after next which is the path of the forward-looking policy interest rate according to the median forecasts
and FF futures widens, the overall level of the US Treasury yield curve tends to increase. The FF futuresindicated that its level at the end of current year also have an effect on yield curve. The reason why thelevels of the explanatory variables are not significant for the median forecasts and low for the FF futures,
despite the fact that the dependent variable is the level of the overall yield curve (𝛽 ), is that the zero interest
rate policy was in place from 2012 to 2015 during the sample period, and during that period the market wasmore focused on interest rates in the more distant future than on interest rates in the near future, which is
the level of the median forecasts and FF futures. Therefore, it can be said that the median forecasts in thedot plot had effects on interest rates under the zero-interest-rate policy. Adjusted 𝑅 is 0.13 for the median
forecasts and 0.31 for the FF futures, confirming that the FF futures have more than twice as much
explanatory power as the median forecasts.
Second, the slope (𝛽 ) is also confirmed that for both the median forecasts and the FF futures, the slopes
have significantly negative impact. The coefficient values are -0.27 at the 1% significance level for the
median forecasts and -0.61 at the 1% significance level for the FF futures. The coefficient value for thelevel of FF futures is -0.15 at the 1% significance level, indicating a negative impact. The adjusted 𝑅 is
0.15 for the median forecasts and 0.33 for the FF futures, again confirming a difference of more than twotimes.
The curvatures (𝛽 and 𝛽 ) are also affected by both the median forecasts and the FF futures. The
coefficient value of curvature 1 (𝛽 ) is not significant for the median forecasts, and it is -0.22 at the 1%
significance level for FF futures. For curvature 2 (𝛽 ), it is -0.47 at the 5% significance level for the median
forecasts, and -1.05 at the 1% significance level for the FF futures. As mentioned earlier, curvature 1 (𝛽 )10Although the reference index calculated using market interest rates shows the same characteristics of the yield curve shape as the parametersfrom the NSS model, the values do not necessarily coincide due to different definitions.

p. 19

Table 3: Results of Regression Analysis of Yield Curve
Level(β 0 )MedianForecasts
Constant

Slope(β 1 )FF Futures

MedianForecasts

Curvature2 (β 3 )Curvature1 (β 2 )FF Futures

MedianForecasts

FF Futures

MedianForecasts

FF Futures

1.04***

0.95***-1.04***-0.96***-0.35***-0.29***-2.32***-2.17***(11.37)(11.83)(-11.50)(-12.03)(-8.05)(-7.58)(-12.26)(-12.58)

End of Current Year Forecast

0.05

0.14**-0.06-0.15***

0.03

-0.01

0.00

-0.14

(Explanatory Variable: Level)(1.12)(2.68)(-1.22)(-2.83)(1.23)(-0.33)(0.01)(-1.24)0.26***

0.6***-0.27***-0.61***-0.07-0.22***-0.47**-1.05***(2.86)(4.46)(-3.03)(-4.65)(-1.62)(-3.42)(-2.50)(-3.66)

0.18

0.34

0.19

0.36

0.16

0.32

0.17

0.29

0.13

0.31

0.15

0.33

0.11

0.28

0.12

0.25

4.09**

9.96***

4.59**

10.84***

3.56**

8.86***

3.82**

7.77***

0.02

0.00

0.02

0.00

0.04

0.00

0.03

0.00

Diff of End of Year After Next and Next
Year(Explanatory Variable: Slope)2R2

Adjusted R
F valueSignificance probability of F-value***. ** and * indicate that the respective coefficients are statistically significant at the 1%, 5%, and 10% level. Parentheses indicate t-values.

(Source: Genereated by Authors from Factset data)

represents the curvature mainly on the 3 year Treasury rate, curvature 2 (𝛽 ) represents the curvature mainlyon the 10 year Treasury rate, indicating that the median forecasts and FF futures have a strong influence on
the curvature 2 (𝛽 ), in a relatively long term zone of the yield curve. This is, as suggested by the results
for level (𝛽 ), because more forward-looking information from the median forecasts and FF futures isincorporated in the market. The adjusted 𝑅 for the curvature 1 (𝛽 ) is 0.11 for the median forecasts and0.28 for FF interest rate futures. For curvature 2 (𝛽 ), the adjusted 𝑅 is 0.12 for the median forecasts and0.25 for the FF interest rate futures, and the explanatory power of the FF futures are much greater than thatof the median forecasts in terms of curvature as well.
Thus, with respect to the parameters representing the characteristics of the US Treasury yield curve as
estimated by the NSS model, it is confirmed that the slope is more strongly incorporated into the market
than its level, for both the median forecasts and FF futures. The reason for this can be attributed by the factthat market participants are focusing on longer-term interest rate trends rather than the near future in bothcases. However, both estimates indicated that the explanatory power of the FF futures is more than twiceas that of the median forecasts. Therefore, although the US Treasury market has already incorporated thepath of policy interest rates in the median forecasts released quarterly based on the FOMC's forward
guidance, the FF futures, which are priced forward by a wide range of market participants, has the greater
explanatory power than that of the median forecasts.

6. Conclusion and Implication
This paper analyzed whether changes in policy rates have been factored into market interest rates since2015, when the zero-interest rate policy was lifted in the United States, and found that the relationshipbetween policy rates and market rates has been maintained. In addition, three analyses were conducted. The

p. 20

first analysis of the relationship between the median forecasts in the dot plot and market interest rates andeconomic indicators using Granger causality test confirmed that the median forecasts are set to reflectmarket interest rates and economic indicators, and that there is no effect from the median forecasts onmarket interest rates and economic indicators on a quarterly basis. The second analysis of the predictive
power of the future policy interest rates showed that the median forecasts have better predictive power thanthe FF futures for periods of less than 1 year ahead. The third analysis, using the NSS model, of how levels
and slopes in the median forecasts and FF futures are incorporated into the yield curve shape, showed thatwhile the median forecasts are incorporated into all levels, slopes, and curvatures of the yield curve at thetime of publication, the level and slope of FF futures received more attention from the market. The results
indicate that the market is paying more attention to the level and slope of the FF futures.
The implications of the analysis are as follows. The median forecasts have predictive power for policy
interest rates in the near future, and it is useful to use its median value to predict the direction of monetary
policy for about 1 year ahead. The VAR model analysis clearly shows that the median forecasts are set
according to market and economic developments, and as pointed out in Section 2.1, there are doubts fromsuccessive Fed chairs as to whether the median forecasts are functioning as intended by the FOMC as acommunication tool. In fact, the NSS model analysis showed that FF futures, which reflect the outlook by
a broader range of market participants, are more incorporated into the yield curve than the median forecasts,
which is a policy interest rate forecast by FOMC participants only. Although the dot plot has been intended
to act as forward guidance of policy interest rates, its effect has been limited for the median forecasts. Basedon the above, it is considered more effective to refer to market interest rates and economic indicators such
as FF futures rather than the median forecasts in the dot plot in quantitative analysis of the bond market.

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p. 22

Appendix A: Forecast Accuracy of the Median Forecasts and FF
Futures - 1
The accuracy of the median forecasts in the dot plot forecast of the policy interest rate 1 month (or less)ahead is defined as the difference between the December median forecasts of each year (the end of currentyear) and the actual policy interest rate at the end of the year and is calculated for 10 samples from 2012 to
2021. The 3 months forward forecast accuracy is defined as the difference between the September median
forecast (the end of current year) and the actual policy interest rate at the end of the year and is calculated
for 10 samples from 2012 to 2021. The forecast accuracy for 33 months ahead will be calculated in thesame way. The forecast accuracy for FF interest rate futures will be calculated using the same definition.
1 month (or less) forecast accuracy= December FOMC median forecast (the end of current year) – December end policy interest rate
3 months forecast accuracy= September FOMC median forecast (the end of current year) – December end policy interest rate
6 months forecast accuracy= June FOMC median forecast (the end of current year) – December end policy interest rate
9 months forecast accuracy= March FOMC median forecast (the end of current year) – December end policy interest rate
12 months forecast accuracy= December FOMC median forecast (the end of next year) – policy interest rate of 1 year later at the end of
December
15 months forecast accuracy= September FOMC median forecast (the end of next year) – policy interest rate of 1 year later at the end of
December
30 months forecast accuracy= June FOMC median forecast (the end of year after next) – policy interest rate of 2 year later at the end of
December
33 months forecast accuracy= March FOMC median forecast (the end of year after next) – policy interest rate of 2 year later at the end of
Decemberp. 23

Appendix B: Forecast Accuracy of the Median Forecasts and FF
Futures – 2
The "1 year ahead forecast accuracy" of the policy interest rate by the median forecasts is calculated as follows
for each month the FOMC meeting was held. The "2 year ahead forecast accuracy" is calculated in the sameway.

Estimated 1 year ahead median forecast as of March FOMC
= current year end median forecast+ 0.25*(next year end median forecast - current year end median forecast)
1 year forecast accuracy of March median forecast= Estimated 1 year ahead median forecast – policy interest rate realized in March of the following year
Estimated 1 year ahead median forecast as of June FOMC
= current year end median forecast+ 0.5*(next year end median forecast - current year end median forecast)
1 year forecast accuracy of June median forecast= Estimated 1 year median forecast – policy interest rate realized in June of the following year
Estimated 1 year ahead median forecast as of September FOMC
= current year end median forecast+ 0.75*(next year end median forecast - current year end median forecast)
1 year forecast accuracy of September median forecast= Estimated 1 year median forecast – policy interest rate realized in September of the following year
Estimated 1 year ahead median forecast as of December FOMC
= end of next year median forecast
1 year forecast accuracy of December median forecast= Estimated 1 year median forecast – policy interest rate realized in December of the following year

Appendix C: Estimation of the NSS Model
Figure C1 shows the shape of differentiated level (𝛽 ), slope (𝛽 ) and curvature (𝛽 , 𝛽 ). The horizontal
axis shows the term of the Treasury bond, and the vertical axis is the value of the parameters for each term.
The level (𝛽 ) has a constant effect regardless of the term, whereas the slope (𝛽 ) shows that the effect isgreater on short term interest rates, while the effect decreases as the term increases. Each curvature (𝛽 , 𝛽 ),shows the convex shape of the yield curve, and according to the decay factors λ and κ, the term at which
the maximum value is reached change.
Therefore, by setting λ and κ to maximize

1

𝑒

⁄𝜆𝜏

𝑒

and

1

𝑒

⁄𝜅𝜏

𝑒

in theperiod of years (τ) to be analyzed, it is possible to analyze the variation of curvature in the target period.
(Diebold and Li [2006]).

p. 24

Level(β_0)

Curvature1(β_2)

Curvature2(β_3)

50 year

30 year

20 year15 year

12 year0.0
10 year

0.0
9 year

0.2

7 year

0.2

5 year

0.4

4 year

0.4

3 year

0.6

2 year0.6

1 year0.8

9 month

0.8

6 month1.0

3 month1.0

2 month1.2

1 month

1.2

Slope(β_1)(Source: Generated by Authors from Factset data)

Figure C1 Parameter Characteristics of the NSS model
Table C2 shows λ and κ values that maximizes the curvature in each term. For the analysis in Section 5,
to consider the impact on the median forecast for 3 years, which had the greatest price volatility by terms,
and 10 year as the longer period, we used λ0.60 and κ

0.18.

Table C2 Decay Factor Values by Term

Term

1 year

2 year

3 year

5 year

7 year10 year

30 year

τ

1

2

3

5

7

10

30

λ/κ

1.79

0.90

0.60

0.36

0.26

0.18

0.06

(Source: Generated by Authors from Factset data)

Note that in the estimation of the NSS model, if the yield (𝑟) itself is estimated, for example, an estimation
error of 1 basis point for a 3 year rate and 1 basis point for a 10 year rate are treated as equivalent, anderrors cannot be handled according to the level of interest rates by each term. Therefore, we transformed
the par value of 100 into the bond price using the yield as in equation (C3) and estimated the parameters of
the NSS model for its present value.

𝑦 𝜏

100 ∗ 𝑒

𝑟𝜏

(C3)

p. 25