Next Article in Journal
How Do Sustainability Stakeholders Seize Climate Risk Premia in the Private Cleantech Sector?
Previous Article in Journal
Role of Governance in Developing Disaster Resiliency and Its Impact on Economic Sustainability
Previous Article in Special Issue
The Governance and Disclosure of IFRS 9 Economic Scenarios
 
 
Font Type:
Arial Georgia Verdana
Font Size:
Aa Aa Aa
Line Spacing:
Column Width:
Background:
Article

Stylized Facts of the FOMC’s Longer-Run Forecasts †

School of Advanced International Studies, Johns Hopkins University, 1740 Massachusetts Ave. N.W., Washington, DC 20036, USA
This paper was presented at the Joint Meetings of the American Statistical Association (August 2022) and at the 24th Meeting of the Federal Forecasters Conference (September 2022).
J. Risk Financial Manag. 2023, 16(3), 152; https://0-doi-org.brum.beds.ac.uk/10.3390/jrfm16030152
Submission received: 20 December 2022 / Revised: 13 February 2023 / Accepted: 15 February 2023 / Published: 24 February 2023
(This article belongs to the Special Issue Uncertainties, Risks and Economic Forecasts)

Abstract

:
Conventional explanations of monetary policy decisions in the United States assume that the longer-run Federal funds rate is determined by a representative central banker (i.e., the Fed) using longer-term forecasts of economic activity and unemployment. This assumption is inconsistent with the federalist structure of the Federal Reserve in which the Federal funds rate is determined by a committee made up of the Federal Reserve Board and the Federal Reserve Banks. This inconsistency would be irrelevant if differences in the Fed participants’ longer-run projections were small or constant, but they are not: disparities in these longer-run projections are large and volatile. This finding raises several questions: Are FOMC participants relying on the same forecasting framework (i.e., model or rules of thumb) but using different values for the forecast drivers? Or are these participants using the same forecast drivers but relying on different frameworks?

1. Introduction

Conventional explanations of monetary policy in the United States assume a representative central banker who relies on longer-run projections of GPD growth, inflation, and unemployment to determine the appropriate longer-run Federal funds rate.1 Though this assumption is not consistent with the federalist structure of the Federal Open Market Committee (FOMC),2 using it would still be valid if the longer-run forecasts of FOMC participants were close to each other. However, they are not: their differences are large and volatile. For example, the FOMC projections from the December 2022 FOMC meeting show that the appropriate interest rate for 2025 ranges between 225 basis points and 575 basis points.3 Because differences of this magnitude are not a one-off event, they raise several questions. First, how can monetary policy be useful to the private sector when the very policymakers deciding monetary policy disagree among themselves about future monetary policies? Second, what is the source of such forecast disagreements? Is it because policymakers are using different forecasting frameworks (i.e., models or rules of thumb) in their forecasts or is it because they have the same forecasting framework but use different forecasts for GDP growth and unemployment? This paper studies these questions by offering the first statistical analysis of the distributions of longer-run projections of individual participants of the FOMC for GDP growth, the unemployment rate, and the appropriate interest rate from 2012 to 2022.
To be sure, interest in the forecasts of individual members of the FOMC is not new. Romer (2010) offered the first framework to address the question of whether FOMC participants have a shared forecasting framework. Using FOMC participants’ forecasts from 1992 to 1998, Romer finds that over this period, FOMC participants did not have a common forecasting framework.
Romer’s work generated a substantial interest in the literature. For example, Rülke and Tillmann (2011) examine whether FOMC participants exhibit herd behavior. Tillmann (2011) and Nakazono (2013) examine the possibility of extreme forecasts. Shen (2015) studies the forecasts made by individual members of the Federal Open Market Committee (FOMC) for the period of 1992–2003. Shen finds a substantial level of variation in the members’ forecasts and argues that one reason is the potential conflict of interests between the Federal Reserve Banks and the Federal Reserve Board.
This body of work does not incorporate the implications of the 2008 financial crisis for the FOMC’s forecasting protocol, which includes the introduction of “forward guidance,” the quarterly release of forecasts (instead of semi-annual), and the extension of the forecast horizon. Kalfa and Marquez (2019, 2021) and Marquez and Kalfa (2021) extend the previous literature by using a sample period that includes the 2008 financial crisis and the resulting changes to U.S. monetary policy. Further, they study the modeling and forecasting of FOMC forecasts using publicly available data which are, arguably, a relevant consideration for judging the progress of forward guidance. The appeal of their approach is their focus on short-term forecasts by computing the accuracy of the FOMC’s forecasts once they are released.
In contrast to previous work, I focus here on the FOMC’s longer-run projections which were first released in 2012. The inclusion of these projections reflects a re-orientation of U.S. monetary policy to meeting long-run objectives as part of the FOMC communications strategy; Clarida (2019) and Cecchetti and Schoenholtz (2019) examine the role played by FOMC forecasts in this strategy. Bernanke (2016) argues that “As I discussed here, other key long-run parameters about which the SEP [Summary of Economic Projections] is informative by including the so-called natural rate of unemployment (the rate of unemployment consistent with stable inflation); the potential output growth rate; and the “neutral” or equilibrium value of the federal funds rate, which correspond to the long-run projections of unemployment, output growth, and the funds rate, respectively. …” Powell (2018) notes that longer-run forecasts serve as though they are “fixed stars” used for navigation, but he also notes that “Guiding policy by the stars in practice, however, has been quite challenging of late because our best assessments of the location of the stars have been changing significantly”.
Powell’s analogy, correct as it might be, does not point out what is perhaps the most important stylized fact of these longer-run forecasts: the numerically large and historically persistent disagreement that exists among FOMC participants’ views on the long run. In short, there is a multiplicity of fixed stars that are potentially relevant for navigation and there is no obvious argument to select one set over another.
One would think that reliance on the accuracy of these forecasts would identify which set of stars is reliable for navigation. Yet this approach is not feasible because these projections are not designed to predict a verifiable outcome for a given date but, rather, to characterize a macroeconomic equilibrium in the absence of shocks.4 Arguably, the date when such an equilibrium is reached is not known in advance and thus the associated forecast error cannot be computed, undermining attempts at assessing their reliability.
The data for this project come from both the FOMC’s transcripts and the Summary of Economic Projections (SEP). Section 2 of this paper relies on the FOMC transcripts, which provide each participant’s longer-run forecasts for GDP growth, the appropriate interest rate, and the unemployment rate from each meeting between January 2012 and December 2016. Given the participants’ forecasts from each meeting, I construct the associated empirical distributions and document the evolution of their moments (median, variance, and skewness). To examine whether FOMC participants have a common forecasting framework for generating their longer-run forecasts, I use Romer’s (2010) framework.
I find that FOMC’s participants exhibit substantial disagreements regarding the longer-run performance of the U.S. economy. In addition, these disagreements are persistent and volatile, showing no tendency to converge among participants. Further, I do not find evidence of FOMC participants sharing a common framework—confirming the findings of Romer (2010). The seeming lack of information in these forecasts is not new and has been explained as resulting from “extreme forecasts” and “herd behavior.” Thus, as an alternative to studying participant-by-participant forecasts subject to these behaviors, I focus on whether the moments of their forecast distributions are informative about the longer-run structure of the U.S. economy.
To that end, Section 3 relies on the Summary of Economic Projections (SEP), which reports the medians of the forecast distributions along with their upper and lower bounds from 2017 to 2022. Combining the data from both the transcripts and the SEP yields a time-series of the median of the distribution of longer-run forecasts from 2012 to 2022 for GDP growth, the appropriate interest rate, and the unemployment rate. To provide a reference point to judge these forecasts, I compare them to the FOMC’s short-term forecasts and the observed values for inflation and unemployment; I use Granger causality tests to detect the direction of causality, if any, among them. Finally, given that the longer-term forecast errors are not observable, I replicate the published moments of the longer-run forecasts as a second-best criterion for judging their reliability.

2. Distributions of Individual FOMC Participants’ Forecasts: 2012–2016

Figure 1 shows the distributions of longer-run forecasts for the appropriate interest rate for two policy meetings: December 2012 and December 2016.
The figure shows that the assumption of a representative central banker for the case of the United States is not met for these two dates: disagreements among participants for the longer-run forecast for the appropriate interest rate are pronounced and persistent. Figure 2 shows the distributions of the longer-run appropriate interest rate for each of the meetings from January 2012 to December 2016. These distributions show no tendency to converge to a single value, or to a narrow range of values, which is what one would expect to see if the representative central banker were a useful approximation.
There are several potential explanations for the dispersion of these forecasts. First, FOMC participants share a forecasting framework but assign different values to the associated forecast drivers. Intuitively and greatly simplified, the longer-run forecast for the appropriate interest rate from the ith participant R i could be modeled as R i t = β · X i t + ε i t ,   where β is a vector of the parameter values shared by all participants, X i t is the vector of the values of the longer-run forecast drivers for the ith participant as of time t, and ε i t is a participant-specific random term with a mean of zero reflecting the effect of unforeseen events (i.e., COVID-19) on the appropriate interest rate. Note that, simple as it is, this formulation is consistent with the FOMC protocol: “The Committee’s primary means of adjusting the stance of monetary policy is through changes in the target range for the federal funds rate. … Therefore, the Committee’s policy decisions reflect its longer-run goals, its medium-term outlook, and its assessments of the balance of risks, including risks to the financial system that could impede the attainment of the Committee’s goals. …”5 Second, participants have different forecasting frameworks (i.e., equations or rules of thumb) but use the same values for the forecast drivers: R i t = β i · X + ε i t . Third, participants share neither the forecasting framework nor the values of the forecast drivers—that is, R i t = β i · X i t + ε i t .
Figure 3 and Figure 4 show that the participants disagree substantially about the values for their longer-run forecasts for growth and unemployment (i.e., the forecast drivers   X i ). For GDP growth, the sustained leftward shift in the densities between January 2012 and December 2016 reveals that the FOMC has had a pessimistic outlook for U.S. economic growth (bottom row of Figure 3). Further, the downward trend is accompanied by an increase in both the standard deviation and a positive skewness. FOMC participants also lack a common outlook for the longer-run forecast of the unemployment rate (Figure 4). Though the median of the distribution declines over time, the data also indicate a decline in the standard deviation (bottom row). These two properties confirm the absence of a representative central banker.
Arguably, such differences in longer-run forecasts need not be surprising given the ambiguities built into the definition of the longer run (see note 6). Another factor explaining these attributes is the heterogeneity of the experiences of the FOMC participants, as Romer (2010) and Marquez and Kalfa (2021) have noted. Such heterogeneity induces differences in participants’ identification of the sources of macroeconomic shocks (i.e., aggregate supply, aggregate demand, fiscal, monetary, permanent, transitory, foreign or domestic), which could then give rise to different forecasts.
This evidence, however, does not rule out that FOMC participants have a common forecasting framework. Specifically, if participants are sharing a forecasting framework, then differences in the longer-run forecasts for growth and unemployment could explain the differences in their forecasts for the longer-interest rate. Thus, an interesting question is whether the participants are sharing a forecasting framework.
To examine this possibility, Figure 5 shows the scatterplots of the FOMC participants’ longer-run forecasts from January 2012 to December 2016 for growth, unemployment, and the appropriate interest rate. These scatterplots reveal that the unconditional contemporaneous correlations among the three variables are positive and large, suggesting that one cannot rule out, a priori, a shared framework among participants. To be sure, sharing a forecasting framework is not the same as having identical forecasts. For example, the scatterplots suggest that participants view a higher longer-term interest rate as directly associated with a higher longer-term unemployment rate, but that tendency is far from precise. Indeed, given a longer-run forecast for the interest rate of two percent, the longer-run forecast for the unemployment rate varies from 4.75 to 5.75 percentage points. Arguably, that range is potentially influenced by unusual events (e.g., the euro crisis of 2011) and by the influence of the Chair of the FOMC. To assess whether these correlations are indeed reflecting a relation, or they are being driven by the influence of outliers, I use Romer’s model augmented by who the FOMC chair is.
r i , t u i , t y i , t = t = 2 17 δ t D t + β B C B t + β Y C Y t + e i , t r e i , t u e i , t y ;   e i , t r e i , t u e i , t y N 0 , Σ
r i , t : longer-term appropriate interest rate forecast of the ith participant made in period t; i ranging from 1, …, N t ; N t 19   for all t from 1 (January 2012) to 17 (December 2016).
u i , t : longer-term unemployment forecast of the ith participant made in period t
y i , t : longer-term GDP growth of the ith participant made in period t
D t : Dummy variable equal to one for period t and zero otherwise
C B t : Dummy variable equal to one for Bernanke’s tenure as FOMC Chair; zero otherwise
C Y t : Dummy variable equal to one for Yellen’s tenure as FOMC Chair; zero otherwise
The model accounts for FOMC participants’ longer-run forecasts in terms of the date of each FOMC meeting, to control for unexpected events, and the holder of the FOMC Chair. Following Romer (2010), I use the associated estimation residuals to detect if FOMC participants use a shared forecasting framework. Intuitively, finding that the residuals are correlated would be consistent with the view that there is a set of variables, common to all participants, which is omitted from Equation (1). If there is no correlation among the residuals, then there is not an obvious set of omitted variables. Figure 6 shows that, after controlling for the date of the meetings and the holder of the FOMC chair, the associated residuals are not correlated with each other. In other words, the residuals do not reveal an obvious theory, shared by all participants, explaining these longer-run forecasts.
Finding that the dispersion of FOMC participants’ forecasts cannot be explained by a single framework raises the question of whether the longer-run forecasts offer any useful information regarding the future of the U.S. economy.6 As mentioned earlier (and detailed below), two factors could be responsible for this seeming lack of information: extreme forecasts and herd behavior. Thus, as an alternative to studying participant-by-participant forecasts, I examine whether the moments of the participants’ forecast distributions are informative about the longer-run structure of the U.S. economy.
With this consideration in mind, Figure 7 shows the medians, standard deviations, and the skewness of the distributions of longer-run forecasts. The most important feature of Figure 7 is that the narrative of a representative central banker is not grounded in facts. Indeed, the degree of disagreement among participants, measured by the standard deviation, shows no sustained tendency to decline to zero. Figure 7 also shows the swings in skewness in the distributions for the interest rate and GDP growth. These swings fit the views of Rülke and Tillmann (2011) who examine whether FOMC participants exhibit herd behavior.7 Third, the skewness for the distribution of the unemployment rate is positive (forecasts exceeding the mean) and has an upward trend, meaning that the excess of the ith participant’s forecast relative to the mean is increasing. This observation fits the findings of “extreme” forecasts as noted by Tillmann (2011) and Nakazono (2013). They argue that FOMC participants who are not voting during the meeting might submit “extreme” forecasts as a way of registering their disagreements. These extreme forecasts and herd behavior are two manifestations of the absence of a representative central banker.
Finally, Figure 7 raises the question of whether the trends in the median continue after 2016. To address this question, the section combines the information from the FOMC transcripts with the information from the SEP to assemble the time-series of the medians of the distributions of longer-run forecasts from 2012 to 2022.

3. Moments of FOMC Participants’ Forecast Distributions: 2012–2022

Figure 8 shows the evolution of these medians along with the upper and lower bounds of the associated distributions.8 The figure shows three features of interest.
First, the median for each variable shows a downward trend. Second, the range between the upper and lower bounds is not constant over time. Indeed, periods when the median is close to one of the bounds reflect instances of possible extreme forecasts, as noted earlier. Third, there is a statistically significant change in the FOMC’s view of the longer run. Specifically, the forecast distributions for unemployment and the appropriate interest rate in 2012 do not overlap with their own distributions in 2022. These observations are relevant for two reasons. First, because these longer-run forecasts are used as signposts to judge the pace of the adjustment of the balance sheet of the Federal Reserve, changes in such forecasts undermine judgments based on them. For example, Ferrara et al. (2018) assess the progress of the normalization of the Fed’s balance sheet by comparing the historical interest rate to the FOMC’s longer-run forecast of the interest rate. Thus, if the associated forecast is changing, then the role of the forecasts as signposts is undermined. Second, structural changes in longer-run forecasts are, effectively, reflecting perceived structural changes in the economy, which, arguably, are informative about the direction of monetary policy. However, one cannot judge independently the reliability of these long-run changes because they are not accompanied by a specific date.

3.1. Comparison to the FOMC’s Current-Year Forecasts

Another approach to assess the informational value of the longer-run forecasts is to compare them to the median of the FOMC’s current-year forecasts and to the recorded values for these macroeconomic variables (Figure 9). I find that the evolution of the longer-run forecasts seems invariant to changes in the current-year forecasts. Note that the current-year forecast is informative about movements in the recoded data for these variables.

3.2. Granger Causality

To study whether there is a direction of (Granger) causality among these forecasts, I implement Granger causality tests. To this end, I assume that the behavior of all these nine variables is adequately represented by a VAR of order one:
z t x t c x t x t r = A · z t 1 + Γ · C t + c o v i d   d u m m i e s + ε t ;   ε t N 0 , Φ
where
  • x t c = u t c   y t c   r t c   π t c
  • x t = u t   y t   r t
  • x t r = u t r   π t r  
  • C t = C B t   C Y t   C P t
  • C B t : Dummy variable equal to one for Bernanke’s tenure as FOMC Chair; zero otherwise
  • C Y t : Dummy variable equal to one for Yellen’s tenure as FOMC Chair; zero otherwise
  • C P t : Dummy variable equal to one for Powell’s tenure as FOMC Chair; zero otherwise
Covid Dummies: 2020:Q2, 2021:Q1–2021:Q4
  • t = 2012:Q1 … 2022:Q2
  • u t : median of the longer-run forecast for the unemployment rate for period t
  • r t : median of the longer-run forecast for the appropriate nominal interest rate for period t
  • y t : median of the longer-run forecast for the GDP growth rate for period t
  • u t c : median of the current-year forecast for the unemployment rate for period t
  • r t c : median of the current-year forecast for the appropriate nominal interest rate for period t
  • y t c : median of the current-year forecast for the GDP growth rate for period t
  • π t c : median of the current-year forecast for the inflation rate for period t
  • u t r : recorded data for the unemployment rate for period t
  • π t r : recorded data for the PCE inflation rate for period t
This model controls for the tenure of each of the three FOMC Chairs (the C′s) and for the disruptions associated with COVID-19. The model has 153 unrestricted parameters (excluding Φ);9 I use OLS for the parameter estimation with observations from 2012: Q1 to 2022: Q2 (369 observations for all nine equations). Note that I exclude longer-run forecasts for the inflation rate from the model because the FOMC has been setting the longer-run forecasts for inflation to a value of 2 over this sample.
I postulate several Granger causality hypotheses, all of which are described in Table 1;10 the table also reports the number of parameters that are set to zero (n) and the p-value for the statistic χ2(n) needed to reject the null hypothesis.
The results reveal several features of interest. First, lines 2 and 4 suggest that movements in the FOMC’s forecasts (current year and longer-term) are informative in explaining movements in recorded inflation and unemployment. Second, lines 1 and 5 suggest that neither current-year forecasts nor the realized values of inflation and unemployment are informative in accounting for movements in longer-run forecasts. Third, line 3 suggests that movements in longer-run forecasts account for movements in current-year forecasts.
Taken as a group, the results suggest that movements in the longer-run forecasts help explain (i.e., Granger cause) movements in both the current-year forecasts and in the recorded values of inflation and unemployment but not the other way around; this finding is consistent with Bernanke’s interpretation of the longer-run forecasts as parameters and with Powell’s interpretation of longer-run forecasts as navigational “fixed” stars.

3.3. Replication of FOMC Longer-Run Forecasts

By design, longer-run forecasts from the FOMC cannot be evaluated by examining their forecast errors. Unlike the short-term forecasts, longer-term forecasts are not predictions for a given date but, instead, depict a situation of macroeconomic equilibrium that might be reached at an unspecified date that, in turn, could be extended from one FOMC meeting to the next. Thus, assessing the usefulness of longer-run forecasts calls for a different criterion. I argue that the replicability of these forecasts is a necessary condition for their usefulness, independently of their accuracy.
To that end, I use Equation (2) to study whether the FOMC’s longer-run forecast can be replicated. This equation offers two approaches to replicate the longer-run forecasts. The first approach relies on generating dynamic simulations from 2022: Q3 to 2040: Q3 and using the prediction for 2040: Q3 as the numerical estimate of the longer-run forecast. The second approach relies on the analytical solution to the steady state of the equation as (I−A)−1⋅Γ⋅ℂ. To be sure, these two approaches are intimately related, but the numerical simulation provides information on the profile of the convergence path along with the lapse of time needed to reach the steady state. The analytical approach provides estimates of the longer-run forecasts for each of the FOMC Chairs.
Figure 10 reports the 95 percent confidence intervals for the forecasts for all nine variables.11 The model’s s-step ahead simulations exhibit dampening oscillations owing to the negative roots of (I − A)−1; these oscillations vanish by 2040. Comparing these simulations to the FOMC’s own longer-run projections (vertical red bars) shows that the model underpredicts the appropriate interest rate; this limitation needs to be considered when judging the usefulness of the results.
Table 2 reports the analytical and numerical estimates of the FOMC’s longer-run forecasts along with the FOMC’s own estimates as of both September and December of 2022. The results indicate that the two approaches pursued here are close, numerically and statistically, to the FOMC’s longer-run forecasts from both the September 2022 and December 2022 FOMC meetings. Specifically, I cannot reject the null hypothesis that the FOMC values and the ones generated here are equal.

4. Conclusions

This paper offers the first statistical analysis of the stylized facts for the longer-run forecasts provided by the Federal Open Market Committee (FOMC). These forecasts are relevant because, as Bernanke notes, they “may be interpreted as estimates of the economy’s longer-run potential growth rate and the longer-run normal rate of unemployment”. But the literature, as far as I know, has not examined the informational value of these forecasts, which is what I have done here. I find that the distributions of longer-run forecasts reveal a lack of consensus about the long structure of the U.S. economy among FOMC participants; the results also suggest that this lack of consensus reflects the absence of a shared forecasting framework guiding the participants’ forecasts.
These findings carry two implications. First, reliance on a narrative based on the representative central banker for the United States is incomplete at best because it is not grounded in facts. Second, assessing the usefulness of longer-run forecasts calls for a different criterion based on their replicability. To be sure, I was not able to replicate the FOMC’s longer-run forecast of 50 basis points.
These findings, however, are based on assumptions that need to be relaxed in the future. For example, the sample period is brief, and it needs to be extended to assess the reliability of the statistical tests of stationarity and the statistical quality of the specification of the VAR model. In addition, I invoked the “extreme forecasts” and “herd behavior” hypotheses from the literature to argue the advantages of analyses based on the median of the forecast distributions. A profitable approach in future research would be to assess these two hypotheses in greater detail. Doing so is likely to alter the details of the findings reported here but, at the same time, emphasize the need for additional work on assessing the usefulness of FOMC longer-run forecasts as part of the FOMC’s communication strategy to the private sector.

Funding

This research received no external funding.

Data Availability Statement

Data used here are available from public sources. For the individual participants forecasts, see https://www.federalreserve.gov/monetarypolicy/fomc_historical.htm For the Summary of Economic Projections, see https://www.federalreserve.gov/newsevents/pressreleases.htm; the data for GDP growth are available at Bureau of Economic Analysis of the U.S. Department of Commerce, All of these sites were accessed on 23 February 2023.

Acknowledgments

All the calculations in this paper are carried out with PcGive and Oxmetrics 8.03; see (Hendry and Doornik 1999; Doornik and Hendry 2018). I also want to express my gratitude to two anonymous referees for their suggestions.

Conflicts of Interest

The author declares no conflict of interest.

Appendix A

Appendix A.1. Time-Series Properties of Longer-Term Forecasts

As noted earlier, the median of the longer-run forecast for the three variables steadily declines over time from 2012 to 2022 and raises the question of whether the medians are non-stationary. To examine whether the median of the moments is stationary, Figure A1 shows the autocorrelation coefficients for the longer-run forecasts; I include the autocorrelation coefficient for the recorded data and the current-year forecasts to serve as reference points.
Figure A1. Autocorrelation coefficients for record data (left column), current-year forecasts (middle column), longer-run forecasts (right column).
Figure A1. Autocorrelation coefficients for record data (left column), current-year forecasts (middle column), longer-run forecasts (right column).
Jrfm 16 00152 g0a1
An inspection of the results reveals that the longer-term forecasts exhibit pronounced persistence, lasting for about ten quarters (right column). Further, there is a strong similarity between the autocorrelations for the recorded data (left column) and the autocorrelations for the current-year forecasts (middle column); the exception is for the unemployment rate.
To test whether these series are integrated of order one, I apply an augmented Dickey–Fuller (ADF) test using eight lags:
Δ w t = θ + μ w t 1 + j = 1 8 η j Δ w t j
where w is the variable of interest; the null hypothesis is that w is integrated of order one—that is, H0: μ = 0; Figure A2 shows the associated ADF test statistics and the rejection values.
Figure A2. Augmented Dickey–Fuller tests for current-year and longer-run forecasts of the FOMC. Dashed green lines are the critical values for rejecting the null hypothesis.
Figure A2. Augmented Dickey–Fuller tests for current-year and longer-run forecasts of the FOMC. Dashed green lines are the critical values for rejecting the null hypothesis.
Jrfm 16 00152 g0a2
Based on the results, I cannot reject the hypothesis of non-stationarity for either the longer-run forecasts or the current-year forecasts, except for GDP growth.

Appendix A.2. Model Reliability

The reliability of the model depends on its explanatory power, the properties of the residuals, dynamic stability, and parameter constancy.

Appendix A.2.1. Model Reliability: Explanatory Power

I find that the correlation between the actual and fitted values is sufficiently high to view the model as having enough explanatory power to be of interest (Table A1): the lowest correlation coefficient is 0.980.
Table A1. Correlation Between Fitted and Actual Values: Sensitivity to Covid Dummies.
Table A1. Correlation Between Fitted and Actual Values: Sensitivity to Covid Dummies.
Equation for→ π t c u t c r t r y t r u t r t y t π t r u t r
With Dummies0.990.990.980.990.990.990.980.980.99
No Dummies0.960.90.940.720.990.990.980.970.86
To make sure that these correlations are not an artifact of using Covid dummies, I also report the correlation coefficients between actual and fitted when the model excludes these dummy variables. For most cases, the exclusion of these dummies induces a marginal decline in these correlations. The reduction is, however, noticeable for the current-year forecast of GDP growth and the recorded unemployment rate.

Appendix A.2.2. Model Reliability: Properties of Residuals

Figure A3 shows the autocorrelation coefficients for the residuals. Generally, these autocorrelations are below 0.5 (absolute value), suggesting the absence of serial correlation of residuals.
Figure A3. Autocorrelation coefficients for regression residuals.
Figure A3. Autocorrelation coefficients for regression residuals.
Jrfm 16 00152 g0a3
To examine the hypothesis of whether the variance of the residuals is constant, Figure A4 shows the autocorrelation of the squared residuals. Generally, these autocorrelations are small, suggesting that the variance of the residuals is not changing over time.
Figure A4. Autocorrelation of residuals squared.
Figure A4. Autocorrelation of residuals squared.
Jrfm 16 00152 g0a4
To assess the extent to which the empirical distributions of the residuals are normal, Figure A5 shows the empirical distribution of the scaled residuals and compares them to the N(0,1) distribution. Apart from the distributions for the current-year forecasts for inflation and the appropriate interest rate, the results suggest that deviations from normality are small.
Figure A5. Empirical distribution of residuals—histograms, density, and density of N(0,1).
Figure A5. Empirical distribution of residuals—histograms, density, and density of N(0,1).
Jrfm 16 00152 g0a5
When taken together, the results suggest that the residuals are consistent with the maintained assumptions for parameter estimation.

Appendix A.2.3. Model Reliability: Dynamic Stability

To study the dynamic stability of the model, I use impulse responses with three types of shocks:
  • Revisions to the current-year interest rate forecast.
An upward revision of the current-year forecast for the federal funds rate of one percentage point lowers the recorded inflation rate by nearly the same percentage and raises the unemployment rate by 20 basis points. These responses exhibit cycles that dampen over time with the variables returning to their equilibrium after 10 years (Figure A6).
2.
Revisions to the longer-run interest rate forecast.
A one percentage point upward revision of the longer-run forecast for the appropriate interest rate lowers the recorded inflation rate by more than one percentage point and raises the recorded unemployment rate by 75 basis points; these responses exhibit cycles that dampen over time with the variables returning to their equilibrium after 10 years (Figure A6).
3.
Exogenous shocks to the recorded values of inflation and unemployment.
An increase of one percentage point of the recorded inflation rate raises the current-year forecast of the federal funds rate by 40 basis points (Figure A7); the corresponding effect on the longer-run forecast for that rate is negligible, as one might expect from the Granger causality test results.
An increase of one percentage point of the recorded unemployment rate lowers, after ten quarters, the current-year forecast for the federal funds rate by 15 basis points; the corresponding effect on the longer-run forecast for that rate is negligible. The negligible effects on the longer-run forecasts is what one should expect from the Granger causality tests reported above, showing that the longer-run forecasts are not Granger caused by the other variables.
Figure A6. Response of Recorded Inflation and Unemployment rates to changes in the current-year and longer-run forecasts of interest rates.
Figure A6. Response of Recorded Inflation and Unemployment rates to changes in the current-year and longer-run forecasts of interest rates.
Jrfm 16 00152 g0a6
Figure A7. Response of current-year and longer-run forecasts of interest rates to a one percentage point increase in Recorded Inflation and Unemployment rates.
Figure A7. Response of current-year and longer-run forecasts of interest rates to a one percentage point increase in Recorded Inflation and Unemployment rates.
Jrfm 16 00152 g0a7

Appendix A.2.4. Model Reliability: Parameter Constancy

To test whether changes in the estimation sample period affect the longer-run forecasts, I combine recursive least squares with s-step ahead predictions. This procedure begins with an initial sample used to estimate the parameters and then, using the last date of that first subsample as the initial condition, I generate the s-step simulations. Then the procedure augments the estimation sample by one observation, re-estimates the parameters, updates the initial condition, and re-generates another s-step prediction. This process is repeated until all the observations are used. Figure A8 shows the results on the long-run estimates from changing both the parameter estimates and the initial conditions for the ex-ante simulations.
Figure A8. Sensitivity of simulations to estimation sample and starting value. Green dashed line represents the path based on the full estimation sample and 2022: Q2 as the initial condition for simulation. Vertical red segments represent the range of the FOMC longer-run forecasts. Each blue line represent the s-step ahead prediction associated with each starting date.
Figure A8. Sensitivity of simulations to estimation sample and starting value. Green dashed line represents the path based on the full estimation sample and 2022: Q2 as the initial condition for simulation. Vertical red segments represent the range of the FOMC longer-run forecasts. Each blue line represent the s-step ahead prediction associated with each starting date.
Jrfm 16 00152 g0a8
The figure shows that estimating parameters using a sample ending in the middle of the Covid-19 crisis and then using those sample dates as initial conditions for model extrapolations results initially in large departures for all the variables except the current-year forecast for GDP growth. As the estimation sample period is augmented and the initial conditions are updated, however, subsequent predictions cluster together in their convergence to a narrow range of values by 2029 which are quite close to the longer-run forecasts from the FOMC.

Notes

1
“‘Appropriate monetary policy’ is defined as the future path of policy that each participant deems most likely to foster outcomes for economic activity and inflation that best satisfy his or her individual interpretation of the statutory mandate to promote maximum employment and price stability”. See https://www.federalreserve.gov/newsevents/pressreleases/monetary20221214b.htm (accessed on 22 February 2023).
2
The FOMC consists of 19 participants: 12 presidents from the Federal Reserve Banks and 7 Governors from the Board of Governors of the Federal Reserve System. Only 12 participants vote in a given FOMC meeting; the voting participants are the seven governors of the Federal Reserve Board, the President of the New York Federal Reserve Bank, and four other reserve bank presidents on a rotating basis. The federalist structure consists of the Regional Federal Reserve Banks, who look out for the interests of the private sector, and the Federal Reserve Board who looks out for the interest of the whole country. For additional details, see https://www.federalreserve.gov/monetarypolicy/fomc.htm (accessed on 23 February 2023).
3
4
Specifically, “Longer-run projections represent each participant’s assessment of the rate to which each variable would be expected to converge under appropriate monetary policy and in the absence of further shocks to the economy.” Emphasis added. https://www.federalreserve.gov/monetarypolicy/files/fomcprojtabl20211215.pdf (accessed on 23 February 2023).
5
These long-run objectives were ratified at the FOMC meeting of January 2023; for details see https://www.federalreserve.gov/monetarypolicy/files/FOMC_LongerRunGoals.pdf (accessed on 23 February 2023).
6
Faust (2016) argues that the SEP is not suited as a communication tool for FOMC forecasts. Specifically,
“The SEP [Summary of Economic Projections], in my view, deserves a special place in the annals of obfuscation in the service of transparency. The SEP is purely a depiction of the policymakers’ different views on the outlook and appropriate policy, with no hints about how any differences may be resolved.”
7
To be sure, further work is needed before classifying the FOMC as exhibiting herd behavior. Specifically, drawing inferences about collective behavior based on a small group is tricky: members may become aware of their tendency to have herding behavior and thus alter it before it becomes observable. In addition, herds lack a final known destination whereas FOMC participants generate their forecasts based on policies to attain the FOMC’s dual mandate.
8
Powell (2018, 2019) offers a comparable comparison and includes longer-term forecasts from other institutions. Powell does not report the bounds of the distribution and, further, it is not clear (to me at least) which measure of the longer-run forecast he is reporting.
9
A has 81 parameters; the Covid Dummies have 45 parameters (five dummies for each equation), and the FOMC Chairs (Bernanke, Yellen, Powell) carry 27 parameters.
10
The Appendix A reports the results regarding the reliability of this model. I find that the correlation between the actual and fitted values is sufficiently high to view the model as having enough explanatory power to be informative about the questions raised in this paper; that the residuals are consistent with the maintained assumptions for parameter estimation (serial independence, homoskedasticity, and normality); that, based on impulse responses, the model is dynamically stable; that estimating the model with data through the Covid quarters and using those quarters as initial conditions for simulation yields several paths that converge to a value somewhat different from the FOMC’s longer-run forecasts.
11
The simulations allow for two sources of uncertainty: model specification and parameter estimation.

References

  1. Bernanke, Ben. 2016. Federal Reserve Economic Projections: What Are They Good for? Brookings. Available online: https://www.brookings.edu/blog/ben-bernanke/2016/11/28/federal-reserve-economic-projections/ (accessed on 23 February 2023).
  2. Cecchetti, Stephen, and Kermit Schoenholtz. 2019. Improving U.S. Monetary Policy Communications. Available online: https://www.federalreserve.gov/conferences/conference-monetary-policy-strategy-tools-communications-20190605.htm (accessed on 23 February 2023).
  3. Clarida, Richard. 2019. Models, Markets, and Monetary Policy. Paper presented at the Conference on “Strategies for Monetary Policy,” a Hoover Institution Monetary Policy Conference, Stanford University, Stanford, CA, USA, May 3. [Google Scholar]
  4. Doornik, Jurgen A., and David F. Hendry. 2018. Empirical Econometric Modeling. 3 vols. London: Timberlake Consultants Press. [Google Scholar]
  5. Faust, Jon. 2016. Oh What Tangled Web we Weave: Monetary Policy Transparency in Divisive Times. Hutchison Center Working Paper #25. Available online: https://www.brookings.edu/wp-content/uploads/2016/11/wp25_faust_monetarypolicytransparency_final1.pdf (accessed on 23 February 2023).
  6. Ferrara, Laurent, Ignacio Hernando, and Daniela Marconi. 2018. International Macroeconomics in the Wake of the Global Financial Crisis. Financial and Monetary Policy Studies vol. 46. Berlin/Heidelberg: Springer. Available online: https://www.bde.es/f/webpi/SES/staff/hernandocastelletignacio/files/10.1007_978-3-319-79075-6.pdf (accessed on 23 February 2023).
  7. Hendry, David F., and Jurgen Doornik. 1999. Empirical Econometric Modelling Using PcGive. London: Timberlake. [Google Scholar]
  8. Kalfa, S. Yanki, and Jaime Marquez. 2019. FOMC Forecasts: Are They Useful for Understanding Monetary Policy? Journal of Risk and Financial Management 12: 133. [Google Scholar] [CrossRef] [Green Version]
  9. Kalfa, S. Yanki, and Jaime Marquez. 2021. Forecasting FOMC Forecasts. Econometrics 9: 34. [Google Scholar] [CrossRef]
  10. Marquez, Jaime, and S. Yanki Kalfa. 2021. The Forecasts of Individual FOMC Members: New Evidence after Ten Years. H.O. Stekler Research Program on Forecasting, Working Paper No. 2021-003. Washington, DC: The George Washington University, Department of Economics. [Google Scholar]
  11. Nakazono, Yoshiyuki. 2013. Strategic Behavior of Federal Open Market Committee Board Members: Evidence from Member’s Forecasts. Journal of Economic Behavior & Organization 93: 62–70. [Google Scholar]
  12. Powell, Jerome. 2018. Monetary Policy in a Changing Economy. Board of Governors of the Federal Reserve System, Remarks at the Jackson Hole Meetings, August 24. Available online: https://www.federalreserve.gov/newsevents/speech/files/powell20180824a.pdf (accessed on 23 February 2023).
  13. Powell, Jerome. 2019. Challenges for Monetary Policy. Board of Governors of the Federal Reserve System, Remarks at the Jackson Hole Meetings, August 23. Available online: https://www.federalreserve.gov/newsevents/speech/powell20190823a.htm (accessed on 23 February 2023).
  14. Romer, David. 2010. A New Data Set on Monetary Policy: The Economic Forecasts of Individual Members of the FOMC. Journal of Money, Credit, and Banking 42: 951–57. [Google Scholar] [CrossRef] [Green Version]
  15. Rülke, Jan-Christoph, and Peter Tillmann. 2011. Do FOMC Members Herd? Economic Letters 11: 176–79. [Google Scholar] [CrossRef]
  16. Shen, Simon. 2015. Evaluating the Economic Forecasts of FOMC Members. International of Forecasting 31: 165–75. [Google Scholar] [CrossRef]
  17. Tillmann, Peter. 2011. Strategic Forecasting of the FOMC. European Journal of Political Economy 27: 547–53. [Google Scholar] [CrossRef] [Green Version]
Figure 1. Marginal densities for the FOMC’s longer-run forecast for the Appropriate Interest Rate—December 2012 and December 2016.
Figure 1. Marginal densities for the FOMC’s longer-run forecast for the Appropriate Interest Rate—December 2012 and December 2016.
Jrfm 16 00152 g001
Figure 2. Marginal densities for the FOMC’s longer-run forecast for the Appropriate Interest Rate—January 2012–December 2016. Panels with vertical lines correspond to three moments of the distributions: median, standard deviation, skewness.
Figure 2. Marginal densities for the FOMC’s longer-run forecast for the Appropriate Interest Rate—January 2012–December 2016. Panels with vertical lines correspond to three moments of the distributions: median, standard deviation, skewness.
Jrfm 16 00152 g002
Figure 3. Marginal densities for the FOMC’s longer-run forecast for GDP Growth—January 2012–December 2016. Panels with vertical lines correspond to three moments of the distributions: median, standard deviation, skewness.
Figure 3. Marginal densities for the FOMC’s longer-run forecast for GDP Growth—January 2012–December 2016. Panels with vertical lines correspond to three moments of the distributions: median, standard deviation, skewness.
Jrfm 16 00152 g003
Figure 4. Marginal densities for the FOMC’s longer-run forecast of the Unemployment Rate—January 2012–December 2016. Panels with vertical lines correspond to three moments of the distributions: median, standard deviation, skewness.
Figure 4. Marginal densities for the FOMC’s longer-run forecast of the Unemployment Rate—January 2012–December 2016. Panels with vertical lines correspond to three moments of the distributions: median, standard deviation, skewness.
Jrfm 16 00152 g004
Figure 5. Unconditional correlations among longer-run FOMC forecasts for the Interest Rate (R), the Unemployment Rate (U), and GDP Growth (Y)—January 2012–December 2016.
Figure 5. Unconditional correlations among longer-run FOMC forecasts for the Interest Rate (R), the Unemployment Rate (U), and GDP Growth (Y)—January 2012–December 2016.
Jrfm 16 00152 g005
Figure 6. Correlations of residuals based on Romer model for longer-run FOMC forecasts for the Interest Rate (VR), Unemployment (VU), and GDP Growth (VY)—January 2012–December 2016.
Figure 6. Correlations of residuals based on Romer model for longer-run FOMC forecasts for the Interest Rate (VR), Unemployment (VU), and GDP Growth (VY)—January 2012–December 2016.
Jrfm 16 00152 g006
Figure 7. Medians (top row), standard deviations (middle), and skewness of marginal densities for forecasts of the longer Interest rate (left), GDP Growth (center), and Unemployment rate (right)—January 2012–December 2016.
Figure 7. Medians (top row), standard deviations (middle), and skewness of marginal densities for forecasts of the longer Interest rate (left), GDP Growth (center), and Unemployment rate (right)—January 2012–December 2016.
Jrfm 16 00152 g007
Figure 8. Evolution of the distributions of the FOMC’s longer-run forecasts. Solid lines in each panel are the bounds of the distribution of the associated variable; the dashed lines are the median of the respective distributions.
Figure 8. Evolution of the distributions of the FOMC’s longer-run forecasts. Solid lines in each panel are the bounds of the distribution of the associated variable; the dashed lines are the median of the respective distributions.
Jrfm 16 00152 g008
Figure 9. Median of longer-run forecasts, current year forecasts, and actual data. Red lines are the median of the distributions of the FOMC’s current-year forecasts; the blue lines represent the median of the distributions of the FOMC’s longer-run forecasts; the black short-dashed line represents the evolution of the recorded values; the black long-dashed line represents the FOMC’s longer-run forecast of the inflation rate.
Figure 9. Median of longer-run forecasts, current year forecasts, and actual data. Red lines are the median of the distributions of the FOMC’s current-year forecasts; the blue lines represent the median of the distributions of the FOMC’s longer-run forecasts; the black short-dashed line represents the evolution of the recorded values; the black long-dashed line represents the FOMC’s longer-run forecast of the inflation rate.
Jrfm 16 00152 g009
Figure 10. 95% confidence band for dynamic simulations of VAR, Equation (2): 2022: Q3 to 2040: Q4. Vertical red segments represent the range of the FOMC longer-run forecasts for September 2022. The shaded bands are the fan charts accounting for 95 percent probability.
Figure 10. 95% confidence band for dynamic simulations of VAR, Equation (2): 2022: Q3 to 2040: Q4. Vertical red segments represent the range of the FOMC longer-run forecasts for September 2022. The shaded bands are the fan charts accounting for 95 percent probability.
Jrfm 16 00152 g010
Table 1. Granger Causality Tests: 2012:1-2022:2.
Table 1. Granger Causality Tests: 2012:1-2022:2.
H0np-ValueDescription of H0
1 x t c x t 120.385current-year forecasts do not Granger-cause longer-run forecasts
2 x t c x t r 80.093current-year forecasts do not Granger-cause GDP growth and unemployment
3 x t x t c 120longer-term forecasts do not Granger-cause current-year forecasts
4 x t x t r 60.108longer-term forecasts do not Granger-cause GDP growth and unemployment
5 x t r x t 60.249GDP growth and unemployment do not Granger-cause longer-run forecasts
6 x t r x t c 80GDP growth and unemployment do not Granger-cause current-year forecasts
Table 2. Estimates of Longer-run Forecasts: Alternative Methods.
Table 2. Estimates of Longer-run Forecasts: Alternative Methods.
AnalyticalNumerical *FOMC
BernankeYellenPowell2040Sep. 2022Dec. 2022
(Range)(Range)
u 5.014.133.733.7344
se0.540.820.650.66(3.5–4.5)(3.5–4.8)
r 3.392.281.921.922.52.5
se0.71.070.850.88(2.3–3.0)(2.3–3.3)
y 2.181.751.761.761.81.8
se0.170.260.20.23(1.6–2.2)(1.6–2.5)
* The simulations allow for two sources of uncertainty: model and parameter estimation.
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Share and Cite

MDPI and ACS Style

Marquez, J. Stylized Facts of the FOMC’s Longer-Run Forecasts. J. Risk Financial Manag. 2023, 16, 152. https://0-doi-org.brum.beds.ac.uk/10.3390/jrfm16030152

AMA Style

Marquez J. Stylized Facts of the FOMC’s Longer-Run Forecasts. Journal of Risk and Financial Management. 2023; 16(3):152. https://0-doi-org.brum.beds.ac.uk/10.3390/jrfm16030152

Chicago/Turabian Style

Marquez, Jaime. 2023. "Stylized Facts of the FOMC’s Longer-Run Forecasts" Journal of Risk and Financial Management 16, no. 3: 152. https://0-doi-org.brum.beds.ac.uk/10.3390/jrfm16030152

Article Metrics

Back to TopTop