2. Model

In a framework with monopolistic competition, menu costs, and staggered price-setting, Rotemberg (Reference Rotemberg1982) and Calvo (Reference Calvo1983) derive the New Keynesian Phillips curve:

(1) \begin{equation} \pi _t=\beta \hat E_t\pi _{t+1}+\kappa x_t+u_t \end{equation}

which relates present inflation $\pi _t$ to expected next-period inflation $\hat E_t\pi _{t+1}$ , contemporaneous output $x_t$ , and a cost-push shock $u_t$ . It is private-sector price-setters’ inflation expectations that are relevant in the Phillips curve, and these may or may not be rational, depending on the case below, so we denote these as $\hat E_t$ to distinguish from $E_t$ , which is usually understood to imply rational expectations. The exogenous shock is assumed to be known to satisfy

(2) \begin{equation} u_t=\rho u_{t-1}+ a_t \end{equation}

where $a_t$ is white noise. The parameters $\beta \in \left ( 0,1\right ), \kappa \gt 0$ , and $\rho \in (0,1)$ are assumed to be known constants. Inflation $\pi _t$ and output $x_t$ are measured in terms of deviations from their flexible-price values, that is, the values they would attain in the absence of nominal rigidities. Hence, as Rotemberg and Woodford (Reference Rotemberg and Woodford1999) and Woodford (Reference Woodford2003) show, minimizing the distortions due to nominal rigidities, reflected by their impact on the utility of a representative consumer, can be accomplished at any time $t=0$ by minimizing

(3) \begin{equation} L_0= E_0\sum _{t=0}^{\infty }\beta ^t l_t \end{equation}

where

(4) \begin{equation} \ l_t = \pi _t^2+\lambda x_t^2 \end{equation}

and $\lambda \gt 0$ is a known constant. Details, and extensions, of this popular framework are discussed by Clarida et al. (Reference Clarida, Gali and Gertler1999), Svensson and Woodford (Reference Svensson and Woodford2002), and Woodford (Reference Woodford2003), among others.

There are several reasons why the public’s expectations might not be rational. It could be that they do not know all the details of the model, are not savvy enough to solve it, or that it is just not worth their time and effort to stay on top of it [rational inattention, see Sims (Reference Sims2003)]. This could easily drive them to be guided by policymakers’ projections, especially if they do not know the exact policy objective (3), or if policymakers are otherwise thought to have any advantage, such as advance or private information about macroeconomic fundamentals. While the underlying reason for why the public might let itself be guided by the projections could affect their behavior, and thus the optimal policy and projections, and even the model itself [see e.g Mackowiak and Wiederholt (Reference Mackowiak and Wiederholt2009)], the present study aims at obtaining general results. It is important to emphasize that at a minimum, these require assuming that the model described above is invariant to the underlying rationale for the public’s expectations not being rational. When this is the case, the underlying motivation is irrelevant when policymakers’ projections are assumed to be believed blindly, as long as this remains true over time. However, the optimal policies and projections with imperfect credibility would still be sensitive to these underlying aspects, so we cannot obtain explicit generic solutions for this case.

From the perspective of any period $t=0$ , the optimal commitment plan is the infinite sequence of current and future inflation $\{\pi _t\}_{t=0}^\infty$ that minimizes the loss function (3) subject to the Phillips curve (1). As shown by Clarida et al. (Reference Clarida, Gali and Gertler1999) and Woodford (Reference Woodford1999), the optimal commitment policy assuming rational expectations is (see Section A.1)

(5) \begin{equation} \pi _0=-\frac{\lambda }{\kappa }x_0 \end{equation}

and

(6) \begin{equation} \pi _t=-\frac{\lambda }{\kappa }x_t+\frac{\lambda }{\kappa }x_{t-1} \end{equation}

for $t=1, 2, 3, \dots$ While this optimal plan minimizes the objective function (3), it is, as argued by Kydland and Prescott (Reference Kydland and Prescott1977), not time-consistent. The reason is that if policymakers reoptimized in any later period $\tau \gt 0$ , they would want to deviate from the promised commitment rule (6) in period $\tau$ and instead enforce

(7) \begin{equation} \pi _\tau =-\frac{\lambda }{\kappa }x_\tau \end{equation}

while committing to implement

(8) \begin{equation} \pi _t=-\frac{\lambda }{\kappa }x_t+\frac{\lambda }{\kappa }x_{t-1} \end{equation}

in all later periods $t=\tau +1, \tau +2, \tau +3, \dots$ If policymakers reoptimized every period, they would implement

(9) \begin{equation} \pi _t=-\frac{\lambda }{\kappa }x_t \end{equation}

in all periods $t=0, 1, 2, \dots$ , making it the optimal discretionary policy. The policy objective (3) is strictly positive under both optimal commitment and discretion. Exactly how much lower it is with commitment depends on the parameters, which there is some disagreement about, particularly with respect to $\kappa$ and $\lambda$ [see Assenmacher-Wesche (Reference Assenmacher-Wesche2006), Dennis (Reference Dennis2004), Givens (Reference Givens2012), Schorfheide (Reference Schorfheide2008), and Söderström et al. (Reference Söderström, Söderlind and Vredin2005)].

3. Optimal misleading projections

This section determines the optimal strategy for policymakers when their projections are fully believed and thus shape public expectations perfectly, even if inconsistent with the policy they actually implement.

Result 1. When policymakers’ projections $\hat \pi _{t+1}$ are believed, so that the public’s policy expectations $\hat E_t \pi _{t+1}$ match these exactly, irrespectively of any deviations with implemented policy and realized outcomes, the optimal policy is to implement

(10) \begin{equation} \pi _t = 0 \end{equation}

in all periods $t=0, 1, 2, \dots$ , while projecting future inflation according to

(11) \begin{equation} \hat \pi _t = -\beta ^{-1} \rho ^{-1}u_t \end{equation}

for $t=1, 2, 3, \dots$ , thus making the optimal projections misleading. The corresponding value of the policy objective ( 3 ) is $L_0=0$ . (Proof in Section A.2 ).

Hence, if policymakers can mislead the public, shaping inflation expectations with projections that are inconsistent with the implemented policy, they can achieve their objectives (3) to a greater extent than with a credible commitment to the optimal plan (5)–(6). For comparison, imagine that in any period $t=0$ policymakers could mislead the public into believing the policy rule

(12) \begin{equation} \pi _t = -\beta ^{-1} \rho ^{-1}u_t \end{equation}

would be implemented in periods $t=1, 2, 3,\dots$ , so that the public’s expectations $\hat E_t \pi _{t+1} =E_t \hat \pi _{t+1} = -\beta ^{-1} u_t$ , while actually implementing equation (10) in all periods $t=0, 1, 2, \dots$ Policymakers would then do better, in terms of the policy objective (3), than with standard commitment (5)–(6). How is this possible? While time-inconsistent, at any point in time the standard commitment solution assumes expectations of future policy are consistent with what policymakers actually plan to implement, and vice versa. This internal consistency is violated in the alternative commitment strategy proposed at the beginning of the present paragraph. In other words, standard commitment is only misleading if policymakers reoptimize and therefore deviate from the original optimal plan. The alternative strategy is misleading even without reoptimization.

If the shock $u_t$ and inflation $\pi _t$ were perfectly observable, it would be obvious that projections generated with equation (11) are inconsistent with the implemented policy (10) whenever $u_t \neq 0$ , and policymakers’ projections would lose credibility. Moreover, if the public could observe the implemented policy (10), deduce it by studying past realizations, or derive it by reproducing the policy problem and policymakers’ logic, the public’s inflation expectations would instead be determined by the implemented policy. In reality, however, there are several factors that can make it difficult for the public to determine whether policymakers’ projections are consistent with the implemented policy. The most obvious is the uncertainty tied to forecasts, and in particular, the difficulty in accurately predicting macroeconomic variables even just a few quarters ahead. In addition, there is model uncertainty and misspecification, unknown parameter values, and the fact that different committee members voting on policy might favor different models, or may be acting strategically.Footnote ⁴ Also, central banks might not be able to achieve exactly the inflation rate they desire, contrary to what is assumed in our model. Because of these difficulties, policymakers could easily get away with manipulating their projections, and due to the potential gains, they have incentives to do so. This, however, means that the public should not trust policymakers’ projections, which renders these all but useless.Footnote ⁵

4. Optimal time-inconsistent projections

Next, we assume that policymakers’ projections must be consistent with both current policy and the one that policymaker’s plan to implement in the future. We assume policymakers’ projections are fully credible and shape public expectations perfectly despite the fact that optimal plans are time-inconsistent.

Assuming perfect credibility, policymakers can influence expectations exactly the same through projections as by committing to a rule and thus yield the same optimal commitment solution. However, both approaches suffer from time inconsistency. The optimal policy to implement in the contemporary period is discretion (9), while the optimal policy to promise to implement in the future, or more generally, to shape policy expectations, is the commitment rule (6). The reason is that $\pi _{\tau +1}$ has an impact on $\pi _\tau$ and $y_\tau$ through expectations $\hat E_\tau \pi _{\tau +1}$ in period $\tau$ and prior, but no such impact in period $\tau +1$ when $\pi _\tau, y_\tau$ and $\hat E_\tau \pi _{\tau +1}$ have already been realized. Thus, from the perspective of any period before $\tau +1$ , the commitment rule (6) is optimal for period $\tau +1$ , but from the perspective of period $\tau +1$ , discretion (9) is optimal for period $\tau +1$ . Hence, from today’s perspective (3), it is optimal for policymakers to implement the commitment rule (6) in all future periods and thus to use it to project ahead and shape expectations about future variables. But when policymakers reconsider at any later time, they would want to implement the optimal discretionary policy (9) in the contemporary period, thus deviating from past projections that assumed the commitment rule (6) would be implemented.Footnote ⁶ Hence, the optimal projections are time-inconsistent for the same reason that the optimal plan is. If the cost to policymakers of deviating from the previously projected path is high enough, for example due to the loss of credibility, or prestige, the projections can serve as a commitment device. However, the same would be true if there were a cost to deviating from a preannounced rule.

From a theoretical point of view, maintaining the public’s trust requires the same whether their expectations are influenced through a commitment to a rule or projections: that the they be able to verify that the optimal commitment rule (6) is actually being implemented, or at least, that they do not observe evidence to the contrary. However, in practice it can be more difficult to check if a preannounced rule is followed, versus determining whether realized outcomes and past and present projected values are mutually consistent, that is, based on the same policy equation. This is especially true when policymakers do not provide details about how their projections are generated, or the underlying model. As long as past realizations of economic variables are observable, it is fairly trivial to plug realizations of $\pi _t, x_t$ , and $x_{t-1}$ into a preannounced rule (6) to verify whether or not the commitment to implement it has been honored. Projections, on the other hand, do not require any public commitment to a particular policy equation, and without knowing the underlying model or implemented policy, it is difficult to determine if previously projected values are mutually consistent with the realized ones. Realized values of $\pi _t$ and $x_t$ depend on the contemporaneous shocks $u_t$ , which projections cannot forecast perfectly (due to the white noise shock $a_t$ ). Hence, projections are almost always going to be off the mark, and even large deviations do not necessarily imply, or prove, manipulation, as they could be caused by large unanticipated shocks. Instead, without additional information, the only way to verify manipulation may be if projection errors are not white noise. This, however, does not necessarily imply manipulation if the underlying model, or future policy, is also unknown to policymakers, who may then be making systematic mistakes in their honest projections.

With manipulation, and deviations from commitment, being more difficult to detect with projections than with an explicit commitment to a rule, policymakers might prefer projections, so as to reap the gains from such deviations. But this also means that it may be harder to establish and maintain credibility with projections, which is required in order to reap the gains from commitment. From this point of view, the two strategies, committing to a rule and providing projections, can complement each other. The preannounced rule provides an easy way to verify that the commitment is being implemented, strengthening also the credibility of projections by providing the public with information that can be used to contrast these against realized values. At the same time, projections tell people exactly what their expectations of future values should be, instead of relying on them to compute these. However, projections can also weaken the credibility of commitments, for example, to an inflation target when policymakers themselves project to miss said target.

5. Projections with imperfect credibility

The present section abandons the extreme assumptions of projections perfectly dictating private-sector expectations or having absolutely no impact on these. In this case with imperfect credibility, we assume that the degree to which official projections influence the public’s expectations depends on their past record. The more accurate past projections have been, the higher the credibility, and the larger the influence of current projections. But if current credibility depends on past projections and policy, then current projections and policy will affect future credibility, and thus future expectations, which policymakers’ decisions must take into account.

The intuition behind Result 3 is the same as for Result 2. In fact, Result 3 holds for any nonzero influence of projections on public’s expectations, including when policymakers’ credibility is perfect. When committing or projecting ahead, policymakers must take into account the effect they can have on all expectations, since doing so allows them to achieve their objectives better. However, when they later choose the inflation rate to implement, some of these expectational effects are in the past, and no longer relevant, and thus ignored, driving a wedge between policy and projections. While some of these effects may be negligible, and thus irrelevant, such as those the current projection about a value far into the future has on current expectations about next-period inflation, the current projection of next-period inflation will have some impact if policymakers’ projections have any credibility.Footnote ⁷

While time inconsistency remains as long as policymakers use their influence to shape the public’s expectations, the optimal discretionary and commitment policies will generally differ from those discussed in the previous sections when credibility is imperfect. The reason is that now policy is assumed to affect expectations about future policy even if policymakers do not commit ahead due to the impact current policy has on future credibility.Footnote ⁸ The optimal policy and projections will depend on exactly how policymakers’ actions are assumed to affect their credibility and hence influence future expectations.

6. Time-consistent projections

Next, we consider whether there is any scope for projections to improve policy outcomes when these are neither used to mislead the public or to try to reap any gains from commitment. We consider three cases. First, we assume the public is fully rational and can forecast economic variables just as well as policymakers and are therefore not affected by policymakers’ projections. Second, we consider the case where the public’s forecasts are noisier than policymakers’, but still consistent with the implemented policy. Finally, we study the situation where the public’s expectations are inconsistent with policymakers’ actions.

In the ideal case where the public can replicate the policy problem perfectly, and thereby form expectations rationally, they would correctly anticipate the optimal discretionary policy (9). Consequently, their own forecasts would be identical to policymakers’ projections. However, when this is not the case, and the public’s expectations are noisier than policymakers’ projections, or inconsistent with the implemented policy, the projections can, if believed, improve policy outcomes (3) even when they are not used as a commitment mechanism or to mislead the public. The following two results show this.

The latter two results assume policymakers use their projections to correct the public’s noisy or inconsistent expectations, while still implementing the standard discretionary policy (9). However, it follows from Results 1–3 that this is a suboptimal strategy. Any influence policymakers have on expectations, through projections or implemented policy, should be exploited to optimize the policy objective (3). As is shown above, doing so makes the optimal projections be inconsistent with the optimal policy.

7. Projecting multiple variables

In the stylized model above, only inflation expectations are relevant for economic outcomes and the policy objective (3), but in practice policymakers typically include also projections of other variables. One reason might be that they have a more general framework in mind. For example, if the policy objective includes the interest rate, either due to rate smoothing or a desire to keep it at its flexible-price value, the New Keynesian IS curve [see McCallum and Nelson (Reference McCallum and Nelson1999)]

(13) \begin{equation} x_t = E_t x_{t+1} - \sigma r_t \end{equation}

becomes relevant. It hypothesizes that a change in the interest rate $r_t$ , measured in terms of deviations from its flexible-price value (also known as the natural rate of interest), drives a wedge between current and expected next-period output due intertemporal substitution, the degree of which is governed by the parameter $\sigma \gt 0$ . Furthermore, expectations about the future value of the policy interest rate become relevant through the yield curve when the rate $r_t$ in the IS equation (13) is of longer maturity than the typical overnight policy rate. While such changes to the model would affect the optimal policies and projections derived above, it would not change the general results.

Projecting several key variables in the economy might also help strengthen credibility by showing a bigger picture. For example, a projection of higher future inflation might be more plausible if a buoyant economy with low unemployment is expected. Moreover, the relationships between variables implies that they are somewhat interchangeable. For instance, the Phillips curve (1) can alternatively be expressed as:

(14) \begin{equation} \pi _t = \beta ^{J+1} \hat E_t\pi _{t+J+1} + \kappa x_t + u_t +\sum _{j=1}^J \beta ^j \hat E_t \left ( \kappa x _{t+j} + u_{t+j}\right ) \end{equation}

after substituting forward $J$ periods and applying the law of iterated expectations. Here, it is expectations of output $x_{t+j}$ and the shock $u_{t+j}$ , both $J$ periods into the future, that are the protagonists instead of next-period inflation explicitly.

8. FOMC projections and survey forecasts

Finally, we turn to studying projections in practice and compare with actual private-sector forecasts. Since its 2007 October meeting, the FOMC has published projections of real GDP growth, unemployment, and inflation after some of its policy meetings. These have been released with its policy statement, at the Chairman’s press conference within hours of the meeting, or in the minutes released 3 weeks afterward.Footnote ⁹ Projections of the future target federal funds rate were included starting in 2012. Projections have been provided about four times a year, for the January, March/April, June, and October/November/December FOMC meetings, with the schedule changing slightly over time. The projections cover the concurrent year, and 1 and 2 years ahead. Each FOMC member, whether or not voting in that particular meeting, submits a projection. These individual submissions are not publicly available until transcripts are released 5 years later. Instead, the FOMC makes immediately available the range of the individual projections, and what it calls the central tendency, that is, the minimum and maximum projected values after eliminating the three lowest and three highest ones. Since September 2015, the FOMC has included the median projection in the immediate releases.

The FOMC projects the average fourth-quarter civilian unemployment rate, and fourth-quarter over fourth-quarter growth rates of real GDP and prices for personal consumption expenditures (PCE). This makes it difficult to compare with survey forecasts, which typically focus on annual averages and the consumer price index (CPI). The FOMC’s particular, and changing, schedule further complicates comparison, as the surveys follow more regular patterns. For example, the Survey of Professional Forecasters (SPF) operates with deadlines in the middle of February, May, August, and November.Footnote ¹⁰ Consequently, the FOMC’s January and March projections are both compared with the SPF February forecast, the FOMC’s April and June projections are compared with SPF May, the FOMC’s September value is compared with SPF August, while the FOMC’s October, November, and December projections are all compared with the SPF November forecast. This way the predictions are at most a month apart. Even if close in time, predictions can vary significantly, especially if new data is released in between.Footnote ¹¹ Comparing with Greenbook projections, Romer and Romer (Reference Romer and Romer2000) find that these small differences in timing do not appear to have much impact. We find that even differences as short as a month can make a difference and therefore check for robustness by comparing FOMC projections also with one-period leads and lags of the matched-up SPF forecast. This is particularly important with time trends in the data, which are prevalent. The dates used in the figures below are those of the second day of the FOMC meetings for which the corresponding projections were produced. We do not know the exact dates the projections and forecasts were generated, which could vary across respondents.Footnote ¹²

The Wall Street Journal’s Economic Forecasting Survey (EFS) provides monthly forecasts. It samples more than 60 economists, with responses due on the Tuesday following the Bureau of Labor Statistics release of the Employment Report on the first Friday of the month, making the deadline anywhere between the 5th and 11th day of the month. It provides individual data, which were used to determine median forecasts.Footnote ¹³ Due to differences in timing, we compare with both the forecast immediately preceding and succeeding the corresponding FOMC projection. Since only three FOMC meetings involving projections during the period 2008–2019 ended before the 12th day of the month, surveys from the month the meeting was held are referred to as the preceding forecast, and the survey from the following month as the succeeding one. The only exceptions are the three early November FOMC meetings in 2009–2011, for which we use forecasts from the month of the meeting and the prior month.

Each of the four figures compare forecasts and projections for each of the following variables: (1) unemployment, (2) GDP growth, (3) PCE inflation, and (4) the federal funds rate target. Each figure has one panel for each of the individual years 2008–2019, plotting predictions for that year against the time at which these were produced (corresponding FOMC meeting), together with the realized value (latest revised). In all figures, the FOMC median projection is plotted in solid black dots connected by solid black lines. SPF survey median forecasts are red circles, with smaller red squares for the financial services subgroup and small red diamonds for respondents not employed in financial services.Footnote ¹⁴ EFS preceding forecasts are orange multiplication signs ( $\times$ ), while the succeeding ones are plus signs ( $+$ ). A star ( $\ast$ ) means the forecasts preceding and succeeding a given meeting coincide. Greenbook (now Tealbook) projections prepared ahead of each FOMC meeting by staff at the Board of Governors are plotted as green squares (at the time of writing released only up to December 2017). The straight dotted black line represents the realized value of the variable being forecast.

To evaluate whether any observed deviations between FOMC and survey expectations are statistically significant, we rely on binomial tests to compute the probability of $x$ out of $N$ observations deviating in the same direction, ignoring the order, and throwing out any ties. The reported p-values are for two-tailed hypothesis tests, that is, the two-sided probability of results being at least as lopsided as observed, assuming that the underlying distributions were truly the same (50–50% probability of being above or below when not identical). The binomial test does not require many observations to be able to yield statistically significant results, potentially just six at the usual 5% significance level, which is an advantage given the limited number of observations in our data set. It also does not require any assumptions about the underlying data generating process.

8.1. Civilian unemployment rate

Figure 1 shows projections and forecasts of the fourth-quarter average unemployment rate from 2008 to 2019. The SPF only asks about unemployment expectations 1 year ahead, so there are only 60 observations to compare with FOMC projections. The EFS focuses on June and December unemployment, only sporadically asking for fourth-quarter average unemployment, thus yielding only four comparable observations.

Figure 1. Projections and forecasts of unemployment.

While the binomial test for the 2008–2019 period as a whole rejects that the observed differences in SPF and FOMC predictions of unemployment are exclusively due to noise, with the SPF median forecast above that of the FOMC in 35 out of 51 non-tied observations (p-value 0.01), the result is not robust to comparing with the one-period lead and lag of the matched-up SPF forecast. Hence, we cannot be confident that the result is not an artifact of imprecise matching, a serious danger with the time trends in the data. Looking at the subgroups of the SPF reveals that it is the nonfinancial services respondents that push the SPF median forecast above that of the FOMC (on average predicting 0.08 percentage points higher unemployment), illustrating that there are important differences between these two subgroups. We cannot find any significant patterns in the differences between FOMC projections and those from the Greenbook, or between the SPF and Greenbook.

The mean squared errors (MSE) of the matched-up SPF forecasts are a mere 3% lower than for FOMC projections (14% lower for financial services subgroup), but 133% higher for the lagged SPF forecast and 61% lower for the one-period lead.Footnote ¹⁵ Greenbook MSE are 17% higher than those of FOMC projections.

8.2. Real GDP growth

Figure 2 plots projections and forecasts of fourth-quarter over fourth-quarter real GDP growth for 2008–2019 together with the realized values. The SPF only forecasts GDP 1 year ahead on a quarterly basis. In addition, it asks for GDP levels, so the implied fourth-quarter to fourth-quarter growth rate can only be computed unambiguously for surveys from the first and fourthquarters. Because of this, the SPF only provides 23 comparable observations. For the EFS survey, we have 115 matching preceding forecasts and 122 succeeding ones.

Figure 2. Projections and forecasts of real GDP growth.

For the 2008–2019 period as a whole, there are no statistically significant deviations between the different forecasts and projections of GDP growth. However, splitting the sample into two periods, we find that FOMC projections are systematically above EFS forecasts for 2008–2015 and below for 2016–2019, in statistically significant ways, both for surveys preceding and succeeding meetings (largest p-value is $1\times 10^{-5}$ ). These results are robust to ignoring the crisis years 2008 and 2009 (largest p-value is $8\times 10^{-6}$ ). For individual years, the differences are statistically significant for both EFS surveys preceding and succeeding FOMC meetings for 2013, 2014, 2017, and 2018.

FOMC projections are generally not more accurate than the EFS. In fact, the MSE of the EFS are 12% and 18% lower than the MSE of FOMC projections for preceding and succeeding surveys, respectively, but these are not statistically significant differences. Greenbook MSE are 3% lower than those of the FOMC, but still 10% higher than for preceding EFS (in sample where all three are available).

Greenbook forecasts do not deviate systematically from those of the FOMC in a statistically significant way, except for the single year 2011 (p-value 0.02), but Greenbook forecasts are systematically above both preceding and succeeding EFS over the period 2008–2015 (largest p-value is 0.012). We could not find any significant differences between SPF forecasts and any of the other measures.

On average over the period 2008–2019, FOMC median projections of GDP growth were higher than the EFS median forecasts by 0.04 percentage points in terms of the preceding ones and by 0.07 for the succeeding ones. For 2008–2015, the corresponding numbers are 0.17 and 0.21, while they are −0.13 and −0.13 for 2016–2019. Annual averages deviate as much as 0.39 for 2011 and −0.19 for 2018. In terms of absolute deviations, which give a better picture of the typical size of the deviations without positive and negative ones canceling each other out, we have 0.22 for both preceding and succeeding surveys. Annual averages of absolute deviations are all within the 0.07–0.39 range. The single largest deviation is of 0.9 percentage points in 2011, but deviations of half a point or more occurred at least once for all years before 2016. As Figure 2 shows, there is much more variation in the magnitude of deviations between GDP growth forecasts and projections than in their sign.

8.3. PCE inflation

Figure 3 plots projections and forecasts of fourth-quarter over fourth-quarter PCE inflation rates. Of the surveys, only the SPF asked for PCE inflation during our sample period and yields 135 comparison points. None of the surveys included core PCE inflation at the time, which the FOMC also projects.

Figure 3. Projections and forecasts of PCE inflation.

The figure shows that the FOMC systematically projected lower inflation than the SPF in the period 2010–2015, and not always correctly so (2011 and 2012). The binomial test reveals that FOMC projections for inflation being lower than the corresponding SPF forecasts in 96 out of 123 cases (excluding ties), as we observe from 2008 to 2019, has a p-value of $3\times 10^{-10}$ . This result is robust to shifting the timing of the SPF forecasts by one period in either direction so that FOMC projections are compared with SPF forecasts produced at least 2 months prior (p-value less than $2\times 10^{-12}$ ), or at least 2 months after (p-value $2\times 10^{-5}$ ), respectively. The results remain unchanged when ignoring the crisis years 2008 and 2009 (p-value $3\times 10^{-11}$ ). On a year-by-year basis, the differences between FOMC projections and SPF forecasts are statistically significant for 2011–2015, but only for 2012–2014 are they also significant for both the one-period lead and lagged SPF. There are significant differences between SPF forecasts from respondents in the financial services industry and others, with the latter group consistently predicting higher inflation during the 2008–2014 period (by 0.28 on average). However, both groups systematically forecast higher inflation than FOMC projections (p-values of $5\times 10^{-4}$ and $5\times 10^{-11}$ , respectively, for 2008–2019).

Greenbook inflation forecasts are systematically lower than FOMC projections in a statistically significant way for each individual year 2011–2018 (highest p-value is 0.03) and also for the 2008–2019 period as a whole, with only 2 out of 107 non-tied observations being higher (p-value below $2\times 10^{-12}$ ). Greenbook forecasts are also systematically lower than those of the SPF, with only 11 out of 119 non-tied observations being higher (p-value below $2\times 10^{-12}$ ).

On average over the period 2008–2019, the FOMC median projection for inflation was 0.15 percentage points below the SPF median, but annual averages vary between −0.34 for 2008 and 0.29–0.31 for 2010–2013. In terms of absolute deviations, the average was 0.21 percentage points. The single largest deviation was a full percentage point in 2008, but deviations of half a point occurred at least once in all years 2008–2015. As Figure 3 shows, there is much more variation in the magnitude of deviations between inflation forecasts and projections than in their sign. Greenbook projections of PCE inflation were for the period 2008–2019 on average 0.2 percentage points below the FOMC median, with annual averages varying between 0.32 for 2011 and 0.03 in 2008. In terms of absolute deviations, the numbers are almost identical, since there are only two instances of positive deviations. The single largest deviations are of 0.7 percentage points in 2011, and half a point at least once in each of the years 2012–2016. Greenbook forecasts were on average 0.35 percentage points below SPF forecasts during 2008–2019.

MSE for SPF forecasts are 7% higher than those for FOMC projections for the 2008–2019 period as a whole, while Greenbook MSE are practically the same as for the FOMC. Year by year, the SPF MSE are usually slightly higher than for the FOMC, but much lower for 2008 and 2011, years in which the FOMC grossly underestimated and overestimated inflation, respectively. The same applies for Greenbook forecasts. None of the differences in terms of MSE are statistically significant.

8.4. Federal fund rate target

Figure 4 plots projections and forecasts of the federal funds rate target from 2012 to 2019. The EFS is the only survey to include this variable, yielding 87 comparable preceding forecasts and 84 succeeding ones.

Figure 4. Projections and forecasts of the federal funds rate target.

While the binomial test finds that succeeding EFS forecasts have a statistically significant tendency to be below FOMC forecasts (p-value $5\times 10^{-4}$ ), it cannot reject the null hypothesis of no systematic deviations for preceding ones. This fits with the downward time trend in predicted values in our sample and again illustrates the need for caution with respect to the timing of forecasts when comparing these. On average, succeeding EFS forecasts are 0.07 percentage points below the corresponding FOMC projections, while preceding ones are just 0.01 below.

The binomial test does not find systematic deviations between Greenbook forecasts and FOMC projections for the 2012–2019 period as a whole, or for any individual year. MSE for Greenbook, FOMC, and EFS forecasts are basically identical (except for succeeding EFS, which are about 12% lower).