Forecasting FOMC Forecasts

Summarizing Hendry's forty years of work on taming uncertainty is "clear and distinct": Test, test, test. Sure - but test what? Test the maintained assumptions of the disturbances. Test the parameter restrictions of a given model. Test the explanatory power of a model against a rival model. In brief, test everything that is not clear and distinct. We implement Hendry's view to forecast FOMC forecasts. Specifically, monetary policy is forward looking and, in its pursuit of transparency, it communicates its economic projections to the public at large. As a result, there is interest in whether these projections are credible. We argue that central to that credibility is the public's ability to replicate FOMC's projections using publicly available data only. In other words, is it possible to anticipate, reliably and independently, what the FOMC will anticipate for the federal funds rate? To address this question, we assemble FOMC projections from 1992 to 2017; examine their statistical properties; postulate models to predict FOMC projections; estimate the parameters of these models; and generate out-of-sample predictions for inflation, unemployment, and the federal funds rate for 2018. As the reader will soon realize, there is a lot more testing to be done.

Importantly, these projections are not mere extrapolations of existing trends but the result of an FOMC directive to participants to craft appropriate monetary policies: 2 "Appropriate monetary policy is defined as the future policy most likely to foster outcomes for economic activity and inflation that best satisfy the participant's interpretation of the Federal Reserve's dual objectives of maximum employment and price stability." 3 That FOMC participants disagree on the appropriate federal funds rate is clear from   What is not clear is how these disagreements enhance the FOMC's accountability or the public's understanding of monetary policy: if FOMC participants disagree to this extent about what is appropriate, why would they expect the public to understand their decisions?
We are not the first to note the tension between the intended transparency of the SEP and the dispersion of appropriate policies. Faust (2016) notes that The SEP, in my view, deserves a special place in the annals of obfuscation in the service of transparency. The SEP is the paradigm case of the second type of communication: it 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. (Faust 2016 p. 17) The question we address here is whether there is a suitable approach to bypass Faust's critique. Developing this approach involves addressing several obstacles. The first one is the FOMC's idiosyncratic data-release protocol. Greatly simplified, the FOMC releases summaries of economic projections in real time but the underlying details are released with a lag of at least five years. To document this idiosyncratic protocol, we offer a brief description of the FOMC with an emphasis on both its structure and its data-release protocol. Our examination yields a data set of FOMC projections from 1992 to 2017 which we use in our modeling work.
The second obstacle is how to model a process that, by design, is secretive. To address this obstacle, we argue that FOMC projections can enhance the public's understanding if they are, at a minimum, replicable by the public. If so, that would mean that both the FOMC and the public share an understanding of both the goals of monetary policy and the functioning of economy. This shared understanding allows the public to anticipate decisions about interest rates and to understand unexpected departures from those anticipations. 4 We illustrate the applicability of our framework by assessing the credibility of Forward Guidance. Specifically, after the federal funds rate reached "zero" in 2009, the FOMC issued a string of increasingly ambiguous FOMC statements about the duration of the exceptionally low interest rates. Then, in December 2012, the FOMC issued a statement that removed the ambiguities. We use SEP data to generate an ex-ante prediction of the date when the unemployment rate would cross the announced threshold and find very supportive results.
The third obstacle is how to assess the quality and/or usefulness of our work. Indeed, asking if FOMC projections are replicable amounts to asking whether it is possible to extract a narrative of the FOMC's views of the economy's functioning. But we want a narrative that is consistent with the FOMC record, that can be rejected by the data, that uses publicly available data, that is statistically reliable, and that helps mapping FOMC projections into FOMC interest-rate decisions. Again, we find that such an objective is feasible and useful in understanding policy decisions.
The projections also include a long-run horizon defined as "· · · 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." 7

Data-Release Protocol
Details about FOMC projections are released on separate schedules. This difference creates a distinction between real-time and delayed data releases.
• Real-time data: Correspond to the information included in the FOMC release: range and central tendency from FOMC participants for GDP growth, inflation, and unemployment. Further since 2012, FOMC releases include projections for the appropriate federal funds rate; since 2015, FOMC releases include the median of forecasts from FOMC participants.
• Delayed data: Correspond to the projections from FOMC participants considered individually. These data are released in two stages: -With a five year lag, the FOMC releases the numerical projections of FOMC participants without attribution -With a ten-year lag, the FOMC releases the numerical projections of FOMC participants with attribution A delay of five years in releasing these details contradicts the goal of accountability stated in the SEP. Again, we are not the first to note this contradiction. Thus, following Romer (2010), we report in figures 2 and 3 participant-specific projections of inflation and unemployment from 1992 to 2012 the present along with recent FOMC's SEP. 8 This record shows several features of interest. First, disagreements about the outlook among FOMC members are the norm: the 2008 financial crisis only exacerbated them. In other words, Faust's critique applies to the history of FOMC forecasts, not just to the SEP. Second, FOMC projections are notoriously inaccurate and thus the public cannot rely on the accuracy of these projections as a substitute for understanding monetary policy or its credibility. 9 Third, there is no information about the dispersion of projections after 2012. This absence reflects the FOMC's protocol for data release in which information about participants' projections is released with a delay of at least five years. This protocol contradicts the goal of accountability stated in the SEP. This contradiction violates a central tenet of social relations: Trust but Verify. 8 The data assembled by Romer (2010) contains participant-specific projections for 1992 to 2006 with attribution. We replicated his data, added the observations for 2007 with attribution, and extended the data to include FOMC participants through 2012 but without attribution because they are not available. Note that there are no comparable data for the interest rates. 9 Note, however, that forecast accuracy is not an FOMC mandate. Intuitively, FOMC participants are not impartial observers of their own forecasts but rather must influence the economy so as to meet their dual mandate. As a result, a narrow interpretation of forecast accuracy is not useful if that accuracy means high inflation and high unemployment. Further, forecasts revisions cannot be unambiguously interpreted as reactions to news. As indicated earlier, FOMC participants' projections depend on their assessments of the appropriate monetary policy. Thus, even if FOMC participants had and released a shared knowledge of the economy, its usefulness to the public would be transitory because the makeup of the FOMC participants changes over time. New participants would bring their own interpretation of appropriate monetary policy which would translate into different interest-rate projections, even in the absence of economic news.  These observations fit the views Rulke and Tillman (2011) who examine whether FOMC participants exhibit herd behavior. Neverthless, 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 herding behavior and thus alter it. In addition, herds lack a final known destination whereas FOMC participants generate their forecasts based on policies to attain the FOMC dual's mandate.
The forecasts also exhibit instances of seemingly extreme values. Indeed, forecasts for unemployment in 2010 made during the April 2009 meeting might be construed as extreme. Tillman (2011) and Nakazono (2013) have noted such instances and they attribute them to the differential behavior of FOMC participants who are not voting during the meeting. Indeed, they argue that these participants might submit "extreme" forecasts as a way of registering their disagreements. Again, further work is needed because declaring a forecast as extreme involves two considerations: First one needs a benchmark to judge whether the forecast is extreme. Second, one needs a method to differentiate between mood swings and interpretations of an appropriate policies. 10

Empirical Analysis
Because the FOMC has not released the data needed to compute the median forecast for 2013-2015, one would have to wait three years to have a complete series of medians for these two variables given the FOMC's release protocol. The alternative of using the available data on mid-points could, potentially, entail a loss of information. For example, if the extreme views do not change over time but the distribution of forecasts for other participants does, then the same range is consistent with different medians The operational question, then, is whether there is a loss of information when the public relies solely on real-time FOMC projections of the midpoints for unemployment and inflation to anticipate, or understand, FOMC projections for the federal funds rate?
To answer that question, we examine whether movements in the median of FOMC projections for inflation and unemployment projections can be explained by movements of in publicly available data: recorded values of inflation and unemployment available prior to the FOMC meeting; projections from the Survey of Professional Forecasters for inflation and unemployment; and mid-points of the FOMC projections. Finally, we include Greenbook forecasts as an alternative to publicly available data in real time. Although Greenbook forecasts are released with a five-year delay, and thus are not available in real time, they are available through 2012 and thus represent an alternative to publicly available data. Figure 4 represents the timeline of available information for the variables:  Inspection of the data reveals that the median of the forecast distribution for inflation is not, in general, closely related to alternative measures of inflation (figure 5), not even to the Greenbook forecasts. Furthermore, the character of the relation depends on the inflation rate itself: there is a break in the correlation for large values of the inflation rate. The exception is the mid-point of the distribution suggesting that the distribution of projections is fairly symmetrical. For unemployment, movements in the alternative measures are closely related among themselves with unconditional correlations exceeding 0.94 ( figure 6). Nevertheless, a closer inspection of the data reveals that the correlation is sensitive to large values of the unemployment rate.

The Informational Loss of the FOMC's Data Protocol
We now carry out a formal statistical analysis to assess whether reliance on publicly real-time data carries a loss of information. But a loss of information relative to what? Relative to the Greenbook forecasts which are not available publicly in real time. We quantify that loss using two approaches. The first is a single equation approach to assess whether we can replace the missing medians for 2013-2015 with their mid-points. The second approach relies on a system of equations to assess whether the delay in releasing the Greenbook forecasts carries a deterioration of forecast accuracy.

Equivalence Between Median and Midpoints of FOMC Forecast Distributions
We postulate that Assessing whether there is a loss of information involves testing whether  13 =  23 = 1 and all the other  0  equal to zero. If so, then the mid-points serve as sufficient statistics for the medians and thus there is no loss of information. If  14 6 = 0;  24 6 = 0 then Greenbook forecasts are needed to predict the median of the forecast distribution. In this case, one cannot rely solely on publicly available information.
For parameter estimation we apply ordinary least squares to equations (1) and (2) using observations from FOMC meetings held from 1992 January to November 2012 (49 meetings). To avoid the statistical pitfalls associated with the joint nature of model specification and parameter estimation, we use Autometrics, a computer-automated algorithm, developed by Doornik and Hendry (2013). 12 Their algorithm combines least squares with a selection criteria that excludes insignificant coefficients and tests for both parameter constancy and white-noise residuals; the critical values for rejection are not fixed in advance but, rather, are calculated sequentially. Table 1 reports results for equations (1) and (2), labeled the General formulation, and for the simplified formulation, labeled the Specific formulation, using a significance level of five percent.
The results for inflation indicate that    is a sufficient statistic for    : the intercept is no different from zero, the slope is no different from one, and the other coefficients are zero. Furthermore, the residuals are consistent with maintained assumptions for inference. For unemployment,    is also a sufficient statistic    : the intercept is no different from zero but the slope is statistically different from one. Furthermore, the residuals are consistent with maintained assumptions for inference. Taken together, the results suggest that the mid-points of the distributions are suitable substitutes for the median of the distributions over from 1992 to 2012. Thus we use the real time midpoints over 2013-2015 to replace the missing median values over the same period.

Delays in Data Release and Forecast Accuracy
To quantify the loss of information from delaying the release of the Greenbook forecasts, we focus on the forecast accuracy of two models that differ in the use of conditioning variables: publicly available and Greenbook. We also use the two measures of central tendency: median and mid-point. The general formulation is where    is the current-period projection of the inflation rate for the  FOMC meeting where  =median or midpoint    is the current-period projection of the unemployment rate for the  FOMC meeting where  =median or midpoint To quantify the loss of information, we focus on forecast accuracy of using two types of information: Greenbook forecasts only (model M1) and publicly available data only (model M2). For parameter estimation we use ordinary least squares with observations from FOMC meetings held from 1992 January to July 2007. The estimation results are reported in table 3: For inflation, the parameter estimates indicate no evidence of an inverse association with unemployment regardless of how it is measured. But measurement matters in terms of fit: reliance on Greenbook forecasts alone yields smaller SERs with virtually no difference between the mid-point and the median. So what matters is the conditioning variable. For unemployment, the parameter estimates indicate no evidence of an inverse association with inflation regardless of how it is measured. But again, measurement matters greatly in terms of fit: formulations using the Greenbook forecasts have much lower SERs.
Given the parameter estimates, we use s-step forecasts from October 2007 to November 2011. Given these forecasts, we quantify the loss of information as the root mean squared forecast error. Table 4 reports that, regardless of whether one uses the mid-point or the median of the forecasts, the availability of Greenbook forecasts for parameter estimation yields lower RMSFE for inflation and unemployment. To assess the sensitivity of the results, we apply Autometrics to the system (i.e., not equation by equation) using three levels of significance. Table 4 shows a deterioration of forecast performance in response to the application of increasingly tigther significance levels.

Credibility of Forward Guidance
Forward Guidance is an FOMC announcement indicating the likely stance of monetary policy in the foreseable future and how this stance may respond to departures from the FOMC's dual objectives. Forward Guidance was introduced during the 2008 financial crisis to influence long-term interest rates by anchoring expectations of the future federal funds rate. Initial annoucements focused on the end date of the period of unusually low interest rates but were not concise. But the FOMC issued in December 2012 a statement that removed the ambiguities: In particular, the Committee decided to keep the target range for the federal funds rate at 0 to 1/4 percent and currently anticipates that this exceptionally low range for the federal funds rate will be appropriate at least as long as the unemployment rate remains above 6-1/2 percent, inflation between one and two years ahead is projected to be no more than a half percentage point above the Committee's 2 percent longer-run goal, and longer-term inflation expectations continue to be well anchored. Figure 7 shows that at the time of the announcement, the actual unemployment rate was close to eight percent, which was very close to the mid-point of the projections for the current-year unemployment rate. The unemployment rate declined subsequently but the pace of decline was subdued at best. By April 2014 the unemployment rate was above the 6.5 threshold but the FOMC forecast was below the threshold. By May 2014, the unemployment rate, both actual and FOMC forecasts were below the threshold and the FOMC statements did not refer to the threshold afterwards. These observations suggest that, ex-post, the FOMC's forward guidance was credible: the federal funds rate was raised in December of 2015 after the unemployment rate fell below the 6.5% threshold. But this type of ex-post verification involves the public waiting for the actual unemployment rate to cross the announced threshold and then verifying the reaction of the FOMC. Waiting to verify means that the public may be late to benefit from this change in policy. Thus a fair question to ask is whether the public, relying only on public available data, can anticipate the date the unemployment rate will reach 6.5 and is that date consistent with what the FOMC anticipates?
To answer these questions, we model the mid-point of FOMC projections from 1992 to 2012, which are available in real time. Specifically, we postulate that where    is the mid-point of the current-year projection of inflation for the  FOMC meeting and    is the mid-point of the current-year projection of unemployment for the  FOMC meeting. Note that we cannot include the interest rate because they began to be released in 2012.
We estimate the parameters with three methods: • FIML with no-cross persistence ( 13 =  23 = 0) and constant variance-covariance for the disturbances (A = C = 0) • OLS with cross persistence and constant variance-covariance for the disturbances (A = C = 0) • MGARCH with no-cross persistence ( 13 =  23 = 0) Reliance on MGARCH recognizes that the disturbances are influenced by two considerations: mismatch of mid-points among participants and rotation protocol of participants in the FOMC process. A mismatch of mid-points occurs when the participant associated with the mid-point inflation is not the same participant associated with the mid-point unemployment rate. If the mismatch were fixed over time, then the intercept would capture it. But the mismatch is unlikely to be fixed over time because participants change over time or because their projections are reflecting strategic considerations. Rotation of participants is built-in in the FOMC protocol because participants whose tenure expire are replaced by other participants who ma. the FOMC rotation protocol. In other words, in the that Table 5 shows the estimation results using FOMC meetings from February 1992 to December 2012. The fitted values in figures 8-9 reveal a fairly good level of accuracy.  Electronic copy available at: https://ssrn.com/abstract=3303817 Regardless of estimation method, the results indicate that, using the SEP forecasts along with publicly available data, the public would have been able to obtain a fairly accurate prediction of the date when the unemployment rate would be below 6.5 percent (April 2014). Furthermore, all three formulations predict that the FOMC projection for the unemployment rate in April of 2014 was (1) close to the actual and (2)   The above remarks raise several questions. First, why do Faust, Bernanke, and Wessel and Olson use the singular when referring to the reaction function? Indeed, the FOMC directive associated with the SEP allows for the possibility of 19 reaction functions. 13 Thus, in the absence of compelling evidence or acquiesence to authority, adherence to a single reaction function contradicts 13 Heuristically, the  FOMC participant determines the appropriate interest rate that minimizes the welfate loss of deviations of inflation and unemployment from the dual mandate. Subject to the behavior of the economy, the FOMC participant would solve where   is the participant's welfare loss associated with a deviation from the dual mandate,   is the  FOMC participant's appropriate federal funds rate; the  FOMC's participant pojections for inflation is  and for unemployment is   ;  is vector if exogenous variables with publicly available data; Θ  is the vector of coefficients relevant to the  participant;  * is the FOMC's target inflation rate (2%);  *  is the  0  participant estimate of the the FOMC directive embodied in the SEP. Second, even if knowledge of a single reaction function were available, how would it help the public? A reaction function that depends on variables that the public cannot observe directly -the FOMC's own forecasts -is not a reaction function helpful to the public: We want to anticipate decisions and react to the gap between decisions and expectations. Third, an important obstacle in implementing Bernanke's "consensus function" is, at the risk of stating the obvious, the lack of consensus among FOMC participants. Figure 13 shows three measures of the dispersion of the appropriate federal funds rate for the current and one-year ahead. The dispersion of appropriate policies, measured as the coefficient of variation, has declined considerably since 2012 but it is not zero. 14 Importantly, Tillman (2011) and Nakazono (2013) argue that the dispersion of forecasts may be due to FOMC participants who are not voting during the meeting and submit "extreme" forecasts as a way of registering their disagreements. If taken at face value, these observations suggest that the public's effort in scrutinizing the SEP is misplaced, that the FOMC's effort in assembling them is wasteful, and that the FOMC's communication policy embodies a potential contradiction (diversity of views versus single reaction function). Missing from the discussion so far, however, is the role evidence. What evidence is offered by Faust to conclude that a "depiction of policymakers views with no hint about differences may be resolved" automatically means that the SEP "deserves a special place in the annals of natural unemploument rate;   (·) and   (·) are  participant's specific functional forms. The appropriate policy is  *  =   ( *   *    Θ  ) but note that the existence of the solution is not guaranteed. We interpret Faust as suggesting that the dispersion of  * 0   is large enough to undermine the usefulness of a function that combines the 19  * 0   into a single  *  period after period without a significant loss of information. See additional evidence of the plurality of reaction functions in the May 2018 Papers and Proceedings of the American Economic Association. obfuscation in the service of transparency."?

Taylor Rules as Verification Devices
Lacking a single "official reaction function," one could assess whether FOMC decisions on interest rates are consistent with their SEP's projections using the Taylor rule: 15 where   is the median of the distribution of the FOMC projections for the current-year federal funds rate made at time ;   and   are the median of the current-year projections for inflation and unemployment made made at time . 16 Recognizing the uncertainties associated with  and   (Bernanke 2016, Powell 2018), we consider three values for  (0, 1, 2) and two value for   (4, 5). The Taylor rule with  = 0 and   = 4 yields remarkably close interest-rate predictions for meetings since 2016 but not before then (  15 We focus on these two variables because the record of press releases of FOMC decisions and Bluebooks, documenting the alternative options over which FOMC members vote, indicates that the outlook for economic activity (i.e. unemployment) and inflation are the most important considerations for determining the outlook for interest rates. See page 52 of https://www.federalreserve.gov/monetarypolicy/files/FOMC20090128bluebook20090122.pdf 16 Note that the median of  need not correspond to a participant with the median of  or  Mismatch of medians can be solved if FOMC released the participant specific projections with attribution. So the problem is secrecy and not a techical one. It is one thing not to reveal the reaction function. It is another not to release the data so that the public can craft their own reaction function.
Whether these projections are consistent with the FOMC process is impaired by an identification problem: is the FOMC's behavior inconsistent with its goals or is the FOMC consistent with its goals but the assumed coefficients prevent us from detecting. To study this issue further, we assume that the Taylor rule used here is correct but that the coefficient values are not. Thus, as an alternative, we apply OLS to  (2016) notes, indirect information about the reaction function. 18 Indeed, the parameter estimates suggest that an increase in the FOMC forecast for inflation raises the FOMC forecast for the federal funds rate and that an increase in the FOMC forecast for the unemployment rate lowers the FOMC forecast for the federal funds rate; these results are robust to measurement and consistent with the dual mandate. Second, the coefficient estimates are remarkably close to those of the Taylor rule reported above. Third, the estimates are congruent: residuals are white noise and parameter estimates are constant. Fourth, FOMC-Chair effects are both positive and significant.
Despite their appeal, these results fall short of what is needed for verification. First, the Taylor rule only helps to detect ex-post inconsistencies between the rule and FOMC decisions. Even if we could forecast the explanatory variables of the Taylor rule, we do not know whether the implied interest rate from these forecasts is consistent with the FOMC forecasts. If one wants an exante prediction of the interest rate that can then be compared to the FOMC decisions, then one needs to model these SEP measures; we do that below. Second, arguably the SEP's projections for inflation and unemployment are jointly determined along with the appropriate interest rate. But the Taylor rule takes FOMC projections for inflation and unemployment as given. Third, the FOMC's projection horizon extends the current year: there is thus a potential endogeneity of across forecast horizons.  Addressing these limitations involves tradeoffs among computational feasibility, details about transmission channels, and econometric reliability. To this end, we consider models that differ in design and estimation approaches.

Replication as Verification
We now develop empirical models that explain the median of FOMC projections for inflation, unemployment, and the federal funds rate in terms of publicly available data; we focus on current and one-year ahead projections for FOMC meetings held from 2012 to 2017 (figure 9). 19 effr(t) effr(t+1) The data show two properties of interest. First, differences between current and one-year ahead projections have been, over this period, one-sided. For example, the median projection for the appropriate federal funds rate for the one-year ahead is effectively equal to the current-year plus a fairly constant "term" premium. For inflation, the one-year ahead projections are well anchored around two percent, even though projections for the current-year departs from their target. For unemployment, the projections reveal sustained optimism that next year will have a lower unemployment rate. Second, the projections reveal an FOMC that expects to meet its dual mandate next year despite evidence to the contrary in the current year.
Though the FOMC provides this information in real time, it is released along with the interestrate decision. So, if what we want is to anticipate that decision, then we need to forecast the FOMC's own forecasts. Thus we postulate a model that treats FOMC projections as jointly determined. To be sure, we are not arguing that the FOMC participants determine their projections using econometric formulations only. Further, even a casual reading of FOMC transcripts reveals that the FOMC considers many variables in their decision-making process: term structures (foreign and domestic), exchange rates, interest rates (foreign and domestic), among others. Instead, we argue is that these equations are the ones that the public could use to replicate FOMC's forecasts. 20

Vector Autoregresive Approach
We begin with a VAR to explain current and one-year ahead projections for inflation, unemployment, and the federal funds rate for a total of six endogenous variables: 21 ⎡ where   and  +1 are the inflation projections for the current and one-year ahead, respectively, made during the   FOMC meeting   and  +1 are the unemployment projections for the current and one-year ahead, respectively, made during the   FOMC meeting   and  +1 are the federal funds rate in the current and one-year ahead projections, respectively, made during the   FOMC meeting This formulation • treats FOMC projections as jointly determined • includes • allows Chair-specific effects.

"Incredible Restrictions" Formulation
As an alternative to the VAR, we introduce incredible (but hopefully useful) parameter restrictions. Specifically, we assume a recursive structure in which current-year projections influence the one-year ahead projections but not the other way around; this assumption is motivated by the profile of the current-and one-year ahead predictions discussed in figure 15 above: where Θ : vector of unknown coefficients that need to be estimated  : vector of exogenous variables with publicly available data in real time and prior to the FOMC meeting: recorded data for inflation and unemployment Note that FOMC projections for a given horizon are jointly determined. With these considerations in mind, the structure for current-year projections isThus we postulate a model that treats FOMC projections as jointly determined. Specifically, the model has six endogenous variables that are grouped into a recursive structure in which projections for the current-year determine the oneyear ahead projections but not the other way around. For parameter estimation we postulate a model that is linear in the parameters. The structure for the current-year projections is The structure for one-year ahead projections is This formulation has several features of interest: • The equation for   generalizes the conventional Taylor rule by using endogenously determined FOMC projections • Chair-specific effects are included • Publicly available information is targeted: inflation data affects directly inflation projections but not unemployment projections and vice versa • Persistence is present but there is no cross-persistence.

Single Equation: Rules of Thumb Approach
A fair question to ask is whether we need to rely at all on the above models to predict    As an alternative, we could just regress   on the pre-determine variables and then forecast them to generate the forecast of    Though appealing in principle, this approach removes the links between the modeling of the FOMC projections and the forecast for   : In other words, one would not know if the forecast for   is consistent with the forecasts for inflation and unemployment. And the question is whether our modeling of those links above helps anticipating interest-rate decisions.
To that end, we consider For estimation we apply OLS to data on the median of FOMC's participants projections for FOMC meetings held from 2012 to December 2017. Again, we also report results using Autometrics; the results are shown in table 8: Reliance on Autometrics removes the actual values for both inflation,   −1  and unemployment,   −1 but it retains the SPF forecasts; both persistence and chair-specific effects are quite significant. In terms of congruency, the residuals' distributions are consistent with the assumptions needed for statistical inference.
Having implemented the three models, we now ask whether they are equally suitable for addressing Faust's critique for predicting interest rates. Answering that question involves examining the properties of these models.

Reduced Form Coefficients
We now use the long-run, reduced-form coefficients for   from each model and estimation method. The results are sensitive to both model specification and estimation method. Nevertheless, they share three features of interest: • A combined increase of one percentage point in the actual and SPF inflation rate raises the federal funds rate ranging from 40 to 50 basis points.
• A combined increase of one percentage point in the actual and SPF unemployment rate reduces the federal funds rate from 26 to 50 basis points.
• Chair-specific effects are significant and positive; the value of Yellen's tenure is lower than the one for Bernanke by about 60 basis points.
In the absence of a universally accepted point estimate these results are not helpful in discriminating among models.

Dynamic Stability
We now use impulse responses to examine how much of a revision in FOMC projections for one variable are reflected as revisions in other variables.

Ex-ante Forecasting Accuracy
We now implement 1-step ahead out-of-sample forecasts of the FOMC forecasts for the March and June 2018 meetings. 23 In doing so, we assume that Chair Powell has the same view of the world as Chair Yellen; we examine this assumption in the next section. For both meetings, the model's prediction for   is a bit below the lower bound of the FOMC's range of appropriate interest rates. Such an underprediction owes to two factors. First, the model shows a slight underprediction for   , which then lowers   via the interest-rate equation. Second, the forecast assumes that Powell's approach is the same as that of Yellen, which need not be correct.
We now re-examine this assumption.

Autometrics Redux: Occam's Razor
We postulate the following General Unrestricted Model (GUM) and use data including Powell as the Chair of the FOMC: + 8 ·   +  9 ·   +  10 ·   +  11 () ·   +  12 () ·  +1 +     ˜ (0  2 ) where () is a polynomial of degree one in the lag operator,   is the Chair effect for Powell and, to assess the empirical relevance of Faust's critique for forecasting, we include   −1 and   −1+1 which represent the degree of disagreement among FOMC participants of the appropriate interest rate; we measure this disagreement using coefficient of variation of the distribution of FOMC participants' appropriate federal funds rate shown earlier in figure 13. Note that the equation includes the FOMC's current-year predictions for inflation and unemployment. Thus, if  60 () =  70 () = 0 then information about the FOMC's inflation and unemployment forecasts is not needed for predicting    Similarly, if  11 () =  12 () = 0then the force of Faust's critique for forecasting would be attenuated.
The estimation results reveal several features of interest. First, sole reliance on the GUM suggests that the previous value of the federal funds rate is the most important factor in explaining movements in that interest rate; neither FOMC-Chair effects nor participants' difference, nor economic data (FOMC's or public) are statistically important. Second, the implementation of Autometrics reveals a different characterization: Chair effects and   −1 are important and their long-run values are robust to the choice of target size. Third, FOMC's current-year forecasts of inflation and unemployment are not relevant for forecasting FOMC rate decisions. In other words, one cannot reject the null hypothesis that  60 () =  70 () = 0 Estimates using a 0.01% target size show that persistence is no longer relevant and information about both inflation and unemployment play statistically important roles. The exclusion of persistence sounds like a limitation until one realizes that persistence is already embodied in the FOMC Chair. But the Chair embodies more than history: It embodies the power to persuade participants around the Chair's view. Yellen's approach is illustrative: And the question is, are we ever going to converge? I would feel my job is to get everybody to see that off-white is not a bad alternative. (Laughter) As brilliant as your choice was, maybe you could live with off-white, and it's not so bad. And we can converge on that and it's going to function just fine and maybe we can agree. Yellen (2018) 24 Given this persuasive power, it is not surprising to find that one cannot reject the null hypothesis that  11 () =  12 () = 0   These differences in estimation results are relevant for forecasting. Specifically, as the cost of including irrelevant variables is assumed to be increasingly greater than the cost of excluding relevant variables (declines in target size), we note a reduction in both the level and the change of the forecasts. Second, combining lowest target size with super-saturation miss the level of interest rates but predict the change in the interest-rate announcements while lowering the standard error of the forecast.

Conclusions
This paper is not about invalidating Faust's critique: The SEP offers no way to reconcile the dispersion of appropriate interest rate policies. To Faust and Bernanke, the way to reconcile these differences is for the FOMC to provide its reaction function. We argue that providing a reaction function that relies on variables the public does not observe is not helpful. This paper is about the feasibility of bypassing the absence of the FOMC reaction function. The results show that it is possible to replicate accurately the FOMC projections, to obtain results that are consistent with expectations, and to extract simple rules of thumb to predict interest-rate decisions. There are many objections to our findings. First, FOMC participants' projections rely on their assessments of the appropriate monetary policy. We do not have access to the solutions of participants' optimization problem, much less the aggregate of such solutions. Second, there is no guarantee that a replicable, but unknown, model even exists. Indeed, our work is subject to the criticism that we are testing a joint hypothesis: that the mapping exists and that our approach offers a characterization of it. Third, from a modeling standpoint, our mapping treats SPF forecasts as given. Fourth, the sample period is brief and the number of observations is small and correspond to an unusual circumstances in U.S. history. Finally, we have not undertaken an exhaustive sensitivity analysis of our econometric results. Thus, taken as whole, these limitations underscore the undeniably tentative character of our results.