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Finance and Economics Discussion Series

Divisions of Research & Statistics and Monetary Aﬀairs

Federal Reserve Board, Washington, D.C.

Real-Time Properties of the Federal Reserve’s Output Gap

Rochelle M. Edge and Jeremy B. Rudd

2012-86

NOTE: Staﬀ working papers in the Finance and Economics Discussion Series (FEDS) are preliminary

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are those of the authors and do not indicate concurrence by other members of the research staﬀ or the Board of Governors. References in publications to the Finance and Economics Discussion Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers.

Real-Time Properties of the Federal Reserve’s Output Gap Rochelle M. Edge Jeremy B. Rudd Federal Reserve Board∗ Federal Reserve Board∗∗ December 3, 2012 Abstract This note considers the reliability of Federal Reserve Board staff estimates of the output gap after the mid-1990s, and examines the usefulness of these estimates for inﬂation forecasting. Over this period, we ﬁnd that the Federal Reserve’s output gap is more reliably estimated in real time than previous studies have documented for earlier periods and alternative estimation techniques. In contrast to previous work, we also ﬁnd no deterioration in forecast performance when inﬂation projections are conditioned on real-time estimates of the output gap.

∗ Corresponding author. Mailing address: Mail Stop 155-C, 20th and C Streets NW, Washington, DC

20551. E-mail: rochelle.m.edge@frb.gov.

∗∗ E-mail: jeremy.b.rudd@frb.gov. We thank Athanasios Orphanides for helpful comments on an earlier version of this work. The views expressed are our own and do not necessarily reﬂect the views of the Board of Governors or the staff of the Federal Reserve System.

I Introduction In a 2002 paper, Orphanides and van Norden contend that it is not possible to obtain reliable estimates of the output gap in real time. As they demonstrate, standard detrending procedures yield gap measures that are subject to large subsequent revisions, primarily because trend extraction becomes quite difﬁcult at the endpoint of a given sample. In addition, based on data available for the 1980s and early 1990s, Orphanides (1998) concludes that Federal Reserve staff estimates of the output gap are similarly unreliable.

The purpose of this note is to consider whether these conclusions obtain for more recent vintages of the outputgap estimates produced by the Federal Reserve staff. Narrative evidence suggests that the Federal Reserve’s ability to recognize and quantify the mids acceleration in trend productivity in a reasonably timely manner was an important contributor to the successful conduct of monetary policy over that period.1 This points to an improved ability to estimate the gap, which should in turn be evident in the data.

A related issue concerns the usefulness of real-time estimates of the output gap for inﬂation forecasting. In companion work, Orphanides and van Norden (2005) ﬁnd that over the post-1983 period, inﬂation forecasting models that use real-time estimates of the output gap typically perform worse than models that condition on ﬁnal estimates of the gap. We therefore also examine whether the Federal Reserve staff estimates of the GDP gap provide a useful predictor of future inﬂation movements in real time.

II Real-Time Estimates of the Federal Reserve Board Output Gap Before each meeting of the Federal Open Market Committee (FOMC), the Federal Reserve Board’s staff produce a detailed projection of various U.S. economic aggregates.

See Meyer (2004, ch. 6) for a ﬁrsthand account.

This projection, which is known as the Greenbook forecast, is judgemental in the sense that it is not explicitly derived from a single model of the economy.2 In particular, the staff’s estimates of potential GDP pool and judgementally weight the results from a number of estimation techniques, including statistical ﬁlters and more structural model-based procedures.3 Our set of real-time output gap estimates starts with the June 1996 Greenbook forecast; these estimates extend back to 1975:Q1 for every vintage of the forecast. The Greenbook projection is only made public with a ﬁve-year lag; hence, the most recent estimate of the gap in our dataset comes from the December 2006 Greenbook. Because the Greenbook is produced eight times a year, there will be eight sets of output gap estimates for each year (typically two per quarter).

Deﬁne the December 2006 estimates of the gap to be the gap’s “ﬁnal” value. We then deﬁne the corresponding real-time estimate of the quarter-t gap to be the estimate of the gap from the forecast round whose closing date falls in quarter (t + 1). (Obtaining the period-t gap estimate from a Greenbook in the following quarter ensures that in most cases an advance estimate of GDP—or a relatively full set of monthly indicators— would have been available for estimating the quarter-t gap.) For example, the June 1997 Greenbook forecast was completed in 1997:Q2. We therefore call the 1997:Q1 value of the gap from the June 1997 round the real-time estimate of the gap in that quarter. This means, of course, that there can be multiple real-time observations for a given quarter; for instance, we will obtain real-time estimates of the 1997:Q1 gap from both the May 1997 Starting in June of 2010, the staff’s forecast document was renamed the Tealbook forecast, as it now combines elements of the original Greenbook with topics related to the conduct of monetary policy that were formerly presented to the FOMC in the so-called “Bluebook.” (During the entire period we consider, the staff’s projection was contained in the Greenbook, so we refer to it by this title.) See Mishkin (2007) for a description of how the Federal Reserve Board staff estimate potential output.

and June 1997 Greenbook forecasts. We ignore the informational asymmetry generated by these timing deﬁnitions—speciﬁcally, we ignore the fact that rounds that occur later in a given quarter will enjoy an informational advantage over those that occur earlier—as such asymmetries will be roughly constant across years. (As we document in the next section, our main conclusions are robust to alternative assumptions regarding timing.) III The Magnitude of Revisions to the Federal Reserve’s Gap Estimates We deﬁne the gap revision as the difference between the ﬁnal and real-time gap estimates.

Lines 1 and 2 of Table 1 give the mean, standard deviation, and root-mean-square error (RMSE) for these revisions, together with two measures of the noise-to-signal ratio: the ratio of either the standard deviation or the RMSE of the gap revisions to the standard error of the ﬁnal estimate of the gap.4 As can be seen from the table, the mean error over the full sample is small (less than a tenth of a percentage point). The standard deviation (and RMSE) of the revisions is around 0.7 percentage point; while this is large in absolute terms, it is only about half the size of the corresponding standard deviation of the ﬁnal estimate of the gap.5

**These standard deviation and RMSE values are also small relative to the corresponding estimates found by Orphanides (1998) in his analysis of the Greenbook output gap:**

Over the 1980-1992 period, Orphanides reports a RMSE of 2.8 percentage points for revisions to the Greenbook’s real-time output gap estimates, which is actually greater than Recall that the mean-square error contains an adjustment for the squared bias (here, the mean error).

Thus, when the mean error is small, the standard deviation of the gap revisions and the RMSE should be quite close.

To compute the mean and standard deviation of the ﬁnal gap estimate, we “duplicate” the observations on the ﬁnal gap in line with the number of Greenbook forecasts that fall in a given quarter. However, the computed mean and standard deviation are essentially identical if we instead just allow one observation on the ﬁnal gap per quarter.

the 2.4 percentage point standard deviation of his “ﬁnal” (end-of-1994) gap estimate. Part of this difference no doubt reﬂects our use of a different sample period: Relative to the 1980s, GDP in our sample period is less volatile. However, this explanation is tempered somewhat by the observation that the Federal Reserve appears to have had greater difﬁculty forecasting real GDP movements in recent decades (see Tulip, 2005).

Of course, another explanation for the observed reduction in the size of gap revisions is simply that the Federal Reserve staff’s ability to estimate the GDP gap in real time has improved relative to the period that Orphanides examined. To assess this possibility, we used real-time GDP data to examine whether purely statistical methods for estimating the output gap yield a decline in the size of gap revisions that is comparable to what we ﬁnd for the Greenbook output gap. In particular, we produced real-time estimates of the output gap using each of the six univariate detrending procedures considered by Orphanides and van Norden (2002). These procedures include three deterministic approaches (ﬁtting a linear trend, a broken-linear trend, and a quadratic trend to log real GDP) and three unobserved-components approaches (the Hodrick-Prescott ﬁlter and the trend GDP models of Watson, 1986 and of Harvey, 1985 and Clark, 1987). The noise-to-signal ratios that obtain for these various gap estimates—which are shown in the upper panel of Table 2—imply that for all but one of the six detrending methods, the size of the real-time gap revisions relative to the volatility of the gap itself either remains about unchanged or increases somewhat from 1980-1992 to 1992-2006. Hence, these purely statistical procedures do not yield an improvement in the reliability of real-time gap estimates that is similar to what we observe for the Federal Reserve’s measure, which in turn suggests that some element particular to the the Fed’s estimation procedure—such as the use of judgement or the pooling of results from multiple sources—is responsible.6 In line with Orphanides (1998), however, we ﬁnd that the autocorrelation of the Greenbook gap revisions is quite high: about 0.91 over the period we consider.7 It turns out that part of the autocorrelation over our sample period is attributable to a persistent string of negative errors (that diminish in magnitude) up until around 1998. Very likely, this string of errors reﬂects slow learning about the 1990s speedup in trend productivity growth; dropping the pre-1999 observations from the sample reduces the estimated autocorrelation coefﬁcient to 0.70. Interestingly—and as shown in Table 3—when we compute real-time gap estimates using the univariate approaches in Orphanides and van Norden (2002), we ﬁnd that the gap revision is as highly autocorrelated over the 1996-2006 period (line 2) as it is over the 1980-1992 period (line 1), with autocorrelation coefﬁcients on the order of 0.9. For these gap measures, however, dropping the pre-1999 observations from the latter period (line 3) reduces the estimated autocorrelation coefﬁcient for only two of the six methods (the linear and piecewise-linear detrending procedures).

As was noted above, the publication of two Greenbook forecasts per quarter implies that we will have multiple gap estimates in each quarter. In addition, even though we have obtained each time-t gap estimate from a Greenbook published in period (t + 1), there will be occasions where an advance estimate of GDP will not have been available to produce the gap estimate for a given quarter.8 We therefore considered two modiﬁcations to our timing assumptions. First, we recomputed the statistics in Table 1 using the One reason we are not fully willing to advance such an optimistic conclusion is that it implicitly suggests that previous techniques for estimating potential GDP were less sophisticated. However, as Solow (1982) documents, the methodology used by the Council of Economic Advisers to estimate potential output as far back as the 1960s would not be out of place in a contemporary policy institution.

In his sample, Orphanides (1998) ﬁnds an autocorrelation coefﬁcient in excess of 0.8 for revisions to the Federal Reserve’s gap estimates.

For example, one of the two 2006:Q3 estimates of the GDP gap is taken from the October 2006 Greenbook; an advance estimate of third-quarter GDP was not available when this Greenbook was ﬁnalized.

time-t gap estimate from the time-(t + 2) Greenbook; this ensures that a complete set of GDP data for quarter t would have been available for producing the Greenbook estimate.

Unsurprisingly, doing this (not shown) lowers the mean, standard deviation, and RMSE of the gap revisions, but only by a very small amount (on the order of 0.02 or 0.03 percentage point in each case). Next, we recomputed the statistics in Table 1 using only the gap estimate from the second Greenbook in each quarter. Once again, the mean, standard deviation, and RMSE of the gap revisions are little changed by this modiﬁcation (not shown). However, the autocorrelation of the revisions declines slightly (to 0.84), and is considerably lower (only 0.41) if the pre-1999 revisions are excluded.