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Federal Reserve Bank of Chicago
How Professional Forecasters View
Shocks to GDP
Spencer D. Krane
WP 2006-19
How Professional Forecasters View Shocks to GDP
by
Spencer D. Krane
Federal Reserve Bank of Chicago
November 29, 2006
The views expressed are those of the author and not necessarily those of the Federal
Reserve Bank of Chicago or the Federal Reserve System. I would like to thank Jeff
Campbell, Tim Cogley, Leland Crane, Cristina De Nardi, Charlie Evans, Hesna Genay,
David Marshall, Dick Porter, Tara Rice, and Dan Sullivan for helpful comments and
assistance.
1
Abstract
Economic activity depends on agents’ real-time beliefs regarding the persistence
in the shocks they currently perceive to be hitting the economy. This paper uses an
unobserved components model of forecast revisions to examine how the professional
forecasters comprising the Blue Chip Economic Consensus have viewed such shocks to
GDP over the past twenty years. The model estimates that these forecasters attribute
more of the variance in the shock to GDP to permanent factors than to transitory
developments. Both shocks are significantly correlated with incoming high-frequency
indicators of economic activity; but for the permanent component, the correlation is
driven by recessions or other periods when activity was weak. The forecasters’ shocks
also differ noticeably from those generated by some simple econometric models. Taken
together, the results suggest that agents’ expectations likely are based on broader
information sets than those used to specify most empirical models and that the
mechanisms generating expectations may differ with the perceived state of the business
cycle.
2
1. Introduction
Economic activity depends crucially not just on the actual source of the shocks to
the economy, but also on economic agents’ real-time perceptions of the nature of these
shocks. In particular, the behavior of households and businesses will depend on the
degree to which they believe the economy is experiencing a permanent shift in its
productive capacity as opposed to a transitory fluctuation about a trend path for output.
For example, regardless of its ultimate persistence, a fluctuation in labor income that
currently is perceived to be permanent will have a larger immediate impact on
consumption and overall economic activity than one that is thought to be transitory.
Accordingly, agents’ perceptions of shocks and how well they compare with the eventual
path for actual output are important for the historical interpretation of business cycles.
Furthermore, learning about factors influencing economic agents’ perceptions of shocks
can help business cycle researchers specify theoretical and empirical models with
expectational structures that are consistent with those observed in the economy.
There is a long history of empirical studies investigating the decomposition of
actual GDP into permanent and transitory components; and today the economic and
statistical identification of these shocks are standard features of most models used in
business cycle analysis. 1 But there has been little work on identifying how economic
agents have viewed fluctuations in GDP in real time.2 This paper does so by examining
how one group of well-informed agents--professional economic forecasters--have
interpreted the shocks to the economy that they have experienced over the past twenty
years. Specifically, I estimate the persistence and propagation patterns in the shocks to
GDP perceived by the panel of forecasters comprising the Blue Chip Economic
Indicators Consensus Outlook. I do so using a statistical model of the revisions to the
short-, medium-, and long-horizon Blue Chip projections. I also consider how the
1
Early statistical decompositions, such as those by Beveridge and Nelson (1981), Nelson and Plosser
(1982), Watson (1986), Campbell and Mankiw (1987a, 1987b), Clark (1987), and Cochrane (1988), were
based on univariate time series models for output. Later, Shapiro and Watson (1988), Blanchard and Quah
(1989), Cochrane (1994) and others extended the analysis to multivariate frameworks. These studies
produced a wide range of estimates of the relative importance of permanent and transitory shocks to GDP
and in the patterns over which these impulses affect macroeconomic aggregates.
2
On example is Edge, Laubach, and Williams (2004), who examine how forecasters revise their views of
long-run productivity growth.
3
forecasters’ views of shocks compare with the results from some simple econometric
specifications that have been used in the academic literature to identify permanent and
transitory shocks to GDP.
There are three broad statistical findings. First, the Blue Chip forecasters attribute
more of the variance in the shock to the level of GDP to permanent factors than they do
to transitory developments. Second, the shocks to the Blue Chip forecasts differ in a
number of ways from those identified by the statistical GDP models. Third, both the
permanent and transitory Blue Chip shocks are significantly correlated with incoming
high-frequency indicators of economic activity; and for the permanent component, the
relationship varies with the state of the business cycle.
Turning to the details of the results, on average, the forecasters comprising the
Blue Chip Consensus perceive that about 30 percent of the current shock to real GDP
reflects transitory factors while about 70 percent is due to a permanent change in the level
of output. This estimate of the relative importance of permanent versus transitory shocks
is in the upper half of the range found in the literature that estimates such decompositions
in the published GDP data and is larger than the estimates generated by most of the GDP
models that I consider.3 The transitory shocks are thought to have an economically and
statistically significant impact on output for at least 1-1/2 years while the full effect of
permanent shocks become incorporated into GDP in about one year. These impulse
response patterns are similar to those from most of the GDP models that I estimate.
By construction, the revision to the forecast from an econometric model is a
function of the model’s most recent forecast errors. In contrast, both the permanent and
transitory shocks to the Blue Chip forecasts are essentially uncorrelated with last-period’s
forecast error. Instead, the Blue Chip revisions are more heavily influenced by the
incoming high-frequency data on economic activity. Such data are not included in the
statistical GDP models I consider; nor are they generally included in larger forecasting
models, which usually project GDP based solely on quarterly aggregates from the
national accounts. Furthermore, there are some economically interesting relationships
3
As discussed below, the variance decomposition of the current-period forecast revision differs from the
forecast-error-based variance decompositions of GDP itself made in the papers cited in footnote 1. Section
5 adjusts for the differences and compares the Blue Chip forecast revisions to comparable revisions from
4
between the high-frequency indicators and the shocks to the Blue Chip forecasts. The
correlation between the indicators and the transitory shocks does not appear to vary
cyclically, but the correlation with the permanent shock appears to be driven largely by
behavior during recessions or periods of sluggish growth. There also are relatively large
perceived permanent shocks following the 1987 stock market crash, the onsets of the
1990 and 2001 recessions, and following September 11, 2001--events that forecasters
thought would be associated with weak economic activity. Though sample-size
limitations mean these results are tentative, they do suggest that forecasters view
recessions or shocks associated with unusual, but identifiable, events more as permanent
reductions in output than transitory deviations in production from trend or a reallocation
of production across time.
The results relating past forecast errors and high-frequency indicators to the Blue
Chip shocks suggest that there is an important difference between the information sets
used by professional forecasters and the national income accounts data generally used to
estimate quarterly econometric models of aggregate economic activity. In addition,
forecasters may process information differently if they see data or events suggesting the
economy is threatened with a recession than if it is in the midst of an expansion. Such
differences can not be captured by linear econometric models with identically distributed
error terms. These results also are relevant for researchers seeking to construct
expectationally consistent models of business cycle behavior.
My empirical findings are generated using a relatively flexible unobserved
components model of the revisions to the Blue Chip forecasts. The model exploits the
simple observation that only permanent shocks can affect output in the very long run.
Thus the revision made today to the projection of GDP at a far-distant forecast horizon
reflects only the shocks that forecasters think will be permanent. The difference between
these permanent shocks and the revision to the projection for current GDP then identifies
the transitory shock. Finally, the correlations between the revisions to projections at
different forecast horizons reveal the impulse response patterns that describe how
forecasters think the effects of the shocks on output will play out over time.
four time-series models that calculate permanent and transitory shocks to GDP. I find that the Blue Chip
attributes a larger proportion of the forecast revision to permanent factors than do three of the four models.
5
Working with the observed forecast revisions eliminates the need for a detailed
analysis of how the projections actually are constructed. This is useful because the Blue
Chip forecast is not the simple unadulterated output of a single statistical model with a
corresponding mechanical representation of shocks and impulse responses. Instead,
many forecasters comprise the Blue Chip panel, and virtually all of them make
judgmental adjustments to model projections or base their forecasts on a wide range of
statistical and anecdotal sources. Nonetheless, regardless of how the forecasts are
constructed, any time a forecaster revises a projection, he or she takes a stand on the new
information they think will influence GDP and the degree to which the shocks will either
dissipate over time or become permanently embedded into the economy. These
judgments can be inferred from the observed forecast revisions. Throughout the paper I
will refer to these judgments as forecasters’ perceptions of the permanent and transitory
shocks. This terminology highlights the fact that the shocks are not generated by any
particular statistical model and that they are real-time evaluations that never undergo expost adjustments to calibrate them to the actual path for GDP that eventually transpired.
2. The Data
2.1 The Blue Chip panel and data availability
Many private- and public-sector economists regularly sell macroeconomic
forecasts to clients or release them to the public. One of the most widely used summaries
of such projections is the “Consensus Outlook” published by the Blue Chip Economic
Indicators. The Blue Chip Consensus is the simple arithmetic average of the projections
made by the Blue Chip panelists. There are 52 forecasters in the current panel.
The Blue Chip Consensus is interesting for a number of reasons. First, the
forecasts are made by the economic staffs at major investment banks, financial services
firms, large commercial banks, industrial companies, economic consulting firms, and
university-affiliated forecasting projects. Accordingly, the projections encompass
expectations for the macroeconomy held by organizations making large financial
commitments or selling services to business clients. Second, the Blue Chip Consensus is
6
commonly used as a benchmark against which to compare other forecasts. For example,
both the Administration and Congressional Budget Office compare their official forecasts
with the Blue Chip Consensus in their annual analyses of the United States Budget.
Third, the average is likely the most important moment of the distribution of forecasts
with regard to how expectations may feedback onto aggregate activity. One reason is
that the Consensus averages out perennially optimistic or pessimistic forecasters. Indeed,
Bauer, Eisenbeis, Waggoner, and Zha (2003) show that the Consensus does a better job
in predicting calendar-year average growth rates than the projections of most of the
individual forecasters.
On the 10th of each month, Blue Chip publishes a Consensus forecast for each
quarter in the current and subsequent calendar years. This projection period is too short
to separately identify transitory events expected to last a year or two from developments
expected to have a permanent impact on the level of economic activity. However, twice
a year the Blue Chip surveys its respondents for projections covering the next 12 years.
In addition to the regular quarterly projections, each March and October the panel also is
queried for calendar-year annual forecasts for each of the next 6 years and for the average
pace of activity over the subsequent 5-year period (the 7 through 12-year-ahead forecast
period).4 These forecasts thus provide semi-annual information on how forecasters
interpret the effect of incoming shocks on the path of GDP both over the next several
quarters and for many years to come.5 Since I need to observe near-, medium-, and longhorizon forecasts made at the same point in time, this paper uses only the forecasts made
in March and October.
Let gdp(t+k) be the value of the logarithm of real GDP k periods from now and
ftgdp(t+k) be the forecast made in period t of gdp(t+k); k = 0, 1, 2, …K. As a practical
matter, forecasters provide projections for GDP growth, ftΔgdpt(t+k) = ftgdp(t+k) ftgdp(t+k-1). Given that I observe forecasts two times a year, I work with semi-annual
time series of projections for half-year periods. Specifically, when t is in March, the k =
4
The individual Blue Chip forecasts are not available at the quarterly or long-run forecast horizons—they
are only published for the averages of the current and next calendar-year.
5
The Blue Chip a better suited for studying shocks and propagation than another popular forecast data set,
the Survey of Professional Forecasters (SPF). The SPF publishes forecasts for average growth over a 10year period. However, the SPF only began doing so in 1992; it only conducts the long-run survey once a
year; and the SPF medium-term forecasts are limited to the current and subsequent four quarters.
7
0 forecast is of growth between the fourth quarter of the previous year and the second
quarter of the current year; the k=1 forecast is of growth between the second and fourth
quarters, and so on. If t is in October, the k = 0 forecast is for growth between the second
and fourth quarters of the current year. In March, forecasts for k = 0, 1, 2, 3 can be
constructed from the quarterly projections; in October, the quarterly numbers can
generate forecasts for k = 0, 1, 2. For larger k, I interpolated the 2 through 6-year-ahead
annual projections to the half-year frequency to generate semi-annual projections for up
to k = 9. The long-run GDP forecast, ftΔgdp(lr), denotes the forecast of average growth
made at time t for the 7 through 12-year-ahead period. The complete set of short-,
medium- and long-term forecasts begins in March 1982; the sample I use runs through
the first half of 2005. Appendix 1 provides further details regarding timing conventions
and the methodology used to distribute the annual forecasts to a semi-annual basis.
2.2 The historical data
Figure 1 presents some of the data. The time axes in the graphs denote the period
being forecast. The solid lines in each panel are forecasts for half-year growth rates: the
top-left panel plots forecasts made for the current half-year period (k = 0); the top-right
panel the projection of semi-annual growth made one-half year earlier (k = 1); and the
bottom panels the forecasts made one-year earlier (k = 2). The dashed lines in the top
and lower left panels are the actual values for GDP growth as estimated by the third or
final NIPA estimates. 6 The dashed line in the lower-right panel is what forecasters were
assuming for long-run growth at the time the forecast was made. The shading marks
recessions as designated by the NBER.
The figure highlights several characteristics of these forecasts (see Krane 2003 for
further details). First, the short-term forecasts can move around substantially, particular
during periods of economic weakness. In contrast, the medium and longer-run forecasts
are much smoother. Indeed, as seen in the lower-right panel, even the one-year-ahead
forecast appears to be fairly well anchored by the assumptions for longer-run growth.
8
Second, the forecast errors can be large. As seen in table 1, the root-mean-squared error
(RMSE) for growth in the current half-year period is about 1-1/2 percentage point; the
RMSEs for the longer-horizon forecasts are between 1-3/4 and 2 percentage points.
These RMSEs compared with a standard deviation in actual half-year growth of about 2
percentage points. As seen in the graphs, the increase in the RMSEs at longer horizons
largely reflects the fact that these forecasts vary only modestly from the long-run growth
projections and therefore miss recessions. Third, the assumptions concerning long-run
growth exhibit low-frequency variation; notably, they drifted down during the late 1980s
and then moved up rather rapidly around the turn of the millennium.
Although the forecast errors are large, they pass some simple tests for rationality.
As seen on the first column of table 1, the mean errors are not statistically different from
zero. More formally, in the regression:
Δgdp (t + k ) = a + b ft Δgdp (t + k ) + et (k )
(1)
ftΔgdp(t+k) fails as a rational forecast of Δgdp(t+k) if the joint null hypothesis that a = 0
and b = 1 is rejected. As seen in the last column of table 1, one cannot reject this
hypothesis for any value of k in the Blue Chip data. That said, this is not a resounding
victory: with the exception of the k = 0 forecast, a often is well above zero and b well
below one, but the standard errors are large enough that one cannot reject the null.
Figure 2 looks at the relationship between the current state of the economy and
the projected path for GDP growth. The solid lines plot the differences between the
forecasts for semi-annual growth made k periods ahead and the assumption for long-run
growth at that time, ftΔgdp(t+k) - ftΔgdp(lr). The time axis refers to the dates the
forecasts are made. The dashed line is the most recent value of the three-month moving
average in the Chicago Fed National Activity Index, or CFNAI-MA3, that is known at
time t. The CFNAI-MA3 is an index that captures the comovment in 85 monthly
indicators of economic activity. Thus, it measures common information about economic
6
Note that I assume forecasters were not predicting the effects of comprehensive revisions of the NIPA;
accordingly the actual data in 1999, 1995, 1991, and 1985 were adjusted by the average changes in longrun growth that occurred with the comprehensive revisions to the NIPA in those years.
9
activity contained in a wide range of high-frequency indicators available to the
professional forecasters. 7
In the near term (k=0, 1), we see a large positive correlation between ftΔgdp(t+k) ftΔgdp(lr) and the CFNAI-MA3. This indicates that forecasters are building in some
persistence of the current observed strength or weakness in the economy into their
projections for the next year. For longer-run forecasts (k = 2, 4), however, there is a
negative correlation between ftΔgdp(t+k) - ftΔgdp(lr) and the current state of the
economy. This suggests that forecasters are looking for some future offset to current
high or low rates of growth. However, it is not clear from the graphs to what degree
medium-term forecast adjustments offset near-term movements. To the degree that they
do, the forecasters think the shocks hitting the economy are transitory; to the degree that
they do not, the forecasters perceive a permanent element in the shocks hitting the
economy.
Of course, these characterizations are only suggestive. Importantly, we do not
know how much of the swings in the CFNAI-MA3 reflect informational surprises. And,
as just noted, the relative scale of the various adjustments is unclear. For these, I turn to a
more formal statistical model.
3. A Statistical Model to Identify the Perceived Shocks to GDP
3.1 A model of forecast revisions
This section presents a model of forecasters’ real time views regarding the size
and persistence of the shocks to GDP that they observe. The model is based on some
general assumptions about how forecasters view the time series properties for GDP.
Specifically, I assume that the forecast of the logarithm of GDP is the conditional
expectation:
7
The CFNAI is the first principle component of 85 monthly time series measuring production,
employment, sales, construction, orders, and inventories. The index is normalized to have a value of zero
when all of the indicators are moving along their long run trends. Given publication lags, the monthly
10
ft gdp ( t + k ) = E[ gdp (t + k ) | Ωt ]
(2)
where Ωt is the information set used to construct the forecasts. I make no assumptions on
whether or not Ωt encompasses a formal model of economic activity. I do, however,
assume Ωt reflects a view that gdp(t) is the sum of a permanent or trend component,
gdpp(t), and a transitory component, gdptr(t). The change in the permanent component of
GDP includes an expected average trend rate of growth, αt. As in any business cycle
model, the permanent component reflects the underlying production technology and
wealth endowment of the economy, while the transitory component represents monetary
policy shocks, temporary changes in production possibilities, or factors that shift the
allocation of spending across time. Accordingly, as one looks ahead from time t to time
t+k, the actual value of gdp(t+k) will converge to gdpp(t+k) as the transitory factors run
their course and gdptr(t+k) approaches zero. These properties are summarized in the
system of equations (3):
gdp ( t ) = gdp p (t ) + gdp tr (t )
ft gdp ( t + k ) = f t gdp p (t + k ) + ft gdp tr (t + k )
lim ft gdp tr (t + k ) = 0
k →∞
(3)
lim ⎡⎣ f t gdp (t + k ) − ft gdp p (t + k ) ⎤⎦ = 0
k →∞
lim ⎡⎣ f t gdp p (t + k ) − f t gdp p (t + k − 1) ⎤⎦ = α t .
k →∞
In order to isolate the perceived shocks to these components, I will work with the
change made between period t-1 and period t in the forecast of period-t+k GDP; this
forecast revision is denoted ft rgdp(t+k):
ft r gdp(t + k ) = ft gdp (t + k ) − ft −1 gdp (t + k )
= [ ft gdp p (t + k ) − f t −1 gdp p (t + k )] + [ ft gdp tr (t + k ) − ft −1 gdp tr (t + k )] (4)
= ft r gdp p (t + k ) + f t r gdp tr (t + k ).
indicators in the CFNAI-MA3 are generally between one or two months old. For more information on the
CFNAI, see Evans, Chin, and Pham-Kanter (2002).
11
Because the revisions are changes in conditional expectations, they reflect the new
information that forecasters choose to incorporate in their GDP projections. These
shocks cause revisions to the forecasts of both the permanent and transitory components
of GDP, ft rgdpp(t+k) and ft rgdptr(t+k), respectively. 8 The variability in the ft rgdp(t+k)
and the correlations between the ft rgdp(t+k) and ft rgdp(t+j) (revisions made at the same
point in time to projections of GDP at different forecast horizons) thus can be used to
identify both the perceived permanent and transitory shocks to output and how the shocks
are expected to propagate or dissipate over time. But to identify the shocks and response
patterns, I need to specify a parametric time-series model for the forecast revisions.
I assume that two factors may cause forecasters to revise their projections for
permanent GDP. The first is et, a shock that causes a permanent increase in the level of
GDP. The shock is normalized to have a unit impact on the projection for output in the
current period. Forecasters, however, may believe it takes a few periods before et
completely work its way into output; it’s effect on gdpp(t+k)--the impulse response--is
measured by the parameter, θk. 9 The complete impact is assumed to take R periods, so
that θk = θR for all k ≥ R. The second factor that can cause a revision to the outlook for
permanent GDP is a change in forecasters’ assumptions of the average long-run growth
rate in GDP, which I denote wt; after k periods, this would cumulate into a revision in the
outlook for gdpp(t+k) of kwt. I assume that wt is observable and equal to the change in
the long-run forecasts made at time t and t-1, ftΔgdp(lr) – ft-1Δgdp(lr). Because shocks to
tastes and technology that could lead to changes in gdpp(t+k) may cause both a jump in
the level and a permanent change in the growth rate of output, I allow for a covariance,
θlr, between et and wt. In sum, then, the revision in the level of permanent GDP is:
8
See Berger and Krane (1985) for a discussion of the use of forecast revisions to identify the information
sets used by forecasters’ and to test for broader concepts of forecast efficiency.
9
This differs from many univariate models decomposing permanent and transitory changes in GDP, which
assume the full impact of et on permanent output is instantaneous.
12
ft r gdp p (t + k ) = (k + 1) wt + θ k et
wt = f t Δgdp(lr ) − f t −1Δgdp(lr )
θ 0 = 1;
θ k unrestricted for 1 ≤ k ≤ R;
θ k = θ R > 0 for k ≥ R
(5)
E[ wt et | Ωτ ] = θlr .
I also assume that transitory factors influence GDP; the perceived transitory shock
in period t is denoted by ut. The impact of ut on the current level of GDP is normalized to
unity. This shock may influence GDP for some time, and the impulse response on
gdptr(t+k) is measured by the parameter, ρk. However, because it is transitory, the effect
of this shock eventually dissipates to zero; the model incorporates this restriction by
assuming there is some J ≥ 0 such that ρj = 0 for j > J. This means that the revisions to
the forecasts for transitory GDP may be written as:
ft r gdp tr (t + k ) = ρ k ut
(6)
ρ0 = 1;
ρ k unrestricted for 1 ≤ k < J ;
ρ k = 0 for k ≥ J .
I also assume that ut is independent of et and any changes in assumptions about
long-run growth at all leads and lags. All of the shocks are assumed to have conditional
zero means and constant variances:
E[et | Ωt −1 ] = E[ wt | Ωt −1 ] = E[ut | Ωt −1 ] = 0
E[et ut +i | Ωt −1 ] = E[ wt ut +i | Ωt −1 ] = 0
E[et2 | Ωt −1 ] = σ e2 ; E[ wt2 | Ωt −1 ] = σ w2 ; E[ut2 | Ωt −1 ] = σ u2 .
i≥0
(7)
13
Given equations (5), (6), and (7), the observed revisions made at time t to the
forecasts for actual GDP in period t+k can be written as:
k=0: ft r gdp(t ) = wt + et + ut
k < R : f t r gdp (t + k ) = (k + 1) wt + θ k et + ρ k ut
(8)
k ≥ J : ft r gdp(t + k ) = (k + 1) wt + θ R et ,
where, for convenience, I set R = J-1.
Note that if the forecasts were being mechanically generated from a single semiannual statistical model of the economy, then the forecast revisions--and hence wt, et, and
ut--would be functions of only the model’s last forecast error. But there is no such model
underlying the Blue Chip Consensus. Instead, wt, et, and ut reflect any and all
information that forecasters build into their projections at time t. Importantly, the
forecast error learned in period t reflects only the news revealed in gdp(t-1) (since GDP is
published with a lag); but a host of additional factors influencing current and future GDP
also are learned at that time, and these will be included in the shocks in my model.10
Note, though, that a transitory shock learned today that is thought to influence GDP only
in period t-1 would not show through in ut. This means that the variance decomposition
of the k = 0 forecast revision could attribute more variation to the permanent shock than
many of the forecast-error based decompositions of actual GDP estimated in the
literature.
3.2 Identification
The system of equations (8) is my basis for estimation. In particular, the
structural parameters can be recovered from the variance-covariance structure of the
ft rgdp(t+k). This structure is:
10
This is particularly important since I am working with semi-annual data, and a good deal of such
information becomes available during a half-year period. Furthermore, as discussed in appendix 1, the
forecast errors may contain certain measurement errors that are not in the k = 0 revisions.
14
k = 0: Var[ ft r gdp (t )] = σ w2 + σ e2 + σ u2
k ≠ 0 : Var[ f t r gdp (t + k )] = (k + 1) 2 σ w2 + θ k2σ e2 + (k + 1)θ kθlr + ρ k2σ u2
Cov[ f t r gdp (t ), f t r gdpt (t + k )] =
(k + 1)σ w2 + θ kσ e2 + (k + 1 + θ k )θlr + ρ k σ u2
(9)
Cov[ f t r gdp (t + j ), f t r gdp (t + k )] =
( j + 1)(k + 1)σ w2 + θ jθ kσ e2 + [( j + 1)θ k + (k + 1)θ j ]θlr + ρ j ρ k σ u2
k ≥ J : Var[ f t r gdp (t + k )] = (k + 1) 2 σ w2 + θ R2σ e2 .
The system of equations (9) is useful for thinking about identification and estimation. A
natural candidate for an estimator is a method-of-moments system constructed by
substituting the sample analogs for the theoretical moments in (9). Because J is large,
there are enough moment conditions to solve for all of the σ2’s, θk’s, and ρk’s. Indeed,
since there are more equations than unknowns, there exist more efficient estimators then
simple method-of-moments. In particular, similar moment conditions are embedded in
the likelihood function defined by the Kalman filter model described below, and
parameter estimates and can be obtained by maximum likelihood. The Kalman filter also
produces estimates of et, and ut.
As a practical matter, forecasters provide projections for GDP growth. The
revisions to these forecasts, ft rΔgdp(t+k), are:
k = 0:
ft r Δgdp(t ) = wt + et + ut
k<J:
f t r Δgdp(t + k ) = wt + (θ k - θ k -1 ) et + ( ρ k - ρ k -1 ) ut
k=J:
ft Δgdp(t + j ) = wt - ρ k -1ut
k≥J:
f t r Δgdp(t + k ) = wt .
(10)
r
15
I estimate (10) using the Kalman filter and construct ft rgdp(t+k) from Σi≤k ft rΔgdp(t+i).
3.3 Aggregation and measurement error
The Consensus forecast is the simple average of the projections of the individual
members in the Blue Chip panel. As such, the model of forecast revisions is meant to
capture the average perceptions of shocks and propagation patterns. For it to do so, I
need to add measurement error to the model.
Let the subscript “i” denote the ith forecaster’s forecast revisions (fitrΔgdp(t+k)),
perceptions of permanent and transitory shocks (wit, eit, uit), and coefficients on the
dissemination processes (θik, ρik). The fitrΔgdp(t+k) are specified as in (10) with “i”
subscripts on the parameters and shocks. The Consensus values for each of these
variables and parameters are then the simple averages of the N forecaster-specific values.
Consider first the k = 0 Consensus forecast revision:
ft r Δgdp (t ) =
1 N r
1
f it Δgdp (t ) =
∑
N
N i =1
N
∑w
it
i =1
+
1
N
N
∑e
it
i =1
+
1
N
N
∑u
it
i =1
(11)
= wt + et + ut .
Because all the idiosyncratic factors average out, the k = 0 revision reflects the average of
the individual forecasters’ views of the permanent and transitory shocks. Similarly, for k
> J, the consensus revisions accurately reflect wt.
However, for 0 < k ≤ J, the Consensus forecast revision contains forecaster-specific
effects. In particular,
16
ft r Δgdp(t + k ) =
=
1 N r
∑ fit Δgdp(t + k )
N i =1
1
N
N
∑ wit +
i =1
1
N
N
∑ (θik − θik −1 )eit +
i =1
1
N
N
∑ (ρ
ik
i =1
− ρik −1 )uit
(12)
= wt + (θ k − θ k −1 ) et +
1
N
+ ( ρ k − ρ k −1 ) ut +
1
N
N
∑ [(θ
− θik −1 ) − (θ k − θ k −1 ) ] eit
ik
i =1
N
∑ [( ρ
ik
i =1
− ρik −1 ) − ( ρ k − ρ k −1 ) ] uit .
This revision differs from the average effects modeled in equation (10) by the terms in
the summations over eit and uit. Without information on individual forecasts, we cannot
estimate these extra terms. Instead, I model them as measurement errors, vt(k),
vt(k) =
1
N
N
∑ [(θik − θik −1 ) − (θk − θk −1 )] eit +
i =1
1
N
N
∑ [( ρ
i =1
ik
− ρik −1 ) − ( ρ k − ρ k −1 ) ] uit
to be added to equation (10) for 0 < k ≤ J. I assume E[vt(k)2] = σ2vk; E[vt(k) vτ(j)] = 0 for
all t and τ, and j ≠ k, and E[vt(k) et] = E[vt(k) ut] = E[vt(k) wt] = 0 for all k and t.11
3.4 Making the model operational: the state space representation
Define the following matrices:
11
As discussed in appendix 1, measurement error also is induced into the system due to the fact that for
periods beyond which the quarterly forecasts are published, the semi-annual projections are constructed by
distributing annual-average forecasts to the two halves of the year.
17
⎡ ft r Δgdp(t ) ⎤
⎢ r
⎥
⎢ f t Δgdp(t + 1) ⎥
⎥
Ft r ΔGDP = ⎢
:
⎢
⎥
⎢ ft r Δgdp(t +J ) ⎥
⎢ r
⎥
⎣⎢ ft Δgdp(lr ) ⎦⎥
⎡ ut ⎤
St = ⎢⎢ et ⎥⎥
⎢⎣ wt ⎥⎦
⎡σ u2 0
0⎤
⎢
⎥
Σ S = E[ St St' ] = ⎢ 0 σ e2 θlr ⎥
⎢ 0 θlr σ w2 ⎥
⎣
⎦
1
1
⎡
⎢ ρ −1
θ1 − 1
1
⎢
⎢ ρ 2 − ρ1
θ 2 − θ1
⎢
B=⎢
:
:
⎢ ρ J −1 − ρ J − 2 θ J −1 − θ J − 2
⎢
0
⎢ − ρ J −1
⎢
0
0
⎣
⎡ 0 ⎤
⎢ v (1) ⎥
⎢ t ⎥
vt = ⎢ : ⎥
⎢
⎥
⎢vt ( J ) ⎥
⎢⎣ 0 ⎥⎦
1⎤
1⎥⎥
1⎥
⎥
:⎥
1⎥
⎥
1⎥
1⎥⎦
⎡0 0
⎢0 σ 2
v1
⎢
'
Σ v = E[vt vv ] = ⎢ :
:
⎢
⎢0 0
⎢⎣0 0
0 0
0 0
:
:
0 σ vJ2
0 0
0⎤
0 ⎥⎥
: ⎥.
⎥
0⎥
0 ⎥⎦
(13)
The vector St is an unobserved state variable. The observed forecast revision process,
FrΔGDPt, is described by the state-space model:
F r ΔGDPt = BSt + vt .
The log likelihood function for the revision process (excluding constants), L, and the
Kalman filter updating equations for the state variables are:
(14)
18
L= −
1 T
1 T
−1
log B ' Σ s B + Σ v − ∑ F r ΔGDPt ' ( B ' Σ s B + Σ v ) F r ΔGDPt
∑
2 t =1
2 t =1
St|t −1 = 0
(15)
St|t = Σ s B ( B ' Σ s B + Σ v ) F r ΔGDPt .
−1
Estimates of the θ’s, ρ’s, σ2’s can be obtained by maximizing the likelihood function and
estimates of the fundamental shocks ut, et, and wt can then be found by applying the
Kalman filter updating equations.
Note that because k = 0, 1, … 9, I set J = 9. The full set of revision series run
from the second half of 1982 the first half of 2005. This means I have 23 years of semiannual data and 10 revisions with each observation, leaving 460 observations. Of course,
given that the half-year forecasts are interpolated from annual data beyond k = 3, as a
practical matter, I am effectively working with 322 independent observations. The model
contains 29 parameters.
4. Estimation Results
4.1 The revision process
Table 2 shows the model estimates. The first and third columns show the
parameters directly estimated by (15), the revisions to growth (in annual rates), ρk - ρk-1,
and θk - θk-1, while the second and fourth columns give the implied revisions (in
percentage points) to the level of GDP.12 The bottom rows give estimates for σ2u, σ2e, σ2w,
and θlr. Bootstrapped standard errors are in parentheses.
Consider first the transitory shocks. After raising growth on impact, these shocks
have little effect on projected growth for the next year. They then reduce growth over the
following year and a half as GDP returns to its permanent level. In terms of the level of
GDP, the ρk indicate the transitory shocks have an economically meaningful influence for
12
Because the forecasts are recorded as semi-annual growth at an annual rate, I need to multiply the ρk and
θk by 0.5 to calculate the effects on the level of GDP.
19
about 2 years but then dissipate quickly. The effect of the shock is statistically significant
for 1-1/2 years. The sum of the coefficients is 1.15. This means that integrating over
time, the transitory factors are perceived on average to produce a net positive or negative
change in GDP from its permanent level as opposed to a zero-sum shift in the timing of
output between today and tomorrow.
Turning to the permanent shock, one interesting result is that its projected effect
does not occur entirely at the time of the shock: θ1 - θ0 = 0.27, indicating an additional
27 basis point (annual rate) increase in output in the half year following the shock. But
with a t-ratio of 1.6, this extra growth effect has only marginal statistical significance.
That said, the extra boost does not dissipate; this is seen in the coefficients for the effects
on the level of output, which are above 0.6 for all k > 0. Accordingly, there is some
suggestive evidence that forecasters believe et is not a simple random walk, though given
the standard errors, one cannot reject the hypothesis that these gains are no greater than
the impact effect at the usual levels of statistical significance.
As seen in the bottom row of the table, the variance of the permanent shock, σ2e,
is more than twice as large as the variance of the transitory shock, σ2u. Accordingly, twothirds of the changes that forecasters make to their projections of GDP in the current halfyear reflect perceptions of permanent gains or losses in output. Finally, θlr = 0.04; this
correlation between et and wt indicates that forecasters see a small positive relationship
between a permanent shock to the level of output and a perceived change in the trend
growth in GDP. This relationship, however, is not statistically significant.
4.2 The scaled responses and variance decomposition
Figure 3 combines the shock and response information by plotting the revisions to
the k-period-ahead forecasts of the level of GDP scaled by the standard errors of the
shocks. The upper panel plots the effect of the transitory shock, σu ρk; the middle panel
the effect of the permanent shock, σe θk; and the bottom panel the combined effects of the
permanent shock and the shock to long-run growth, k[σ2e (θk - θk-1) + σ2w + 2 θlr]1/2. The
horizontal axes plot the forecast horizon, k. The panels also plot two-standard error
bounds for each set of responses; these are calculated from bootstrapping the σuρk, σeθk,
20
and [σ2e (θk - θk-1) + σ2w + 2 θlr]1/2. Table 3 gives the corresponding decomposition of
the variance of the revision between transitory and permanent components and
measurement error.
As seen in the upper panel of the figure, the scaled transitory effects are
statistically significant for up to a year and a half. Furthermore, any noticeable future
offsetting response in production is of marginal statistical significance. As seen in the
middle panel, the upslope in the response to the permanent level shock, et, differs from
the flat line one would see if gdpp(t) were a random walk; though given the standard
errors, there is little statistical significance in this pattern. Finally, in the long-run, the et
and wt shocks together add to growth at a rate of one-tenth of a percentage point per year
(lower panel).
With regard to the variance decomposition (table 3), the variance of the revision
to the level of output in the current half year period is 0.33 percentage point (not at an
annual rate). 13 Of this, about one-quarter is assumed to reflect transitory factors, twothirds the permanent et shocks, and the remaining 6 percent the shock to long-run growth,
wt, and its interaction with et. Only between 12 and 15 percent of the k = 1 and k = 2
revision variance reflects transitory factors, while et accounts for 58 to 66 percent.
Naturally, over time, the revisions to the trend growth become increasingly import; wt
and cov(et,wt) account for nearly 30 percent of the level revision by 2-1/2 years.
Measurement error accounts for about 15 percent of the variance in the k ≥ 2 revisions.
Recall the interpretation of measurement error as the variability in forecaster-specific
views of shocks and impulse responses about the average view captured by the
Consensus. The small amount of variability in the total revision that this error accounts
for suggests a strong tendency for individual forecasters’ perceptions of economic events
to cluster around a viewpoint common to all of the Blue Chip panelists.
To sum, forecasters believe that transitory shocks influence the path of real GDP
over the next 1-1/2 to 2 years. The transitory factors are perceived to largely reflect net
positive or net negative influences on production for some limited period of time as
opposed to a shift in a fixed level of output between today and tomorrow. Even in the
21
near-term, however, permanent shocks are believed to be a more important influence on
output than transitory shocks. Finally, the forecasters may not believe that the permanent
factors are best modeled as a simple random walk, but may instead take some time to
become fully reflected in GDP.
4.3 The time series of the shocks
Figures 4a and 4b plot the perceived shocks to GDP. The solid lines in the top
panel of each figure are the transitory shocks, ut, the solid lines in the middle panels are
the permanent shocks to the level, et, and the solid lines in the bottom panels are the
changes in the long-run growth rate, wt. The ut and et plotted here are the values of the
unobserved components generated by the Kalman smoother.14 The shaded periods mark
NBER recessions. Figure 4a compares ut, et, and wt with the error learned in time t for
the k = 0 forecast made in time t-1, gdp(t-1) – ft-1gdp (t-1) (shown by the dashed lines in
each panel). The bottom panel of figure 4a also compares wt with the average revisions
to historical growth in the GDP that occurred with comprehensive revisions to the
national income accounts in 1985, 1991, 1996, and 1999 (the bars; see appendix 1).
Figure 4b compares the shocks to the incoming information on the current state of the
economy as summarized by the CFNAI-M3 in the second month of semi-annual period t
(the dashed lines).
First, comparison of the ut and et in the top two panels of both figures highlights
the greater variability in the permanent shock. For example, 17 values of et are greater
than 3/4 percentage point in absolute value and 10 are greater than 1 percentage point; the
corresponding counts for ut are just 10 and 3. Second, there are some large negative
permanent shocks at the times of discrete events that hit the economy; notable ones occur
with the stock market crash in 1987, the onsets of the recessions in late 1990 and early
13
Recall that the revisions to the level are not at annual rates. The revision in the level is 0.5 times the
revision to the semi-annual growth rate, so the 0.33 percentage point level revision variance equals 0.25
times the 1.31 percentage point variance in the k=0 growth rate revision cited earlier.
14
By construction, the forward filtered ut and et are serially uncorrelated, but there is no reason for the
smoothed estimates to be. Still, a regression of ut, on ut-1 finds a small and statistically insignificant
coefficient. The et are also serially uncorrelated. That said, ft rΔgdp(t) itself exhibits some serial
correlation; a regression of it on ft-1 rΔgdp(t-1) yields a coefficient on the lag of 0.37 and an adjusted R2 of
0.14. However, the ft rΔgdp(t+k) for k>0 are not correlated with any ft-1 rΔgdp(t+j), j ≥ 0.
22
2001, and the forecast following September 11, 2001. Indeed, if these four observations
are excluded, σ2u changes little but σ2e falls by about one-third. Apparently, forecasters
saw these events as unusual but identifiable discrete shocks that had the potential to
noticeably and permanently disrupt economic activity without any offsetting recovery in
production once events had run their course.
Next, consider the relationships between the shocks and the forecast errors shown
in figure 4a. There are not any obvious regular relationships between these errors and ut,
et, or wt. There are, however, a few interesting case studies. One was in the mid 1980s,
when there appears to be some negative correlation between the forecast errors and both
shocks. Apparently forecasters were having trouble judging the timing of the strong
recovery from the 1981-1982 recession. This episode seemed to influence forecasters
later in the decade, when there were several negative valuations for both et and wt.
Another interesting period was during the boom of the late 1990s. Here, a string of
positive forecast errors led to two years of small upward revisions to the permanent level
of output and an upgrading of views regarding long-run growth. Finally, the
comprehensive revisions to the national income accounts appear to have influenced
forecasters to revise their perceptions of the long-run growth rate of output, particularly
so with the 1999 revision.
Turning to figure 4b, the CFNAI-MA3 and ut exhibit some positive comovement
throughout the sample period, consistent with the evidence shown in figure 2. The
CFNAI-MA3 and et move together during recessions, but no clear pattern emerges during
other periods. And other than during the late 1990s, the changes in perceptions of longrun growth and the CFNAI-MA3 appear to be uncorrelated.
In order to provide some statistical description of these relationships, table 4
presents a regression of the k = 0 forecast revision on the forecast error in last period’s k
= 0 forecast and the last four months of CFNAI-MA3 data that became available between
the times the t-1 and t forecasts were made. The first column considers the total revision
while the second and third columns run separate regressions for the revisions due to the
transitory and permanent shocks.
As seen by the p-values reported in the table, despite the examples in the 1980s
and 1990s noted above , the previous half-year’s GDP forecast error has virtually no
23
statistical explanatory power for the current-period revisions. In the eyes of the Blue
Chip forecasters, their previous forecast error does not consistently reveal useful
information about the course of activity going forward. In contrast, the CFNAI-MA3
data are highly statistically significant in all three regressions. The effect is strongest in
the equation for the transitory shock; indeed a simple regression of ut on the CFNAI-M3
terms has an R2 of nearly 40 percent.
Furthermore, there is some statistical support for the pattern found in figure 4b of
forecasters reacting more to incoming data during periods of economic weakness. The
third and fifth columns in table 4 allow for a separate coefficient on the most recent
CFNAI-MA3 value known at time t if it is less than -0.5. This occurs in 7 of the 46 semiannual observations.15 The coefficient is statistically significant in the regressions for the
overall revision; indeed, it drives out the statistical significance of the other CFNAI-MA3
variables. In the regression for the transitory shock, the threshold CFNAI-MA3 variable
has a coefficient of -0.22, indicating that forecasters perceive some offset to recessionary
declines in output from higher production in latter periods. However, the magnitude of
this offset is small and the coefficient is not close to being statistically significant. In
contrast, the threshold variable has a coefficient of 1.26 and a p-value of 0.02 in the
regression of the permanent shock; its inclusion even drives out the statistical influence
of the other CFMAI-MA3 variables in the regression.16
These regressions are consistent with forecasters believing that large permanent
declines in output characterize recessions. This contrasts with say Friedman’s (1964)
“plucking” model in which recessions represent a drop in output and then a recovery to
trend--and thus reflect a temporary loss in production--as well as alternative models in
which the lost output is made up for by above trend production sometime during the
subsequent expansion. It is, however, consistent, with the permanent losses in output
found in Hamilton’s (1989) Markov-switching model of recessions. Furthermore, the
large negative values for et following the stock market crash in 1987 and September 11,
15
The specific dates are 1982:H2, 1990:H2, 1991:H1, 1992:H1, 2001:H1, 2001:H2, and 2003:H1.
Accordingly, 5 fall during recessions and 2 during periods of sluggish recovery.
16
A univariate regression of et on the negative threshold CFNAI-MA3 variable has an R2 of 0.23, the same
as the base regression. Note also that if I instead put a positive threshold CFNAI-MA3 variable (values
greater than 0.5) in the regression, its coefficient is small and statistically insignificant (-0.32 with a p-value
of 0.21).
24
2001 are consistent with the idea that forecasters think such special and readily
identifiable adverse shocks will generate unusually large permanent reductions in
economic activity. Of course, with only three recessions and a couple of such special
events in the sample, one should not overemphasize the statistical substance of these
results. Still, they suggest that forecasters think that the data generating process for GDP
differs between recessions and expansions. Linear models with independent and
identically distributed error processes cannot encompass such a view of the business
cycle.17
In addition, the correlations between forecast revisions and incoming highfrequency measures of economic activity are instructive for empirical modeling. First,
the correlations suggest that these indicators may be useful additions to the lagged
endogenous variables typically employed to instrument expectational variables in Euler
equations or current-period variables in structural vector autoregressions. Second, the
linkage between expectations and the high-frequency indicators may help explain why
such variables prove helpful in modeling the term structure of interest rates (see, for
example, Ang and Piazzesi (2003) and Evans and Marshall (2002)). Namely, the term
structure incorporates expectations for the path of economic activity from today through
the long run; and according to my results, high frequency indictors appear to be important
determinants of changes in agents’ expectations of both transitory fluctuations in GDP
and permanent shifts in economic activity.
5. Comparing the Results to Time Series Models for GDP
5.1 Some statistical models for permanent and transitory shocks to GDP
The specification above motivates the separation of forecast revisions into
permanent and transitory components from a simple univariate time series model for
GDP. So it is natural to ask how the Blue Chip revisions compare with the
17
This result also suggests that the state-space model (13) can be improved by incorporating some type of
non-standard specification for σ2e that recognizes the possibility of large negative realizations of et during
recessions or periods following unusual economic events.
25
decompositions into permanent and transitory shocks generated from statistical
specifications of the process for actual GDP. Are forecasters patterning their perceptions
of shocks along the lines estimated by these models?
This section compares the Blue Chip forecast revisions with comparable forecast
revisions from four time-series models for GDP. Because these models generally are
estimated using quarterly data, one needs to aggregate their impulse responses to the
semi-annual frequency. As described in appendix 2, if the Wold representation of a
quarterly univariate statistical model for forecasting GDP growth
(1 − L) gdp(t ) = ω * ( L)ε (t )
(16)
where ω*(L) is a square sumable lag polynomial with ω*0 = 1 and ε(t) is the shock or
vector of shocks to GDP, then there exists the following semi-annual correspondence
between the Blue Chip revisions and those from the quarterly statistical model:
Blue Chip : ft r gdp (t + k ) = ft gdp (t + k ) − f t −1 gdp (t + k )
Statstical Model : fτr gdp(t + k ) =
2( k +1) +1
∑
ωiε (τ - 2) +
i =1
2( k +1)
∑ ω ε (τ - 1)
i
i =1
i
ωi = ∑ ω *j
(17)
j =0
τ - 2 = first quarter of half − year period t - 1
τ - 1 = second quarter of half − year period t - 1.
I consider four simple econometric models that are designed to identify both a
permanent and a transitory shock to real GDP and how these shocks propagate over time:
the Beveridge-Nelson (1981) decomposition; a univariate unobserved components (UC)
model similar to Clark (1987) or Campbell and Mankiw (1987a, b); the Blanchard-Quah
(1989) bi-variate structural VAR in GDP growth and the level of the unemployment rate;
and the Campbell-Krane (2005) multivariate structural VAR. The Beveridge-Nelson
decomposition assumes gdpp(t) follows a random walk and that Δgdp(t) can be described
by an ARMA model. The UC model assumes both Δgdpp(t) and gdptr(t) follow ARMA
26
processes. The Blanchard-Quah model identifies the transitory shock to GDP through the
assumption that it has no effect on the long-run level of GDP. The Campbell-Krane
model is a 6-variable VAR in private GDP, nondurables and services consumption,
durables consumption and residential investment, the federal funds rate, core PCE
inflation, and food and energy inflation. In the spirit of Cochrane (1994), it identifies the
permanent shock by restricting it to be the only shock in the VAR that has a long-run
influence on the level of consumption. It is the only one of the models also explicitly
designed for forecasting. Appendix 2 describes the models in more detail.
5.2 Estimation results
I use AIC and BIC information criteria to identify the models, picking an AR(2)
model in the growth rate in GPD in the Beveridge-Nelson case; a simple random walk for
gdpp(t) and an AR(2) for gdptr(t) in the UC model, and a third-order VAR in the
Blanchard-Quah case. Campbell-Krane used similar specification criteria to choose lag
length and contemporaneous zero restrictions in their model.18
Figure 5a compares the Blue Chip forecast revisions to permanent and transitory
shocks (scaled by the standard deviations of the shocks) with those implied by the two
univariate models for GDP. The black and blue lines in each panel replot the scaled Blue
Chip revisions shown in figure 3 and their two-standard error bounds. The green lines in
the top two panels are the GDP model estimates of the impulse responses of a transitory
shock on the level of GDP; the green lines in the bottom panels are the model responses
to a permanent shock. Figure 5b shows plots for the multivariate models. As seen in the
graphs, there are noticeable differences between the scaled impulse responses of the
models and of the Blue Chip forecasts.
18
The first three models are estimated using currently published quarterly data for the period 1967-2005. I
chose to start in 1967 because in 1982, the first year in my Blue Chip sample, forecasters undoubtedly
would have been considering the history of the previous 15 years when making there assessments of the
shocks hitting the economy. I also decided to give the model some “extra” information by estimating 3
different constant terms to allow for changes in long-term growth—one for the period 1967-1973; one for
1974-1995, and one for 1996 and on. This was done since αt is observed to change over time. For reasons
discussed in their paper, the Campbell-Krane model is estimated using data from 1984 onwards. Note that
the Campbell-Krane model does not identify a single transitory shock; the transitory shock referred to in
this paper is the covariance weighted average of the 5 transitory shocks found in the model.
27
Qualitatively, the pattern of the Blue Chip revisions to transitory shocks
resembles those in the UC, Blanchard-Quah, and Campbell-Krane models: the entire
initial shock remains in the level of GDP for about a year and then dissipates quickly
towards zero. However, the magnitudes of the responses are much different. All three of
these models see the transitory shock inducing forecast revisions of between 1 and 1-1/2
percentage points of GDP over the next year, while the Blue Chip innovation in response
to a transitory shock is about 1/3 percentage point. The initial response of the Blue Chip
forecasters to a transitory shock is of similar magnitude to that from a Beveridge-Nelson
decomposition. However, the Beveridge-Nelson transitory shock only has a palpable
effect on the k = 0 forecast, as compared with longer-lived effects in the Blue Chip.
With regard to the permanent shock, both univariate models assume et follows a
random walk, while the multivariate models share the Blue Chip feature that the impulse
from a permanent shock takes some time to feed into GDP. The Blue Chip and
Blanchard-Quah impulses share a similar upward sloping pattern, while the CampbellKrane impulses exhibit some hump shaped behavior. The variances of the permanent
shock are of similar magnitude in all of the forecasts with the exception of the BeveridgeNelson decomposition, where it is about three times the size of the Blue Chip.
5.3 The influence of high-frequency data on the differences between the revisions from
the Blue Chip Consensus and the econometric models
One reason that the impulses and shocks differ across the Blue Chip and model
forecasts is the difference in conditioning sets. The revisions to the statistical GDP
models’ projections are functions of lagged forecast errors. Accordingly, they are
functions only of GDP in the Beveridge-Nelson and unobserved components models, of
GDP and the unemployment rate in the Blanchard-Quah specification, and of private
GDP, consumption, durables and residential investment, interest rates, and inflation in the
Campbell-Krane model. In contrast, the revisions to the Blue Chip forecasts encompass
any information forecasters care to incorporate.
As seen in section 4, the Blue Chip forecasters appear to discount the persistence
of past forecast errors but revise their projections noticeably in response to the
28
information contained in high-frequency indicators of economic activity. By
construction the econometric models do not ignore their past errors; but what would the
responses of these models look like if they incorporated high-frequency data?
I reran all of the time series models using the value of the CFNAI-MA3 in the
third month of quarter t-1 as an exogenous explanatory variable. Table 5 shows the
standard deviations of the k = 0 forecast revisions--which are the sum of all the period-t
shocks--for the Blue Chip forecasts, the base case statistical models, and the statistical
models that include the CFNAI.
The base-case (left-hand columns) illustrate the results cited in the discussion of
the impulse responses in section 5.2: with the exception of the transitory BeveridgeNelson and permanent Blanchard-Quah shocks, both the permanent and transitory shocks
to the Blue Chip are smaller than the corresponding shocks in the models’--and often
substantially so. And the Beveridge-Nelson model is the only specification that attributes
at least as high of a share of the revision variance to the permanent shock as the Blue
Chip does.19
The standard deviations of the GDP models’ k = 0 revisions are markedly smaller
when the CFNAI is added to their specifications (right-hand columns). Furthermore,
incorporation of the CFNAI eliminates all of the transitory shock estimated by the
univariate Beveridge-Nelson and UC models. The standard deviations of both shocks in
the Blanchard-Quah model are now nearly identical to those in the Blue Chip, and the
variation in the transitory shock Campbell-Krane model is much closer to the Blue Chip.
That said, the pattern of the impulse responses in the Blue Chip and adjusted BlanchardQuah models (not shown) differ substantially: the adjusted Blanchard-Quah transitory
response declines linearly to zero instead of having a hump shaped. Furthermore, the
correlation between that model’s k = 0 forecast revision and the Blue Chip’s is small (10
percent). In contrast, the impulse response pattern in the Campbell-Krane model does not
19
Of course, part of the reason that the Blue Chip revision may be small is that the Consensus forecast is
the simple arithmetic average of about 50 individual forecasts. To the extent that averaging smooths out
idiosyncratic reactions, the variance in the Consensus’ forecast revisions will be less the average variance
of the revisions made by the individual forecasters. While individual quarterly forecasts are not available
for the Blue Chip panel, some subgroup averages are. As described in appendix 3, these subgroups can be
used to calculate a potential upper bound for the smoothing effect. The calculations suggest the standard
deviation of the Consensus forecast revision understates the average standard deviation of the individual
forecasters’ revisions by only about 20 percent.
29
change much from the base case; it merely shifts down by the change in the standard
deviation of shocks. Still, like the Blanchard-Quah model, the correlation between the
adjusted model and Blue Chip revisions is small (12 percent).
In sum, the Blue Chip forecast revisions more resemble those of multivariate
models of GDP than the univariate decompositions. Even with these models, however,
there are important differences between the revision processes. Some of the differences
in the variation in the shocks may reflect the use of the incoming high-frequency data by
the Blue Chip forecasters. In particular, the differences in the standard deviations close a
good deal when the CFNAI-MA3 is added to the statistical models; nonetheless, the
models still produce a much different pattern of behavior than is implied by the Blue
Chip forecast revisions.
Conclusions
This paper uses a statistical model of the forecast revisions to infer forecasters’
implicit decomposition of news into permanent and transitory shocks to GDP. According
to this model, on average, the forecasters comprising the Blue Chip Consensus perceive
that about 30 percent of the shock to real GDP reflects transitory changes while about 70
percent is due to a permanent change in the level of output; expect transitory shocks to
dissipate in about 1-1/2 to 2 years; and believe there may be a half-year delay before the
entire permanent shock to GDP is in place in the data. These results differ a good deal
from those of some small-scale models designed to identify permanent and transitory
shocks to GDP: the total shocks to the Blue Chip forecast are smaller than the models’,
and their decompositions generally see a much larger role for transitory shocks.
One reason for the differences between the models’ and the Blue Chip results
likely revolves around the fact the Blue Chip forecasts are much more heavily influenced
by the incoming high-frequency data on economic activity then by past forecast errors.
This effect is particularly pronounced during recessions or periods of economic
weakness. The results also suggest that forecasters see downturns or expected periods of
sluggish activity associated with unusual, but identifiable, events as comprising more
permanent then transitory reductions in output.
30
One lesson of this paper is that even for broad aggregates such as GDP, agents’
expectations are likely based on a good deal more information than what is incorporated
into quarterly econometric models using data from the national income accounts. In
addition, the result that expectations are more sensitive to incoming data during economic
downturns then during expansions suggests that it may be fruitful to consider models that
allow for shock processes or propagation mechanisms to differ according to the state of
the business cycle. These observations are relevant for researchers who are attempting to
build internally consistent expectations into equilibrium models of the business cycle or
are considering how to more efficiently capture expectations in econometric models.
31
Appendix 1. Data Issues
1. The timing relationships between the March and October Blue Chip surveys and the
national income accounts.
I let the data for March represent the first semi-annual period of the year and the
data for October the second semi-annual period. At the time the October Blue Chip is
published, the most recent published National Income and Product Account (NIPA) data
are the third, or “final,” estimates for the second quarter. This means the most recent
history is a final estimate of growth for the previous semi-annual period--the fourth
quarter of last year to the second quarter of the current year. In March, the most recent
historical NIPA semi-annual data are the second estimates for growth between the second
and fourth quarters of the previous year. The revisions between the second and third
estimates of the NIPA usually are small. Accordingly, while the most recent history in
March is not quite the final estimate for growth in the second half of the previous year, it
is not too far from it (annual revisions aside--see below). Still, the October forecasts
contain one more month of data for the t = 0 semi-annual period. I could have accounted
for this difference by including additional measurement errors to the model, but chose not
to do so for reasons of parsimony.
2. Modeling the k = 0 forecast revisions instead of the forecast errors.
As noted in section 3, wt, et, and ut reflect the shocks to the k = 0 forecast, not the
shocks thought to have hit GDP in period t-1. An alternative structure would have been
to start the model with the forecast error for last-period’s GDP, which is also the k = -1
forecast revision,
ft r gdp (t − 1) = gdp(t − 1) − f t −1 gdp(t − 1).
(18)
Note that this error is learned at time t.
As discussed in section 3.1, one reason to prefer the k = 0 over the forecast errors
is that the latter exclude important information relevant to the GDP forecast. Others
relate to well-known difficulties in defining forecast errors that mean they likely contain
measurement error that is not be present in the k = 0 revisions. In order to isolate the true
forecast error, one needs to know if forecasters are predicting the first-published GDP
32
estimate or a revised number (see McNees, 1973). If they are predicting revised data,
then it is necessary to substitute a value for gdp(t-1) learned after period t into equation
(18). So one must decide on the appropriate revised value to use--the one associated with
the final quarterly number, or perhaps one following an annual revision--and also
separately identify the information learned with each revision to the estimate of GDP.
Errors in specifying the data being forecast or differences between the vintages of GDP
being projected by the panelists add measurement error to the model and thus complicate
the identification of shocks. The issue is particularly problematic for this paper because
at the semi-annual frequency, forecasters learn two quarters of data instead of one
between each observation. The use of forecast revisions starting with period k = 0 avoids
all such issues: Since no published values for GDP are needed to construct the revisions,
there is no need make any judgment on the vintage of GDP that is being forecast.
Major revisions to the national accounts are another problem. Annual revisions
are published each July, and four comprehensive revisions to the NIPA also occurred
during the sample.20 The annual and comprehensive revisions fold in a wide range of
information from annual surveys, quinquennial economic censuses, and other data
sources that do not strictly reflect new information learned between time t-1 and t. The
revisions--particularly the comprehensive ones--can also include changes in statistical
methodologies. Accordingly, the forecast errors made in periods spanning these
revisions will reflect a variety of measurement issues in addition to the fundamental
economic shocks affecting activity and thus their use would add measurement error to my
model. In contrast, the k = 0 revisions that span such periods will reflect only the
information forecasters think are of consequences for future growth.
3. Distribution of annual forecasts to semi-annual frequency.
I first construct the annual average levels implied by the k = 0 through k = 3
forecasts made in March or the k = -1 through k = 2 forecast made in October. I then
20
This means that any forecast errors between the March and October projections reflect the effects of the
annual revisions. The comprehensive NIPA revisions took place in December 1985, December 1991,
January 1996, and October 1999, which influences forecast errors for the second halves of 1985, 1991,
1995, and 1999. In general, no annual revisions are made to the NIPA if a comprehensive benchmark is to
come later in the year.
33
apply the published Consensus average annual growth rate forecasts for 2 through 5-yearahead to these data to calculate annual levels for these years.
I then distribute the annual numbers to half-year levels according to an algorithm
that minimizes the difference in the change in GDP between adjacent semi-annual
periods subject to the constraint that the averages of half-year levels equal the annual
level. That is, it chooses ftgdpl(t+k) and ftgdpl(t+k+1) to minimize Σ ηt+k2 subject to the
constraint ftgdpl(t+k) + ftgdpl(t+k+1) = ftgdpl(t+k,t+k+1) where the “l” superscript refers
to the level of GDP, k is the first half-year period, k+1 is the second half-year period,
ftgdpl(t+k,t+k+1) is the published annual forecast, and
ftΔgdpl(t+k) = ftΔgdpl(t+k-1) + ηt+k
ftΔgdpl(t+k+1) = ftΔgdpl(t+k) + ηt+k+1
The resulting levels are used to construct half-year growth rates for k ≥ 4 (for March) and
k ≥ 3 (for October).21 I generate forecast up through k = 9. Conceptually, the 6-yearahead forecasts would allow me to interpolate values for k = 10 and k = 11 as well; I
chose not to do so to avoid any end-point issues that may arise with the interpolation
procedure.
This procedure produces the following forecasts:
ftgdpl(t+k+1) = λftgdpl(t+k,t+k+1) + β1(L)ftgdpl(t+k-1) + β2(L-1)ftgdpl(t+k+2)
ftgdpl(t+k) = (1-λ)ftgdpl(t+k,t+k+1) + β3(L)ftgdpl(t+k-1) + β4(L-1)ftgdpl(t+k+2)
λ is a weight between 0 and 1, the βi(L) are second-order lag polynomials that capture the
smoothing of changes, and β1(L) + β3(L) = β2(L) + β4(L) = 0. So while this smoothing
adds some measurement error to the resulting forecasts, by construction, the errors
21
This means there is a slight difference between how the semi-annual growth rates are measured for small
k—which are second-to-fourth and fourth-to-second quarter changes—and the larger k—which are firsthalf-to-second half and second half-to-first-half changes. Any measurement errors due to differences
between two-quarter and half-year growth rates will be absorbed by the vt(k). (This difference could have
been avoided by distributing the annual data to the quarterly frequency; the cost of doing so would have
been additional measurement error induced by the distribution process.)
34
average out over the two halves of the year. Note, too, that any such measurement error
will be absorbed in the vt(k).
As an alternative to this procedure, one could estimate the model using the
published revisions to annual-average forecasts. The revision to the annual forecast for
the log level of GDP is log[0.5*{exp((k+1)wt + θk+1et + ρk+1ut) + exp(kwt + θket + ρkut)}],
which does not lend itself to the linear structure of the Kalman filter described in section
3. One could instead use the first-order Taylor expansion of the annual forecast revision
about wt = et = ut = 0, which is 0.5*[(2k+1)wt + (θk+1+θk)et + (ρk+1+ρk )ut] + vt’(k+1,k),
where vt’(k+1,k) is measurement error. But by construction, vt’(k+1,k) will be correlated
with wt, et, and ut;; accounting for these correlations requires a significant number of
parameters and complicates the structure of the Kalman filter. In contrast, any
measurement error added by the distribution algorithm described above averages out over
the two halves of the year. This means while the individual θk and ρk may be bias for k ≥
3, the estimates of θk+1 + θk and ρk+1 + ρk will be unbiased.
35
Appendix 2: Econometric Models
1. The Beveridge-Nelson (1981) decomposition.
This decomposition notes that equation (16) can be written as
gdp(τ ) = ω * (1) [ε (τ ) + ε (τ − 1) + .... + ε (1) ] + φ ( L)ε (τ )
∞
φ j = −∑ ω *j +i
(19)
i =1
ω * (1) [ε (τ ) + ε (τ − 1) + .... + ε (1) ] represents the permanent component of GDP and
φ ( L)ε (τ ) is the transitory component. The decomposition is calculated by first
estimating an ARIMA model for the growth in GDP, finding the Wold representation,
and then calculating (19).
2. Univariate unobserved components model.
ρ ar ( L) gdp tr (t ) = ρ ma ( L)ut
(20)
θ ar ( L)(1 − L) gdp p (t ) = α + θ ma ( L)et
ut is the shock to transitory output and et is the shock to permanent output. This implies
an observation equation for gdp growth:
Δgdp (t ) = α '+
(1 − L) ρ ma ( L)
θ ma ( L)
u
+
e
t
ρ ar ( L)
θ ar ( L) t
(21)
where α’ = α/θ(1). The ρar(L), ρma(L), θar(L), θma(L), α’, σ2e and σ2u can be estimated
using the Kalman filter.
3. Blanchard-Quah bivariate VAR representation of GDP and the unemployment rate.
The Wold representation of this model is:
36
⎡ (1 − L) gdp(τ ) ⎤ ∞
⎢
⎥ = ∑ C ( j )υ (τ − j )
un(τ )
⎣
⎦ j =0
(22)
where C(0) is a 2 by 2 identity matrix and ν(t) is a 2 by 1 vector of reduced form errors
with covariance matrix Φ. This model can be used to separate permanent from transitory
shocks to GDP by assuming that shocks to the unemployment rate can not have a
permanent effect on the level of GDP. This is done by considering the Wold
representation of the structural VAR:
⎡ (1 − L) gdp(τ ) ⎤ ∞
⎢
⎥ = ∑ A( j )ε (τ − j )
un(τ )
⎣
⎦ j =0
(23)
where the ε(τ) are a 2 by 1 vector of structural errors. The Blanchard-Quah assumption is
equivalent to saying that the lower right-hand entry of A(1) equals zero. This imposes the
restriction that lower right hand entry of C(1)A(0) is zero and that A(0)A(0)’ = Φ.
4. The Campbell-Krane model.
This model is a 6 variable VAR in: 1) the log difference in personal consumption
expenditures for nondurables and services excluding housing (C); 2) the log ratio of
private GDP (Y) to C; 3) the log ratio of expenditures for consumer durables and
residential investment (D) to C; 4) the federal funds rate; 5) PCE inflation excluding food
and energy; 6) inflation in PCE food and energy. The model is based on the ideas that: 1)
the permanent income hypothesis implies that any permanent shock to the productive
capabilities of the economy will alter C and; 2) balanced growth implies that Y/C and
D/C will be stationary.22 This means the permanent shock to production can be identified
by restricting it to be the only shock that has a long-run impact on C and by restricting
22
As a practical matter, the ratios Y/C and D/C and PCE inflation excluding food and energy exhibit some
important low-frequency variation. Accordingly, as discussed in Campbell and Krane, the model is
estimated in deviations of these variables from their 40-quarter lagged moving average.
37
any shock in the model from having a long-run impact on Y/C, D/C, or the other
variables in the VAR. 23
A couple modifications are necessary to make the model compatible with the other
data presented in the paper. First, the impulses to log Y are calculated by adding the
impulses to log(Y/C) and log C. Second, the impulses to transitory shocks represent the
weighted sum of the responses of Y to all other shocks in the system other than the
permanent income shock. Finally, the impulse responses of Y are multiplied by the ratio
of the standard deviation of total GDP to the standard deviation of private GDP to give
appropriate scaling relative to the impulses presented in the papaer.
5. Derivation of equation (17).
Consider the Wold representation of a quarterly univariate statistical model for
forecasting GDP growth:
(1 − L) gdp(t ) = ω * ( L)ε (t )
(24)
where ω*(L) is a square sumable lag polynomial with ω*0 = 1. It is convenient to work
with the following representation for the level of GDP:
gdp(t ) = ω ( L)ε (t )
i
ωi = ∑ ω *j
(25)
j =0
so that the revision to the q-quarter-ahead forecast made at time t can be written as:
f r gdpτ (t + q ) = ωqε (t )
(26)
The k = 0 Blue Chip projection is the outlook for real GDP in the second quarter
of the current half-year period. Since data for the first quarter of the half year are not yet
known (see appendix 1), this corresponds to a two-quarter-ahead (q = 2) forecast. In
23
The relative importance of transitory shock to the one-step-ahead forecast error estimated by the
Campbell-Krane model is similar to that found in Cochrane (1994), who used data for 1947-1989. Both of
these models identify the permanent shock by allowing it to be the only one affecting consumption in the
long run. These results thus indicate that the use of consumption to identify permanent shocks generalizes
from Cochrane’s simple bivariate system to a larger-scale restricted VAR and to the “post-greatmoderation” sample period (see also, Campbell and Krane).
38
general, the k-period-ahead semi-annual forecast corresponds to a 2k+2-quarter-ahead
forecast. In terms of forecast revisions, the k = 0 revision, for example, reflects the
difference between the q = 4 forecast made in semi-annual period t-1 and the q = 2
forecast made in semi-annual period t. In terms of quarterly forecasts this is the sum of
the revisions between consecutive q = 4 and q = 3 forecasts and q = 3 and q = 2 forecasts.
Suppose period t is the first half of the year; then this revision is the sum of the influence
of first e(Q3) and then e(Q4) onto the projection for GDP in the following second quarter.
In terms of (1.11), the total revision is:
ω1ε (Q3) + ω2ε (Q3) + ω3ε (Q3) + ω1ε (Q 4) + ω2ε (Q 4)
More generally, we have the following correspondence between the semi-annual Blue
Chip revisions and those from the quarterly statistical model:
Blue Chip : ft r gdp (t + k ) = ft gdp (t + k ) − f t gdp (t + k )
Statstical Model : fτr gdp(t + k ) =
2( k +1) +1
∑
i =1
ωi e(τ - 2) +
2( k +1)
∑ ω ε (τ - 1)
i
i =1
τ - 2 = first quarter of half − year period t - 1
τ - 1 = second quarter of half − year period t - 1
(27)
39
Appendix 3 The Influence of Averaging Forecasts
The Consensus forecast is the simple arithmetic average of about 50 individual
forecasts. To the extent that averaging smooths out idiosyncratic reactions, the
Consensus’ forecast revisions will be less variable that the revisions that the individual
forecasters make. How might this smoothing influence the empirical results?
The k = 0 period forecast revision of each individual forecaster i, fitrgdp(t), may
be written as the sum of the Consensus (average) forecast and an idiosyncratic
component, zit, which reflects the range of views on the permanent and transitory shocks
to output. By construction Σ i=1,50 zit = 0. As a statistical matter, I assume the zit are mean
zero and independently and identically distributed across forecasters and are independent
from the consensus revision:
fitr gdp(t ) = f t r gdp (t ) + zit
zit = ( wit − wt ) + ( eit − et ) + ( uit − ut )
E[ zit ] = 0; Var[ zit ] = σ z2 for alli
(28)
Var ⎡⎣ f i r gdpt (t ) ⎤⎦ = Var ⎡⎣ f t r gdp (t ) ⎤⎦ + σ z2
Note that the set up in equation (28) allows for the possibility for forecaster fixed effects;
that is, for some forecasters to always predict that growth will be higher or lower than
average. These fixed effects, however, are differenced out in the forecast revisions.
Individual forecasters’ quarterly projections are needed to calculate σ2z directly,
and the only individual forecasts published by the Blue Chip are for growth on a
calendar-year average basis for the current and subsequent year.24 However, since 1992
24
For example, in terms of the semi-annual frequency I am working with, the forecast made in March for
calendar-year average growth in the current year is [fgdplM(H1) + fgdplM(H2)]/[gdpl(H1t-1) + gdpl(H2t-1)],
where gdpl(H1t) is the level of gdp in half-year i of year t and the subscript M refers to the fact that the
forecast is being made in March. In October, the forecast (the subscript O) for calendar-year average
growth in the current year is [gdpl(H1t) + fgdplO(H2t)]/[gdpl(H1t-1) + gdpl(H2t-1)]. Accordingly, the forecast
revision between March and October reflects both the forecast error for growth in the first half of the year
40
Blue Chip has been publishing quarterly forecasts for the average of the highest 10
forecasts made by the panelists and for the average of the lowest 10 forecasts. If these
forecasters were the same individuals each time period, then the assumptions behind
equation (28) would mean that the differences between the revisions to the consensus
forecasts and the revisions to the group made up by combining the top-10 and bottom-10
forecasters would be observations on Σi=1,20 zit/20 and the variances of the differences
would be estimates of σ2z/20. The forecasters in the top and bottom 10 averages are not
the same across periods. But the forecasters moving into and out of these groups are
more likely to have done so because they made a larger revision than the average
forecaster. This means that the variance of the differences between the consensus and
subgroup revisions likely overestimate σ2z/20, and so can be used to bound σ2z. 25
I constructed time series of Σ zit/20 from the top 10 and bottom 10 averages and
estimated σ2z’s from a 5000 replication boostrap of this time series. This gave an
estimate for σ2z of 0.16. The bootstrap estimate of Var[ft rgdpt(t)] of 0.28, so that under
the assumptions in equation (28), the average standard deviation of the individual
forecasters’ k = 0 revisions is 0.66 percentage point. This compares with a 0.55
percentage point standard deviation for the Consensus revisions over the 1992-2005
period. So the Consensus forecast understates the average variability of the individual
forecasters by only about 20 percent.26
Furthermore, it is unlikely that smoothing out the idiosyncratic variation means
that the relationships between individual forecaster’s revisions and the incoming data
differs substantially from what was estimated using the Consensus outlook. I regressed
the time series for Σ zi/N from the top 10, bottom 10, and combined subgroups on the
same CFNAI data and realized forecast error as shown in table 4. None of the variables
were statistically significant in explaining the Σ zi/N. This supports the view that the
and the revision to growth in the second half of the year, and so cannot be used to back out the appropriate
semi-annual series.
25
Intuition also says that Σ Δzit/10 > 0 for the top ten average and Σ Δzit/10 < 0 for the bottom ten.
However, Σ Δzit/10 is -0.03 for both series.
26
Of course, the bottom and top 10 averages likely are not random draws from the consensus pool. Indeed,
one would not want to assume that the forecasts themselves are random distributed about the consensus
outlook: some forecasters will always be optimistic and some will always be pessimistic. However, the
assumption that the revisions are randomly distributed about the consensus revision is less stringent since
the revisions difference out any forecaster fixed effects. Combining the top 10 and bottom 10 averages also
should help produce more efficient estimates of σ2z.
41
idiosyncratic components of individual forecasters’ revisions are relatively random
disturbances about the Consensus and not systematically related to the incoming data.
42
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44
Table 1: Summary Statistics for the Blue Chip Consensus Forecast Errors
Errors
Δgdp(t + k ) = a + b ft Δgdp (t + k ) + et (k )
Forecast
Mean
RMSE
p-value
a
b
Horizon, k
a=0, b=1
0
0.33
1.53
0.38
0.97
0.37
(0.23)
(0.49)
(0.17)
1
0.20
1.85
0.93
0.71
0.70
(0.28)
(1.18)
(0.43)
2
0.17
1.95
2.11
0.30
0.43
(0.29)
(1.64)
(0.57)
3
0.28
1.86
1.12
0.69
0.58
(0.28)
(1.28)
(0.42)
4
0.38
1.70
0.65
0.90
0.37
(0.26)
(1.61)
(0.52)
Standard errors in parentheses. p-values for a=0, b=1 test based on Newey-West
corrections for autocorrelation in et(k)
45
Table 2: The Revision Process
Forecast
Horizon, k
Response to Transitory Shock
Response to Permanent Shock
Growth
ρk - ρk-1
1.00
NA
Level
0.5 ρk
0.50
NA
Growth
θk – θk-1
1.00
NA
Level
0.5 θk
0.50
NA
1
-0.06
(0.27)
0.47
(0.13)
0.27
(0.17)
0.63
(0.08)
2
-0.06
(0.26)
0.44
(0.17)
-0.00
(0.15)
0.63
(0.11)
3
-0.33
(0.16)
0.28
(0.22)
0.04
(0.12)
0.65
(0.15)
4
-0.46
(0.21)
0.05
(0.27)
0.08
(0.15)
0.69
(0.20)
5
-0.41
(0.20)
-0.16
(0.30)
0.07
(0.15)
0.72
(0.26)
6
-0.11
(0.15)
-0.22
(0.26)
-0.02
(0.09)
0.71
(0.27)
7
0.13
(0.23)
-0.15
(0.16)
-0.09
(0.11)
0.67
(0.25)
8
0.18
(0.20)
-0.06
(0.07)
-0.06
(0.09)
0.63
(0.23)
9
0.13
NA
0.00
NA
0.36
0.01
0.00
NA
0
0.63
(0.23)
0.87
Shock
σ2 u
σ2 e
2
0.04
Variances
θlr
σw
(0.03)
Forecast horizon k corresponds to semi-annual periods. Standard errors in parentheses.
NA indicates a fixed parameter with no standard error.
46
Table 3: GDP Level Forecast Revision Variance Decomposition
Forecast
Horizon
k
0
Revision
Contribution to the Variance of the Forecast Revision
Variance
(share of revision variance)
(percentage Transitory
Permanent Shocks:
Measurement
points)
Shock, ut
Errors, vt
,w
)
cov(e
wt
et
t t
0.33
0.27
0.66
0.01
0.05
0.00
1
0.53
0.15
0.66
0.02
0.08
0.08
2
0.58
0.12
0.58
0.05
0.11
0.15
3
0.63
0.04
0.58
0.07
0.14
0.16
4
0.70
0.00
0.58
0.11
0.17
0.14
5
0.78
0.01
0.54
0.13
0.18
0.13
6
0.83
0.02
0.49
0.17
0.19
0.13
7
0.83
0.01
0.42
0.22
0.20
0.15
8
0.85
0.00
0.37
0.26
0.21
0.15
9
0.93
0.00
0.34
0.30
0.22
0.15
47
Table 4: The Influence of Forecast Errors and the Current State of the Economy
on the k = 0 Blue Chip GDP Forecast Revisions
Revision
Total
Lagged Error
Σ CFNAI’s
p-values in parentheses
Permanent Shock
ut
et
-0.07
-0.03
-0.16
-0.17
-0.04
0.04
(0.48)
(0.72)
(0.19)
(0.17)
(0.84)
(0.84)
0.42
0.11
0.68
0.81
0.45
-0.29
(0.00)
(0.42)
(0.00)
(0.01)
(0.03)
(0.24)
CFNAI < -0.5
R2
Transitory Shock
0.37
0.52
-0.22
1.26
(0.03)
(0.48)
(0.02)
0.43
0.41
0.43
0.23
0.33
48
Table 5: Effect of Including CFNAI in the GDP Models
Standard Deviations of k = 0 Forecast Revisions
Base Models
Total
Models with CFNAI
Transitory
Permanent
Shock
Shock
Total
Transitory
Permanent
Shock
Shock
Beveridge-Nelson
1.65
0.12
1.53
1.03
0.00
1.03
Unobserv. Comp.
1.41
0.91
0.65
0.99
0.00
0.99
Blanchard-Quah
1.71
1.19
0.29
0.64
0.42
0.46
Campbell-Krane
1.52
1.33
0.56
0.77
0.60
0.37
Memo: Blue Chip
0.57
0.31
0.46
0.57
0.31
0.46
49
Figure 1: GDP Forecasts
Half-Year Growth (annual rate)
Forecast for Growth in the Current Period
Forecast for Growth Made One-Half Year Earlier
9.6
9.6
8.0
8.0
6.4
6.4
4.8
4.8
3.2
3.2
1.6
1.6
0.0
0.0
Forecast
Actual
-1.6
Forecast
Actual
-1.6
1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004
Forecast for Growth Made One Year Earlier
1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004
Forecast for Growth Made One-Year Earlier and Long-Run Growth
9.6
9.6
8.0
8.0
6.4
6.4
4.8
4.8
3.2
3.2
1.6
1.6
0.0
0.0
Forecast
Actual
-1.6
Forecast
Long-run Forc.
-1.6
1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004
1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004
50
Figure 2: The Current State of the Economy and the GDP Forecasts
Deviations from Long-Run Growth Forecast
Forecast for Growth in the Current Period
3
2
1
1.5
3
1.0
2
0.5
0
Forecast for Growth One Half Year Ahead
1.0
1
0.5
0
0.0
-1
0.0
-1
-0.5
-2
-0.5
-2
-1.0
-3
-4
Diff. from LR Gr
CFNAIM3
-5
Forecast for Growth One Year Ahead
3
2
1
-1.0
-3
-1.5
-4
-2.0
-5
1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004
-1.5
Diff. from LR Gr
CFNAIM3
-2.0
1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004
1.5
3
1.0
2
0.5
0
Forecast for Growth Two Years Ahead
1.5
1.0
1
0.5
0
0.0
-1
0.0
-1
-0.5
-2
-0.5
-2
-1.0
-3
-4
1.5
Diff. from LR Gr
CFNAIM3
-5
1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004
-1.0
-3
-1.5
-4
-2.0
-5
Diff. from LR Gr
CFNAIM3
-1.5
-2.0
1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004
51
Figure 3: Responses to Shocks: Revisions to Forecasts for the Level of GDP
Scaled by Standard Deviation of Shocks; with Two Std-Error Bounds
Response to TransitoryShock
1.12
0.96
0.80
0.64
0.48
0.32
0.16
0.00
-0.16
-0.32
0
1
2
3
4
5
6
7
8
9
6
7
8
9
7
8
9
Response to Permanent Shock
1.12
0.96
0.80
0.64
0.48
0.32
0.16
0.00
-0.16
-0.32
0
1
2
3
4
5
Response to Permanent and Long-Run Growth Shocks
1.50
1.25
1.00
0.75
0.50
0.25
0.00
0
1
2
3
4
5
6
52
Figure 4a: Perceived Shocks to GDP and Forecast Errors
Transitory Shocks to the Level of GDP
2.4
1.2
0.0
-1.2
-2.4
-3.6
Shock
1982
Forecast Error
1984
1986
1988
1990
1992
1994
1996
1998
2000
2002
2004
2000
2002
2004
Permanent Shock to the Level of GDP
2.4
1.2
0.0
-1.2
-2.4
-3.6
Shock
1982
Forecast Error
1984
1986
1988
1990
1992
1994
1996
1998
Shock to LR Growth Rate
2.4
0.50
1.2
0.25
0.0
0.00
-1.2
-0.25
-2.4
Shock
Forecast Error
NIPA Rev.
-0.50
-3.6
-0.75
1982
1984
1986
1988
1990
1992
1994
1996
1998
2000
2002
2004
53
Figure 4b: Perceived Shocks to GDP and the Current State of the Economy
TransitoryShocks to the Level of GDP
2.4
1.5
1.0
0.5
0.0
-0.5
-1.0
-1.5
-2.0
1.2
0.0
-1.2
-2.4
Shock
CFNAI-MA3
-3.6
1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005
Permanent Shock to the Level of GDP
2.4
1.5
1.0
0.5
0.0
-0.5
-1.0
-1.5
-2.0
1.2
0.0
-1.2
-2.4
Shock
CFNAI-MA3
-3.6
1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005
Shock to LR Growth Rate
0.50
0.25
0.00
-0.25
-0.50
Shock
CFNAI-MA3
-0.75
1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005
1.5
1.0
0.5
0.0
-0.5
-1.0
-1.5
-2.0
54
Figure 5a: Responses to Shocks: Blue Chip and Univariate Models
Responses Scaled by Standard Deviations of the Shocks
Response to Transitory Shock
Response to Transitory Shock
Compared with Beveridge-Nelson
2.0
Compared with UC Model
2.0
Blue Chip
Blue Chip
+2 std. error
-2 std. error
1.5
+2 std. error
-2 std. error
1.5
Beveridge-Nelson
UC Model
1.0
1.0
0.5
0.5
0.0
0.0
-0.5
-0.5
0
1
2
3
4
5
6
7
8
9
0
1
2
Response to Permanent Shock
4
5
6
7
8
9
Response to Permanent Shock
Compared with Beveridge-Nelson
2.0
3
Compared with UC Model
2.0
Blue Chip
Blue Chip
+2 std. error
-2 std. error
1.5
+2 std. error
-2 std. error
1.5
Beveridge-Nelson
UC Model
1.0
1.0
0.5
0.5
0.0
0.0
-0.5
-0.5
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
55
Figure 5b: Responses to Shocks: Blue Chip and Multivariate Models
Responses Scaled by Standard Deviations of the Shocks
Response to Transitory Shock
Response to Transitory Shock
Compared with Blanchard-Quah
2.0
Compared with Campbell-Krane
2.0
Blue Chip
Blue Chip
+2 std. error
-2 std. error
1.5
+2 std. error
-2 std. error
1.5
Blanchard-Quah
Campbell-Krane
1.0
1.0
0.5
0.5
0.0
0.0
-0.5
-0.5
0
1
2
3
4
5
6
7
8
9
0
1
2
Response to Permanent Shock
4
5
6
7
8
9
Response to Permanent Shock
Compared with Blanchard-Quah
2.0
3
Compared with Campbell-Krane
2.0
Blue Chip
Blue Chip
+2 std. error
-2 std. error
1.5
+2 std. error
-2 std. error
1.5
Blanchard-Quah
Campbell-Krane
1.0
1.0
0.5
0.5
0.0
0.0
-0.5
-0.5
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
Working Paper Series
A series of research studies on regional economic issues relating to the Seventh Federal
Reserve District, and on financial and economic topics.
A Proposal for Efficiently Resolving Out-of-the-Money Swap Positions
at Large Insolvent Banks
George G. Kaufman
WP-03-01
Depositor Liquidity and Loss-Sharing in Bank Failure Resolutions
George G. Kaufman
WP-03-02
Subordinated Debt and Prompt Corrective Regulatory Action
Douglas D. Evanoff and Larry D. Wall
WP-03-03
When is Inter-Transaction Time Informative?
Craig Furfine
WP-03-04
Tenure Choice with Location Selection: The Case of Hispanic Neighborhoods
in Chicago
Maude Toussaint-Comeau and Sherrie L.W. Rhine
WP-03-05
Distinguishing Limited Commitment from Moral Hazard in Models of
Growth with Inequality*
Anna L. Paulson and Robert Townsend
WP-03-06
Resolving Large Complex Financial Organizations
Robert R. Bliss
WP-03-07
The Case of the Missing Productivity Growth:
Or, Does information technology explain why productivity accelerated in the United States
but not the United Kingdom?
Susanto Basu, John G. Fernald, Nicholas Oulton and Sylaja Srinivasan
WP-03-08
Inside-Outside Money Competition
Ramon Marimon, Juan Pablo Nicolini and Pedro Teles
WP-03-09
The Importance of Check-Cashing Businesses to the Unbanked: Racial/Ethnic Differences
William H. Greene, Sherrie L.W. Rhine and Maude Toussaint-Comeau
WP-03-10
A Firm’s First Year
Jaap H. Abbring and Jeffrey R. Campbell
WP-03-11
Market Size Matters
Jeffrey R. Campbell and Hugo A. Hopenhayn
WP-03-12
The Cost of Business Cycles under Endogenous Growth
Gadi Barlevy
WP-03-13
The Past, Present, and Probable Future for Community Banks
Robert DeYoung, William C. Hunter and Gregory F. Udell
WP-03-14
1
Working Paper Series (continued)
Measuring Productivity Growth in Asia: Do Market Imperfections Matter?
John Fernald and Brent Neiman
WP-03-15
Revised Estimates of Intergenerational Income Mobility in the United States
Bhashkar Mazumder
WP-03-16
Product Market Evidence on the Employment Effects of the Minimum Wage
Daniel Aaronson and Eric French
WP-03-17
Estimating Models of On-the-Job Search using Record Statistics
Gadi Barlevy
WP-03-18
Banking Market Conditions and Deposit Interest Rates
Richard J. Rosen
WP-03-19
Creating a National State Rainy Day Fund: A Modest Proposal to Improve Future
State Fiscal Performance
Richard Mattoon
WP-03-20
Managerial Incentive and Financial Contagion
Sujit Chakravorti and Subir Lall
WP-03-21
Women and the Phillips Curve: Do Women’s and Men’s Labor Market Outcomes
Differentially Affect Real Wage Growth and Inflation?
Katharine Anderson, Lisa Barrow and Kristin F. Butcher
WP-03-22
Evaluating the Calvo Model of Sticky Prices
Martin Eichenbaum and Jonas D.M. Fisher
WP-03-23
The Growing Importance of Family and Community: An Analysis of Changes in the
Sibling Correlation in Earnings
Bhashkar Mazumder and David I. Levine
WP-03-24
Should We Teach Old Dogs New Tricks? The Impact of Community College Retraining
on Older Displaced Workers
Louis Jacobson, Robert J. LaLonde and Daniel Sullivan
WP-03-25
Trade Deflection and Trade Depression
Chad P. Brown and Meredith A. Crowley
WP-03-26
China and Emerging Asia: Comrades or Competitors?
Alan G. Ahearne, John G. Fernald, Prakash Loungani and John W. Schindler
WP-03-27
International Business Cycles Under Fixed and Flexible Exchange Rate Regimes
Michael A. Kouparitsas
WP-03-28
Firing Costs and Business Cycle Fluctuations
Marcelo Veracierto
WP-03-29
Spatial Organization of Firms
Yukako Ono
WP-03-30
Government Equity and Money: John Law’s System in 1720 France
François R. Velde
WP-03-31
2
Working Paper Series (continued)
Deregulation and the Relationship Between Bank CEO
Compensation and Risk-Taking
Elijah Brewer III, William Curt Hunter and William E. Jackson III
WP-03-32
Compatibility and Pricing with Indirect Network Effects: Evidence from ATMs
Christopher R. Knittel and Victor Stango
WP-03-33
Self-Employment as an Alternative to Unemployment
Ellen R. Rissman
WP-03-34
Where the Headquarters are – Evidence from Large Public Companies 1990-2000
Tyler Diacon and Thomas H. Klier
WP-03-35
Standing Facilities and Interbank Borrowing: Evidence from the Federal Reserve’s
New Discount Window
Craig Furfine
WP-04-01
Netting, Financial Contracts, and Banks: The Economic Implications
William J. Bergman, Robert R. Bliss, Christian A. Johnson and George G. Kaufman
WP-04-02
Real Effects of Bank Competition
Nicola Cetorelli
WP-04-03
Finance as a Barrier To Entry: Bank Competition and Industry Structure in
Local U.S. Markets?
Nicola Cetorelli and Philip E. Strahan
WP-04-04
The Dynamics of Work and Debt
Jeffrey R. Campbell and Zvi Hercowitz
WP-04-05
Fiscal Policy in the Aftermath of 9/11
Jonas Fisher and Martin Eichenbaum
WP-04-06
Merger Momentum and Investor Sentiment: The Stock Market Reaction
To Merger Announcements
Richard J. Rosen
WP-04-07
Earnings Inequality and the Business Cycle
Gadi Barlevy and Daniel Tsiddon
WP-04-08
Platform Competition in Two-Sided Markets: The Case of Payment Networks
Sujit Chakravorti and Roberto Roson
WP-04-09
Nominal Debt as a Burden on Monetary Policy
Javier Díaz-Giménez, Giorgia Giovannetti, Ramon Marimon, and Pedro Teles
WP-04-10
On the Timing of Innovation in Stochastic Schumpeterian Growth Models
Gadi Barlevy
WP-04-11
Policy Externalities: How US Antidumping Affects Japanese Exports to the EU
Chad P. Bown and Meredith A. Crowley
WP-04-12
Sibling Similarities, Differences and Economic Inequality
Bhashkar Mazumder
WP-04-13
3
Working Paper Series (continued)
Determinants of Business Cycle Comovement: A Robust Analysis
Marianne Baxter and Michael A. Kouparitsas
WP-04-14
The Occupational Assimilation of Hispanics in the U.S.: Evidence from Panel Data
Maude Toussaint-Comeau
WP-04-15
Reading, Writing, and Raisinets1: Are School Finances Contributing to Children’s Obesity?
Patricia M. Anderson and Kristin F. Butcher
WP-04-16
Learning by Observing: Information Spillovers in the Execution and Valuation
of Commercial Bank M&As
Gayle DeLong and Robert DeYoung
WP-04-17
Prospects for Immigrant-Native Wealth Assimilation:
Evidence from Financial Market Participation
Una Okonkwo Osili and Anna Paulson
WP-04-18
Individuals and Institutions: Evidence from International Migrants in the U.S.
Una Okonkwo Osili and Anna Paulson
WP-04-19
Are Technology Improvements Contractionary?
Susanto Basu, John Fernald and Miles Kimball
WP-04-20
The Minimum Wage, Restaurant Prices and Labor Market Structure
Daniel Aaronson, Eric French and James MacDonald
WP-04-21
Betcha can’t acquire just one: merger programs and compensation
Richard J. Rosen
WP-04-22
Not Working: Demographic Changes, Policy Changes,
and the Distribution of Weeks (Not) Worked
Lisa Barrow and Kristin F. Butcher
WP-04-23
The Role of Collateralized Household Debt in Macroeconomic Stabilization
Jeffrey R. Campbell and Zvi Hercowitz
WP-04-24
Advertising and Pricing at Multiple-Output Firms: Evidence from U.S. Thrift Institutions
Robert DeYoung and Evren Örs
WP-04-25
Monetary Policy with State Contingent Interest Rates
Bernardino Adão, Isabel Correia and Pedro Teles
WP-04-26
Comparing location decisions of domestic and foreign auto supplier plants
Thomas Klier, Paul Ma and Daniel P. McMillen
WP-04-27
China’s export growth and US trade policy
Chad P. Bown and Meredith A. Crowley
WP-04-28
Where do manufacturing firms locate their Headquarters?
J. Vernon Henderson and Yukako Ono
WP-04-29
Monetary Policy with Single Instrument Feedback Rules
Bernardino Adão, Isabel Correia and Pedro Teles
WP-04-30
4
Working Paper Series (continued)
Firm-Specific Capital, Nominal Rigidities and the Business Cycle
David Altig, Lawrence J. Christiano, Martin Eichenbaum and Jesper Linde
WP-05-01
Do Returns to Schooling Differ by Race and Ethnicity?
Lisa Barrow and Cecilia Elena Rouse
WP-05-02
Derivatives and Systemic Risk: Netting, Collateral, and Closeout
Robert R. Bliss and George G. Kaufman
WP-05-03
Risk Overhang and Loan Portfolio Decisions
Robert DeYoung, Anne Gron and Andrew Winton
WP-05-04
Characterizations in a random record model with a non-identically distributed initial record
Gadi Barlevy and H. N. Nagaraja
WP-05-05
Price discovery in a market under stress: the U.S. Treasury market in fall 1998
Craig H. Furfine and Eli M. Remolona
WP-05-06
Politics and Efficiency of Separating Capital and Ordinary Government Budgets
Marco Bassetto with Thomas J. Sargent
WP-05-07
Rigid Prices: Evidence from U.S. Scanner Data
Jeffrey R. Campbell and Benjamin Eden
WP-05-08
Entrepreneurship, Frictions, and Wealth
Marco Cagetti and Mariacristina De Nardi
WP-05-09
Wealth inequality: data and models
Marco Cagetti and Mariacristina De Nardi
WP-05-10
What Determines Bilateral Trade Flows?
Marianne Baxter and Michael A. Kouparitsas
WP-05-11
Intergenerational Economic Mobility in the U.S., 1940 to 2000
Daniel Aaronson and Bhashkar Mazumder
WP-05-12
Differential Mortality, Uncertain Medical Expenses, and the Saving of Elderly Singles
Mariacristina De Nardi, Eric French, and John Bailey Jones
WP-05-13
Fixed Term Employment Contracts in an Equilibrium Search Model
Fernando Alvarez and Marcelo Veracierto
WP-05-14
Causality, Causality, Causality: The View of Education Inputs and Outputs from Economics
Lisa Barrow and Cecilia Elena Rouse
WP-05-15
5
Working Paper Series (continued)
Competition in Large Markets
Jeffrey R. Campbell
WP-05-16
Why Do Firms Go Public? Evidence from the Banking Industry
Richard J. Rosen, Scott B. Smart and Chad J. Zutter
WP-05-17
Clustering of Auto Supplier Plants in the U.S.: GMM Spatial Logit for Large Samples
Thomas Klier and Daniel P. McMillen
WP-05-18
Why are Immigrants’ Incarceration Rates So Low?
Evidence on Selective Immigration, Deterrence, and Deportation
Kristin F. Butcher and Anne Morrison Piehl
WP-05-19
Constructing the Chicago Fed Income Based Economic Index – Consumer Price Index:
Inflation Experiences by Demographic Group: 1983-2005
Leslie McGranahan and Anna Paulson
WP-05-20
Universal Access, Cost Recovery, and Payment Services
Sujit Chakravorti, Jeffery W. Gunther, and Robert R. Moore
WP-05-21
Supplier Switching and Outsourcing
Yukako Ono and Victor Stango
WP-05-22
Do Enclaves Matter in Immigrants’ Self-Employment Decision?
Maude Toussaint-Comeau
WP-05-23
The Changing Pattern of Wage Growth for Low Skilled Workers
Eric French, Bhashkar Mazumder and Christopher Taber
WP-05-24
U.S. Corporate and Bank Insolvency Regimes: An Economic Comparison and Evaluation
Robert R. Bliss and George G. Kaufman
WP-06-01
Redistribution, Taxes, and the Median Voter
Marco Bassetto and Jess Benhabib
WP-06-02
Identification of Search Models with Initial Condition Problems
Gadi Barlevy and H. N. Nagaraja
WP-06-03
Tax Riots
Marco Bassetto and Christopher Phelan
WP-06-04
The Tradeoff between Mortgage Prepayments and Tax-Deferred Retirement Savings
Gene Amromin, Jennifer Huang,and Clemens Sialm
WP-06-05
Why are safeguards needed in a trade agreement?
Meredith A. Crowley
WP-06-06
6
Working Paper Series (continued)
Taxation, Entrepreneurship, and Wealth
Marco Cagetti and Mariacristina De Nardi
WP-06-07
A New Social Compact: How University Engagement Can Fuel Innovation
Laura Melle, Larry Isaak, and Richard Mattoon
WP-06-08
Mergers and Risk
Craig H. Furfine and Richard J. Rosen
WP-06-09
Two Flaws in Business Cycle Accounting
Lawrence J. Christiano and Joshua M. Davis
WP-06-10
Do Consumers Choose the Right Credit Contracts?
Sumit Agarwal, Souphala Chomsisengphet, Chunlin Liu, and Nicholas S. Souleles
WP-06-11
Chronicles of a Deflation Unforetold
François R. Velde
WP-06-12
Female Offenders Use of Social Welfare Programs Before and After Jail and Prison:
Does Prison Cause Welfare Dependency?
Kristin F. Butcher and Robert J. LaLonde
Eat or Be Eaten: A Theory of Mergers and Firm Size
Gary Gorton, Matthias Kahl, and Richard Rosen
Do Bonds Span Volatility Risk in the U.S. Treasury Market?
A Specification Test for Affine Term Structure Models
Torben G. Andersen and Luca Benzoni
WP-06-13
WP-06-14
WP-06-15
Transforming Payment Choices by Doubling Fees on the Illinois Tollway
Gene Amromin, Carrie Jankowski, and Richard D. Porter
WP-06-16
How Did the 2003 Dividend Tax Cut Affect Stock Prices?
Gene Amromin, Paul Harrison, and Steven Sharpe
WP-06-17
Will Writing and Bequest Motives: Early 20th Century Irish Evidence
Leslie McGranahan
WP-06-18
How Professional Forecasters View Shocks to GDP
Spencer D. Krane
WP-06-19
7
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