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This paper advances beyond the prediction of the probability of a recession by also considering its severity in terms of output loss and duration. First, Probit models are used to estimate the probability of a recession at period t + h from the information available at period t. Next, a Vector Autoregression (VAR) augmented with diffusion indices and an inverse Mills ratio (IMR) is fitted to selected measures of real economic activity. The latter model is used to generate two forecasts: an average forecast, and a forecast under the pessimistic assumption that a recession occurs at the forecast hori-zon. The severity of recessions is then predicted as the gap between these two forecasts. Finally, a zero-inflated Poisson model is fitted to historical durations of recessions. Our empirical results suggest that U.S. recessions are fairly predictable, both in terms of occurrence and severity. Out-of-sample experiments suggest that the inclusion of the IMR in the VAR model significantly improves its forecasting performance.
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Probability and Severity of Recessions
Rachidi KotchoniDalibor Stevanovic
November 18, 2013
Abstract
This paper advances beyond the prediction of the probability of a recession by also
considering its severity in terms of output loss and duration. First, Probit models are
used to estimate the probability of a recession at period t+hfrom the information
available at period t. Next, a Vector Autoregression (VAR) augmented with diffusion
indices and an inverse Mills ratio (IMR) is fitted to selected measures of real economic
activity. The latter model is used to generate two forecasts: an average forecast, and a
forecast under the pessimistic assumption that a recession occurs at the forecast hori-
zon. The severity of recessions is then predicted as the gap between these two forecasts.
Finally, a zero-inflated Poisson model is fitted to historical durations of recessions. Our
empirical results suggest that U.S. recessions are fairly predictable, both in terms of
occurrence and severity. Out-of-sample experiments suggest that the inclusion of the
IMR in the VAR model significantly improves its forecasting performance.
JEL Classification: C3, C5, C35, E27, E37
Keywords: Duration of recessions, Forecasting Real Activity, Probability of Recessions, Pro-
bit, Vector Autoregression, Zero Inflated Poisson.
We thank Yvon Fauvel, Mark Watson and Jonathan Wright for useful discussions and comments.
Thema, Universit´e de Cergy-Pontoise, 33 boulevard du port F-95000. email: rachidi.kotchoni@u-cergy.fr
Universit´e du Qu´ebec `a Montr´eal, D´epartement des sciences ´economiques, 315, rue Ste-Catherine Est,
Montr´eal, QC, H2X 3X2. e-mail: dstevanovic.econ@gmail.com
HIGHLIGHTS
1. Predicting the probability and severity of US recessions using a large data set.
2. Modeling economic activity using a vector autoregression (VAR) model augmented
with diffusion indices (i.e., PCA factors) and an inverse Mills ratio (IMR).
3. Generating forecasts that are conditional on the future state of the economy (pes-
simistic and optimistic scenarios).
4. Predicting the depth of a recession as the gap between the forecasts associated with
the pessimistic and the average scenario.
5. Predicting the duration of a recession using a zero-inflated Poisson model.
6. The inclusion of the IMR and PCA factors in the VAR model improves its out-of-
sample forecast performance by up to 40%.
2
1 Introduction
The world economic history consists of an endless succession of business cycles characterized
by swings across peaks and troughs of real economic activity. A period running between any
given peak and the next trough is called a recession while a period between a trough and the
next peak is an expansion. Although quite simple, this definition raises two practical issues.
The first issue concerns the precise meaning of the expression “real economic activity”. The
Business Cycle Dating Committee of the National Bureau of Economic Research (NBER)
does not provide a precise definition of this expression. Rather, the NBER defines a recession
as “a significant decline in economic activity spread across the economy, lasting more than a
few months, normally visible in real GDP, real income, employment, industrial production,
and wholesale-retail sales.” The second issue concerns the identification of the peaks and
troughs of real economic activity from observed data. The Business Cycle Dating Committee
does provide a precise response to the latter issue by regularly publishing recession dates
with six months to one year lag1.
The general objective of this paper is to examine the predictability of economic recessions
in the United States from three different perspectives. The first perspective concerns the
probability of recessions, i.e., how likely is a recession to occur at a given forecast horizon.
The two other perspectives pertains to the expected severity of a forthcoming recession.
The severity of a recession can be measured in terms of its duration, but also in terms of
its impact on output growth and unemployment rate. Each of the dimensions of a reces-
sion identified above is analyzed by combining well-established econometric methods. Thus,
the contribution of our paper resides in the approach to combine simple econometric tech-
niques to address important forecasting issues rather than in the novelty of the techniques
themselves.
One strand of the literature related to this topic focuses on predicting the probability
of a recession using financial indicators. For example, (Estrella & Mishkin 1998) examined
1The announcement dates can be found at http://www.nber.org/cycles.html.
1
the individual performance of financial variables such as interest rates, spreads, stock prices,
and monetary aggregates in predicting the probability of a recession. They found that stock
prices are good predictors of recessions at one to three quarters horizon while the slope of
the yield curve emerges as a better predictor beyond one quarter horizon. (Anderson &
Vahid 2001) applied nonlinear models to predict the probability of U.S. recession using the
interest-rate spread and growth in M2 as leading indicators. Using (Fair 1993) definitions
of a recession, they found that “conditional on the spread, the marginal contribution of M2
growth in predicting the probability of recessions is negligible2.
Another strand of the literature focuses on the computation of coincident and leading
indicators of economic activity. Coincident indicators are aimed at nowcasting the current
state of the economy while leading indicator are devised for forecasting future economic
activity3. For instance, (Issler & Vahid 2006) used the information content in the NBER
dates to construct a coincident and leading index of economic activity. Their coincident
(leading) index is devised as a fixed-weight linear combination of coincident (leading) series.
(Stock & Watson 1989) combined these two approaches to construct a recession index. An
excellent overview of the literature on real time prediction of the state of the economy is
provided by (Hamilton 2011).
Our paper advances one step beyond the prediction of the probability of a recession
by also considering its severity. As mentioned earlier, the severity of a recession can be
measured in terms of output loss or increased unemployment. Of two recessions with six
months duration, the more severe is arguably the one that resulted in a higher output loss
and unemployment rate. Alternatively, the severity of a recession can also be measured in
terms of its duration. A recession that lasts 12 months is more harmful than a recession that
lasts six months, assuming that output and jobs are destroyed at the same pace for both
2(Fair 1993) defines a recession as either “at least two consecutive quarters of negative growth in real
GDP over the next five quarters” or “at least two quarters of negative growth in real GDP over the next
five quarters.” This definition is not retained by the NBER.
3For the definition of coincident and lead economic indicators, see (Burns & Mitchell 1946) and (Stock
& Watson 1989).
2
recessions.
In this paper, we shall not attempt to identify the business cycle turning points as
done in (Chauvet 1998), (Chauvet & Hamilton 2006), (Chauvet & Piger 2008), (Stock &
Watson 2010) or (Stock & Watson 2012), nor shall we try to identify the variables that
lead future economic activity as in (Ng & Wright 2013). Rather, we devise a black-box
that predicts the probability and severity of a recession as indicated by the NBER dates.
More precisely, we employ the Principal Component Analysis to summarize a large number of
candidate predictors into a few number of factors, which is in line with (Ng 2013). Identifying
the candidates predictors individually is appealing in theory but difficult in practice because
the transmission mechanisms might be different across recessions. Our approach circumvents
this difficulty by letting the statistical method choose a linear combination of candidates
predictors. The list of predictors considered includes the most widely used variables in
this literature, as well as the realized volatility and skewness of the SP500 and DJIA. The
principal components selected at this step are then used in subsequent models as leading
indicators of real economic activity.
We design an empirical framework in three steps for analyzing the NBER business cycles.
The first step relies on a Probit model that predict the probability of a recession. Regressors
observed on a quarterly basis are used to predict the probability of a recession up to two
years ahead. The second step uses a Vector Autoregression (VAR) model to predict future
economic activity. Rather than constructing a single index of real economic activity, we
consider predicting different measures of economic activity jointly. The estimating equation
from our second step is a VAR augmented with PCA factors (i.e., diffusion indices) that
summarize a large number of candidate predictors plus an inverse Mills ratio (IMR) deduced
from the Probit. The inclusion of the IMR allows us to generate forecasts that are condi-
tional on the future state of the economy. As a result, the model is capable of generating
an optimistic forecast (assuming that an expansion occurs at the forecast horizon) as well as
a pessimistic forecast (assuming that a recession occurs at the forecast horizon). Our IMR
3
augmented VAR framework provides a simple approach to incorporate qualitative informa-
tion in a standard VAR model and as such, it is reminiscent of the (Dueker & Wesche 2010)’s
Qual VAR approach to forecasting macro variables. The third step of the analysis is con-
cerned with the prediction of the severity of a recession in terms of its duration. In real
life, the NBER recession durations are known only ex-post. However, historical data can be
used to investigate the ex-ante predictability of the duration of recessions. We construct the
duration variable Ntas the number of recessionary periods lying ahead at time t. We fit
a zero-inflated Poisson model to this variable and use the output to construct an estimate
of the conditional expected duration of a recession, which combines the probability and the
(unconditional) expected duration of a recession into a single index.
We apply our methodology to U.S. macroeconomic and financial series. Our results
support that U.S. recessions are predictable to a great extent, both in terms of occurrence
and severity. Recession dates are reasonably well predicted up to 5 quarters ahead. The
model is capable of correctly predicting 40% of recession dates at up to 2 years horizon
while delivering a very low percentage of bad shots. The unemployment rate, employment
growth, GDP deflator inflation, and industrial production growth are predictable at quite
long horizons. GDP growth and SP500 returns appear to be less predictable. Interestingly,
the Great Recession of 2007-2009 has been more severe than our pessimistic forecast. Also,
the SP500 has outperformed our optimistic forecast during the period that preceded the
Great Recession (approx. 2003-2007).
We perform an out-of-sample analysis to assess the extrapolation capabilities of the pro-
posed empirical framework. The inclusion of the IMR and diffusion indices in the VAR model
reduces the out-of-sample mean square forecast error by up to 38% for measures of real ac-
tivity (GDP, Industrial production and Employment growth, and Unemployment rate) and
by 41% for GDP Deflator inflation.
The remainder of the paper is organized as follows. Section 2 presents our framework.
Section 3 presents our empirical application and Section 4 summarizes our findings. Esti-
4
mation outputs and graphs are shown in the appendix.
2 The Framework
This section presents the three-step empirical framework that we employ to analyze the U.S.
recession episodes.
2.1 Probability of Recessions
Let Rtbe a variable such that Rt= 1 if the NBER Dating Committee identifies period tas
a recession time and Rt= 0 otherwise. We would like to use a large number of economic
indicators gathered in a N-dimensional vector Xtto predict recessions. Ideally, Xtshould
contain real economic activity as well as financial activity indicators, and coincident as
well as leading indicators. The candidate predictors may be partially redundant or highly
correlated (e.g., GDP deflator versus CPI inflation, or SP500 versus DJIA), but they should
all be observable at time tor a few periods before time t+h, where his the forecast horizon.
In order to reduce the dimensionality of Xtand by the same token avoid multicolinearity
issues, we consider summarizing Xtinto a smaller number (q) of principal components Ft.
By abuse of language, we refer to Ftas factors although we do not pretend that Xtobeys a
formal factor model. We interpret each factor Ftby examining the three variables to which
it correlates with the most.
To fix ideas, we assume that the data are observed on a quarterly basis. We augment
Ftwith a constant variable (so that subsequently, FtRq+1) and assume the existence of a
latent leading index Zh,t such that:
Zh,t =γhFt+uh,t,for all t(1)
where uh,t N(0,1) for all h= 1,2, ... and his a forecast horizon. The latent leading index
5
Zh,t predicts the state of the economy hperiods ahead such that:
Rt+h=
1 if Zh,t >0,
0 otherwise.
(2)
This probabilistic approach has been used by (Estrella & Mishkin 1998) to identify lead
indicators of U.S. recession at horizons ranging from 1 to 8 quarters. Hence, it allows us to
predict the probability of a recession in hperiods as:
Pr (Rt+h= 1|Xt) = Φ (γhFt),for all h, (3)
where Φ is the CDF of the standard normal distribution. The predicted probability of
recession may be interpreted as a recession index, as suggested by (Stock & Watson 1989).
Model (1)-(2) can be estimated by Probit based on historical data. If release lags exist, the
Probit model above can still be used for forecasting purposes as long as the release lags are
shorter enough than the horizon h.
2.2 Severity of a Recession: an IMR-Augmented DI-VAR Ap-
proach
In order to assess the severity of a recession, we consider the Diffusion Index VAR model
(DI-VAR) of (Stock & Watson 2002) as starting point:
yi,t+h=αi,hYt+βi,h Ft+δi,h,1Rt+h+vi,t+h, t = 1, ..., T h(4)
where yi,t,i= 1, . . . , M , the ith coordinate of Yt, is a measure of economic activity and
vi,t+hN(0, σ2
i,h) is uncorrelated with Ftand Yt. As a reminder, we recall that Ftincludes
a constant variable and Rt+his the indicator of recession at t+h.
The error term vi,t+his allowed to be correlated with the future state of the economy. In
6
order to avoid the resulting endogeneity problem, we consider taking the expectation yt+h
conditional on the information set at time t, that is:
E(yi,t+h|Yt, Xt) = αi,hYt+βi,h Ft+δi,h,1Φ (γhFt)byt+h.(5)
This allows us to represent yt+has follows:
yi,t+h=αi,hYt+βi,h Ft+δi,h,1Φ (γhFt) + evi,t+h,(6)
where evi,t+hvi,t+h+Rt+hΦ (Ftγh).
Beside the average scenario forecast provided by (5), two other forecasts can be con-
structed. The first forecast is based on the pessimistic assumption that we will effectively
witness a recession at period t+h, i.e. :
E(yi,t+h|Yt, Xt, Rt+h= 1) = αi,hYt+βi,h Ft+δi,h,1+δi,h,2
φ(γhFt)
Φ (γhFt)=yi,t+h.(7)
This expression is obtained by assuming that (uh,t,evi,t+h) are jointly Gaussian, where uh,t
is the error term of the latent variable governing the corresponding Probit. The second
forecasting formula is based on the optimistic assumption that there will be an expansion at
period t+h:
E(yi,t+h|Yt, Xt, Rt+h= 0) = αi,hYt+βi,h Ftδi,h,2
φ(Ftγh)
1Φ (γhFt)=yi,t+h,(8)
The estimating equation that allows us to identify δis:
yi,t+h=αi,hYt+βi,h Ft+δi,h,1Φ (γhFt) + δi,h,2IMRt,h +e
evi,t+h,(9)
where IMRt,h =φ(γhFt)
Φ(γhFt)if Rt+h= 0, and I M Rt,h =φ(γhFt)
1Φ(γhFt)if Rt+h= 1 is the inverse Mills
ratio, and e
evi,t+hevi,t+hE(evi,t+h|Yt, Xt, Rt+h). We shall estimate Equation (9) to identify
7
the parameters and use Equations (5), (7) and (8) for forecasting purposes.
The parameters δi,h,1and δi,h,2are both expected to be negative if yi,t is cyclical and
they should be positive otherwise. For instance, if yi,t denotes the GDP growth, the term
δi,h,1Φ (γhFt) + δi,h,2IMRt,h is expected to be negative as it represents the expected output
loss during a recession. However, if yi,t is the unemployment rate, the term δi,h,1Φ (γhFt) +
δi,h,2IMRt,h is expected to be positive as it measures the rise in unemployment due to
recession.
2.3 Severity of a Recession: a Duration Approach
An alternative approach to gauge the severity of a recession consists of converting the indica-
tor variable Rtinto count data4. Based on historical data, it is possible to tell for any month
tif there had been a recession at month t+1. Thus, let Ntbe an indicator variable such that
Nt= 0 if there is an expansion at period t+ 1 and Nt>0 otherwise. If a recession starts
at period t+ 1, then we let Nt=r, where ris the duration of that particular recession as
indicated by historical data. Afterward, we let Nt+hdenote the number of recession periods
to go starting from t+h+ 1. Hence, for a recession that starts at t+ 1 and ends at t+r,
we have:
Nt+h=rh, for h= 0, ..., r, (10)
Accordingly, an expansion episode starts at period t+r+ 1. Hence,
Nt+h= 0 for rhr+e1,
where eis the duration of the expansion episode.
Our idea is to fit a zero-inflated Poisson model to the count process Nt. By noting that
4(Watson 1994) has investigated several explanations for the postwar duration stability. Here, our focus
is to forecast the duration.
8
Rt+1 = 0 if and only if Nt= 0 and Rt+1 = 1 otherwise, we have:
Pr (Nt= 0) = 1 Φ (γ1Ft) and (11)
Pr (Nt=n|Xt, Nt1) = exp (λt)
1exp (λt)
λn
t
n!, n 1,(12)
where Φ (γ1Ft)Pr (Rt+1 = 1|Xt), λt= exp θ˜
Ftis the time-varying parameter of the
Poisson model and ˜
Ftis a subset of Ft. Φ (γ1Ft) is already obtained from the Probit model
of Section 2.1. Hence, it only remains to estimate (12) using strictly positive realizations of
Nt. The sample on which the estimation of θrelies is much shorter than the original sample.
Thus, we shall not use too many predictors in model (12) for the sake of degrees-of-freedom.
Interestingly, our multi-step estimation procedure allows us to use different number of factors
at each step: more factors in the Probit model and less factors in the Poisson model.
Equation (12) gives the probability of the next nconsecutive periods belonging to a
recessionary episode under the pessimistic assumption that recession is unavoidable at the
next period. If no a priori assumption is made, the probability of a recession is computed
as:
Pr (Nt=n|Xt) = Φ (γ1Ft) exp (λt)
1exp (λt)
λn
t
n!, n 1,(13)
At any period t, the expected duration of a recession can be calculated under the pessimistic
assumption that recession is unavoidable. This leads to the conditional expected duration
given by
E(Nt|Xt, Nt1) = λt
1exp (λt).(14)
The unconditional expected duration of a recession is given by:
E(Nt|Xt) = Φ (γ1Ft)λt
1exp (λt)Nt.(15)
The probability Φ (γ1Ft) is the recession index proposed by (Stock & Watson 1989). Our
9
indicator Ntgoes one step further in that it combines the probability of a recession with its
expected severity as measured by the conditional expected duration.
One may consider undertaking the counterfactual exercise which consists of calculating
E(Nt|Xt, Nt1) for periods where Nt= 0 has actually been observed. However, this
exercise tends to predict exaggerately high conditional durations at periods where Nt= 0.
This happens because:
E(Nt|Xt, Nt1) = E(Nt|Xt)
Φ (γ1Ft).
As an estimator of the probability of a recession one period ahead, Φ (γ1Ft) exploits very
imminent information when the data are quaterly. Hence, its tends to be very small compared
to E(Nt|Xt) when no recession is actually going to occur at quater t+ 1. In our empirical
application, (14) is computed only when Ntis strictly positive while (15) is constructed for
the all sample.
3 Application to NBER Recession
For this application, we use the quarterly NBER recession indicator from the FRED2
database. The time series included in Xtas candidate predictors are presented in Table
9. The time span starts in 1967Q2 and ends in 2012Q35. We perform a full sample analysis
as well as an out-of-sample exercise to assess the forecasting abilities of our methodology.
3.1 Full Sample Analysis
The first subsection below presents the results of the principal component analysis of Xt. The
second subsection is devoted to the prediction of NBER recessions using a Probit model. The
third subsection presents the estimation results of our IMR-augmented diffusion index VAR
(IMR-DI-VAR) model while the fourth subsection presents the results for the zero-inflated
5We start only in 1967Q2 since one of important leading indicators, that is often used to assess the
probability of a recession, Initial Claims (IC4WSA) is available from that date. We stop at 2012Q3 because
of the availability of the Consumer Sentiment (ConsMICH) computed by the University of Michigan.
10
Poisson model.
3.1.1 Principal Component Analysis
We employ the Principal Component Analysis to reduce the dimensionality of Xt. Subse-
quently, Ftconsists of 16 principal components of Xt.6Table 1 contains the three series
with which each principal component is correlated the most.
The first factor (F1) is mainly related to employment growth and external finance pre-
mium. The second factor (F2) is in line with inflation and FED funds rate. The third
factor (F3) is correlated with consumption and stock prices. Echoing (Hamilton 2011), (Ng
& Wright 2013) noted that “the track record of forecasting models using asset prices is not
good, or at least not consistent.” However, the fact that stock prices greatly contribute to the
formation of F3suggests that robust predictors of the state of the economy can be obtained
by taking their linear combinations with other variables. The fourth factor (F4) captures
money growth as measured by M1 and unemployment rate. The fifth factor (F5) is mostly
correlated with money growth as measured by M2 and stock market volatility. The sixth
factor (F6) combines GS5 and stock market returns’ skewness. The oil price growth is highly
correlated with F7, along with house starts and construction permits. The factor F8recom-
bines again the M2 growth and the stock market skewness. The unemployment rate in the
mining sector and the GS1-FFR spread appear to be strongly correlated with F9.F10 is
mainly correlated with M1 growth, unemployment rate in the mining sector and also the
investment growth rate.
The remaining factors are mainly recombinations of the variables mentioned above.
Hence, selecting the 16 most important principal components ensures us that we bring the
most relevant part of the information content of Xtto our forecasting models. It is inter-
esting to note that the stock market returns, volatility and skewness are related to different
factors, namely, F3,F5and F6respectively. Likewise, the monetary aggregates M1 and M2
6At this step, the number 16 is selected in order to obtain a good in-sample fit. Later on, the choice of
the number of principal components to include in Ftis based on out-of-sample performance criteria.
11
are related to different factors, the most important ones being F4and F5respectively.
Table 1: Most correlated variables with PCs
F1MANEMPgr BAA-GS10 PAYEMSgr
F2CPIAUCSLinfl FEDFUNDS CPILFELinfl
F3RPCEgr DJIAret SP500ret
F4NAPMPRI M1SLgr UNRATE
F5M2SLgr SP500-RV DJIA-RV
F6GS5 DJIA-SK SP500-SK
F7OILPRICEgr PERMIT HOUST
F8M2SLgr SP500-SK DJIA-SK
F9GS1-FFR NAPMSDI USMINEgr
F10 M1SLgr INVESTgr USMINEgr
F11 SP500ret OILPRICEgr INVESTgr
F12 RPCEgr INVESTgr RPCEDGgr
F13 M2SLgr DJIAret DJIA-RV
F14 INVESTgr M2SLgr OILPRICEgr
F15 AWOTMAN USMINEgr M1SLgr
F16 PCEPIgr CPIAUCSLinfl USMINEgr
3.1.2 Predicting the Probability of a Recession
Table 2 presents the in-sample goodness-of-fit of the Probit model that predicts the proba-
bility of a recession. Detailed estimation results are presented in Table 10 of the Appendix.
The goodness-of-fit measures considered are McFadden’s pseudo R2, Estrella’s R2, the per-
centage of good shots (calling for a recession when Rt= 1) and the percentage of bad shots
(calling for a recession when Rt= 0).
Table 2: Predicting NBER recessions: in full-sample goodness-of-fit
Quarter h= 1 h= 2 h= 3 h= 4 h= 5 h= 6 h= 7 h= 8
McFadden pseudo-R2 0,753 0,619 0,614 0,657 0,474 0,390 0,346 0,395
Estrella R2 0,692 0,558 0,554 0,598 0,422 0,345 0,306 0,352
% of good shots 0,778 0,667 0,815 0,778 0,630 0,407 0,296 0,407
% of bad shots 0,026 0,033 0,020 0,020 0,027 0,027 0,047 0,034
We call for a recession when the estimated probability is higher than 0.5. The forecasting
horizons considered are h= 1 through h= 8 quarters. Recession dates are reasonably well
12
predicted up to 5 quarters ahead. The model is capable of correctly predicting 40% of
recessions dates at up to 2 years horizon while delivering a very low percentage of bad shots
(see Figure 1).
3.1.3 Predicting the Severity of a Recession using the IMR-DI-VAR
We fit the predictive equation (9) to the data by SURE. The variables included in Ytare:
real GDP growth rate (GDP growth), industrial production growth rate (INDPRO growth),
unemployment rate (UNRATE), employment growth rate (EMPL growth), GDP Deflator
growth rate (GDPDEF inflation) and SP500 returns. The first four variables measure the real
activity while the last two variables are proxies for the price level and the financial activity.
Table 3 presents the R2sof the regressions for each of the measures of economic activity. At
one year horizon, the most predictable variable is the unemployment rate (92.6%), followed
by employment growth (79.4% ), GDP deflator inflation (77.9%) and industrial production
growth (66.8%). The R2of the prediction of GDP growth and SP500 returns one year
ahead are 45.9% and 21.1% respectively. Figures 11 and 12 in appendix plot the actual and
predicted values of all six series at horizons h= 4 and h= 8.
Table 3: Predicting economic activity: R2from DI-VAR predictive regressions
1 quarter 2 quarters 3 quarters 4 quarters
GDP growth 0,574 0,523 0,494 0,459
INDPRO growth 0,704 0,638 0,621 0,668
UNRATE 0,989 0,972 0,950 0,926
EMPL growth 0,877 0,825 0,805 0,794
GDPDEF inflation 0,847 0,821 0,817 0,779
SP500 returns 0,395 0,309 0,279 0,211
5 quarters 6 quarters 7 quarters 8 quarters
GDP growth 0,451 0,440 0,433 0,448
INDPRO growth 0,631 0,592 0,579 0,595
UNRATE 0,906 0,869 0,823 0,765
EMPL growth 0,766 0,718 0,678 0,657
GDPDEF inflation 0,754 0,729 0,711 0,700
SP500 returns 0,202 0,188 0,207 0,160
13
Figure 1: Predicting US recessions
1970 1980 1990 2000 2010
0
0.2
0.4
0.6
0.8
1
Predicting a recession 1 quarter ahead
1970 1980 1990 2000 2010
0
0.2
0.4
0.6
0.8
1Predicting a recession 2 quarters ahead
1970 1980 1990 2000 2010
0
0.2
0.4
0.6
0.8
1Predicting a recession 3 quarters ahead
1970 1980 1990 2000 2010
0
0.2
0.4
0.6
0.8
1Predicting a recession 4 quarters ahead
1970 1980 1990 2000 2010
0
0.2
0.4
0.6
0.8
1Predicting a recession 5 quarters ahead
1970 1980 1990 2000 2010
0
0.2
0.4
0.6
0.8
1Predicting a recession 6 quarters ahead
1970 1980 1990 2000 2010
0
0.2
0.4
0.6
0.8
1Predicting a recession 7 quarters ahead
1970 1980 1990 2000 2010
0
0.2
0.4
0.6
0.8
1Predicting a recession 8 quarters ahead
Notes: Predicted in-sample probabilities of NBER recessions from Probit models.
We also compute the “optimistic” and “pessimistic” scenarios according to equations (7)
and (8), respectively. Figure 2 presents the graphs for h= 2. The graphs for horizons h= 1,
14
h= 4, and h= 8 are shown in the Appendix. For illustrative purposes, we focus on the
period 2000-2012 which covers the last two recessions. The Great Recession of 2007-2009
has been more severe than our pessimistic forecast. It is also interesting to note that the
financial market has outperformed our optimistic forecast during the period that preceded
that recession (approx. 2003-2007). This result suggests perhaps a simple methodology to
identify financial bubbles, which consists of examining the gap between the actual value of
the market index and its most optimistic forecast based on real activity measures.
Figure 3 presents the estimated cost of recessions at horizon h= 2, as defined in the
paragraph following Equation (9).7The drop in output (GDP and industrial production)
growth predicted by the model for the Great Recession appears to be smaller than the one
predicted for the 2001 downturn. Likewise, the rise in unemployment rate predicted for the
Great Recession is smaller than in 2001. However, Figure 2 shows that the Great Recession
has been more severe. This suggest that the severity of the latter recession is less predictable
than that of the preceding recession.
3.1.4 Predicting the Severity of a Recession using the Duration Approach
We now present the estimation results for the duration approach. As discussed in Section
2.3, we fit an inflated Poisson to the NBER durations. The estimation is done by setting
λt= exp θ˜
Ftwhere ˜
Ftconsists of the first three principal components and a constant. We
use much less factors than in the Probit because the sample contains only 27 observations
with strictly positive duration (i.e. we only have 27 recessionary dates in the sample). The
expected duration of a recession conditional on the event Rt+1 = 1 is E(Nt|Xt, Nt1). The
expected duration can also be calculated unconditionally, that is, as E(Nt|Xt). Although
both expectations are conditional on Xt, we refer subsequently to E(Nt|Xt, Nt1) as the
“conditional expected duration” and to E(Nt|Xt) as simply the “expected duration.”
Note that Nt1 when Rt+1 = 1. Consequently, E(Nt|Xt, Nt1) is always larger than
7See the Appendix for horizons h= 1, h= 4 and h= 8.
15
Figure 2: Predicting US economic activity: 2-quarters ahead scenarios
GDP growth
2000 2002 2004 2006 2008 2010 2012
−2
−1
0
1
2
INDPRO growth
2000 2002 2004 2006 2008 2010 2012
−6
−4
−2
0
2
4
UNRATE
2000 2002 2004 2006 2008 2010 2012
4
5
6
7
8
9
10
11
EMPL growth
2000 2002 2004 2006 2008 2010 2012
−1.5
−1
−0.5
0
0.5
GDPDEF inflation
2000 2002 2004 2006 2008 2010 2012
−0.2
0
0.2
0.4
0.6
0.8
1
SP500 returns
2000 2002 2004 2006 2008 2010 2012
−20
−10
0
10
20
Notes: Predicted in-sample optimistic and pessimistic scenarios from DI-VAR forecasting models.
16
Figure 3: Predicting US economic activity: 2-quarters ahead loss due to recession
GDP growth
2000 2002 2004 2006 2008 2010 2012
−1.2
−1
−0.8
−0.6
−0.4
−0.2
0
0.2
INDPRO growth
2000 2002 2004 2006 2008 2010 2012
−2.5
−2
−1.5
−1
−0.5
0
UNRATE
2000 2002 2004 2006 2008 2010 2012
0
0.1
0.2
0.3
0.4
0.5
0.6
EMPL growth
2000 2002 2004 2006 2008 2010 2012
−0.6
−0.5
−0.4
−0.3
−0.2
−0.1
0
0.1
GDPDEF inflation
2000 2002 2004 2006 2008 2010 2012
−0.1
−0.05
0
0.05
0.1
SP500 returns
2000 2002 2004 2006 2008 2010 2012
−6
−5
−4
−3
−2
−1
0
Notes: Predicted in-sample losses during recessions in US economic activity from DI-VAR forecasting models.
one. The expected duration is equal to the probability of a recession times the conditional
expected duration. Figure 4 plots the expected duration and conditional expected duration
as defined in equations (15) and (14) respectively, as well as the observed NBER duration.
Recall that the expected duration is calculated for the whole sample while the conditional
expected duration is computed only for recession periods. The conditional expected duration
17
better approximates the actual duration, particularly at the beginning of the recessionary
episodes. The MSE of the conditional expected duration is 1.38 while the MSE of the
expected duration is 3.01. This suggests that the conditional expected duration is more
informative than its unconditional version when a recession is imminent.
Figure 4: Observed versus fitted NBER recession durations
year
quarters
1970 1975 1980 1985 1990 1995 2000 2005 2010
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
6
Expected duration
Conditional duration
Observed duration
Notes: We fit an inflated Poisson to NBER durations. The dashed asterisk black line is the observed NBER duration. The
solid diamond blue line is the expected duration conditional on the next period belonging to a recessionary episode. Finally,
the solid red line is the expected duration computed for the all sample. The MSE of conditional expected duration is 1.38 while
the MSE of expected duration is 3.01.
3.2 Out-of-Sample Analysis
We perform an out-of-sample analysis aimed at assessing the extrapolation capabilities of
the proposed empirical framework. For this purpose, we compare the IMR-DI-VAR model
to alternative specifications. The competing models retained are:
18
- Our IMR-DI-VAR model, which is the multivariate version of (9):
Yt+h=αhYt+βhFt+δh,1Φ (γhFt) + δh,2IMRt,h +εt+h
- The DI-VAR model, an extension of the univariate diffusion indices model of (Stock
& Watson 2002), that is a IMR-DI-VAR from which the fitted probability of recession and
IMR are omitted:
Yt+h=αhYt+βhFt+εt+h
- The IMR-VAR, which is another version of the IMR-DI-VAR without the factors:
Yt+h=αhYt+δh,1Φ (γhFt) + δh,2IMRt,h +εt+h
- And finally, the standard VAR:
Yt+h=αhYt+εt+h.
The out-of-sample evaluation period is 2000Q1 - 2012Q3, which leaves us with 131 periods
for model training, and 51 periods for forecasting evaluation. We use an expanding window
scheme by re-estimating the model as a new quarter is added to the training period. The
forecasting horizon is set at 4 quarters.
We consider selecting the number of factors (q1) to include in the Probit independently
from the number of factors (q2) to include in the prediction of Yt+h. Moreover, q1and q2are
selected independently for each of the models above and for each target variable in Yt. Note
that only q1matters for IMR-VAR model while only q2matters for DI-VAR. We choose q1
and q2that minimize the out-of-sample MSE.
The results are reported in Table (4). Interestingly, the IMR-DI-VAR model delivers the
smallest out-of-sample MSE for all targets except the SP500 returns. The latter variable
is better predicted by the IMR-VAR model. We perform Diebold-Mariano tests for the
19
purpose of judging whether the observed differences in out-of-sample MSEs truly reflect
different forecasting abilities across models. Table (5) presents the p-values computed for
pairwise tests for the null case that two given models deliver identical forecasts. As the
four models being compared are nested, we follow (Alquist & Kilian 2010) by adjusting the
p-values as in (Clark & West 2006). We also compare our competing models to a random
walk (RW). We find that the forecasts from all four models are mutually different and are
also different from the predictions of a RW8.
Table 4: Out-of-sample exercise: MSE results with expanding window
GDP Growth IP Growth
MSE q1q2MSE q1q2
IMR-DI-VAR 0.5077 15 4 1.9781 15 12
DI-VAR 0.5555 . 18 2.3524 . 4
IMR-VAR 0.5305 15 . 2.1390 15 .
VAR 0.6708 . . 2.6786 . .
RW 0.8834 . . 5.1295 . .
Unemployment Rate Employment Growth
MSE q1q2MSE q1q2
IMR-DI-VAR 0.4826 13 17 0.1670 15 12
DI-VAR 0.5272 . 17 0.2061 . 18
IMR-VAR 0.6174 9 . 0.2071 15 .
VAR 0.7729 . . 0.2701 . .
RW 1.4688 . . 0.3772 . .
GDPD Inflation SP500 Returns
MSE q1q2MSE q1q2
IMR-DI-VAR 0.0775 2 3 52.3303 16 1
DI-VAR 0.1303 . 18 57.1233 . 3
IMR-VAR 0.0993 2 . 51.2833 16 .
VAR 0.1326 . . 56.8302 . .
RW 0.0999 . . 107.5507 . .
These empirical results suggest four important conclusions. First, the IMR is an impor-
tant lead indicator of economic activity; its inclusion as the predictor in a VAR model permits
the significant reduction of the out-of-sample error. In particular, adding only the IMR to
the VAR improves the forecasting precision of the GDP growth rate one year ahead by 20%
(ratio of IMR-VAR and VAR MSEs), while considering the full IMR-DI-VAR model reduces
8As discussed in (Diebold 2012), these tests do not compare models but the forecasts.
20
Table 5: Out-of-sample exercise: p-values for testing the equal predictive accuracy with
expanding window
GDP Growth IP Growth
IMR-DI-VAR DI-VAR IMR-VAR VAR IMR-DI-VAR DI-VAR IMR-VAR VAR
DI-VAR 0.0000 . - - 0.0000 . - -
IMR-VAR 0.0011 0.0000 . - 0.0001 0.0010 . -
VAR 0.0063 0.0000 0.0022 . 0.0003 0.0008 0.0033 .
RW 0.0208 0.0113 0.0275 0.0156 0.0171 0.0254 0.0166 0.0394
Unemployment Rate Employment Growth
IMR-DI-VAR DI-VAR IMR-VAR VAR IMR-DI-VAR DI-VAR IMR-VAR VAR
DI-VAR 0.0000 . - - 0.0000 . - -
IMR-VAR 0.0011 0.0000 . - 0.0001 0.0010 . -
VAR 0.0063 0.0000 0.0022 . 0.0003 0.0008 0.0033 .
RW 0.0208 0.0113 0.0275 0.0156 0.0171 0.0254 0.0166 0.0394
GDPD Inflation SP500 Returns
IMR-DI-VAR DI-VAR IMR-VAR VAR IMR-DI-VAR DI-VAR IMR-VAR VAR
DI-VAR 0.0000 . - - 0.0000 . - -
IMR-VAR 0.0011 0.0000 . - 0.0001 0.0010 . -
VAR 0.0063 0.0000 0.0022 . 0.0003 0.0008 0.0033 .
RW 0.0208 0.0113 0.0275 0.0156 0.0171 0.0254 0.0166 0.0394
Note: All p-values refer to a pairwise test of equal forecasts obtained from two models. Following (Alquist & Kilian 2010), we
produce adjusted p-values based on (Clark & West 2006).
the MSE by 25%. In case of IP growth, Unemployment rate, and Employment growth, the
improvements of IMR-DI-VAR specifications are 24%, 37%, and 38%, respectively. Second,
including the IMR and principal components is especially important to forecast the inflation
rate, which is a variable very difficult to predict, see discussion in (Faust & Wright 2012).
Not only the IMR-DI-VAR improves over the VAR model by 41%, but it reduces the MSE
with respect to the Random Walk by 22%. Third, the SP500 returns do not seem to be
linearly predictable by the PCA factors. In fact, the inclusion of these factors as predictors
in a VAR model increases the out-of-sample MSE. The best forecasts are delivered by the
IMR-VAR model which reduces the MSE by 10% compared to the VAR. Finally, note that
the out-of-sample evaluation period covers the biggest financial crisis and the global economic
downturn since the Great Depression. Hence, the flexibility of IMR-DI-VAR approach in
including information from different sources to a VAR is an important advantage.
To check the robustness of the results, we repeat the out-of-sample exercise but now
using a rolling window scheme (as opposed to an expanding window). As shown by Table
21
(6), the IMR-DI-VAR model has the smallest out-of-sample tracking error for unemployment
and inflation rates, as well as for the SP500 returns, while the IMR-VAR model is more
successful at tracking the other targets. However, the performances of these two models are
quite close.
We also consider using the mean absolute error (MAE) as loss function (as opposed to
the MSE). This choice of loss function implicitly assumes that the quantity being tracked is
the conditional median of the target while the models have been trained to correctly track its
conditional mean. The results for the expanding window are shown in Table (7) while those
for the rolling window are shown in Table (8). The results suggest that the IMR-DI-VAR
model has superior performance at predicting all six targets under expanding windows. This
model also dominates the other benchmarks under the rolling window scheme, except for
the employment growth. The latter variable is better predicted by the IMR-VAR model.
Overall, this robustness check exercise confirms the relevance of including the IMR (and
possibly, diffusion indices) as predictor in VAR models. Our results can be related to those
of (Dueker 2005) and (Dueker & Wesche 2010), who show that including information about
a qualitative variable (i.e., the indicator of NBER recession) in a standard VAR improves
the forecasts of the system.
4 Conclusion
We propose an empirical framework for analyzing the probability and severity of U.S. reces-
sions in a data rich environment. The severity of a recession is measured in two dimensions:
its depth (impact on economic activity) and its length (duration). We consider a frame-
work where a large number of candidate predictors of economic activity is available to the
econometrician. The range of candidate predictors considered includes financial spreads, con-
sumption expenditures, monetary aggregates, and measures of stock market performance.
This large number of predictors is summarized into a fewer number of principal components
22
Table 6: Out-of-sample exercise: MSE results with rolling window
GDP Growth IP Growth
MSE q1q2MSE q1q2
IMR-DI-VAR 0.5047 15 1 2.1556 16 1
DI-VAR 0.5887 . 3 2.4212 . 1
IMR-VAR 0.4937 17 .2.0529 16 .
VAR 0.6651 . . 2.4744 . .
RW 0.8834 . . 5.1295 . .
Unemployment Rate Employment Growth
MSE q1q2MSE q1q2
IMR-DI-VAR 0.5192 16 6 0.1757 16 1
DI-VAR 0.5768 . 18 0.2312 . 1
IMR-VAR 0.5522 4 . 0.1601 16 .
VAR 0.7288 . . 0.2376 . .
RW 1.4688 . . 0.3772 . .
GDPD Inflation SP500 Returns
MSE q1q2MSE q1q2
IMR-DI-VAR 0.0817 2 3 53.6018 17 3
DI-VAR 0.1104 . 1 60.8804 . 6
IMR-VAR 0.1040 2 . 55.3633 17 .
VAR 0.1120 . . 59.4742 . .
RW 0.0999 . . 107.5507 . .
23
Table 7: Out-of-sample exercise: MAE results with expanding window
GDP Growth IP Growth
MAE q1q2MAE q1q2
IMR-DI-VAR 0.5306 1 4 0.9568 1 4
DI-VAR 0.5425 . 18 1.0679 . 1
IMR-VAR 0.5340 1 . 1.0432 1 .
VAR 0.6140 . . 1.1503 . .
RW 0.6914 . . 1.5361 . .
Unemployment Rate Employment Growth
MAE q1q2MAE q1q2
IMR-DI-VAR 0.4286 9 1 0.3055 1 18
DI-VAR 0.4905 . 4 0.3286 . 12
IMR-VAR 0.4793 9 . 0.3134 10 .
VAR 0.6080 . . 0.3587 . .
RW 0.8216 . . 0.4333 . .
GDPD Inflation SP500 Returns
MAE q1q2MAE q1q2
IMR-DI-VAR 0.2232 2 2 5.1764 17 3
DI-VAR 0.2748 . 17 5.5699 . 3
IMR-VAR 0.2520 2 . 5.1915 16 .
VAR 0.2875 . . 5.6465 . .
RW 0.2639 . . 7.5608 . .
24
Table 8: Out-of-sample exercise: MAE results with rolling window
GDP Growth IP Growth
MAE q1q2MAE q1q2
IMR-DI-VAR 0.5057 1 4 1.0110 1 1
DI-VAR 0.5627 . 1 1.0891 .1
IMR-VAR 0.5125 1 . 1.0166 1 .
VAR 0.5968 . . 1.1193 . .
RW 0.6914 . . 1.5361 . .
Unemployment Rate Employment Growth
MAE q1q2MAE q1q2
IMR-DI-VAR 0.4477 3 1 0.3064 1 1
DI-VAR 0.4968 . 3 0.3376 . 1
IMR-VAR 0.4971 7 . 0.3023 1 .
VAR 0.6215 . . 0.3421 . .
RW 0.8216 . . 0.4333 . .
GDPD Inflation SP500 Returns
MAE q1q2MAE q1q2
IMR-DI-VAR 0.2242 2 2 5.3618 17 3
DI-VAR 0.2670 . 1 5.5288 . 6
IMR-VAR 0.2615 4 . 5.5019 16 .
VAR 0.2669 . . 5.7361 . .
RW 0.2639 . . 7.5608 . .
25
or factors. Each factor is interpreted by examining the variables with which it is correlated
the most. Among others, we find that the first factor is related to employment growth and
external finance premium, the second factor is correlated with inflation and FED fund rate,
and the third factor captures the movements of consumption and stock prices. This step
provides a summary description of the data while eluding the multicolinearity problems that
would have resulted from including highly correlated variables in the information set (e.g.,
GDP deflator and CPI inflation).
To analyze the probability of recessions, we advocate Probit models in which the infor-
mation available at time t (as summarized by the factors) conditions the indicator of NBER
recession at horizon t+h, where hvaries between 1 and 8 quarters. Our in-sample analysis
suggests that recession dates are fairly predictable at up to 5 quarters horizon. Second, we fit
an IMR-DI-VAR model to the GDP growth, industrial production growth, unemployment
rate, employment growth, inflation rate, and SP500 returns. The IMR-DI-VAR model is
obtained by augmenting the standard diffusion index vector autoregression model of (Stock
& Watson 2002) by an Inverse Mills Ratio deduced from the Probit models. This model
allows us to construct an average forecast scenario as well as an optimistic and a pessimistic
forecast scenarios. The severity of a recession is predicted as the gap between the forecasts
associated with the pessimistic and the average scenarios. Third, we fit a zero-inflated Pois-
son model to the duration of NBER recessions. The estimation output is used to construct
an estimate of the expected duration of a recession.
We perform an out-of sample experiment aimed at optimally selecting the number of
factors to include in the analysis. The optimal numbers of factors to use in the Probit
model and in the IMR-DI-VAR model are assumed to be distinct. We compare the IMR-
DI-VAR model to three alternative specifications: the standard DI-VAR, the IMR-VAR (a
VAR augmented with an IMR), and a standard VAR model. The results suggest that the
IMR-DI-VAR has the best out-of-sample forecast performance for all target variables under
an expanding window scheme and a quadratic loss function. Particularly, important findings
26
include a reduction of up to 38% in MSE when forecasting several measures of real activity,
and 41% in the case of GDP Deflator inflation. Under alternative schemes, the IMR-VAR
outperforms the IMR-DI-VAR for certain targets (e.g., SP500 returns). The main lesson
learned from this study is that the IMR conveys valuable information about future states of
the economy.
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Appendix A: Description of the data
The transformation codes are: 1 - no transformation; 2 - first difference; 4 - logarithm;
5 - first difference of logarithm; 0 - variable not used in the estimation (only used for trans-
forming other variables). A * indicate a series that is deflated by the Personal Consumption
Expenditures: Chain-type Price Index. GDP and GDPDEF are observed quarterly and are
not in Xt.
29
Table 9: Data used to construct the diffusion indices
INDPROgr 5 Industrial Production Index
UNRATE 1 Civilian Unemployment Rate
PAYEMSgr 5 All Employees: Total nonfarm
MANEMPgr 5 All Employees: Manufacturing
USMINEgr 5 All Employees: Mining and logging
IC4WSA 4 4-Week Moving Average of Initial Claims
RPCEgr 5* Real Personal Consumption Expenditures
RPCEDGgr 5* Real Personal Consumption Expenditures: Durable Goods
AWHMAN 1 Average Weekly Hours: Manufacturing
AWOTMAN 1 Average Weekly Overtime Hours: Manufacturing
NAPM 1 ISM Manufacturing: PMI Composite Index
NAPMOI 1 ISM Manufacturing: New Orders Index
NAPMEI 1 ISM Manufacturing: Employment Index
NAPMII 1 ISM Manufacturing: Inventories Index
NAPMSDI 1 ISM Manufacturing: Supplier Deliveries Index
NAPMPRI 1 ISM Manufacturing: Prices Index
CUmftg 1 Capacity Utilization: Manufacturing
CPILFEL 5 Consumer Price Index for All Urban Consumers: All Items
CPIAUCSL 5 Consumer Price Index for All Urban Consumers: All Items Less Food & Energy
PCEPI 5 Personal Consumption Expenditures: Chain-type Price Index
M1SL 5 M1 Money Stock
M2SL 5 M2 Money Stock
HOUST 4 Housing Starts: Total: New Privately Owned Housing Units Started
PERMIT 4 New Private Housing Units Authorized by Building Permits
ConsMICH 1 University of Michigan: Consumer Sentiment
OILPRICEgr 5 Spot Oil Price: West Texas Intermediate
FFR 1 Effective Federal Funds Rate
INVEST 5 Securities in Bank Credit at All Commercial Banks
TB3MS 1 3-Month Treasury Bill: Secondary Market Rate
GS1 0 1-Year Treasury Constant Maturity Rate
GS5 1 5-Year Treasury Constant Maturity Rate
GS10 0 10-Year Treasury Constant Maturity Rate
SP500 5 S&P 500 Stock Price Index
DJIA 5 Dow Jones Industrial Average
BAA 0 Moody´s Seasoned Baa Corporate Bond Yield
AAA 0 Moody´s Seasoned Aaa Corporate Bond Yield
BAA-GS10 1
BAA-AAA 1
BAA-FFR 1
GS10-TB3MS 1
GS5-FFR 1
GS1-FFR 1
SP500-RV 1 S&P500: realized volatility
SP500-SK 1 S&P500: realized skewness
DJIA-RV 1 DJIA: realized volatility
DJIA-SK 1 DJIA: realized skewness
GDP 5 Real Gross Domestic Product
GDPDEF 5 GDP Deflator
Appendix B: Estimation results
30
Table 10: Predicting NBER recessions: full-sample results
1 quarter ahead 2 quarters ahead 3 quarters ahead 4 quarters ahead
coefficients p-value coefficients p-value coefficients p-value coefficients p-value
const -2,934 0,000 -2,183 0,000 -2,208 0,000 -3,054 0,000
F1-0,328 0,001 -0,055 0,305 0,247 0,096 0,524 0,004
F20,594 0,000 0,393 0,000 0,386 0,000 0,518 0,000
F3-0,714 0,001 -0,531 0,000 -0,330 0,029 -0,342 0,087
F40,065 0,707 0,183 0,147 0,097 0,421 -0,010 0,951
F5-0,164 0,376 -0,097 0,509 -0,408 0,155 -0,281 0,395
F6-0,154 0,464 -0,128 0,456 -0,184 0,541 0,558 0,078
F70,539 0,032 -0,131 0,494 0,098 0,687 -0,237 0,321
F8-0,082 0,753 -0,269 0,210 -0,580 0,062 -0,363 0,172
F90,016 0,952 -0,238 0,290 -0,362 0,190 -0,227 0,422
F10 0,430 0,142 -0,018 0,928 -0,047 0,858 -0,234 0,497
F11 0,225 0,323 0,308 0,173 0,466 0,064 0,848 0,011
F12 -0,231 0,495 -0,079 0,767 0,349 0,254 0,013 0,966
F13 -0,371 0,249 0,225 0,319 -0,369 0,367 -1,278 0,033
F14 0,281 0,395 0,107 0,705 -0,210 0,491 -1,402 0,001
F15 0,342 0,447 0,206 0,566 -0,178 0,640 -0,440 0,277
F16 0,731 0,078 0,985 0,008 1,126 0,006 1,701 0,001
5 quarters ahead 6 quarters ahead 7 quarters ahead 8 quarters ahead
coefficients p-value coefficients p-value coefficients p-value coefficients p-value
const -1,953 0,000 -2,035 0,000 -2,277 0,000 -2,685 0,000
F10,208 0,004 0,280 0,008 0,386 0,002 0,594 0,000
F20,265 0,000 0,249 0,003 0,285 0,001 0,296 0,002
F3-0,143 0,121 0,096 0,573 0,155 0,396 0,467 0,051
F40,035 0,706 0,259 0,086 0,340 0,044 0,521 0,012
F50,124 0,366 0,089 0,748 0,311 0,258 0,107 0,727
F60,370 0,024 0,588 0,010 0,415 0,091 0,340 0,312
F7-0,586 0,002 -0,283 0,186 0,128 0,563 0,334 0,186
F8-0,410 0,018 -0,169 0,436 -0,165 0,492 -0,353 0,297
F9-0,135 0,378 0,019 0,907 0,153 0,363 0,302 0,196
F10 -0,392 0,045 -0,211 0,387 -0,502 0,036 -0,576 0,041
F11 0,055 0,762 0,214 0,297 0,076 0,695 0,076 0,717
F12 0,545 0,016 0,520 0,028 0,593 0,013 0,637 0,016
F13 -0,158 0,517 -0,191 0,573 0,166 0,600 0,041 0,911
F14 -0,369 0,152 -0,347 0,143 -0,361 0,116 -0,256 0,276
F15 -0,626 0,033 -0,698 0,016 -0,753 0,009 -0,576 0,063
F16 0,260 0,290 -0,191 0,457 -0,344 0,191 -0,093 0,735
31
Table 11: Predicting economic activity 4 quarters ahead: estimation results
GDP growth INDPRO growth UNRATE
coefficients p-value coefficients p-value coefficients p-value
const -1,878 0,061 -5,632 0,000 6,728 0,000
F1,t 0,026 0,760 -0,097 0,436 -0,272 0,000
F2,t 0,054 0,349 -0,001 0,989 0,121 0,003
F3,t -0,117 0,292 -0,317 0,047 0,163 0,039
F4,t 0,283 0,007 0,659 0,000 -0,453 0,000
F5,t 0,149 0,115 0,235 0,085 -0,292 0,000
F6,t 0,057 0,498 0,149 0,217 -0,205 0,001
F7,t 0,124 0,157 0,261 0,038 -0,275 0,000
F8,t -0,105 0,100 -0,346 0,000 0,176 0,000
F9,t 0,027 0,720 0,068 0,539 -0,189 0,001
F10,t 0,153 0,061 0,337 0,004 -0,070 0,228
F11,t -0,020 0,831 -0,092 0,500 0,181 0,007
F12,t 0,112 0,305 0,176 0,265 0,020 0,799
F13,t 0,206 0,093 0,338 0,056 -0,094 0,280
F14,t -0,082 0,305 0,093 0,418 0,058 0,308
F15,t -0,025 0,752 -0,235 0,039 0,123 0,029
F16,t 0,000 0,998 -0,065 0,661 0,117 0,107
y1,t 0,080 0,491 0,139 0,405 -0,094 0,255
y2,t 0,249 0,018 0,448 0,003 -0,031 0,675
y3,t 0,402 0,011 0,855 0,000 -0,053 0,639
y4,t -0,150 0,713 0,469 0,426 -0,226 0,437
y5,t 0,150 0,556 0,733 0,046 0,063 0,728
y6,t -0,011 0,827 0,004 0,953 -0,028 0,431
Φ(Ftγh) -1,297 0,000 -2,244 0,000 0,346 0,108
IMRt-0,647 0,000 -1,463 0,000 0,386 0,000
EMPL growth GDPDEF inflation S&P500 returns
coefficients p-value coefficients p-value coefficients p-value
const -3,093 0,000 -0,217 0,639 -6,158 0,503
F1,t 0,082 0,020 0,030 0,452 0,674 0,397
F2,t 0,016 0,509 0,120 0,000 0,238 0,654
F3,t -0,158 0,000 -0,085 0,095 -0,771 0,448
F4,t 0,257 0,000 -0,052 0,288 0,508 0,599
F5,t 0,185 0,000 0,110 0,011 0,349 0,688
F6,t 0,096 0,005 0,108 0,005 -0,850 0,268
F7,t 0,175 0,000 0,129 0,001 0,520 0,517
F8,t -0,118 0,000 -0,061 0,040 0,474 0,421
F9,t 0,107 0,001 0,075 0,034 0,331 0,637
F10,t 0,176 0,000 0,107 0,005 -0,417 0,577
F11,t -0,071 0,065 0,018 0,684 -0,239 0,784
F12,t 0,014 0,757 -0,048 0,340 -0,168 0,867
F13,t 0,139 0,005 0,055 0,332 0,919 0,416
F14,t -0,009 0,778 0,059 0,107 -0,472 0,519
F15,t -0,098 0,002 -0,027 0,460 -0,293 0,686
F16,t 0,008 0,847 -0,051 0,281 0,998 0,288
y1,t 0,071 0,132 0,005 0,926 0,105 0,921
y2,t 0,096 0,024 0,047 0,329 -0,809 0,401
y3,t 0,515 0,000 0,116 0,114 1,448 0,321
y4,t 0,274 0,098 0,261 0,166 -0,963 0,798
y5,t 0,150 0,148 0,229 0,052 0,728 0,756
y6,t 0,023 0,265 0,037 0,111 0,108 0,814
Φ(Ftγh) -0,703 0,000 0,135 0,334 -8,032 0,004
IMRt-0,365 0,000 -0,089 0,154 0,210 0,866
32
Table 12: Predicting economic activity 8 quarters ahead: estimation results
GDP growth INDPRO growth UNRATE
coefficients p-value coefficients p-value coefficients p-value
const 0,902 0,376 0,012 0,994 10,553 0,000
F1,t 0,121 0,169 0,162 0,246 -0,107 0,323
F2,t -0,018 0,764 0,057 0,551 0,122 0,095
F3,t 0,189 0,098 -0,017 0,926 0,255 0,068
F4,t 0,080 0,458 0,080 0,641 -0,780 0,000
F5,t -0,064 0,510 0,000 0,998 -0,419 0,000
F6,t 0,067 0,423 -0,016 0,905 -0,183 0,075
F7,t -0,093 0,311 0,055 0,704 -0,721 0,000
F8,t 0,012 0,860 -0,063 0,557 0,208 0,012
F9,t -0,060 0,438 0,165 0,178 -0,324 0,001
F10,t -0,107 0,199 0,010 0,938 -0,228 0,025
F11,t -0,088 0,367 -0,136 0,379 0,093 0,437
F12,t 0,000 1,000 -0,090 0,611 0,045 0,744
F13,t 0,143 0,256 0,064 0,747 -0,367 0,017
F14,t -0,164 0,055 -0,110 0,415 -0,117 0,266
F15,t -0,007 0,932 -0,105 0,433 0,119 0,251
F16,t 0,168 0,094 0,324 0,042 -0,039 0,751
y1,t -0,018 0,877 -0,140 0,452 0,155 0,283
y2,t -0,024 0,829 -0,117 0,504 -0,314 0,020
y3,t 0,050 0,757 0,220 0,386 -0,583 0,003
y4,t -0,573 0,174 -0,457 0,494 -1,091 0,034
y5,t 0,106 0,681 0,042 0,919 -0,015 0,963
y6,t -0,067 0,191 0,005 0,953 -0,042 0,507
Φ(Ftγh) -1,795 0,000 -3,482 0,000 0,638 0,176
IMRt-0,731 0,000 -1,691 0,000 0,376 0,003
EMPL growth GDPDEF inflation S&P500 returns
coefficients p-value coefficients p-value coefficients p-value
const -0,999 0,058 -0,407 0,456 3,939 0,681
F1,t 0,003 0,942 0,085 0,073 0,007 0,994
F2,t 0,024 0,443 0,051 0,113 0,356 0,527
F3,t -0,002 0,971 -0,036 0,558 -0,323 0,763
F4,t 0,114 0,040 -0,052 0,370 -0,497 0,625
F5,t 0,042 0,399 0,144 0,006 0,082 0,929
F6,t 0,064 0,138 0,111 0,013 -0,014 0,986
F7,t 0,106 0,026 0,133 0,007 -0,359 0,680
F8,t -0,063 0,073 -0,117 0,001 0,863 0,176
F9,t 0,082 0,040 0,126 0,002 -0,278 0,703
F10,t 0,071 0,099 0,185 0,000 0,120 0,878
F11,t -0,063 0,213 -0,069 0,186 -0,102 0,911
F12,t 0,018 0,753 0,060 0,315 -0,346 0,743
F13,t 0,159 0,014 0,009 0,895 0,324 0,784
F14,t -0,019 0,667 -0,044 0,338 0,071 0,929
F15,t -0,050 0,254 -0,037 0,414 1,010 0,204
F16,t 0,166 0,001 -0,095 0,077 -0,422 0,655
y1,t -0,062 0,308 -0,018 0,772 0,891 0,422
y2,t 0,099 0,084 0,013 0,828 0,125 0,904
y3,t 0,222 0,007 0,185 0,032 -0,259 0,864
y4,t 0,178 0,414 0,003 0,990 -0,448 0,910
y5,t 0,108 0,419 0,148 0,285 0,005 0,999
y6,t -0,004 0,882 0,017 0,530 0,110 0,820
Φ(Ftγh) -1,232 0,000 0,227 0,271 -8,237 0,023
IMRt-0,518 0,000 0,056 0,311 -2,054 0,036
33
Figure 5: Predicting US economic activity: 1-quarter ahead scenarios
GDP growth
2000 2002 2004 2006 2008 2010 2012
−2.5
−2
−1.5
−1
−0.5
0
0.5
1
1.5
INDPRO growth
2000 2002 2004 2006 2008 2010 2012
−6
−4
−2
0
2
UNRATE
2000 2002 2004 2006 2008 2010 2012
4
5
6
7
8
9
10
11 EMPL growth
2000 2002 2004 2006 2008 2010 2012
−1.5
−1
−0.5
0
0.5
GDPDEF inflation
2000 2002 2004 2006 2008 2010 2012
−0.2
0
0.2
0.4
0.6
0.8
1
SP500 returns
2000 2002 2004 2006 2008 2010 2012
−25
−20
−15
−10
−5
0
5
10
15
Notes: Predicted in-sample optimistic and pessimistic scenarios from DI-VAR forecasting models.
34
Figure 6: Predicting US economic activity: 4-quarters ahead scenarios
GDP growth
2000 2002 2004 2006 2008 2010 2012
−5
−4
−3
−2
−1
0
1
INDPRO growth
2000 2002 2004 2006 2008 2010 2012
−10
−8
−6
−4
−2
0
2
UNRATE
2000 2002 2004 2006 2008 2010 2012
4
5
6
7
8
9
10
11
12
EMPL growth
2000 2002 2004 2006 2008 2010 2012
−3.5
−3
−2.5
−2
−1.5
−1
−0.5
0
0.5
GDPDEF inflation
2000 2002 2004 2006 2008 2010 2012
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
SP500 returns
2000 2002 2004 2006 2008 2010 2012
−25
−20
−15
−10
−5
0
5
10
Notes: Predicted in-sample optimistic and pessimistic scenarios from DI-VAR forecasting models.
35
Figure 7: Predicting US economic activity: 8-quarters ahead scenarios
GDP growth
2000 2002 2004 2006 2008 2010 2012
−6
−5
−4
−3
−2
−1
0
1
INDPRO growth
2000 2002 2004 2006 2008 2010 2012
−12
−10
−8
−6
−4
−2
0
2
UNRATE
2000 2002 2004 2006 2008 2010 2012
4
5
6
7
8
9
10
11
12
EMPL growth
2000 2002 2004 2006 2008 2010 2012
−4
−3
−2
−1
0
GDPDEF inflation
2000 2002 2004 2006 2008 2010 2012
−0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
SP500 returns
2000 2002 2004 2006 2008 2010 2012
−25
−20
−15
−10
−5
0
5
10
Notes: Predicted in-sample optimistic and pessimistic scenarios from DI-VAR forecasting models.
36
Figure 8: Predicting US economic activity: 1-quarter ahead loss due to recession
GDP growth
2000 2002 2004 2006 2008 2010 2012
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4 INDPRO growth
2000 2002 2004 2006 2008 2010 2012
−2
−1.5
−1
−0.5
0
UNRATE
2000 2002 2004 2006 2008 2010 2012
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35 EMPL growth
2000 2002 2004 2006 2008 2010 2012
−0.35
−0.3
−0.25
−0.2
−0.15
−0.1
−0.05
0
GDPDEF inflation
2000 2002 2004 2006 2008 2010 2012
−0.06
−0.05
−0.04
−0.03
−0.02
−0.01
0
SP500 returns
2000 2002 2004 2006 2008 2010 2012
−3.5
−3
−2.5
−2
−1.5
−1
−0.5
0
Notes: Predicted in-sample losses during recessions in US economic activity from DI-VAR forecasting models.
37
Figure 9: Predicting US economic activity: 4-quarters ahead loss due to recession
GDP growth
2000 2002 2004 2006 2008 2010 2012
−1.2
−1
−0.8
−0.6
−0.4
−0.2
0
INDPRO growth
2000 2002 2004 2006 2008 2010 2012
−2.5
−2
−1.5
−1
−0.5
0
UNRATE
2000 2002 2004 2006 2008 2010 2012
−0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
EMPL growth
2000 2002 2004 2006 2008 2010 2012
−0.7
−0.6
−0.5
−0.4
−0.3
−0.2
−0.1
0
GDPDEF inflation
2000 2002 2004 2006 2008 2010 2012
−0.05
0
0.05
0.1
SP500 returns
2000 2002 2004 2006 2008 2010 2012
−7
−6
−5
−4
−3
−2
−1
Notes: Predicted in-sample losses during recessions in US economic activity from DI-VAR forecasting models.
38
Figure 10: Predicting US economic activity: 8-quarters ahead loss due to recession
GDP growth
2000 2002 2004 2006 2008 2010 2012
−1.5
−1
−0.5
0
INDPRO growth
2000 2002 2004 2006 2008 2010 2012
−3
−2.5
−2
−1.5
−1
−0.5
0
UNRATE
2000 2002 2004 2006 2008 2010 2012
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
EMPL growth
2000 2002 2004 2006 2008 2010 2012
−1
−0.8
−0.6
−0.4
−0.2
0
GDPDEF inflation
2000 2002 2004 2006 2008 2010 2012
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
SP500 returns
2000 2002 2004 2006 2008 2010 2012
−6
−5
−4
−3
−2
−1
0
Notes: Predicted in-sample losses during recessions in US economic activity from DI-VAR forecasting models.
39
Figure 11: Predicting US economic activity: 4 quarters ahead
1970 1980 1990 2000 2010
−2
−1
0
1
2
3
GDP growth
Actual
Predicted
1970 1980 1990 2000 2010
−6
−4
−2
0
2
4
INDPRO growth
1970 1980 1990 2000 2010
4
5
6
7
8
9
10
UNRATE
1970 1980 1990 2000 2010
−1.5
−1
−0.5
0
0.5
1
1.5
EMPL growth
1970 1980 1990 2000 2010
0
0.5
1
1.5
2
2.5
GDPDEF inflation
1970 1980 1990 2000 2010
−20
−10
0
10
20
SP500 returns
Notes: Predicted in-sample US economic activity series from DI-VAR forecasting models.
40
Figure 12: Predicting US economic activity: 8 quarters ahead
1970 1980 1990 2000 2010
−2
−1
0
1
2
3
GDP growth
Actual
Predicted
1970 1980 1990 2000 2010
−6
−4
−2
0
2
4
INDPRO growth
1970 1980 1990 2000 2010
4
5
6
7
8
9
10
UNRATE
1970 1980 1990 2000 2010
−1.5
−1
−0.5
0
0.5
1
1.5
EMPL growth
1970 1980 1990 2000 2010
0
0.5
1
1.5
2
2.5
GDPDEF inflation
1970 1980 1990 2000 2010
−20
−10
0
10
20
SP500 returns
Notes: Predicted in-sample US economic activity series from DI-VAR forecasting models.
41
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