Academy of Economic Studies Bucharest
Doctoral School of Finance and Banking
DOFIN
The Yield Curve in Predicting U.S.
Recessions
Supervisor: Professor Dr. Moisa Altar
MSc Student: TIBERIU PIPIRIG
Bucharest, July 2008
Contents

Conceptual considerations
The Yield Curve as a Leading Indicator
Defining Recessions
Measuring the variables

Recession Prediction Using the Yield Curve: Alternative Probit Models
Methodology
Empirical Results
Out of Sample Predictions of Recessions and Expansions
Interpreting the signal
Conclusions
References
Appendix 1
Motivation

In 1996, the Conference Board added the yield curve spread to its index of
leading indicators, focusing on monthly changes in the spread. Note, however,
that it announced in June 2005 that it would adjust its procedure so as to focus
on the level of the spread and not on the change, and for this reason my
analysis is focused on the level of the term spread.

The slope of the Treasury yield curve has often been cited as a leading
economic indicator, with inversion of the curve being thought of as a harbinger of
a recession.

Before each of the last six recessions, short-term interest rates rose above long
term rates, reversing the customary pattern and producing what economists call
a yield curve inversion.

In March 2007, Alan Greenspan stated that there is a 35 percent probability that
the US economy enters a recession before the end of the year.
Literature Review

Analysis of the behaviour of interest rates of different maturities over the
business cycle goes back at least to Mitchell (1913) and Kessel (1965);

Laurent (1988,1989) used term spread to predict GNP growth;

Fama (1990), Mishkin (1990) and Jorion (1991) show that spreads between long
and short term interest rates contain information about future inflation;

Bernanke (1990) and Estrella and Hardouvelis (1991) showed that term spreads
are useful for predicting future real economic growth;

The value of term spreads as an indicator of the likelihood of whether a
recession, as defined by the NBER, will occur in the near future is forcefully
demonstrated by Bernard and Gerlach (1998) and Estrella and Trubin (2006);

More supportive empirical evidence for this argument is recently provided by
Stock and Watson (2003), Wright (2006), Swanson (2007), Estrella and Adrian
(2007) and Rosenberg and Maurer (2008);
The Yield Curve as a Leading Indicator

Current monetary policy has a significant influence on the yield curve spread
and hence on real activity over the next several quarters
Tightening of monetary policy  rise in short term interest rates  intended to
lead to a reduction in inflationary pressures  pressures subside  lower
interest rates  monetary tightening slows down the economy and flattens or
inverts the yield curve

Changes in investor expectations can also change the slope of the yield curve
Rise in short term interest rates  slowing economic activity  increasing the
likelihood of a future easing in monetary policy  expected declines in short
term rates would tend to reduce current long term rates
This scenario is consistent with the observed correlation between the yield curve
and recessions.
Defining Recessions

A recession is 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 (NBER).

The 2001 recession thus lasted 8 months, which is somewhat less than the average
duration of recessions since World War II. The post-war average, excluding the 2001
recession, is 11 months.

The standard dating of U.S. recessions derives from the cyclical peaks and troughs
identified by the National Bureau of Economic Research (NBER). To convert the
NBER monthly dates into a monthly recession indicator, I classify as a recession
every month between the peak and the subsequent trough, as well as the trough
itself. The peak is not classified as a recession month because the economy would
have grown from the previous month.

Other conventions may lead to different results, for example, Wright (2006) classifies
peaks as recession periods.
Measuring the variables

Term spread measured as 10 years Treasury Bond less the 3 month Treasury
Bill

Maximum accuracy and predictive power are obtained with the secondary
market three month rate expressed on a bond equivalent basis, rather than the
constant maturity rate, which is interpolated from the daily yield curve for
Treasury securities. To convert the three month discount rate to a bond
equivalent basis, I apply the transformation:
100 * 365 * discount / 100
Bond  equivalent 
360  91* discount /100
where “discount” is the discount yield expressed in percentage points.

Historically, the nominal federal funds rate (annualized using a 360 day year)
has exhibited a positive statistical relationship with the odds of a recession
Treasury spread: Ten Year Bond Rate minus Three Month Bill Rate Monthly Average
5
4
Percentage points
3
2
1
0
-1
n07
Ja
n04
Ja
n01
Ja
n98
Ja
n95
Ja
n92
Ja
n89
Ja
n86
Ja
n83
Ja
n80
Ja
n77
n74
Ja
-4
Notes: The term spread in February 2007 was -0.45 percentage points. The shaded areas indicate periods
designated national recessions by the National Bureau of Economic Research.
Federal Funds Rate Monthly Average
n07
Ja
n04
Ja
n01
Ja
n98
Ja
n95
Ja
n92
Ja
n89
Ja
n86
Ja
n83
Ja
n80
Ja
n77
Ja
n74
Ja
n71
Ja
n68
20
18
16
14
12
10
8
6
4
2
0
Ja

Ja
Ja
-3
Ja
n71
n68
-2
Recession Prediction Using the Yield Curve: Alternative
Probit Models

Model A
PNBERt ,t h  1   (~0  ~1SPREADt10Y 3M )
where is the dummy that takes on a value 1 if and only if there is an NBER defined
recession at some point during months or quarters t+1 through t+h, inclusive,
denotes the average ten year over three month constant maturity Treasury term
spread during quarter t and denotes the standard normal cumulative distribution
function.

Model B
PNBERt ,t h  1   ( 0  1SPREADt10Y 3M   2 FFt )
where the denotes the average effective federal funds rate during month or quarter
t.
Each of the monthly models is estimated using data from Jul 1960 to Jul 2007
The quaterly model is estimated using data from Q3:1960 to Q2: 2007.
Measure of fit

The measure of fit used, that is, the pseudo R2, is calculated from a formula
proposed in Estrella (1995)
 log Lu
pseudoR  1  
 log Lc
2




2
log Lc
n
where is the value of the likelihood of the estimated model and is the value of a
model containing only the constant term .
Empirical Results

Chart shows that the estimated probability of recession exceeded 27 percent in the
case of each recession and ranged as high as 98 percent in the 1981-82 recession.
Recession Probability in 12 months
Recession
-0
7
Ja
n
-0
4
Ja
n
-0
1
Ja
n
-9
8
Ja
n
-9
2
-9
5
Ja
n
Ja
n
-8
9
Ja
n
-8
6
Ja
n
-8
3
Ja
n
-8
0
Ja
n
-7
7
Ja
n
-7
4
Ja
n
-7
1
Probability spread
Ja
n
Ja
n
-6
8
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

Model A now puts the odds of a recession in the next twelve months at over 30
percent, starting from October 2007 until April 2008. Model B predict odds of a
recession of around 20 percent, which is actually in the range of the unconditional
probability of a recession in any twelve months period.

At the most recent Survey of Professional Forecasters (May 2008) the forecasters see
a 49 percent chance of negative growth this quarter, up from 43 percent in the last
survey
12 Months Horizon
Note: ***Statistically significant at the 1 percent level
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Recession
-0
4
-0
1
-9
8
-9
5
-9
2
-0
7
Ja
n
Ja
n
Ja
n
Ja
n
Ja
n
-8
6
-8
3
-8
0
-8
9
Ja
n
Ja
n
Ja
n
Ja
n
-7
4
-7
7
Ja
n
Ja
n
-7
1
Prob spread_FFR
Ja
n
-6
8
In model A, the coefficient on the ten year
over the three month term spread is
statistically highly significant at the 12
months horizon, reaffirming the underlying
historical statistical association. In model B,
both the federal funds rate and term spread
are highly significant. The fit of the
regression, judging from the pseudo Rsquared and McFadden R-squared is better
than using the term spread alone.
Recession Probability in 12 months
Ja
n

Charts show the fitted probabilities of a
recession from models A and B, at the 12
months ahead horizon. Both models have
generally quite good fit, with actual
recessions following periods when the fitted
probability of a recession was high.
Ja
n

Model (12
months lag)
A
B
Constant
-0.73***
-1.64***
Term spread
-0.78***
-0.57***
0.11***
Fed funds rate
Pseudo R2
0.25
0.28
McFadden R2
0.33
0.37
4 Quarters Horizon
PNBERt ,t h  1   (1.40  0.63SPREADt10Y 3M  0.11FFt )
Recession
Probability
Value of
Spread
5
1.42
10
0.97
15
0.67
20
0.24
25
0.02
30
-0.05
40
-0.30
50
-0.64
60
-0.95
70
-1.42
80
-1.88
90
-2.18
R e c e s s io n P ro ba bilit y in 4 qua rt e rs
1.00
0.90
0.80
0.70
0.60
0.50
0.40
0.30
0.20
0.10
0.00
Q
3/
6
Q 1
3/
6
Q 4
3/
6
Q 7
3/
7
Q 0
3/
7
Q 3
3/
7
Q 6
3/
7
Q 9
3/
8
Q 2
3/
8
Q 5
3/
8
Q 8
3/
9
Q 1
3/
9
Q 4
3/
9
Q 7
3/
0
Q 0
3/
0
Q 3
3/
06
Estimated Recession Probabilities for Probit Model
Using the Yield curve Spread Four Quarters
Ahead
Recession
Probability_spread
R e c e s s io n P ro ba bilit y in 4 qua rt e rs
Q
3/
6
Q 1
3/
6
Q 4
3/
6
Q 7
3/
7
Q 0
3/
7
Q 3
3/
7
Q 6
3/
7
Q 9
3/
8
Q 2
3/
8
Q 5
3/
8
Q 8
3/
9
Q 1
3/
9
Q 4
3/
9
Q 7
3/
0
Q 0
3/
0
Q 3
3/
06
1.00
0.90
0.80
0.70
0.60
0.50
0.40
0.30
0.20
0.10
0.00
Recession
Probability_spread_FF
Out of Sample Predictions of
Recessions and Expansions

Danger of overfitting

For each model, and each horizon, I recursively compute predicted recession probabilities in each
month or quarter, beginning with the forecast made in 1980. I then consider the root mean square
error of these predictions. That is, if is the fitted probability of a recession between month or quarter t
and t+h, estimated using data available at time t, then the root mean square prediction error is:
1 T*
2


RMSE h 


NBER
 t
t ,t  h
T * t 1
where is the total number of pseudo out of sample forecasts
Out of Sample Root Mean Square Prediction Errors, 1981-2007 Q2
Horizon
6 Months
12 Months
4 Quarters
Model
A
B
A
B
A
B
Value
0.23
0.21
0.24
0.22
0.25
0.24
Interpreting the signal



The tallest bar from the right panel shows that the value of the spread was
between 2 and 3 percentage points in about 35% of the cases
In the left panel the level of the spread was between -1 and 0 percentage
points in almost 50% of the cases
The left panel suggests that, of the observations followed by a recession
twelve months later, 67% (the sum of the bars to the left of zero) are
negative
One year before recession monthly data
One year before nonrecession months
35
25
Frequency
Frequency
30
20
15
10
5
0
-4

-3
-2
-1
0
1
2
3
4
140
120
100
80
60
40
20
0
-4
-3
-2
-1
Note: the frequency distributions is estimated using data from 1968 to 2006
0
1
2
3
4
Short End versus Long End Changes
Three months Treasury bill rate (percentage points)
Number of
months with
negative
NBER Recession
20
15
Maximum
level of
Federal
Funds Rate
spreads
18 months Bill
10
Minimu
m level
of
spread
Recess
Jan-70
Nov-70
10
-0.51
9.19
Dec-73
Mar-75
6
-1.59
10.78
Feb-80
Jul-80
12
-2.20
13.82
Aug-81
Nov-82
10
-3.51
19.1
Aug-90
Mar-91
3
-0.08
9.02
Apr-01
Nov-01
7
-0.70
6.54
Bill
5
Ju
l-6
8
Ju
l-7
0
Ju
l-7
2
Ju
l-7
4
Ju
l-7
6
Ju
l-7
8
Ju
l-8
0
Ju
l-8
2
Ju
l-8
4
Ju
l-8
6
Ju
l-8
8
Ju
l-9
0
Ju
l-9
2
Ju
l-9
4
Ju
l-9
6
Ju
l-9
8
Ju
l-0
0
Ju
l-0
2
Ju
l-0
4
Ju
l-0
6
0
Ten Year Treasury bond rate (percentage points)
18 months Bond
Recess
Jul-06
Jul-04
Jul-02
Jul-00
Jul-98
Jul-96
Jul-94
Jul-92
Jul-90
Jul-88
Jul-86
Jul-84
Jul-82
Jul-80
Jul-78
Jul-76
Jul-74
Bond
Jul-72
16
14
12
10
8
6
4
2
0
-2
Jul-70

Charts display the level of the three
month Treasuries and the change in
their rates over the 18 months leading
to peak recession signal since 1968.
The timing of the peak signals
corresponds to the low monthly
average spread levels reported in
table.
We could think of every yield curve
inversion as resulting at least partly
from a rise at the short end.
Jul-68

Conclusions






Defining recessions as the periods between NBER peaks and troughs, counting
the throughs but not the peaks produces clear results.
Treasury rates are most likely to produce accurate forecasts
The best maturity combination may be the three months and ten years. The
three month rate is best represented by the secondary market rate, expressed
on a bond equivalent basis to match the ten year rate.
The ten year constant maturity rate produces good results.
The results obtain from a model using both variables are encouraging and
suggest that the yield curve spread can have a useful role in macroeconomic
predictions, particularly with longer lead times. Probit models forecasting
recessions that use both the level of the federal funds rate and the term spread
give better out of sample performance than models with the term spread alone.
The shape of the yield curve that has historically been the strongest predictor of
recessions involves an inverted yield curve with a high level of the nominal
funds rate. While a probit model using the term spread alone predicts high odds
of a recession in the next four quarters, the other probit model that I estimate,
which controls for the level of the funds rate do not.
Further analysis of the correlations between the shape of the yield curve and
growth in foreign industrialized countries is an important topic that is left for
future research.
References
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Appendix 1
Model (4
quarters lag)
A
B
Constant
-0.50***
-1.40***
Term spread
-0.82***
-0.63***
0.11***
Fed funds rate
Pseudo R2
0.29
Model (6
months lag)
A
B
Constant
-0.73***
-2.07***
Term spread
-0.62***
-0.35***
0.16***
Fed funds rate
Pseudo R2
0.20
0.27
McFadden R2
0.26
0.35
Model (12
months lag)
A
B
Constant
-0.73***
-1.64***
Term spread
-0.78***
-0.57***
0.32
0.11**
Fed funds rate
McFadden
R2
0.33
0.37
Pseudo R2
0.25
0.28
McFadden R2
0.33
0.37