david cunanne dissertation final draft
TRANSCRIPT
CAN THE TERM STRUCTURE PREDICT ECONOMIC ACTVITY IN IRELAND OVER A SAMPLE
PERIOD 1933-2012? DAVID CUNNANE, 11428538
AUGUST 31, 2016 NUI GALWAY
Maters International Finance
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Abstract
This study is set out to determine whether the term structure has the capacity to predict economic
activity in the Irish economy over a long time period from 1933 to 2012. The data was taken from
Gerlach and Stuart “Money, Interest and Real Prices” in which the data set had not been previously
applied to a study examining the ability of the term structure to predict economic activity. Two
methods were used in analysing the data, first was a graphical analysis analysing the movements of
the term structure and the second method is a regression analysis.
Declaration of my own work
I hereby confirm that the work submitted is my own work. Any work of other has been cited and
acknowledged within the text of the dissertation.
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Contents 1.0 Introduction ...................................................................................................................................... 3
2.1 Literature Review .............................................................................................................................. 4
3.1 Data Set ............................................................................................................................................. 6
4. Results ................................................................................................................................................. 8
A. Graphical Analysis ........................................................................................................................... 8
4.1 Contraction of GDP1937 &1940-1941 ...................................................................................... 9
1956 Contraction in GDP ................................................................................................................. 9
1983 Recession ............................................................................................................................. 10
2008-2011 Recession .................................................................................................................... 10
4.2 Slow Growth ................................................................................................................................ 11
4.3 Economic Growth ...................................................................................................................... 13
4.4 Results ......................................................................................................................................... 13
B. Regression Analysis ........................................................................................................................... 14
Probit Analysis ................................................................................................................................... 20
Testing for Structural Breaks............................................................................................................. 21
Chow Test ...................................................................................................................................... 21
5.1Discussion ........................................................................................................................................ 25
Conclusion ............................................................................................................................................. 27
References ............................................................................................................................................ 28
Appendix ............................................................................................................................................... 29
Section A: 1933-1979 ........................................................................................................................ 29
Section B: Post 1980 ......................................................................................................................... 31
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1.0 Introduction
The aim of this paper is to determine whether the term structure had the ability to predict future
economic activity in Ireland over a sample period from 1933 to 2012. There exists a long history of
using financial data to predict future economic activity and the term structure/yield spread, i.e the
difference between short-term and long-term securities has become a useful tool in forecasting such
variables as output growth, inflation, consumption, industrial production and recessions and its
ability to predict economic activity has emerged as a “stylised fact” among macroeconomists.
Analysts have long noted that most recessions are preceded by a downward sloping yield curve and
frequently inversion of the yield curve i.e. when short-term securities rise above long-term
securities. On the other hand, periods of strong economic growth are preceded by an upward
sloping yield curve. Today there exists a substantial body of evidence from which various useful
stylised facts have emerged. First is that rates on long term securities are usually higher than short
term securities due to investors who purchase long-term securities wanting to be compensated for
the additional risk they are acquiring with the yield having a higher chance of default due to the
longer holding period. Second both short and long-term securities tend to move together; however,
short-term securities are more variable than long-term. Short rates tend to draw close to long rates
at the start of a recession and then the gap tends to widen again. In other words the yield curve
tends to flatten out just before recessions. Finally interest rates on both short and long term
securities are much lower today than in the 1970’s and early 1980’s.
The information that lies within the yield curve became an extremely useful tool for market
participants. Central Banks in the recent past have been paying increasing amount of attention to
information within the term structure as an indicator for monetary policy due to work of several
authors such Estrella and Hardouvelis who have shown that the slope of the yield curve contains
significant information about the future path of macroeconomic variables . Similar to policymakers,
predictive power of the yield curve heavily influences the decision making process of profit seeking
investors, which must involve the formation of expectation on future inflation and interest rates. In
addition information within the yield curve is important for firms who are deciding on how much
resources will be needed to meet demand. The yield spread is widely regarded as one of the most
effective tools in predicting the economic future.
Most studies looking at the predictive capabilities of the term spread have focused their research on
major economic countries such United States, Germany, United Kingdom, Japan and Canada. With
the exception of Japan, movements in yields between these countries are quite correlated despite
some differences in economic circumstances and central bank mandates. This study will be focusing
on the predicative capabilities of Ireland’s term spread from the earliest years of the state in 1933 to
2012. The findings of this research would expect to be consistent with similar research in countries
like the U.S where flattening of the yield spread or downward sloping will signal the probability of a
recession on the horizon or an upward sloping yield curve would signal a period of economic growth.
This paper will be organised as follows. In section 2 we will review the academic research and
investigations that have been able to prove the predictive power of the term structure and its use as
a leading economic indicator. In section 3, we will review the Irish data set and outline the methods
that will be used in analysing the data; it should be noted that a two-fold empirical strategy will be
applied an observation in the movement of the term structure and a regression method. In section
4, the methods in analysing the data will be put into practice and will look at results of each of the
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methods. In section five, the key finding from the results will be presented and compared with
previous literature. This paper does not explicitly address the question on why there is a relation
between the term structure and GDP, but instead focuses on whether or not information within the
term structure can predict the growth rate of real GDP.
2.1 Literature Review
There have been a number of studies conducted to examine the term structure of interest rates
predictive content of economic activity. This review will focus on the breakthrough studies that have
led to the term structure becoming a leading indicator in economic activity and will also focus on
papers that have had a significant influence on the tests carried out later in this paper. It will be
interesting to find whether or not the ability of the term structure to predict future economic
activity is consistent throughout this sample. Many studies have recorded consistency in the
performance of the term structures predictive capabilities but on occasions the term structure can
provide false signals.
The data set assembled by Gerlach & Stuart in “Money, Interest and Real Prices” allows for the
opportunity to examine long term trends in the Irish economy, particularly the ability of the term
structure to predict economic activity which previously has not yet been examined. The data
stretches from 1933-2012 and includes a variety of macroeconomic variables on broad and narrow
money, real and nominal GDP, short and long term interest rates. Data gathered from IMF also
provides the history of government revenue and expenditure that can be added to the data set.
Before discussing key studies regarding the predictive power of the yield spread it is worth noting
why the yield spread is considered such a valuable tool and leading indicator according to an article
written by Estrella and Mishkin (1996). The yield curve can have a useful role in macroeconomic
prediction, particularly with longer lead times. Policymakers value longer term forecasts because
policy actions typically take effect on the economy with long time lags, so the benefit of being able
to plan in advance is a huge benefit. The yield curve can usefully supplement large econometric
models and other forecasts since the yield curve has the advantage of being quick and simple to
construct, and that most people could look at and understand. On top of that the yield curve can be
used to double check econometric and judgemental predictions by flagging a problem that might
have otherwise gone unnoticed.
When learning about the research that has gone into the term structure it is important to note one
of the first studies looking into the behaviour of the yield curve which was conducted by Reuben
Kessel in 1965. Kessel was one of the first to look at the behaviour of term spreads from a
quantitative perspective. Kessel identified that various spreads between long and short term
maturities tend to be low at the start of recessions and tend to be high as an economy begins to
expand. Off the back of this research many studies turned to look at how many quarters the term
structure had power to predict, whether it was more effective in identifying recessions or economic
expansions, and looked at whether or not the term structure was a lead indicator in predicting
economic performance compared with other tools.
In 1989 Stock and Watson aimed to systematically construct an index of new leading economic
indicators, by combing the variables and selecting the best combination that best predicts future
economic activity. They found that one of the variables that is an important component of their
leading economic indicator is the spread between ten and one year U.S Treasury bond. Stock and
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Watson found that the term spread was a key variable in attempting to predict future economic
activity.
While acknowledging the work done by Kessel and the fact that the term structure has been
included as a leading economic indicator, another paper that must be mentioned is the ground
breaking research done by Estrella and Hardouvelis (1991) where they look at the term structure
alone as a predictor of real economic activity in the United States, examining its ability to signal the
probability of both a recession and economic growth. Along with looking at previous evidence of the
predictive power of the term structure, Estrella and Hardouvelis use their own econometric methods
to predict the basic changes in output over a period from 1955-1988. They use a probit/logit analysis
to calculate the probability of a recession, where a recession is coded as one and all other periods
are coded as zero. Estrella and Hardouvelis report that the spread between 10-year and 3-month U.S
Treasury Bills can predict cumulative changes in real output up to 4 years and marginal economic
growth rates up to 7 quarters in the future. The authors also found that the slope of the yield curve
also has extra predictive power over and above the predictive power of lagged output growth,
lagged inflation, the index of leading indicators and the level of short term interest rates. Further,
they find the spread a useful tool in predicting recessions. The research conducted by Estrella and
Hardouvelis has led to many research papers looking into the term structure as a predictor of
economic activity which have been worked off the findings of this paper.
Drawing on the work of Estrella and Hardouvelis (1991), Estrella and Mishkin (1995) focus on the
ability of the term spread to signal the probability of a recession. Using data from 1959 to 1995, the
spread between the yield on ten-year and three-month Treasury securities has the ability to forecast
recessions in the United States as much as eight quarters in advance. As predictive horizon beyond
one quarter, their study found that there is no match for the term structure as a predictor of
recessions amongst leading indicators. As pointed out by Ang, Piazzesi and Wei (2006) every
recession after the 1960’s in the US was preceded by an inverted yield curve or negative slope within
six quarters of a recession. It should be noted, that there was one false positive in the 1960’s, where
an inverted yield curve was not followed by a recession.
In 2009 Wheelock and Wohar investigate and survey the body of research that exists on the ability
of the term spread to forecast output growth and recessions. They conclude that yield spread is able
to forecast output growth and recessions. They echo the results of earlier studies which used linear
forecasting models with post war U.S data. They find that the term spread performs well for
forecasting output growth especially at 6 to 12 months, and the term spread remains useful even if
other variables, including measures of monetary policy are added to the forecasting model.
Although the yield spread is a reliable indicator of forecasting output growth, this paper finds that
the spread is a more reliable predictor of recessions than output growth and that the spread
provides good recession forecasts, especially up to one year ahead.
Considering the data that will be examined cover an 80 year periods, there is a strong possibility of
structural breaks occurring because of the diverse experience of the Irish economy. To this end we
take the work of Benetrix and Lane (2012) and Mauro Paolo et al (2012). Both papers recognise
structural breaks occurring in the 1990’s. Benetrix and Lane looks at the cyclical patterns in fiscal
policy from 1980 to 2007 for the set of EMU member countries, one of which is Ireland, with
particular attention applied to major shifts in the European Institutional environment (the
Maastricht Treaty and launch of EMU). The authors allow for structural breaks in the data – passing
of the Maastricht Treaty in 1992 and the actual formation of monetary union in 1999. Mauro, Paulo
et al examine countries fiscal positions and also identifying the 1990s as a period in which Ireland
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make adjustments to fiscal policy in response to the Maastricht Treaty along with several other
European Countries.
While there is an enormous amount of research looking into the capabilities and the information
that lies within the term structure, the literature has not yet reached a consensus on how well the
term spread actually predicts the output growth, the meaning of the information within the term
structure and whether the predicting capability of the yield spread will continue into the future.
3.1 Data Set
The data set is taken from Gerlach & Stuart (2012) “Money, Interest and Real Prices”. Data was
assembled from a variety of different sources on broad and narrow money, prices, real economic
activity and interest in Ireland over the period of 1933-2012. The authors discuss in detail where the
data was sourced from and have noted that some uncertainty does lie with the data gathered as to
whether the annual data should be interpreted as averages over the year or as capturing economic
conditions at the end of the year. It should be noted that most other papers looking into the
research regarding the yield spread do use averaged data throughout their sample (mostly
quarterly). According to Estrella and Hardouvelis GNP is more closely associated with average
interest rates over the quarter and echo the work done by Park and Reinganum (1986) who find
evidence that point-in-time data at the turn of the calendar month contain systematic biases. While
it is noted that this data set may not entirely be accurate it is not fair to say that it doesn’t have any
value for economic analysis. Furthermore, modern data is also subject to measurement errors.
Data gathered for short term interest rates were taken from the annual average of the open market
rate of discount in London for the period 1933 to 1962 as a proxy for short term interest rates. Then
further data is taken from IMF discount rate in the period after 1951 and finally data for short term
interest rates are taken from OECD from 1984 to 2012. Long term rates prior to 1952 are proxied
using UK interest rates and thereafter the data is taken form IMF international Financial Statistics.
Since data available is only measured annually and not quarterly we will define a recession as period
where real GDP falls on an annual basis. With a recession being defined as a period where growth
falls on an annual basis as oppose to two quarters, we will also be looking at periods of slow growth
and what the yield curve has to predict about that. In addition we will also be looking at whether or
not the term structure has the capability of predicting a period of economic growth with a steep
curve.
Looking at the figure 3.1, we can see the boxplot of the term structure over the 80 year period. A
few observations can be made. Firstly the term structure shows very little variation up until the mid-
1950’s. We then see periods where the term structure rises and falls on an annual basis. Periods
where the boxplot becomes negative are periods where the yield curve inverted. The inverted yield
curve Ireland experienced looked to be the most downward sloping in the early 1990’s, this could
possibly be explained by pressures from a range of exchange rate pegs within the European
Monetary System and forced many Central Banks, including the Central Bank of Ireland, to tighten
monetary policy sharply.
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Figure 3.1 Term Structure 1933-2012
Looking at figure 3.2, a few observations can be made about the growth of the Irish economy over
the past 80 years. Firstly it can be seen that Ireland experienced little growth in the 1930’s and slow
post war growth, Ireland didn’t experience any significant growth up until the 1970’s. The chart also
highlights Irelands notable surge in growth in the 1990’s, known as the Celtic Tiger, when Ireland
experienced an average annual growth rate of 10%. Low interest rates, growth in foreign direct
investment and adoption of the single currency were the main factors that contributed to this huge
growth. And perhaps the most notable divergence in this chart is decline in GDP towards the end of
the 2000’s as result of the Great Recession in 2008, Ireland experienced four continuous years of
contractions in GDP from 2008 up until 2011. A global recession and fiscal austerity measures which
were introduced to help bail out Irish banks were the main factors contributing to this decline.
Figure 3.2 First Difference of GDP 1933-2012
Two steps will be taken in the process of analysing the data. First, in order to determine the
relationship between short and long term interest rates, we graph the movements between short
and long term interest rates and see how they affect the yield curve/term structure. Second, there
will be a range of linear regressions run to identify the relationships between real GDP, the term
structure and other macroeconomic variables on a more technical basis.
The key findings of these graphs would be whether or not the yield had the capacity to signal the
probability of a recession or a period of economic growth. As seen in figure 4.1 we can see the
relationship between short and long term interest rates and how it shapes the term structure over
the length of our sample from 1933 to 2012. In section 3.2 we will take a closer look at periods
where Ireland experienced a recession. In section 3.3 we will look at periods where Ireland
experienced periods of slow economic growth. In section 3.4 we will look at periods where Ireland
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experienced economic growth and in section 3.5 we will look at periods where the yield curve
inverted.
4. Results
A. Graphical Analysis Looking at the figure 4.1 below few observations can be made in relation to the relationship
between the short term and long term interest rate. First, it can see that both short and long term
interest rates support the stylised fact that they tend to move together (the correlation for the
period above is about 92%), but also that short term interest rates tend to vary more throughout the
sample. Therefore parallel shifts are common. Although short and long term interest rates appear to
move together, there are two interesting periods of marked divergence of short and long interest
rates. First in 1992, when pressure across a range of exchange rate pegs within the European
Monetary System forced many Central Banks, including Ireland to tighten monetary policy sharply.
The other notable deviation came in 2008-2011 as a result of concerns about the state of public
finances which led to increased credit risk premiums on long term bonds.
The second observation we can make from looking at the data is that when short rates rise, the term
structure begins to narrow and the spread flattens and when short rates fall the curve widens and
becomes steeper. A third observation that we can make from looking at the chart is that interest
rates do appear to be much lower now than what they were in the 1970’s/80’s. Low interest that we
see today don’t seem to be a part of a short term trend but in fact part of a long term trend. From
the chart we can see that interest rates were quite low from the 1930’s to the 1970’s until they rose
to their peak in 1981when long term-interest rates stood at 17.24% and have been declining ever
since. This trend is partly explained by the inflation, that Ireland experienced in the 1970’s/1980’s.
All else equal, investors demand high interest rates to compensate for the declining purchasing
power of their money which they expect to be repaid.
Figure 4.1 1933-2012 Yield spread, Short-Term Interest Rates & Long-Term Interest Rates
In the next section we will take the opportunity to take a closer look at the five periods where
Ireland experienced a contraction in GDP and investigate whether or not the yield curve did an
adequate job in predicting the future economic circumstances. It should be noted that factors in
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favour of flattening the yield curve are anticipations of a fall in inflation or anticipation of a
slowdown in economic activity. Factors in favour of steepening the yield curve would be
anticipations of inflation, rising wages, rise in economic activity and rising asset prices.
4.1 Contraction of GDP 1937 &1940-1941
1937
In 1937 Ireland experienced a contraction in GDP when the level of GDP fell from 43.58 in 1936 to
42.18 in 1937. In this instance the yield curve failed to signal a contraction in GDP on the horizon,
with the yield curve rising and the term structure rising to 2.81%.
1940-1941
In 1940 and 1941 Ireland experienced a contraction in GDP when the level of real GDP fell from
44.05 in 1939 to 42.07 in 1940 and continued to fall when it dropped to 41.34 in 1941. Looking at
figure 4.2, it can be seen the yield curve flattening and sloping downward from 1938 to 1940,
signalling a contraction in GDP on the horizon which is what happens as Ireland enters a recession in
1940. In this case, the initial flattening/downward sloping of the yield curve is driven by a rise in
short term interest rates where it continues to 1940 where it is then helped by a fall in short term
interest rates. It is not strange for Ireland to experience a contraction in GDP during this period
considering the impact of World War 2 would had on the state.
Figure 4.2 Yield spread 1935-1945
1956 Contraction in GDP In 1956 Ireland experienced a Contraction in GDP when the level of real GDP fell from 60.69 in 1955
to 59.95 in 1956. In this case, the yield curve begins to slope downward in 1954 and continues to fall
throughout 1955 until it reaches 0.71% in 1956 signalling that a contraction in GDP is on the horizon
which was the case in 1956. It should be noted the reason for the yield curve sloping downward was
due to a rise in short term interest rates.
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Figure 4.3 Yield Spread 1950-1958
1983 Recession Taking a closer look at the recession that Ireland experienced in 1983, we can see a steady rise in the
yield curve up until 1982 when the yield curve begins to flatten out and slope downward signalling a
recession on the horizon. In 1983, the level of real GDP dropped from 161.26 in 1982 to 160.08 in
1983.
Figure 4.4 Yield Spread 1978-1985
2008-2011 Recession Taking a closer look at the recession Ireland experienced between 2007 and 2010, in 2004 we begin
to see a decline in the term structure and the flattening of the yield curve. In this case investors are
more uncertain about the short term economic activity and therefore require a higher rate of
interest for the risk they are taking in buying the treasury. In Ireland’s case, the gap between short
and long term spreads closed from 1.96% in 2004 to 0.03% in 2007 predicting a recession being
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imminent. As seen in figure 4.5 the higher and closer the short term interest came to the long
interest rates, the term structure began to invert and fall downward. In 2008 short term rates finally
rose above long term rates indicating that investors were uncertain about the economy and required
higher interest rates for short term bonds than long term bonds.
In 2008, Ireland entered a period of recession where the level of real GDP fell from 594.2 in 2007 to
581.67 in 2008. This recession was preceded by flattening of the yield curve as seen in figure 4.5. The
fall in the level of real GDP continued up until 2011 when GDP climbed from 545.72 in 2010 to
553.53 in 2011. This is another period of an interesting divergence between short and long term
interest rates when concerns about the state of public finances in Ireland led to a large increase in
the credit risk premium on long term bond yields
It is also important to note that flattening of the term spread was not driven by the long term
interest rates. In this case, the flattening of the term spread occurred due to an increase in short
term interest rates from 2.11% in 2005 to 4.63% in 2008.
Figure 4.5 Yield Spread 2004-2011
4.2 Slow Growth
Since the data assembled by Gerlach and Stuart was annual data, the chances of a contraction in
GDP occurring throughout the sample are limited. Therefore we also take a look at observing the
levels of GDP experienced periods of slow growth throughout the sample. As seen in figure 4.6
below, the grey shaded regions display periods where contractions in GDP occurred and the blue
shaded regions exhibit periods where the Irish economy experienced slow growth
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Figure 4.6 Yield Spread 1933-2012
1964-1966
The period from 1964-1966 saw little growth in the Irish economy when compared with previous
years when real GDP only grew from 82.14 in 1964 to 84.47 in 1966, substantially less than other
years. In the same period the term structure fell from 2.03% in 1963 to -0.3% in 1964 inverting the
yield curve. This inverted yield curve was driven by a rise in short term interest rates which is
consistent.
1973-1975
In the period between 1973 and 1975 we also saw little growth when compared with other years
when the level of real GDP only grew from 118.13 in 1973 to 122.87 in 1975. In the same period the
term structure fell from 1.45% in 1972 to -0.43% in 1973 when it inverted. Yet again the fall in the
term structure was driven by the rise in short term interest rates.
1985-1986
In the period between 1985 and 1986 the level of real GDP only grew from 168.43 in 1985 to 169.15
in 1986, substantially less than previous years. In the same period the term structure fell from 1.37%
in 1984 to 0.7% in 1985 and continued to fall until it inverted in 1986 dropping to a level of -1.46%.
Yet again the flattening of the yield curve began with a rise in short term interest rates, however
when the yield curve inverted in 1986 the change was driven by a drop in long term interest rates.
Similarly, the UK term spread inverted in 1985 but failed to be followed by a recession.
1990-1993
In the period between 1990 and 1993 the level of real GDP only grew from 205.4 in 1990 to 221.25,
substantially less than previous years. In the same period the term structure fell from 1.43 in 1988 to
-1.1% in 1989 to -1.23% in 1991 where the term continued to be negative number throughout this
period. Yet again the inverted yield curve was driven by a rise in short term interest rates. In 1992
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there is a noticeable divergence between short and long term interest rates due to pressures from a
range of exchange rate pegs within the European Monetary System and forced many Central Banks,
including the Central Bank of Ireland, to tighten monetary policy sharply.
4.3 Economic Growth
1994-2007
Ireland experienced massive economic growth over the period from 1994 to 2007, also known as the
Celtic Tiger. The level of real GDP was growing at a remarkable average rate of 10% throughout the
1990’s and continued the momentum up until 2007 when the Celtic Tiger reached its peak at 594.2
growing from its original position at 234.29 in 1994. The growth that Ireland experienced during this
period was down to a number of reasons, which included a period of low interest rates and easy
credit, the strength of the European Union and the adoption of the single currency and increasing
amount of foreign direct investment entering the country.
During this period Ireland (and most Western countries) experienced a drop in both short and long
term interest rates. At the beginning of this period the yield curve sloped upward very steeply
signalling a period of economic growth which occurred. However over the duration of this period,
the yield curve did invert and sloped downward signalling a period of recession, which however in
this case did not occur. One reason to we might be seeing an inverted yield curve in a period of
economic growth is that we can’t expect the yield curve to keep rising forever.
Overall real GDP growth rate was low in other periods, particularly in the 1950’s when it averaged
2.2% and from 1960 to 1980 when it averaged 4.2%.
4.4 Results
Out of the five periods of recession documented throughout this sample, the yield curve, from
observation, flattened and sloped downward at least one year before the recession began in four
out of the five cases. The recession in 1935 was the only one that wasn’t preceded by a flattening or
downward sloping yield curve. In cases of economic slowdown where four cases have been
identified, all four cases of economic slowdown were preceded by a flattening or downward sloping
yield curve.
Although through observation the yield curve does a good job signalling a period of recession or
economic slowdown through the flattening or downward sloping of the yield curve, there are
periods where the yield curve did invert and failed to be followed by a recession. Over the 79 year
sample, the term structure has identified eight periods where the yield curve inverted. Of the eight
periods where the yield curve inverted only one period was followed by a recession which was 2008-
2011. Three of the periods that experienced an inverted yield curve were followed by a period of
slow economic growth in 1973, 1986 and form 1989-1993. Other periods where the yield curve
inverted in 1959, 1967, 1979 and 1998 failed to be followed by a recession or slowdown in economic
growth. Similarly, the UK experienced an inverted yield curve in both 1985 and 1998 where neither
were followed by a recession.
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B. Regression Analysis In this section we identify the strength of the relationships between the macroeconomic variables of
the data set. Variations of the methods used by Estrella and Hardouvelis (1991) are used to examine
the relationship between real GDP and the term structure and other macroeconomic variables. Since
the data set only uses annual data, the dependant variable is equal to real GDP as seen in equation
1.
Yt = Real GDP equation 1
Our measure of the spread is the same as used by Estrella and Hardouvelis where it is difference
between the long-term interest rates and short term interest rates as seen in equation 2.
equation 2
Letting equation 1 equal equation 2, our basic regression equation takes the following form:
Yt = α + αSPREADt-1 + Xt-1 + Ut equation 3
where Yt represent our dependant variable real GDP and where Xt-1 represent added
explanatory variables and Ut represent an error term.
Using equation 3, we examine the relationship between real GDP and the term structure, where we take real GDP and look at it as a function of the lagged (-1) of the term structure. In this
case, the relationship between the term structure and real GDP is not significant
Table 4.1 Regression of real GDP and Term Structure
Since the relationship in table 4.1 was not significant the first differences of both variables are taken.
Since GDP tends to rise overtime due to inflation and increases in production, these huge growths in
GDP run the risk of not being stationary. Since the data is less likely to be stationary, taking the first
differences of both variables means the data is more likely to be stationary. In this case the
relationship between real GDP and the term structure is also not significant. This may be that the
real GDP first differences do not show large variations over time.
Table 4.2 Regression of first differences of real GDP and Term Structure (-1)
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A series of Dummy variables is added to the regression to capture the shocks and unusual data from
this period. In this case, a series of 1’s was added to periods during World War 2 and the Great
Recession in 2008 while a series of 0’s are added to other years. In this case neither coefficients are
significant and the constant term is very similar to the mean independent variable which what would
be expected in the case of no relationship.
Table 4.3 Regression of GDP, Term Structure (-1) and Dummy Variables
Expanding on our original regression, we look at the impact several other macroeconomic variables have on our original regression where we take the lagged values of GDP and look at it as a function of the term structure. In this case, CPI (inflation), government expenditure and broad money M2 will be added to the regression. In Table 4.7, the lagged value of inflation is added to our original regression. In this case, there exists a strong relationship between the term structure and inflation with both variables having significant coefficients and have p values less than .05. Whilst adding more macroeconomic variables to our regression, for robust results we would expect the coefficient of the term structure to remain unchanged. Chart A below displays the results of all the regressions examined through the time period, the results are displayed in greater detail just below it.
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CHART A Time Period Considered: 1934 - 2012
Table Number
Variables included
Significant or not
4.4 TS(-1) , CPI(-1) --
4.5 TS(-1) , GOV_EXP(-1) --
4.6 TS(-1) , M2(-1) **
4.7 TS(-1) , CPI(-1) , GOV_EXP(-1) **
4.8 TS(-1) , GOV_EXP(-1), M2(-1) **
4.9 TS(-1) , CPI(-1), M2(-1) --
4.10 TS(-1) , CPI(-1), M2(-1), GOV_EXP(-1) --
-- Not Significant * Significant at 10% level ** Significant at 5% level
Below is a table of the correlations that exists between the term structure, CPI (inflation),
Government Expenditure and M2 broad money. There exists a strong correlation between the
variables of CPI, M2 and Government Expenditure with CPI and M2 (0.8749), CPI and Government
Expenditure (0.5083) and M2 and Government Expenditure (0.2916).
These correlations lead to suspect colinearity and this could lead to instability in estimated
parameters if all these variables are included as explanatory variables in a regression. It also can be
seen that the term structure is positively correlated with M2 and mildly negatively correlated with
CPI and Government Expenditure. Including any of these with the term structure might not lead to
colinearity problems i.e. instability of parameters but including two or more of them with the term
structure could possibly lead to such problems.
Column1 Column2 Column3 Column4 Column5
Term Structure CPI Gov Exp M2
Term Structure -0.0883 -0.1014 0.1659
CPI -0.0883 0.5083 0.8749
Gov Exp -0.1014 0.5083 0.2916
M2 0.1659 0.8749 0.2916
Since the coefficient of the term structure in Table 4.1 and 4.2 is not significant by itself it may
indicate a possible interaction between the term structure and inflation. Table 4.4 examines the
relationship between real GDP, the term structure (-1) and CPI (-1). In this case the regression fails to
yield a significant relationship with the constant term C being insignificant.
17
Table 4.4 regression of GDP between Term Structure (-1) and CPI (-1)
Looking at table 4.5, where we examine the relationship between real GDP, Term Structure (-1) and
Government Expenditure (-1). The coefficient of the term structure is not significant even though the
coefficient of government expenditure is significant. Again the term structure and the government
expenditure have a negative correlation of -.1014.
Table 4.5 regression of GDP, Term Structure (-1) and Government Expenditure (-1)
Looking at table 4.6, where we examine the relationship between real GDP, Term Structure (-1) and
M2 (-1). On introducing M2 to the regression, its coefficient is significant, although the coefficient of
the term structure is significant it has a negative number which may indicate that the possible
interaction between M2 and the term structure is not a stable relationship.
18
Table 4.6 Regression with GDP, Term Structure (-1) and M2 (-1)
Looking at table 4.7, where we examine the relationship between real GDP, Term structure (-1), CPI
(-1) and Government Expenditure (-1). In this case all three variables coefficients are significant,
including that of the constant. It should also be noted that there was a minor change in the
coefficient of the term structure when the variable of government spending was added to the
regression in comparing table 4.4 and table 4.7.
Table 4.7 Regression of GDP, Term Structure (-1), CPI (-1) and Government Expenditure (-1)
Looking at table 4.8, we examine the relationship between real GDP, Term structure (-1)
Government Expenditure (-1) and M2 (-1). Again all three variable coefficients including the constant
are significant, however the term structure has a negative value which may not be desirable. In this
case the correlation that exists between government expenditure and M2 is .2916.
19
Table 4.8 Regression of GDP, Term Structure (-1), Government Expenditure (-1) and M2 (-1)
Looking at table 4.9, we examine the relationship between real GDP, term structure (-1),
Government Expenditure (-1) and M2 (-1).In this case the coefficient of the term structure is not
significant and cannot be regarded as satisfactory since the term structure is the primary
independent variable. In this case the correlation between CPI and M2 has a strong correlation of
.8749.
Table 4.9 Regression of GDP, Term Structure (-1), CPI (-1) and M2 (-1)
Looking at table 4.10, we examine the relationship between real GDP, term structure (-1), CPI 9-1),
government expenditure (-1) and M2 (-1). When all three variables are included with the term
structure two out of the four coefficients including the term structure are not significant.
20
Table 4.10 Regression of GDP, Term Structure (-1), CPI (-1), Government Structure (-1) and M2 (-1)
Tables 4.1 and 4.2 show that there no significant relationship between real GDP and the term spread
or between the first differences. This is disappointing because Estrella and Hardouveils found that
such relationships did exist with their quarterly data. By adding in additional explanatory variables
CPI, Government Expenditure and narrow money M2, some significant relationships were found
between GDP and subsets of the four variables. However the coefficient of the spread was not very
robust as in some cases it was positive and in others negative.
Probit Analysis In this form of probit analysis it is assumed that a relationship of the form (taken from Estrella and
Hardouveils equation 5)
where Xt=1 is a recession, t= time and i= lag
In the case of quarterly data Estrella and Hardouveils used i=4 (i.e k=4 in their terminology)
indicating a 1 year lag. In the current case with annual data we assume i=1. The result of regression
is as follows
Table 4.11 Probit regression of Term Structure
21
The calculated coefficients are not significant and this effectively means that the probability of a
recession cannot be calculated from these data by a probit analysis. As can be expected the logit
analysis is no more successful.
Testing for Structural Breaks Drawing on the work of of Benetrix and Lane (2012) and Mauro Paolo et al, a recursive estimate of
errors is run in figure 4.1 to test for structural breaks that occurred towards the end of the century
due to Ireland’s signing of the Maastricht Treaty and adoption of the single currency. In figure 4.1
below the cusum line begins to rise steadily from the 1960's, but rises more rapidly from the early
1990's onwards and crosses the 5% significance level around the late 1990's indicating that a
structural break has occurred.
Figure 4.1
CHOW TEST A Chow breakpoint test is also applied in order to identify if a real world event at some point
throughout the sample may have affected the trend and affected it in such a way that if we were to
split the regression into two sub samples, there then is a stronger possibility of getting stronger
results. In this case, we have identified 1980’s and Ireland’s entry into the ERM/euro membership as
a significant moment in Ireland’s history throughout this sample as a possibility where a structural
break may have occurred. Below the Chow test is run from 1933 to 1979 and from 1980 to 2012.
Table 4.12 Chow Breakpoint Test 1980
The Chow test shows that there is a break specified in 1980 and a null hypothesis of no breaks at the
specified breakpoint is rejected with a high degree of significance where the p value = 0.00001. Table
4.13 and table 4.14 show the original equation again, both either side of 1980. In this case the
relationship post 1980 shows a much more significant relationship with the coefficient of the term
structure being significant at the 5% level as oppose to the coefficient of the term structure from the
22
period 1933 to 1979 not being significant. This result indicates that the term structure is a significant
factor in determining GDP post 1980 observations.
Table 4.13 Pre 1980 Regression of GDP and Term Structure
Table 4.14 Post 1980 Regression of GDP and Term Structure
While examining the period between 1933 and 1979, we also add a variety of macroeconomic variables to the regression. Of these regression, there are seven relationships examined and results are shown in table 4.15 to 4.21 found in section A of the appendix. Because of the correlation between variables, not all combinations yield significant results. There are four significant results. Table 4.15, regression of GDP on the term structure (-1) and CPI (-1). Table 4.16 regression of GDP on the term structure (-1) and m2 (-1). Table 4.18, regression of GDP on the term structure (-1), CPI (-1) and Government Expenditure (-1). Table 4.20, regression of GDP on the term structure (-1), government expenditure (-1) and m2 (-1). ). Chart B displays the results of all the regressions examined pre 1980, the results are displayed in greater detail in section A of the appendix.
23
CHART B Time Period Considered: 1934 - 1979
Table Number
Variables included
Significant or not
4.15 TS(-1) , CPI(-1) *
4.16 TS(-1) , M2(-1) *
4.17 TS(-1) , GOV_EXP(-1) --
4.18 TS(-1) , CPI(-1) , GOV_EXP(-1) *
4.19 TS(-1) , CPI(-1), M2(-1) --
4.20 TS(-1) , GOV_EXP(-1), M2(-1) *
4.21 TS(-1) , CPI(-1), M2(-1), GOV_EXP(-1) --
-- Not Significant * Significant at 10% level ** Significant at 5% level
While examining the period between 1980 and 2012, we also add a variety of macroeconomic variables to the regression. Of these regression, there are seven relationships examined and results are shown in tables 4.22 to tables 4.28. Because of the correlation between the variables, not all combinations yield significant results. Table 4.22, table 4.24 and table 4.25 show the only three significant relationships that is, regression of GDP on the term structure (-1) and CPI (-1), GDP on the term structure (-1) and Government expenditure (-1) and GDP on the term structure (-1), Government Expenditure (-1) and M2 (-1). Chart C displays the results of all the regressions examined post 1980, the results are displayed in greater detail in section B of the appendix. The combinations that were significant at the 5% level are shown by ** and combinations significant at the 10 % level are shown by *in the following chart.
CHART C Time Period Considered: 1980 - 2012
Table Number
Variables included
Significant or not
4.22 TS(-1) , CPI(-1) *
4.23 TS(-1) , M2(-1) --
4.24 TS(-1) , GOV_EXP(-1) *
4.25 TS(-1), GOV_EXP(-1), M2(-1) **
4.26 TS(-1) , CPI(-1) , GOV_EXP(-1) --
4.27 TS(-1) , CPI(-1), M2(-1) --
4.28 TS(-1) , CPI(-1), M2(-1), GOV_EXP(-1) -
-- Not Significant * Significant at 10% level ** Significant at 5% level
With the Chow test indicating a significant relationship between GDP and the term structure post
1980, a probit analysis is undertaken to analyse the predictability of the term structure. Table 4.29
displays a probit analysis of one lagged period term structure in which case the coefficient for the
term structure is not significant; however in table 4.30 when the term structure not lagged is
included in the regression the coefficient of the term structure is significant at 5% level with a p
value is equal to 0.0206.
24
Table 4.29 Probit Analysis of Term Structure (-1)
Table 4.30 Probit Analysis of Term Structure
Based on the significant relationship in table 4.30 with term structure not lagged, we arrive at the
following results where
P (Xt=1 /SPREAD) = F (α + ΒSPREAD)
= F (-1.666 + 0.346 SPREAD)
The coefficient of the spread is positive in this case. If it were negative it would enhance the
calculated value of probability of contraction in GDP when spread is negative. The probabilities
calculated from this equation are displayed on figure 4.2 alongside the term structure. The
probability of a recession occurring is shown in the orange line and it is clear that it tends to follow
the term structure. Since the term structure in this case is not lagged, its significance of predicting
economic activity is not as valuable considering it is predicting the probability of a recession in the
year it occurs, not in the years before.
25
Figure 4.2 Probability of recession based on term structure of current period
5.1Discussion
The aim of this paper was to determine whether the term structure had the ability to predict future
economic activity in Ireland over a sample period from 1933 to 2012. Data was taken from Gerlach
and Stuart 2012 “Money, Interest and Real prices”. Two methods were used to examine this ability,
one being a graphical method and the other a regression analysis method. The graphical method
was used based on the stylised facts that have emerged regarding the term structure namely that
the term structure tends to flatten out leading up to a recession, short and long term interest rates
move together, short term interest rates vary more than long term and that interest rates are a lot
lower than the 1970's. Our regression analysis follows the pattern of studies from authors of
previous research papers such as Estrella and Hardouveils (1991).
Working with the entire data set, it was found to be impossible to find any coherent set of
relationships for predicting GDP from the term structure from other economic variables. Based on
the manner the original data set was compiled there is a possibility that the entire series may not be
homogenous in its origins. This prompts the question as to whether there could be in later years
more attention to data compilation economic data series. Another limitation of working with this
data set is that whether annual values for interest rate and real GDP contain the same information
as quarterly data which is used in most other research papers regarding the predictability by the
term spread.
As mentioned by Estrella and Mishkin (1997) one of the reasons why the yield spread is considered a
leading economic indicator is its simplicity to understand from looking at a chart, which is the first
method we use in analysing the data. From this analysis, it was shown that four out of five
contractions in GDP were preceded by a flattening or downward sloping yield curve, and four
periods of slow growth identified where the yield spread flattened or sloped downward. However
there were several periods where the yield spread sloped downward and were not followed by a
recession.
The year 1980 was considered as a possible breakpoint in the sample, considering it was a period of transition for Ireland by joining the EU/EMF euro membership. This lead to the Irish pound breaking
-0.2
0
0.2
0.4
0.6
0.8
1
-6
-4
-2
0
2
4
6
8
10
1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020
Term STructure Probit Probs
26
away from Sterling. Alternatives were considered after high inflation in the 1970’s threatened price stability in Ireland. The Irish pound joined the European Monetary System at its inception in 1979. The UK chose not to join and this resulted in a sharp appreciation of their currency leading to Ireland break away from the sterling in the coming weeks. Although it did not happen immediately price stability did arrive with Euro membership. When tested using the Chow breakpoint test it was found that a breakpoint could have been considered to occur in 1980. Therefore both periods leading up to 1980 and post 1980 were used in testing the relationships between the GDP and the term structure and other macroeconomic variables. Some significant relationships were found in each period. Looking at the term structure on its own, it was not a significant predictor of GDP in the early period whereas it was a significant predictor in the later period. This latter finding is in keeping with the finding of authors such as Estrella and Hardouvelis. However the evidence from the present data is not quite as strong or convincing as it was in the paper of Estrella and Hardouvelis. Another observation is that the term structure (-1) and CPI (-1) together were significant predictors of GDP in both early and later periods, but surprisingly were not significant predictors in the entre data set taken as a whole. None of the other combinations that were found to be significant predictors of GDP were common to pre and post 1980 periods. The probit analysis that was carried out for the post 1980 data gave a positive multiplier for the spread term whereas a negative value may have been anticipated because a negative value would lead to a larger probability of recession when the spread was negative. This is an area that could be investigated further with other data sets. Another method that could have been used to give a more sophisticated result would be the use of long horizon VAR forecasting instruments that would help in predict GDP. In addition, it is also possible to use the Consumption Capital Asset Pricing Model to explain the correlation between the term structure and economic growth which has been used in other studies such as Harvey (1988) and HU(1993). While there is an enormous amount of research looking into the capabilities and the information
that lies within the term structure, the literature has not yet reached a consensus on how well the
term spread actually predicts the output growth. In recent years doubts have been raised over the
ability of the yield curve to predict economic activity. Although the yield curve is one of the leading
indicators of recessions, there are no guarantees in financial markets. Overseas bond markets have
not signalled oncoming recessions with an inverted yield curve. The German yield curve failed to
predict the Great Recession in 2008 when the term structure went to zero but did not invert,
similarly the Japanese yield curve failed to invert before The Great Recession. Additionally the level
of Central Bank involvement in financial markets and extraordinary policy measures may hinder the
effectiveness of this tool. Nevertheless, the message form the yield curve still holds, that a flatter
yield curve means slower growth. The meaning of the information within the term structure and
whether the predicting capability of the yield spread will continue to be an area of research into the
future.
27
Conclusion This study was set out to determine whether the term structure had the capacity to predict
economic activity in the Irish economy over a long time period from 1933 to 2012. The data was
taken from Gerlach and Stuart “Money, Interest and Real Prices” in which the data set had not been
previously applied to a study examining the ability of the term structure to predict economic activity
in Ireland. Two methods were used in analysing the data, first was a graphical analysis in which four
out of the five contractions in GDP were preceded by flattening or downward sloping yield curve. In
the regression analysis, the relationship between GDP and the term structure was not significant,
however after testing for structural break we found the relationship to be significant post 1980. This
indicates that if there was to be another study analysing the predictive power of the term structure,
the authors may decide to only look at the data post 1980. The term structure and CPI together were
significant predictors of GDP in both early and later periods, but surprisingly were not significant
predictors in the entre data set taken as a whole. None of the other combinations that were found
to be significant predictors of GDP were common to pre and post 1980 periods.
28
References 1. Estrella, Arturo and Hardouvelis, Gikas A. “The Term Structure as a Predictor of Real
Economic Activity.” Journal of Finance, June 1991, 46(2), pp. 555-76
2. Estrella, Arturo and Mishkin, Frederic S. “The Predictive Power of the Term Structure of
Interest Rates in Europe and the United States: Implications for the European Central Bank.”
European Economic Review, July 1997, 41(7), pp. 1375-401
3. Kessel, Reuben, A. “The Cyclical Behaviour of the Term Structure of Interest Rates.”
4. David C. Wheelock and Mark E. Wohar , Can the Term Spread Predict Output Growth and
Recessions? A Survey of the Literature. Federal Reserve Bank of St. Louis Review,
September/October 2009, 91(5, Part 1), pp. 419-40.
5. Ben Bernanke, 2006. Reflections on the Yield Curve and Monetary Policy,
https://www.federalreserve.gov/newsevents/speech/bernanke20060320a.htm
6. Estrella, Arturo “The Yield Curve as a Leading Indicator: Frequently Asked Questions”
https://www.newyorkfed.org/medialibrary/media/research/capital_markets/ycfaq.pdf
7. Ang, Andrew; Piazzesi, Monika and Wei, Min. “What Does the Yield Curve Tell Us About GDP
Growth?” Journal of Econometrics, March/April 2006, 131(1/2), pp. 359-403
8. Stock, James H. and Watson, Mark W. “Forecasting Output and Inflation: The Role of Asset
Prices.” Journal of Economic Literature, September 2003, 41(3), pp. 788-829
9. Bénétrix, Agustín S., and Philip R. Lane. "Fiscal cyclicality and EMU." Journal of International
Money and Finance 34 (2013): 164-176
10. “Bernard and Gerlach 1996“DOES THE TERM STRUCTURE PREDICT RECESSIONS? THE
INTERNATIONAL EVIDENCE”
11. Mauro, Paolo, et al. "A modern history of fiscal prudence and profligacy." Journal of
Monetary Economics 76 (2015): 55-70.
29
Appendix
Section A: 1933-1979 Table 4.15 pre 1980 Regression of GDP, Term Structure (-1) and CPI (-1)
Table 4.16 Pre 1980 Regression of GDP, Term Structure (-1) and M2 (-1)
Table 4.17 Pre 1980 Regression of GDP, Term Structure (-1) and Government expenditure (-1)
Table 4.18 pre 1980 Regression of GDP, Term Structure (-1), CPI (-1), Government expenditure (-1)
30
Table 4.19 pre 1980 Regression of GDP, Term Structure (-1), CPI (-1) and m2 (-1)
Table 4.20 pre 1980 Regression of GDP, Term Structure (-1), Government expenditure (-1) and M2 (-1)
Table 4.21 Pre 1980 Regression of GDP, Term Structure (-1), CPI (-1), Government expenditure (-1) and M2 (-1)
31
Section B: Post 1980 Table 4.22 Post 1980 Regression of GDP, Term Structure (-1) and M2 (-1)
Table 4.23 Post 1980 Regression of GDP, Term Structure (-1) and M2 (-1)
Table 4.24 Post 1980 Regression of GDP, Term Structure (-1) and Government expenditure (-1)
Table 4.25 Post 1980 Regression of GDP, Term Structure (-1), Government expenditure (-1) and M2 (-1)
32
Table 4.26 Post 1980 Regression of GDP, Term Structure (-1), CPI (-1) and Government expenditure (-1)
Table 4.27 Post 1980 Regression of GDP, Term Structure (-1), CPI (-1) and M2 (-1)
33
Table 4.28 Post 1980 Regression of GDP, Term Structure (-1), CPI (-1), Government expenditure (-1) and M2 (-
1)