Forecasting Economic Activity using Asset Prices

University of Piraeus
Department of Banking & Financial Management
MSc in Banking and Financial Management
Thesis: “Forecasting Economic Activity using Asset Prices”
Graduate Student: Kouvelis Panagiotis
Supervisor: Dr. Christina Christou
Dr. George Diakogiannis
Dr. Dimitrios Kyriazis
Piraeus 2010

Forecasting Economic Activity using Asset Prices
MSc in Banking & Financial Management Σελίδα 2
To my sister

ABSTRACT
This dissertation evaluates how well the asset prices and, in particular the term
spread, the short rate and the real stock returns, forecast the GDP growth and the
Industrial Production. The study is applied with data of seven countries (Canada,
France, Germany, Italy, Japan, United Kingdom and United States) and it covers a
period of time between 1966 until now. The research finds that the asset prices have
forecasting power for one quarter/month but they lose their power when the
forecasting horizon increases. Moreover, the paper evaluates that the real stock return
is the best predictor of the GDP growth and that the short rate has more predictive
content than the term spread.
Keywords: Term spread, short rate, stock returns, output growth, forecasting
horizon, out-of-sample statistics

Acknowledgements
This work would not have been possible without the support and encouragement of
my professor Dr. Christina Christou, under whose supervision I chose this topic and
began the thesis. With her inspiration and her great efforts to explain things clearly
and simply, she helped me to pursue the dissertation. Throughout my thesis-writing
period, she provided encouragement, sound advice, good teaching and she was always
willing to answer any of my questions. I am very grateful also to the PhD student
Christos Bouras who offered me his advice and help. Above all I would like to
sincerely thank my beloved family; my parents, Evangelos and Konstantina, and my
sister, Lily, who supported me throughout the whole year.

PAGE
Abstract 3
Acknowledgements 4
Table of Contents 5
CHAPTER 1 INTRODUCTION 6
CHAPTER 2 LITERATURE REVIEW 8
2.1 Stock Returns, output growth and/or inflation 8
2.2 Term Spread, output growth and/or inflation 13
2.3 Stock Returns and Stock volatility 19
CHAPTER 3 PREVIOUS METHODOLOGY 19
CHAPTER 4 METHODS FOR EVALUATING FORECASTING
ABILITY 24
4.1 In-sample measures 24
4.2 Out-of-sample measures 25
CHAPTER 5 DATA 26
5.1 Data for the Industrial Production 26
5.2 Data for the GDP growth 27
CHAPTER 6 METHODOLOGY AND MODELS 29
6.1 Forecasting Models 29
6.2 Methodology 32
CHAPTER 7 RESULTS 34
7.1 Results from the in-sample tests 34
7.1.1 Industrial Production 34
7.1.2 GDP growth 37
7.2 Results from the out-of-sample tests 39
7.2.1 GDP growth 40
7.2.2 Industrial Production 45
CHAPTER 6 CONCLUSIONS 48
Appendix 51
References 56

1. INTRODUCTION
Many papers were written and a lot of studies were executed in order to find
methods and variables, which can help people to predict the output growth and the
inflation. A lot of researchers consider that the asset prices are forward-looking
variables and as a result of this behavior they constitute a great tool in the technique
of forecasting. But, all those who are interested to create forecasts they need to know
exactly which predictor is the most reliable, which predicts better the GDP growth
than the inflation and which predicts better one quarter than two years ahead.
The purpose of this paper is to evaluate whether the asset prices are good
predictors of the output growth. The study is applied with data of seven countries
(Canada, France, Germany, Italy, Japan, United Kingdom and United States) and it
covers a period of time between 1966 until now. The predictive power of the
candidate variables was evaluated with two methods. Using the Granger causality
method with the whole sample (in-sample) we checked the causality between the
dependent and the independent variable. Using the out-of-sample method we
compared the mean square forecasting error (MSFE) of a benchmark model with the
MSFE of the model, which involved the candidate variable. In our study the variables
we used as candidate predictors are the term spread, the real stock returns and the
short rate.
This study can be useful for anyone who wants to understand the main
methods of the forecasting and how the results of these methods are evaluated. This
work is an effort to extend the research until nowadays using a large sample of data
and to give the opportunity to someone to find a useful guide for the forecasting
power of three main variables. Moreover, it tests in detail the predictive content of
one predictor (the short rate) in which had not been given the appropriate emphasis in
previous studies.
The main results of this paper can be summarized as follows. First, using the
whole sample we can check whether one indicator can be used as a predictor. But,
although, the in-sample tests like the Granger causality test can be helpful and easy to
make this work we cannot be sure about the reliability and the stability of this test.
Second, although, most of the indicators prove to have a predictive power to forecast
the output growth and the industrial production for forecasting period of one quarter
or one month ahead, it seems to lose their ability to forecast when the forecasting

period increases. Third, one indicator appears to be a useful tool to predict a specific
dependent variable for one country, but not for other countries. From the second and
the third results we conclude that some asset prices have substantial and statistically
significant predictive content for some countries and for some specific forecasting
horizon. In this conclusion have Stock and Watson also been led in their paper in
2003. Finally, we can note more thoroughly for our candidate variables that for the
forecasting period of one quarter or one month ahead the research found similar
predictive power in the short rate and the real stock returns when they are used to
predict the GDP growth. However, when the forecasting horizon extend the real stock
returns provide the most accurate forecasts since their predictive content remains
quite stable independent of the horizon. For the Industrial production our results
showed that no variable is a good predictor since their predictive content becomes
really low when the forecasting horizon increases.
The paper is organized as follows. In section 2 we reviewed all the previous
papers that deal with the link between asset prices and other variables. We tried to
separate this section in parts in order to be easier for reading. Thus, we present all the
papers that examined the link between stock returns/term spread/short rate with either
the inflation or output growth. In section 3 we write in detail the previous
methodology of some papers. In section 4 we present the basic methods for evaluating
the predictive content. Section 5 presents all the data that have been used in the
dissertation. In section 6 we describe the models, the variables and the methodology
applied. In section 7 we present the results of our tests and finally the section 8
concludes.

2. LITERATURE REVIEW
The current survey reviews papers that use asset prices (stock returns, yield
curve, short rate and metal and oil prices….) as predictors of economic activity
(industrial production, output growth and / or inflation).
 Forecasts using asset prices:
2.1 Stock returns, output growth and/or inflation.
 Output growth
It has been observed that stock price changes represent the efficient source of
new information. Thus, stock returns could become a useful tool with great ability to
forecast output growth and / or inflation. This link between economic activity and
stock prices was examined by several researchers. Mitchell and Burns (1938),
Grossman and Shiller (1981) and Fischer and Merton (1984) are some of these.
The stock market contains information helpful for predicting GNP. However, this
forecasting ability is not as accurate as someone would want and any predictive
content is decreased by including lagged output growth (Harvey 1989). In another
study, Titman and Warga (1989) observed whether stock returns predict changes in
interest rates. They use both short-term and long-term interest rates on stock returns
lagged one and two months and they execute regressions to examine the results. Their
results show that a positive relation between stock returns and interest rate changes
exists, especially during the period of November 1979 and October 1982. Fama
(1990) used in his test continuously compounded real returns and proved that
monthly, quarterly and annual stock returns are greatly connected with the prospective
production growth rates for 1953-1987. He noted that the degree of correlation
increases with the length of the time period for which returns were calculated. In other
words, he said that annual returns have more predictive ability than quarterly returns
and these with its turn more than monthly returns. He, also, argued that the relation
between current stock returns and future production growth reflects information about
future cash flows, which is impounded in stock prices. Schwert (1990) examined the

constancy of the results that Fama found in his study using an additional 65 years of
data. Following Fama, Schwert used the tests trying to explain the relation between
real stock returns and future production growth rates. The fact that this relation is
confirmed even with 100 years data makes Fama’s results more intense.
All the above researches (Grossman and Shiller (1981), Fischer and Merton
(1984), Harvey (1989), Titman and Warga (1989), Fama (1990), Cochrane (1991))
analyse data of several decades but their results are not influenced from the recent
stock market boom which occurred in the early 1980s. Binswanger (2000) tested if
the Fama’s results also hold up for the period from the early 1980s till now. He ran
regressions for the whole period from 1953 to 1995 and compared the results to
regressions over the subperiods from 1953 to 1965 and 1984 to 1995. He separated
the periods like this because the first one is the first stock market growth period and
the second one consists the second stock market growth period. He presented his
results and he noted that the results of the regressions over the period from 1953 to
1995 seem to confirm the Fama’s findings (1990). But, things seem to change if one
looks at the regressions which specifically cover the recent boom on the stock market
since the early 1980s. Binswanger’s research presents strong evidence that a break
occurred in the relation between stock returns and real activity since 1980s.And this
result is confirmed even if someone uses monthly, quarterly or annual returns or
whether real activity is symbolized by GDP growth rates or production growth rates.
Moreover, one can see in the results that the information the stock returns contain in
the last period (early 1980s until 1995) is different and it is not as significant as it
used to be in previous periods. Binswanger confirmed this difference observing the
correlation between the stock returns and the real activity. The correlation in the first
period (1953 to 1965) is high, but the second high growth period (1984 to 1995) is
characterized by an absence of this correlation. He saw that not even one of
coefficients with a positive sign was significant in the equation. However, these
conclusions cannot be certain because the subperiod 1984-1995 is a short period of
time and the results that occurred can only be temporary. Additionally, Binswanger
gave some possible explanations why this difference happened. Paulo Mauro (2000)
examined the relation between the output growth and lagged stock returns in
seventeen (17) advanced and eight (8) emerging countries. Data used for real stock
returns and GDP were annual for at least 22 years. The results showed that the
correlation for these two variables (GDP and stock returns) is positive and significant

for both emerging and advanced economies. Thus, stock returns contain useful
content to predict the output growth for both types of economies. Furthermore, he
found “stronger link in countries which have high market capitalization, a large
number of listed domestic companies and initial public offerings, and English (or non-
French) origin of the regulations governing the stock market”. Moreover, he has
shown that elements of stock returns exist, which have the power to influence the
strength of the correlation between output growth and lagged stock returns.
Another one who has studied the ability that stock returns have to forecast the
future economic activity is Owen Lamont (2001). He constructed economic tracking
portfolios and with their help examined the relation between the asset prices and
economic variables. According to Lamont economic tracking portfolio “is a
portfolio of assets whose returns track an economic variable, such as expected output,
inflation, returns”. The portfolios he constructed had unexpected returns with high
correlation with economic activities that would occur in the future. He noticed in his
out-of-sample results that it is possible an economic tracking portfolio to give
forecasts for macroeconomic variables but also it can be a useful tool for hedging
these activities. He also suggested that anyone can take daily returns and make an
economic tracking portfolio which will give daily updates for the inflation, GDP and
any other economic variable. Campbell et all. (2001) noted “that the variance of
stock returns rather, than the returns themselves, could have predictive content for
output growth”. Gilchrist and Leahy (2002) performed a number of experiments
using three different models: a real business cycle model, a new Keynesian model and
the RBC model to see the impact of shocks in real economy. Their conclusions were
different from the once we have presented until now. They said that asset prices do
not contain information valuable for forecasting.
Stock and Watson (2003) executed an extensive research on this subject,
using a large number of candidate variables and seven countries in their work. Thus,
we consider that it is useful to describe in detail their paper. Their analysis was
comprised of quarterly data on as many as 43 variables from each of seven developed
economies (Canada, United States, the United Kingdom, France, Japan, Italy and
Germany) over 1959-1999. They collected their data from the International Monetary
Fund IFS database, the OECD database, the DRI Basic Economic Database and the
DRI International Database. They summarized the basic econometric methods used in
bibliography to measure the forecasting ability of economic predictors. They divided

them into two groups: the in-sample measure and the out-of-sample measure of
predictive content. Furthermore, they reviewed all the papers that presented the
relation between the asset prices and economic activity and divided into groups the
indicators that can be useful predictors. Thus, they presented all the bibliography
about the interest rates, the term spread and the output growth, the stock returns, the
default spreads, the dividend yields and other financial variables (like housing prices,
the consumption-wealth ratio). They checked the forecasting ability of all the
variables using both the in-sample statistics and out-of-sample statistics. They applied
the same process to make the out-of-sample forecasts for two periods of time, from
1971 to 1984 and from 1985 to 1999. After this analysis they ended up to four main
conclusions.
First of all, they noted that some asset prices have been useful tools for
predicting output growth in some countries in some time periods. They do not have
the same predictive content all the times for all the countries. As a result of this, one
can say that no one knows a priori which predictor is required for which country and
for which time period. For example in their paper they found that the term spread
could be a useful predictor for the inflation of the USA in the first period of their
study but not in the second period for the USA or not for the first period in the other
countries. In their second conclusion, they noted that forecasts based on individual
indicators are unstable. They found that an indicator which predicts better in the first
out-of-sample period than an autoregression does, will not do the same in the second
period. This instability indeed appears as the normal. These considerations suggest
that one predictor forecasts successfully in one country or in one period, but not in the
next one.
In the third conclusion, they said that although some of the most common
econometric methods of measuring the predictive content rely on in-sample
significance tests, doing so provides little assurance to make stable conclusions.
Indeed, in-sample Granger causality tests contain little or no information about the
forecasting performance of one indicator. They found that although the Granger-
causality test shows that some variables have forecasting power for all the countries
the out-of-sample statistics show that this predictability does not remain for most of
the countries.
Finally, in the fourth conclusion, they noticed that a simple combination of
forecasts improves the forecasting ability upon the benchmark model or the models

with individual predictors. For example, they showed that some simple combination
forecasts – the median and the trimmed mean of the panel of forecasts – were stable
and reliably outperformed a univariate autoregressive benchmark forecast. We will
analyze the methodology that Stock and Watson used in their paper in the next
section.
The last paper that examined the relationship between the stock returns and
economic activity is the paper of Andersson and D’Agostino (2008). In their study,
they checked if the sectoral stock prices give more information for the economic
activity than the traditional asset prices, such as the term spread, the dividend yield,
the exchange rates and money growth, do. They used data for this study from 1973
until 2006 to execute a standard pseudo out-of-sample forecast exercise. The
forecasting power of the candidate variables were evaluated in relation to an
autoregressive model. Their study extends the literature of the forecasting in two new
ways. First, they presented the sectoral prices as useful tools for predicting the GDP
growth. Second, they compared the predictive content of asset prices before and after
the introduction of the euro. Their research concluded in three main findings. They
showed that for the time 1973-1999 the term spread is the best predictor (term spread
produces the lowest MSFE) among all the candidate variables, but after that year
sectoral stock prices became the leading indicator for predicting economic activity
and especially for forecasting horizons above a year. The last finding was that the
introduction of Euro improves the predictability of some variables.
 Inflation
Not a lot of studies exist that they have examined the link between stock returns and
another one economic variable, the inflation. Some of these have been presented
earlier in this text. Titman and Warga (1989) suggested there is a possible relation
between inflation and stock returns for the period 1979-1982.This matter was, also,
analyzed by Lamont (2001) who noted that tracking portfolios can be useful for
forecasting macroeconomic activities, like inflation. Goodhart and Hofmann (2000)
used quarterly data from twelve developed economies for the period 1970-1998 and
found that stock returns do not have significant predictive ability for inflation. Stock
and Watson (2003) were led to the four same conclusions for the inflation as for the
output growth, which previously have been pointed out. Deductively, we can say that

stock returns contain a great deal of information for the change of output growth, but
on the other hand they provide almost no information for the inflation.
2.2 Term spread, output growth and/or inflation.
 Output growth
Another indicator which can be used to predict economic variables is the term
structure. According to Stock and Watson “term spread is the difference between
interest rates on long and short maturity debt, usually government debt”. A lot of
researchers investigated the relationship that term structure and economic activity
have. Fama (1986), Laurent (1989) and Harvey (1989) were some of the first
examiners that studied this matter. Stock and Watson (1989) and Gikas
Hardouvelis and Arturo Estrella (1991) examined this relation for the United
States, Harvey (1991) for the G-7 and Cozier and Tkacz (1994) for Canada. All the
above concluded that the yield spread is one of the most useful indicators and has the
ability to predict output growth for some countries. More specifically, Eugene Fama
used in-sample statistics and found that the term spread has the ability to predict real
rates and this ability strengthens for shorter periods. Gikas Hardouvelis and Arturo
Estrella used quarterly data from 1955 through the end of 1988 so as to observe
whether the dependent variable, which is GNP, has an important correlation with the
term structure. They concluded that the slope of the yield curve has a more significant
predictive content than the lagged output growth, the lagged inflation, the level of real
short-term of interest rates and the index of indicators have. They indicated that the
slope of the yield curve can forecast collective changes in real output for up to 4 years
and consecutive marginal changes in real output up to a year and a half into the future.
Hardouvelis and Estrella noted that the yield curve can predict all elements of real
GNP like consumption, investment and consumer durables. They, also, noticed that
this information can be helpful not only for private investors, but also for the Federal
Reserve; however, they emphasized that it is not clear whether this predictive ability
will continue to exist in the future. Thus, no one knows if the slope is quite useful to
be adopted from Fed as a forecasting indicator. Plosser and Rouwenhorst (1994)
studied data for three industrialized countries in order to confirm the relation between

term structure and output growth. They found that term structure is a great leading
indicator for long-term economic growth. Furthermore, they proved that information,
which is contained in the term structure about future output growth is independent
from information about monetary policy.
Joseph Haubrich and Ann Domborsky (1996) using out-of sample and in-
sample statistics examined reasons that the yield curve might be a good predictor and
compared this predictive skill with other traditional indicators. They used out-of
sample statistics for the United States and they found their data from the Federal
Reserve. They ran out-of-sample statistics for the period from 1961:Q1
through1995:Q3. They decided to take the 10-year CMT rate minus the secondary-
market three-month Treasury bill rate for the spread. Moreover, they based on the
previous work of Estrella and Mishkin (1997) to study how well the yield curve
predicts the severity of recessions. Their results showed that the yield curve had a
significant forecasting power over the years 1955 to 1985. But this predictive content
has diminished since 1985 and they tried to explain the reasons for this phenomenon.
To the same results with the latter had Michael Dotsey (1998) been led using both
out-of-sample and rolling in-sample statistic. Dueker (1997) has noted that the yield
spread has a significant power to forecast recessions in the future. Arturo Estrella
and Frederic Mishkin (1997) studied in their paper the link between the yield curve
and real activity. They took their sample from the major European economies
(Germany, Italy, the United Kingdom and France) and they investigated whether the
information revealed from the term structure is useful for the European Central Park.
They checked the correlation between term spread and GDP but also the relation
between short rate and economic activity and how useful is to use both variables in
the regression. They concluded that in many cases the term structure has a significant
forecasting content which has a time period of two years ahead for predicting real
activity. Moreover, they checked if the term structure had an effect on the monetary
policy actions. Their results showed that this relationship changed over time and as a
consequence, also changed the relation between term structure and real activity.
Taking into consideration all the above, Estrella and Mishkin noted that "a term
spread is a simple and accurate measure that should be viewed as one piece of useful
information which, along with other information (short rate), can be used to help
guide European monetary policy”. Fabio Canova and Gianni De Nicolo (1997)
using in sample Var statistics tried to explain the link between inflation, GDP and

term structure. They used the VAR model, because it is a good approximation to the
GDP, and they examined data from three countries, the United States, Germany and
Japan. They separated the results for each country and they concluded that the
predictive content of the term structure has something to say for the forecasting
economic activity although the power of this content is limited.
Frank Smets and Kostas Tsatsaronis (1997) examined the ability of the yield
curve to forecast the economic activity in Germany and the United States. Their
results were focused in two points relative to the predictive content of the yield curve.
First, they noticed that it is not possible to remain invariant over time because the
factors, which determine the economic conditions, influence the yield curve; if these
factors change the predictive content of the yield curve will also change. Secondly,
the predictive content is not policy-independent. It gets different as the monetary
policy alters. Thus, Smets and Tsatsaronis concluded that it is not secure to say that
the relation between the output growth and the yield curve is stable over time.
James Hamilton and Dong Heom Kim (2002) in their paper re-examined the
ability of the yield spread to predict the economic activity and investigated the results
of previous studies. They used the ten-year T-bond rate and three-month T-bill rate
and real GDP from 1953 to 1998. Finally, they confirmed the usefulness of the term
spread to predict future output growth. Moreover, they noted that the term premium
(“the term spread minus its predicted component under the expectations hypothesis of
the term structure of interest rates”) is also a very good leading indicator with
significant predictive content. Some of the above researchers noticed that the link
between the term structure and the output growth indeed exists. However, most of
them said that this relation perhaps does not remain stable over time. So, Arturo
Estrella, who has examined this link thoroughly, Anthony Rodrigues and Sebastian
Schich (2003) tested the stability of the predictive content of the yield curve. They
used in-sample break tests to see whether this relation was in fact stable. To predict
the economic activity a d recessions they used respectively continuous and binary
models. They found data for two countries, the United States and Germany. Data for
the US was from January 1955 to December 1998 and for Germany from January
1967 to December 1998. After running the models they ended up to some
conclusions. Each time, someone uses the yield curve to predict economic activity or
recessions he first must test the stability of the predictive content of the yield curve
over time. They also showed that binary models have achieved better performance in

the tests than the continuous models. Another paper, which presented the term
structure as a forecasting indicator of economic activity is the work of Andrew Ang,
Monica Piazzesi and Min Wei (2006). They built a dynamic model for GDP growth
which completely characterized the expectations of the GDP. Then, they tried to
check whether the predictability of the term spread was confirmed and if the short rate
is, also, a good predictor of the output growth. They used out-of sample statistics and
zero-coupon yield data for maturities 1,4,8,12,16 and 20 quarters from 1952 to 2001.
They, also, used seasonally adjusted data on real GDP. First, they checked the
forecasting power of the term spread using a simple linear regression model without
lags of the GDP growth. Then, they added into the model the lagged GDP growth and
one more candidate variable, which is the short rate. They involved lags because they
said that the GDP is autocorrelated. Finally, they made out-of sample forecasts and
checked the MSFE of the benchmark and the candidate models and concluded that the
term structure is a good predictor, although the best indicator to forecast US GDP
growth during the 1990s is the short rate.
In October 2001, Ivan Paya, Kent Matthews and David Peel examined
something different from the other papers. Most of the studies examined the link
between the term spread and economic activity in the post-war period. But this
paper aimed to test the stability of this relation and in the inter-war period for the US
economy. They found that the term spread had the ability to forecast economic growth
in that period and this prognostic power was stronger in periods of price instability.
Moreover, they showed that the predictive content of the term structure did not remain
invariant to regime changes
 Inflation
Many researchers, including some of the already named, have dealt with the
subject term spread and inflation. Fama (1984a), Fama (1990), Bernanke and
Mishkin (1992), Canovo and De Nicolo (1997) are some of them. Mishkin has
executed an analytical research on this subject. He has written four papers, which
examine the predictive content of the term spread related to inflation. Taking into
consideration, the importance of the inflation for monetary policy actions Mishkin
(1990a) examined what information one can draw from the term structure of real

interest rates. Moreover, he investigated the movement of the term structure of real
interest rates that is influenced by the change of the term structure of nominal interest
rates. His methodology focused on the “inflation-change equation”. He used the
change between m-period interest rates and n-period interest rates and saw how this
change can give information about the change of the inflation over n-months and m-
months into the future. For his research he used monthly data on inflation rates and
one-to twelve-month U.S. Treasury bills from February 1964 to December 1986. He
concluded that the maturity of the bond played an important role for the predictive
ability of the term structure. Consequently, for maturities of six months or less the
term structure has a very poor predictive power for the inflation changes, however the
term structure of the nominal interest rates provides a great deal of information for the
term structure of real rates. He considered that these results would change if the
maturities became larger. For maturities of nine and twelve months the term structure
is a useful tool to predict the inflation, although it contains little information about the
term structure of real interest rates. In order to confirm his concerns, Mishkin (1990b)
examined again this relation using data from 1953 to 1987 for inflation and U.S.
Treasury bonds with maturities of one to five years. The results he found supported
the aforementioned conclusion that for long maturities the term structure plays an
important predictive role for inflation, but contains a little information for the term
structure of real interest rates.
Elias Tzavalis and M.R. Wickens (1996) presented in their paper new details about
the forecasting skill of the term spread. Data used for the interest rate were monthly
United States zero coupon government bonds with maturity of 1, 3, 6 and 12-month
and for the inflation they were based on the Consumption Price Index. Their results
came in contradiction to previous results arguing that the greater the time horizon the
stronger the predictive power of the term spread. They found that the forecasting
power of the term spread is very limited and that the real interest rate is a far better
indicator than the slope of the yield curve. Arturo Estrella and Frederic Mishkin
(1997) studied in their paper the link between the term spread and inflation. They
showed that in many cases the term spread has the faculty to predict inflation with a
horizon more than two years ahead but it is not a great predictor for one-year horizon.
So, they ended up to the same conclusion for the inflation as for the output growth.
The yield curve is a simple and accurate predictive tool, which becomes more useful
in combination with other indicators. Sharon Kozicki (1997) using data from 1970 to

1996 examined the ability of the term spread and the short rate to forecast output
growth and inflation. Furthermore, she presented in detail the predictive horizon of
the yield spread and studied whether the short rate gives more information about the
future output and inflation than the yield spread does. Initially, she presented three
hypotheses that showed the reasons why the term spread is a good predictor of
inflation and output growth. First, the yield spread reflects the posture of monetary
policy. Second, it contains information on credit market conditions. Finally, the yield
spread moves in the same way with the change of future inflation. Kozicki concluded
to two results in her work. First she noted that the term spread has maximum
predictive power for real growth over the next year or so and three years ahead for
inflation. Moreover, she underlined that the term spread is a better predictor for real
growth than the level of yields, but for the inflation the level of short rates makes
better predictions than the term spread.
An additional paper, which focused on the term structure of interest rates, was
written by Jan Marc Berk (1997). He investigated the link between the yield curve
and inflation and if the yield curve is a useful tool for monetary policy. Furthermore,
he presented why this indicator is worth as a predictor of inflation. Moreover, the
three considerations which establish the usefulness of the yield curve for monetary
policy were noted. These three are stability, predictability and controllability. In his
results he found that the relationship between these two is complicated. He noticed
that, although, the yield curve contains information about the forecasting changes of
the inflation, this information is not stable. Arturo Estrella (2005), again, examined
the roots of the predictive ability of the yield curve for inflation and output growth as
well. He applied an extensive model which was consisted of a Philips curve and IS
equation. This model gives the opportunity to be considered both as a backward-
looking and a forward-looking model. Their results showed that the yield curve has
the ability to predict output growth and inflation. Another result which emanated from
the model was the dependence of the predictive power from the monetary policy and
its changes. More precisely, some reactions of the monetary policy characterize the
yield curve as the optimal predictor of output growth or inflation or both and other
reactions lead the predictive power of the yield curve to disappear. For example, on
the one hand, if we have “strict” or “flexible” inflation the yield curve is a significant
predictor. On the other hand, according to Estrella “if the monetary policy reactions to

both inflation and output deviations approach the infinity” the yield curve is not a
useful tool for predictions any more.
To summarize, the term structure has some predictive power for the changes
of output growth, but every time someone wants to examine the output growth must
test the stability of the link between these two variables. For the inflation changes, the
term structure has something to say to the researchers, but with some lag, and for
better predictions one should use bonds with long maturities (nine months or bigger).
2.3 Stock returns and stock volatility
Hui Guo (2002) tried to show that there is a relation between stock market returns
and volatility and, also, whether there is a link between them and economic activity.
According to Hui Guo “returns relate positively to past volatility, but negatively to
contemporaneous volatility”. As a result, stock market volatility predicts output
growth because it affects the cost of capital through its link with the expected stock
market return. He ran in-sample and out-of-sample regressions using postwar data and
proved that sometimes volatility indeed contains forecasting information, but other
times this predictive ability weakens. And he concluded that if volatility affects the
economic activity only through the cost of capital, stock market returns play a more
significant role than volatility does in forecasting economy.
3. PREVIOUS METHODOLOGY
In this section we present the methodologies that some researchers used to
evaluate the forecasting power of the variables. We show the variables and the
equations the researchers used to find the relationship between the dependent and
independent variables.
Estrella and Hardouvelis (1991) selected quarterly real GNP from 1955
through the end of 1988 as the dependent variable in their regression. They used the
annually cumulative percentage change of real GNP:

where k symbolizes the forecasting horizon in quarters and yt+k the level of real GNP
during quarter t+k. Moreover Yt,t+k indicates the percentage change from t quarter to
t+k. Estrella and Hardouvelis examined the predictive ability of the term spread. To
estimate the term spread they used the difference between two rates; the 10-year
government bond (RL
) and the 3-month T-bill (RS
):
.
Their basic regression equation has the general form:
,
where Yt,t+k and SPREAD are given by the equations above. Xit represents other
information variables available during quarter t. They used in-sample statistics to
check whether the term spread is more significant predictor than the lagged output
growth.
Estrella and Mishkin (1997), also, examined the predictive power between
the term spread and GDP. For the calculation of the term spread they used the
contemporaneous end-of-month observations for the central bank rate (CB), the 3-
month government security rate (BILL) and the 10-year government security rate.
(BOND). Thus, the following regression gives the estimation of the SPREAD:
.
They estimated a regression in which the value of the spread that is calculated above
is used to forecast the change in real economic activity over the following k periods.
This equation has the form:
,
where yt
k
is the variable of economic activity (GDP). They do not take into
consideration the lags of the GDP, because they noticed that they are generally
insignificant. In their model if the a1 is ≠ 0 then the today’s value of the term spread
can be used to predict the value of yt in k periods ahead. They checked the economic
significance of the term spread using the mean R2
. Estrella and Mishkin checked
whether the term spread has better predictive content above and beyond other
variables. To confirm this hypothesis they used the regression equation:
,
where the Xt is the contemporaneous measure of the monetary policy, the short rate
for example. In the same way as above they checked the significance of

and Xt. Furthermore, they used a probit regression to find out whether the
economy will be in a recession.
Sharon Kozicki examined the predictive power of the term spread in seven
countries and compared this skill with the forecasting ability of the level of the yield
curve. He used the following equation:
,
where GDPgrowtht+h-4,t+h is the real GDP growth over the four quarters beginning in
the quarter t+h-4 and ending in the quarter t+h, the SPREADt is the yield spread in the
quarter t, the GDPgrowtht-4, is real GDP growth over the four quarters beginning in
the t-4 and ending in the t quarter and errort is the prediction error in the quarter t and
h is the forecasting horizon in quarters. Kozicki tried to determine whether the term
spread has the ability to forecast one, two and three years ahead. So, the h is set to 4, 8
and 12 quarters respectively. In order to see if the term spread has predictive content
beyond that contained in current growth rates an equation including only the current
real growth was estimated. Kozicki estimated the coefficient of the spread and
underlined the significant coefficients. Also, he estimated R2
which showed the
percent of the variation in real GDP growth that is explained by the term spread and
R2 NO SPREAD
that showed the percent of the variation in real GDP growth that is
explained from the current growth. The difference between R2
and R2 NO SPREAD
reflects the predictive power of the spread.
Moreover, he also used the same methodology to see if the level of the yield curve has
more predictive content than that of the term spread. The equation he used is the
following:
where real ratet is the short rate in t period and is equal to
the product of the spread in quarter t and the short rate in the same period. Testing the
significance of the coefficients on the level of the yield curve and the difference
between and he concluded that the term
spread has predictive content beyond the current growth and the level of the short
rate.

Mathias Binswanger (2000) used the same methodology with the Fama
(1990) to re-examine the results of Fama for a longer period. First of all he used the
Augment Dickey-Fuller unit root test for quarterly stock returns and the quarterly
production and GDP growth rates to see if the series were stationary. The second step
in his research was the Granger causality test. He used this test in order to find out
whether past stock returns still predict future production growth rates. He also chose
two smaller periods (1953-1965, 1984-1995) and applied the same tests. The
estimated equations used have the following form:
, where IPt-T is the production growth rate from t-T to t. Thus, for monthly, quarterly
and annual production growth rate he used T=1, 3, 12 respectively. The term RT-3k+3 is
the stock return for the quarter from t-3k to t-3k+3. To test the predictability of the
stock index he saw whether the coefficients of the regression are significant at the 5%
level and the adjusted R2
.
All the above researchers used in-sample statistics to confirm the link between
the economic activity and the variables they used to make predictions. Stock and
Watson (2003) make both in-sample and out-of sample forecasts to evaluate this
relation. They used data for seven countries from 1959 to 1999. Real GDP and
industrial production are selected to measure the economic activity. The regression
that they used has the form:
, where and Xt is an economic variable
(asset prices). For the in-sample analysis Stock and Watson selected a fixed length of
four lags (Xt….Xt-3 and Yt….Yt-3). They used the whole sample (in-sample statistics) to
make the heteroskedasticity-robust Granger-causality test statistic and the QLR test
for coefficient stability. With the first they tested the statistic and economic
significance of the coefficients. The Granger causality tested the null hypothesis that
β1 (L) =0 and β2 (L) =0. The QLR statistic tests the null hypothesis of constant
regression coefficients against the alternative that the regression coefficients change
over time.

For the out-of sample statistics Stock and Watson used one AR model and the
model with the variable Xt. The lags they
used for the models are data-dependent. They have chosen the number of the lags
from the Akaike (AIC) criteria. Thus, for the AR model the AIC-determined lag
length was restricted between 0 and 4. For the bivariate model, the lags of Yt ranged
between 0 and 4 and between 1 and 4 for the lags of Xt. Then, they computed the
Mean Squared Forecasting Error (MSFE) for both models. From the form
they estimate the reason between the two MSFEs, where Ŷh
i,t+h/t is the ith
candidate pseudo-out-of sample forecasts of Yh
t+h, which was made using data
through time t. If the result of this equation is less than one the candidate forecast is
estimated to have performed better than the benchmark.
Arturo Estrella, Anthony Rodrigues and Sebastian Schich (2003)
examined whether the equations, which were used to predict real activity stayed stable
over time. They selected a linear equation with the following form:
,
,where for the cumulative growth rates and
for the marginal growth rates. They used the spread
between the nominal yields on q and n period bonds to predict the annualized growth
rate in industrial production over the subsequent k periods. The variable k takes the
price k=12, 24, 36 for one, two and three-years horizons respectively and the term
spread was calculated from the difference between the 10,5 or 2-year long rate and 1-
year short rate. For each case they checked the R2
of the equation, the p value of a sup
LM test and the analogous p value of a sup PR test. Estrella, Rodrigues and Schich
also used probit models to see if these models do predict recessions and this ability
stays stable over time.
Magnus Andersson and Antonello D’Agostino (2008) had a specific
purpose in their paper. To test whether the stock prices and, in particular, the sectoral
stock prices can be a useful tool to predict the euro area GDP. To check this
predictability of the sectoral stock prices they tested if the MSFE of a benchmark
model (they applied an AR model as benchmark) improved when the sectoral prices

were included in the model. They used similar models for their study with the
previous work of Stock and Watson. Their basic model has the form:
,
where Xt is the return on the various financial assets, the error term and Q1 and
Q2 the lag lengths having been computed with Akaike criteria. The forecast horizon h
is ranged between one and eight quarters. To estimate the appropriate equation they
used data from 1973;Q1 to 1984;Q4 and they made their out-of sample forecasts until
the end of their sample, namely 2006;Q1. The form that they applied to find the
MSFE for the AR and the candidate model is:
Where r is for the restricted benchmark model and u refers to the unrestricted
candidate model. Then, they looked the result of the form . When this is less
than one, we have better forecasting performance with the candidate model than with
the AR model. Moreover, they tested the predictive accuracy using the MSFE-F
statistic proposed by Clark and McCracken (2005), defined as:
,
where P is the number of observations utilized for the out-of-sample evaluation, h the
forecast horizon and , where
is a quadratic loss differential.
4. METHODS FOR EVALUATING FORECASTING ABILITY
In this section we present the methods that have been used in the previous
bibliography for measuring the predictive content. We can divide in two groups: in-
sample and out-of-sample methods.
4.1 In-sample measures
Using this method we can find whether a candidate variable, X, is useful to forecast
the variable Y. For instance, , could be the value of the real stock returns and we
want to forecast the real GDP. Using one simple linear regression model we can

examine the forecasting ability of the candidate variable. The linear model will have
this form:
where b0 and b1 are unknown parameters and et is the error of the regression. To see
whether the Xt has predictive ability we must examine if b1≠0. The t-statistic can be
used to check the null hypothesis that Xt has no predictive content. Another tool to
measure the economic significance of the candidate variable is the R2
and the adjusted
R2
.
In the aforementioned case we did not take into consideration that Yt+1 can be serially
correlated. However, in the most cases of the time series variables the above
hypothesis is wrong. Thus, the past values of Yt+1 are themselves helpful tools for
forecasting. So, we must examine now if the candidate variable has more predictive
content than the past values of Yt+1. In addition, values of with lag can be useful
predictors. Thus, the linear regression model (1) will change form and the lags of the
variable, Y, and candidate variable, X, will be added in the model. Then the extended
regression model is the autoregressive distributed lag model:
where b1(L) and b2(L) symbolize lag polynomials. To test whether the candidate
variable has predictive content above and beyond the past values of we examine
the null hypothesis that b1(L) =0. This can be done with the F-statistic or Granger
causality test. To generalize, a model must have the following form to forecast h-steps
ahead:
4.2 Out-of-sample measures
This method simulates the real-time forecasting. For example, in order to
make forecasts using a candidate variable(s) for the first month of 2000 a researcher
must estimate a model using data available through the 12th
month of 1999.
Estimating the model is not a simple process, because a researcher must choose
among a large number of models. So, he needs to have something to compare the
ability of the models. Often, they use an information criterion to solve this problem,
such as the Akaike criteria or Bayes criteria (AIC or BIC) and choose the model with

the smallest value. Then he uses this model to forecast the value of the variable Y in
2000m01. This process will continue throughout the sample creating a sequence of
pseudo out-of-sample forecasts. Then, the researcher computes the mean square
forecasting error of the candidate model and that of a benchmark model (an AR model
can be a benchmark model) and he compares these two MSFEs. From the form
(4)
they estimate the fraction between the two MSFEs, where Ŷh
i,t+h/t is the ith candidate
pseudo-out-of sample forecasts of Yh
t+h using data through time t. If the result of this
equation is less than one the candidate forecast is estimated to have performed better
than the benchmark.
5. DATA
In this section we present the data that have been used to examine the relation
between the output growth and the term spread, the stock returns and the short rate.
We focused the research in 7 countries which are Canada, France, Germany, Italy,
Japan, United Kingdom and the United States. The data came in monthly and
quarterly terms from DataStream and IFS. Output growth is measured in industrial
production terms and GDP growth terms. We defined industrial production and GDP
growth as the logarithmic differences. We used real stock returns and computed them
with the form: Real Stock Returns= Stock Returns – Consumer Price Index (we
defined both stock returns and CPI as logarithmic differences). We used levels for the
term spread, which we named as the difference between the 10-year government bond
and the 3-month Treasury bill rate. The 3-month Treasury bill rate was the short rate
in our research; we were not sure whether they should be included in levels or in first
differences, so we use both of them for the short rate.
5.1 DATA FOR THE INDUSTRIAL PRODUCTION
We present now the data that have been used to check whether the industrial
production has a link with the term spread, the real stock returns and the short rate.

For Canada, we used the Industrial Production Total Industry from January 1981
till May 2009 in monthly terms. For the same period we used the term spread and the
short rate and the real stock returns. The General Price Index of Canada was the one
for the stock returns.
For France, the Industrial Production Total Industry, the term spread, real stock
returns and the short rate were measured from January 1973 to December 2008. Also,
the index of DataStream for France was used for the stock returns. The data came in
monthly terms.
As far as Germany is concerned, the period that the data covered for the Industrial
Production and real stock returns was from July 1975 to 15 August 2009. The data for
the term spread and short rate stopped on August 2007. General Index represented the
stock returns.
For Italy, we used for all variables data from February 1977 till December 2008.
The general index of DataStream was concerned as stock returns.
For Japan, Industrial Production Total Industry was used for the Industrial
production and NIKKEI 225 for the stock returns. The period that the data covered
was from October 1966 to May 2009.
For United Kingdom, Industrial Production Total Industry which was chosen for
the UK’s industrial production and the term spread and the short rate were from
January 1968 to May 2009. Stock returns were represented by FTSE 100 Price Index
from January 1988 till August 2009.
Finally, for the United States of America, the Industrial Production, the term
spread, the short rate and the real stock returns were used from January 1966 to March
2009.
For all the countries above we used the Consumer Price Index for the inflation in
order to transform the stock returns to real stock returns. The period of data for the
CPI was the same as the period of the stock returns for each country.
5.2 DATA FOR THE GDP GROWTH
This section contains the data that have been used to examine the link between
GDP growth and the term spread, the real stock returns and the short rate. We used for
all countries the index of the DataStream for the GDP growth. For the stock returns
we used the indices that we reported above for the industrial production for each
country. The same is in effect for the Consumer Price Index, the term spread and the

short rate. Thus, the only change we made for the section of the GDP growth in
relation to the industrial production is the period of the data.
For Canada, the period lasted from the first Quarter of 1965 to the first Quarter
of 2009 for all the variables.
For France we used data from the first Quarter of 1970 to the first quarter of
2009 for the GDP growth, the term spread and the short rate and from the first Quarter
of 1990 until the first Quarter of 2009 for the stock returns.
We have had data from the first Quarter of 1991 to the second Quarter of 2007
for Germany.
For Italy our data begin in the first Quarter of 1981 and reach the first Quarter
of 2009. For Japan they also reach the same point in time, but they begin from the
third Quarter of 1985.
For the United Kingdom we tested the link between GDP growth, the term
spread and the short rate using data from the first Quarter of 1968 until the same
Quarter of 2009. But the data for the stock returns last from the first Quarter of 1988
and stop to the first quarter of 2009.
The last country is the United States of America, for which we have data from
Quarter one of 1996 to Quarter one of 2009.
All the Data are included in the following tables (table 01-table 02):
Πίνακας 1: Δεδομένα για τα μοντέλα με τη Βιομ/κη Παραγωγή ανεξάρτητη
μεταβλητή.
INDUSTRIAL
PRODUCTION
INDEX CPI TERM
SPREAD
SHORT
RATE
OBS.
CANADA 1981M01-
2009M05
1981M01-
2009M05
1981M01-
2009M05
1981M01-
2009M05
1981M01-
2009M05
344
FRANCE 1973M01-
2008M12
1973M01-
2008M12
1973M01-
2008M12
1973M01-
2008M12
1973M01-
2008M12
435
GERMANY 1975M07-
2009M08
1975M07-
2009M08
1975M07-
2009M08
1975M07-
2007M08
1975M07-
2007M08
413-385
ITALY 1977M02-
2008M12
1977M02-
2008M12
1977M02-
2008M12
1977M02-
2008M12
1977M02-
2008M12
387
JAPAN 1966M10-
2009M05
1966M10-
2009M05
1966M10-
2009M05
1966M10-
2009M05
1966M10-
2009M05
515
UNITED
KINGDOM
1968M01-
2009M05
1988M01-
2009M08
1988M01-
2009M08
1968M01-
2009M05
1968M01-
2009M05
500-263
UNITED
STATES
1966M01-
2009M03
1966M01-
2009M03
1966M01-
2009M03
1966M01-
2009M03
1966M01-
2009M03
522
Σημείωση:Γερμανία και Ηνωμένο Βασίλειο δεν έχουν το ίδιο δείγμα για όλες τις
μεταβλητές

Πίνακας 2: Δεδομένα για τα μοντέλα με το Α.Ε.Π. ανεξάρτητη μεταβλητή.
GDP
GROWTH
INDEX CPI TERM
SPREAD
SHORT
RATE
OBS.
CANADA 1965Q01-
2009Q01
1965Q01-
2009Q01
1965Q01-
2009Q01
1965Q01-
2009Q01
1965Q01-
2009Q01
180
FRANCE 1970Q01-
2009Q01
1990Q01-
2009Q01
1990Q01-
2009Q01
1970Q01-
2009Q01
1970Q01-
2009Q01
160-80
GERMANY 1991Q01-
2007Q02
1991Q01-
2007Q02
1991Q01-
2007Q02
1991Q01-
2007Q02
1991Q01-
2007Q02
69
ITALY 1981Q01-
2009Q01
1981Q01-
2009Q01
1981Q01-
2009Q01
1981Q01-
2009Q01
1981Q01-
2009Q01
116
JAPAN 1985Q03-
2009Q01
1985Q03-
2009Q01
1985Q03-
2009Q01
1985Q03-
2009Q01
1985Q03-
2009Q01
98
UNITED
KINGDOM
1968Q01-
2009Q01
1988Q01-
2009Q01
1988Q01-
2009Q01
1968Q01-
2009Q01
1968Q01-
2009Q01
168-89
UNITED
STATES
1966Q01-
2009Q01
1966Q01-
2009Q01
1966Q01-
2009Q01
1966Q01-
2009Q01
1966Q01-
2009Q01
176
Σημείωση:Γαλλία και Ηνωμένο Βασίλειο δεν έχουν το ίδιο δείγμα για όλες τις
μεταβλητές.
6. METHODOLOGY AND MODELS
In this section we present the models that we used to make the predictions and to
test the link between the dependent and independent variables. Moreover, we show
step by step the methodology that we used for the in-sample and the out-of-sample
statistics.
6.1 Forecasting Models
In our analysis seven (7) models have been used for each country; three
models to check the link between the GDP growth and the term spread or the short
rate or the stock returns, another three to check the link between the candidate
variables and the Industrial Production and one benchmark model. Specifically, we
tested the predictability of the real stock returns and the term spread using the h-steps
ahead linear regression model of the form (3).
In this model the dependent variable, Yt+h , represents the output growth, where the
output growth is measured by the real GDP and by the index of industrial production.
The independent variable Xt is either the term spread or the real stock return
depending on the model that we used, the h is the forecasting period in quarters

(1,4,8) or in months(1,12,24), b1(L) and b2(L) symbolize lag polynomials and the et+h
is the error of the model. We used twice the model with the form of (3) to check (a)
whether a relation exists between the industrial production and the term spread/real
stock returns and (b) whether this link exists between the GDP growth and the term
spread/stock returns. Furthermore, we used twice the same model, but adding one
more variable, Zt, that symbolizes the short rate. Thus, this model is:
In this model the variable, Xt , is only the term spread.
The variables are transformed to eliminate stochastic and deterministic trends.
We used the logarithm of output growth and stock returns to make the series
stationary. For the short rate we utilized both the levels and the first differences of the
series to check which has better predictive ability.
Definitions of the dependent variable
For the independent variables we used the GDP growth and the Industrial
Production. We considered two different forms for these variables. The first one is
.
We ran all the regressions having the Yt+h in the (3.1) form and then we transformed
the dependent variable to the second form (3.2) and we followed the same process.
The second form of Yt+h is:
Where the factor of standardizes the units in level to annual
percentage growth rates. The number 400 was used for the GDP that is measured in a
quarterly base and 1200 for the IP that is measured in a monthly base.
Lag lengths
We used in our models past values of dependent and independent variables. To check
which model is the best one to give us useful information about the predictive content
of candidate variables we utilized the Akaike criterion (AIC). For the in-sample
statistics the number of lags ranged between one and five.

Candidate Variables
In our study we checked the forecasting ability of three variables. From the
bibliography we found that the term spread and the real stock returns can be a useful
tool to predict the output growth and we decided to test their predictability. Our last
candidate variable is the short rate that was not examined in detail in the previous
literature, but it was referred to as a possible good predictor.
Yield curve, term spread and short rate
The yield on a government bond is the annual rate of return or the interest rate that
would be earned by an investor, who holds the bond until it matures. The maturity is
an important feature of the bond because yields differ with maturity.
The yield curve describes the relationship between yields and maturities. Yield
curve information is published daily by the financial press. The shape and the level of
the yield curve changes daily as investors reassess the current and expected future
economic conditions.
The yield spread is the difference between yields on two different debt
securities. The yield spread also provides information on the slope of the yield curve.
The larger the spread is between a long-term and a short-term bond, the steeper the
slope of the yield curve will be.
Analysts look at the yield spread as a potential source of information about future
economic conditions. Several hypotheses argue that the information in the yield curve
is forward-looking and therefore, should have predictive power for real growth.
In addition to the spread, the level of the yield curve may also provide useful
information for helping predict real growth. Since overall demand for and supply of
credit are reflected in the general level of interest rates across the maturity range, this
information may provide predictive information in addition to that summarized by the
yield spread. The yield spread does not contain information on the general level of
interest rates because it is constructed as the difference between two rates. The level
of the yield curve as measured by the short rates might help predict real growth
because short rates may provide information on the monetary policy. Short-term
interest rates move closely to the interest rate that serves as an instrument of monetary
policy. While fluctuations in the yield spread may reflect shifts in policy, they may

also be caused by shifts in the risk premium. Thus, the level of short rates may
provide a better measure of the monetary policy than the yield spread does.
6.2 Methodology
First of all, for each country we computed both in-sample and out-of-sample
statistics. Before running the regressions, we test for stationarity of all the variables
included. We utilized the Augment Dickey-Fuller unit root tests. We observed that all
the variables after the transformation (taking logarithms for the IP, GDP and stock
returns) or without transformation (term spread) were stationary. We met a problem
with the short rate which was not stationary for no-one country of our research. Thus,
we took the first differences for the short rate for the in-sample method but for the
out-of-sample we checked both the predictive content of the levels and the first
differences of the short rate.
 In-sample statistics
Using the whole sample we followed a process in three steps for each model and each
country.
First Step: Estimating the best model. We ran a VAR model for each group of the two
variables (IP-term spread/short rate/stock returns and GDP-term spread/short
rate/stock returns) using lags for these two variables. We used the Akaike criterion to
conclude to the well defined VAR model and the lags of the model. Then, we
collected all the prices of the coefficients of this model in tables.
Second Step: Checking the economic significance of the candidate variable. We
tested the economic significance of the (term spread, real stock returns) and
(short rate) looking at the adjusted R2
.
Third step: Checking the causality between the two variables. We wanted to see if the
one variable of the model has a predictive ability to forecast the other variable. This
can be done using the Granger-causality test and looking at the F-statistic (p-value).
The null-hypothesis is that the candidate variable does not granger cause the
dependent variable.
All the results of the in-sample statistics are placed in the tables 3 to 8.

 Out-of-sample statistics
In our exercise we tested whether the predictive ability of a benchmark model
improves when a candidate variable is added to this model. As a benchmark we used
an AR (autoregressive) model with the form:
To consider that a candidate model has better predictive content than the benchmark
model we computed the MSFEB for the AR model and the MSFEC for the candidate
model. To compute these two MSFEs we followed the following process. We
estimate the equation (6) using a sub-sample calling the estimation window. The
estimated coefficients are then used to forecast the dependent variable (GDP or IP) h-
steps outside the estimation window. After that one new observation was included in
the sub-sample, the coefficients were re-estimated and a new h-steps ahead forecast
was computed. This process continued to the end of the sample creating a series of
out-of-sample forecasts. We followed the same procedure for the candidate model and
we have the MSFEs that we need. When the fraction MSFE
is less than one, the inclusion of a candidate variable improves the forecasting
precision of the benchmark model. We followed this process for one period (one
month for the model of IP and one quarter for the model of GDP), one year and two
years ahead forecasting periods for each model and for each country. For most series
the out-of-sample forecasting exercise begins after accumulating fifteen or twenty
years of data. In some countries with a later start date the period begins after ten years
only. For the models that have been applied to forecast the industrial production the
exercise starts between 1988 and 1992 in most cases. For the GDP this period of time
ranges between 1986 and 2001. Overall, we ran our models three hundred and thirty
six times (336) to make out-of-sample forecasts.

7. RESULTS
7.1 Results from the in-sample tests
Most of the researchers of the previous decades used in-sample statistics to
measure the predictive content of the candidate variables. Thus, in the first part of this
section we present the in-sample results of our study. In the second part we show in
detail the out-of-sample findings for each country and each variable for all forecasting
periods. In both parts we try not only to present the results, but also to compare them
with previous findings.
7.1.1 INDUSTRIAL PRODUCTION
We applied the test of Granger causality three times for each country to test the
causality between the IP and the term spread, the short rate and the real stock returns
respectively. Our null hypothesis is that the candidate variable does not granger cause
IP. Our results show that the real stock returns are a statistically significant predictor
for Japan, Italy and the USA at the 1-percent level and for the United Kingdom and
Canada at the 5-percent level; they are not significant for France and Germany (even
at the 10-percent level). For the countries, where the stock returns look like a useful
forecasting tool, the coefficients demonstrate a positive relation between the
dependent and independent variables. Checking previous papers we see that
researchers have had similar results for the stock returns. Fama (1990) and Mathias
Binswanger (2000) examined this relation for the USA. The former showed that the
stock returns were significant in explaining future industrial production for the period
from 1953 to 1987. The latter increased the sample until 1995 and made the Granger
causality test. Indeed, our paper found similar results to his paper for the USA. The F-
statistic for the whole sample shows significance at the 1-percent level with 3 and 6
lags of stock returns. Close to our results is also the work of Stock and Watson, who
showed that the Granger causality test rejected the null hypothesis for 40 percent of
asset prices. Thus, the Granger causality test leads us to the conclusion that it is
helpful to utilize the real stock returns as predictors of Industrial production.

All the above we said, about the results of our test, were pulled together in the
following table 3.
For the term spread the in-sample statistics showed that it might not be helpful
to use it to forecast the industrial production, since we rejected the null hypothesis
that the term spread does not granger cause IP only for two countries; for France it is
rejected at 1-percent level and for the USA at 5-percent level. For all other countries
of our research the test failed to reject the null hypothesis even at 10-percent level.
But, if we use the short rate we can see an improvement in our results. The p-value of
the F-statistic demonstrated that the short rate is a useful tool to predict the industrial
production; we rejected that the coefficients of the candidate variable are equal to zero
for the aforementioned countries (France and USA), but also for the United Kingdom
and Germany at the 5-percent level. For Canada, Japan and Italy neither the short rate
is statistically significant nor the term spread. Thus, we concluded that the in-sample
statistics note that the real stock returns are the most useful predictor for the industrial
production and that the short rate can be a better tool for forecasting than the term
spread.
Table 4 and Table 5 summarized all the above for the term spread and the short rate.
TABLE 3: Granger causality tests ( Ho: Real stock returns do not granger cause Industrial Production)
SAMPLE CANADA
(1981M1-
2009M05)
FRANCE
(1973M02-
2008M12)
GERMANY
(1975M08-
2009M08)
JAPAN
(1966M10-
2009M05)
ITALY
(1977M02-
2008M12)
UK
(1988M01-
200905)
USA
(1966M06-
2009M03)
F-statistic 2.41849 0.95471 0.63260 8.52222 7.75675 3.37521 9.34429
Prob. 0.04848* 0.41407 0.72070 0.0000011** 0.00050** 0.01037* 1.6E-08**
Lags 4 3 2 3 2 4 5
AIC -9.748952 -11.87216 -11.70193 -11.78376 -10.70121 -13.46290 -13.87993
Adj
R-squared
0.316239 0.136025 0.180914 0.151557 0.230047 0.074479 0.230730
Notes: The Granger causality test statistics is heteroskedasticity-robust and was computed in-sample (full
sample). We present only the price of the Akaike criterion of the appropriate model that we estimated.
Asterisks denote significance at the 5% (*) or at 1% (**) level.

We can see in table 4 that the p-value for Germany and United Kingdom is
0.36337 and 0.18036 respectively and changes to 0.01395 and 0.02325 when the short rate is
included in the regression (table 5). If we look at the previous study we can find results
for the forecasting ability of the term spread and the short rate. Sharon Kozicki
(1997), Estrella and Mishkin (1997) and Stock and Watson (2003) used in sample
statistics to compare the term spread and the short rate predictability. The conclusions
of these papers will be presented in detail in the next part of this section, where the
results of the GDP growth are discussed.
TABLE 4: Granger causality tests ( Ho: Term Spread does not granger cause Industrial Production)
SAMPLE CANADA
(1981M1-
2009M05)
FRANCE
(1973M02-
2008M12)
GERMANY
(1975M08-
2007M08)
JAPAN
(1966M10-
2009M05)
ITALY
(1977M02-
2008M12)
UK
(1968M01-
200905)
USA
(1966M06-
2009M03)
F-statistic 1.94056 7.04552 1.01504 1.56618 1.94885 1.71881 3.30880
Prob. 0.10341 0.00098** 0.36337 0.77956 0.10178 0.18036 0.01084*
Lags 4 2 2 4 4 2 4
AIC -12.78949 -15.65873 -16.30884 -16.01751 -14.75179 -15.54090 -17.02628
Adj
R-squared
0.312334 0.140987 0.185976 0.106481 0.223569 0.029216 0.179486
TABLE 5: Granger causality tests ( Ho: Short Rate does not granger cause Industrial Production)
SAMPLE CANADA
(1981M1-
2009M05)
FRANCE
(1973M02-
2008M12)
GERMANY
(1975M08-
2007M08)
JAPAN
(1966M10-
2009M05)
ITALY
(1977M02-
2008M12)
UK
(1968M01-
200905)
USA
(1966M06-
2009M03)
F-statistic 0.11094 3.66601 3.58687 0.65767 0.95961 2.85601 5.95291
Prob. 0.97864 0.01245* 0.01395* 0.65578 0.42966 0.02325* 0.00011**
Lags 4 3 3 5 4 4 4
AIC -21.36245 -24.69139 -26.14800 -26.01026 -23.53568 -24.05668 -26.03385
Adj
R-squared
0.315833 0.165757 0.216000 0.119938 0.216902 0.044798 0.212492
sample). We present only the value of the Akaike criterion of the appropriate model that we estimated.

7.1.2 GDP GROWTH
We used the test of Granger causality three times for each country to test the
causality between the GDP and the term spread, the short rate and the real stock
returns respectively. Our null hypothesis is that the candidate variable does not
granger cause GDP. Our results for the forecasting ability of the real stock returns are
not as good as before for the industrial production, but they demonstrate a strong link
between the dependent and independent variables. The null hypothesis was rejected in
four countries. For Canada, France and the United States at 1-percent level (0.00121-
0.00061-0.00053) and at 5-percent level for Japan (0.03679). For Germany, Italy and
the United Kingdom the Granger causality test accepts the null hypothesis; the
coefficients of the real stock returns are not statistically significant. If we check again
the results of the Binswanger’s paper (2000) we see that for the United States for the
period 1953-1995 the real stock returns have similar power to predict the GDP growth
(0.0000022) as those of our sample. For the term spread we found that causality exists
between itself and GDP growth in four countries again. For Canada, France and the
United States at 1-percent level and for Japan at 5-percent level. Estrella and Mishkin
(1997) ran similar tests for five countries (France, Germany, Italy, United Kingdom
and United States) using data from 1973 to early 1995. Their results are consistent to
ours as they find significance for USA, but not for Italy and the United Kingdom.
However, they found a strong link between the two variables for Germany in contrast
to our results. Stock and Watson (2003) noted that the term spread until 1999 was a
useful predictor of GDP growth in France, United States, Germany and Canada, but
not (even at the 10-percent level) in Italy, Japan and the UK. Paulo Mauro (2003)
also checked the causality between the stock returns and the GDP growth for the
emerging and the developed countries. They found that it appeared a strong link in
France, Canada, Japan, United Kingdom and the United States, but not in Germany
and Italy. From these three papers and from our results we can conclude that the term
spread was and remains a useful forecasting tool of GDP growth in the United States,
Canada and France, but not in Italy and the United Kingdom. The results are not
obvious for Germany and Japan. The Granger causality tests of term spread and stock
returns are summarized in the next two tables (table 6-table 7).

From the table 6 we can see the p-values of Canada, France, Japan and USA, which
shows that the null hypothesis that the index does not granger cause GDP is rejected.
The same results for the same countries we can see in table 7, which includes the
results for the term spread.
Finally, we close this section with the in-sample statistics about the link that
we found between the short rate and the GDP growth. As the previous bibliography
noted (Sharon Kozicki 1997 and Monika Piazzesi 2005) the short rate is a very good
indicator to predict the GDP growth. Our results agree with this statement. We found
a strong link between the GDP growth and the candidate variable in five out of seven
counties. In USA and Germany we rejected the null hypothesis at 1-percent level and
in Canada, UK and France at 5-percent level. In general for GDP we can say that all
the variables that we examined are useful forecasting tools and especially the short
TABLE 6: Granger causality tests ( Ho: Real Stock Returns do not granger cause GDP growth)
SAMPLE CANADA
(1965Q1-
2009Q1)
FRANCE
(1970Q1-
2009Q1)
GERMANY
(1991Q1-
2007Q2)
JAPAN
(1983Q3-
2009Q1)
ITALY
(1981Q1-
2009Q1)
UK
(1968Q1-
2009Q1)
USA
(1966Q1-
2009Q1)
F-statistic 10.8400 6.53788 1.58569 2.96208 2.14593 1.29065 10.9893
Prob. 0.00121** 0.00061** 0.21274 0.03679* 0.14585 0.28090 0.00053**
Lags 1 3 1 3 1 2 2
AIC -12.31920 -13.41012 -12.53454 -11.11788 -11.96789 -13.46527 -12.32978
Adj
R-squared
0.167358 0.452433 0.003637 0.195428 0.258801 0.473224 0.202189
TABLE 7: Granger causality tests ( Ho: Term Spread does not granger cause GDP growth)
SAMPLE CANADA
(1965Q1-
2009Q1)
FRANCE
(1970Q1-
2009Q1)
GERMANY
(1991Q1-
2007Q2)
JAPAN
(1983Q3-
2009Q1)
ITALY
(1981Q1-
2009Q1)
UK
(1968Q1-
2009Q1)
USA
(1966Q1-
2009Q1)
F-statistic 8.78516 6.13170 0.04303 6.38726 0.31299 1.59066 6.28858
Prob. 0.00023** 0.00276** 0.83637 0.01324* 0.81595 0.19392 0.00233**
Lags 2 2 1 1 3 3 2
AIC -15.60130 -16.53554 -18.31691 -16.55000 -17.07701 -15.14910 -15.99670
Adj
R-squared
0.191589 0.344611 -0.027883 0.124204 0.252771 0.044580 0.159950

rate. Table 8 (Appendix) summarizes all the results for the short rate. Thus, the short
rate along with the term spread can be used to help us with predictions of the GDP
growth.
 Discussion
As a conclusion of this section, with the in-sample statistics, we can notice
that the Granger causality test frequently rejects showing that these variables bear a
predictive content. This result does not surprise us if we check the previous literature;
those indicators were chosen in a large part having been identified by researchers as
useful predictors.
7.2 Results from the out-of-sample tests
In this section, which is the most significant of our research, we present the
results of the out-of-sample method. We will discuss them in detail and we will try to
compare this one with previous studies.
In this point, we think that it is useful to remind some things for our out-of sample
statistics methodology. First, we used two variables as independent indicators (the
GDP growth and the Industrial production) and we checked their link with three
candidate predictors (the term spread, the real stock returns and the short rate).
Second, the procedure was repeated seven times for each country (Canada, France,
Germany, Italy, Japan, UK, USA) and three times for each forecasting horizon (h=1,
4, 8 for quarters and h=1, 12, 24 for months).
Third, we used both the forms of that we referred to in section 5 (methodology)
and we made two groups of predictions for each form. No qualitative differences have
occurred in the results of the two groups, so we present in detail these by only the
second form (3.2).
Finally, we took the short rate both as levels and differences, because it is not clear in
bibliography which is better. We present both results in separate tables. The study,
also, examined whether our results are different in the case that the data of the period
of the current crisis (2007-2009) are exempted. The conclusion we drew is that this
period is not long enough to substantially influence the overall results.

7.2.1 GDP GROWTH
Table 9 summarizes the performance of the stock return as the predictor of the GDP
growth for one, four and eight quarter horizons.
We can see that in our results the real stock return is a useful predictor for 5 out of 7
countries for a forecasting horizon of one quarter. More specifically the MSFE of the
model improved when a candidate was involved in Canada, France, Italy, Japan and
the United Kingdom and worsened in Germany and the United States. Similar are the
results we get with four quarters horizon with an exception only in Canada and Japan,
where the MSFEs of the model became worse. In eight quarters ahead we have
exactly the same countries with the four quarters ahead to have MSFE lower than the
benchmark model. We can say as a conclusion that the real stock return can be a
helpful tool for making predictions of the GDP growth. Moreover, the forecasting
power of this indicator stays quite stable independent of the forecasting horizon. To
compare our results we looked back at the bibliography and we found researchers
who tested the link between the GDP growth and the real stock return. Stock and
Watson (2003) followed the same process for two sample periods, 1971-1984 and
1985-1999. Looking at the second period we can notice that they found that the stock
returns can predict the GDP growth successfully in France and the UK, but not in the
United States and Italy as our tests found. The difference in the results probably
appears because the period of data is longer in our research.
Another paper which examined this relation is that of Andersson and D’Agostino
(2008). Because this research was executed recently it is the best one to compare our
results with. They found similar results to our work for the total market index of the
post-euro period, but not for that of the pre-euro period. Our data for the out-of-
sample method in most of the countries commenced in 1995, so we think that it is
preferable to contrast our results to the post-euro period ones in Andersson’s paper.
Indeed they also showed that the MSFE of the model, which has had the total market
index as a candidate variable, became better than the MSFE of the benchmark (by 35-
40%, depending on the forecasting horizon). More specifically, we have three
countries with data from the post-euro period (Germany, France and U.K.) and two
with data close to this period (Italy and Japan). In four of five (except Germany)
countries the relation between the error of the candidate model and the benchmark
model is less than one showing that the stock returns are good predictors of the GDP

growth. Moreover, all the countries except Japan achieved to improve their results
when the forecasting period increased. For example Germany’s relation between the
MSFEs starts in 2.4189 for h=1, became 1.0049 for h=4 and finally we have equal
MSFE for both the benchmark and the candidate models for h=8 . The
equivalent prices for France are 0.6181-0.5304 and 0.1194 showing a big
improvement in the model when the candidate indicator was involved.
Table 10 summarizes the results for the term spread. We can, also, see that the
term spread has predictive power for one quarter forecasting horizon, like the real
stock returns do, but we met different behavior in relation to stock returns as the
horizon increased. Specifically, the predictive ability of the term spread became lower
when the h became higher. Generally, the term spread is a good predictor for 71
percent of the countries for h=1, 42 percent for h=4 and 28 percent for h=8. While in
the beginning we have 5 countries (Canada, France, Italy, Japan and UK) with relative
MSFEs less than one when the forecasting period became four quarters we have three
(France, Japan and the UK) and when it became eight quarters we have only Japan,
and the UK. This shows that the term spread is not the most reliable indicator to make
predictions for the GDP growth. Sharon Kozicki (1997) showed the same thing; the
term spread has predictive power over the next year or so. Nevertheless, the results of
our work for the term spread have some differences with Andersson and D’Agostino
(2008) paper. They found that the term spread has predictive power after two years,
but we show that something like that does not exist. Some explanation could be that in
their paper they check the whole euro area GDP, while in our work we examined only
(4) four countries of Europe, out of which the UK agreed with their results and
Germany has provided not enough data to check the link in two years ahead. So, we
disagree only in relation to Italy and France. Stock and Watson also found that the
predictability of the term spread is eliminated when the forecasting horizon increased.
For forecasting horizon of four quarters ahead they found that the term spread
predicted well only in Canada and the UK. We can say that our results and the results
of other papers confirmed that the term spread is a good predictor, but not the most
reliable over time.
Tables 9 and 10 follow:

TABLE 9: OUT-OF-SAMPLE MEAN SQUARE FORECAST ERRORS ,REAL GDP GROWTH
H= 1 4 8
Canada (1985Q1-2009Q1) 0.9453* 1.5012 1.6573
France (2000Q1-2009Q1) 0.6181* 0.5304* 0.1194*
Germany (2001Q1-2007Q2) 2.4189 1.0049 1.0000
Italy (1991Q1-2009Q1) 0.8321* 0.8444* 0.1215*
Japan (1995Q3-2009Q1) 0.8938* 2.1021 3.5012
United kingdom (1998Q1-2009Q2) 0.7743* 0.9004* 0.8846*
United states (1986Q1-2009Q1) 1.0877 0.9161* 0.8202*
ALL 71% 57% 57%
Notes: The benchmark model has the form: and the Candidate
model: where
and H is the forecasting period in quarters.
H= 1 4 8
Canada (1985Q1-2009Q1) 0.8755* 1.4106 1.4754
France (1990Q1-2009Q1) 0.7855* 0.8477* 2.2119
Germany (2001Q1-2007Q2) 1.4600 4.0278 -
Italy (1991Q1-2009Q1) 0.8541 * 1.8485 4.1037
Japan (1995Q3-2009Q1) 0.5444* 0.4530* 0.4732*
United states (1986Q1-2009Q1) 1.1269 3.5265 1.7420
ALL 71% 42% 28%
Notes: the benchmark model has the form: and the Candidate
model: ,
where and H is the forecasting period in quarters. The data
for the Germany is not enough to make reliable forecasts for 4.
In the model, in which the term spread was included, we added the short rate
and checked whether the forecasting power of the model improved. The summary of
the results for the short rate is given in table 11A. This table has the results from the
model in which the short rate was used as first differences. The table with the short
rate as levels is the table 11B which exists in the Appendix. One thing that we can say
about these two different groups of results is that the model with the short rate as first
differences gave better results than the model with the short rate as levels. This model
now is a trivariate model with lags of GDP, the term spread and the new candidate

variable, namely the short rate. From our results, we can notice that the short rate
followed the behavior of the term spread. For forecasting horizon one (h=1) the short
rate has predictive content for five out of seven countries. However, like in the model
with the term spread when the forecasting horizon increased the forecasting power of
model with the short rate decreased. Nonetheless, we can focus only on the
improvement achieved by the addition of the short rate to the model with the term
spread. If we look at the relative MSFEs of the countries on tables 10 and 11A we
notice that the short rate succeeded to reduce their prices in 4 countries. Only in
Canada and the United Kingdom the term spread has had predictive power bigger
than the short rate. Andrew Ang, Monika Piazzesi, Min Wei (2006) in their paper
showed that the short rate gives additional predictive power to the candidate model.
Stock and Watson (2003) said that a trivariate model gave the same results, which
were characterized with instability, as a bivariate model did.
TABLE 11 A: OUT-OF-SAMPLE MEAN SQUARE FORECAST ERRORS ,REAL GDP GROWTH
H= 1 4 8
Canada (1985Q1-2009Q1) 0.9596* 3.0548 1.6414
France (1990Q1-2009Q1) 0.4373* 0.3890* 2.1397
Germany (2001Q1-2007Q2) 1.4427 - -
Italy (1991Q1-2009Q1) 0.6050* 0.4189* 0.1126*
Japan (1995Q3-2009Q1) 0.2652* 0.2063* 0.1986*
United kingdom (1988Q1-2009Q2) 0.7885* 1.1938 1.7857
United states (1986Q1-2009Q1) 1.0526 1.5327 1.5327
ALL 71% 42% 28%
Notes: the benchmark model has the form: and the candidate
model: ,
where , H is the forecasting period in quarters and the short
rate is used as first differences. The data for the Germany is not enough to make reliable forecasts for
4 and 8 quarters ahead.

We must remind the reader that in all these models the GDP has the form:
. The results of the models where
appeared in the tables 12 for the stock returns, 13 for the
term spread and 14 (A and B) for the short rate. The differences in the results of these
two groups are not qualitative, so we do not need to write a different section for the
model with the second form of the GDP. Simply, we present the table 12 with the
stock returns to show that the results are similar to the table 9. The other tables appear
in the Appendix.
H= 1 4 8
Canada (1985Q1-2009Q1) 0.9448* 2.5414 2.4705
France (2000Q1-2009Q1) 0.6274* 0.5551* 0.2010*
Germany (2001Q1-2007Q2) 1.9341 1.1256 1.0012
Italy (1991Q1-2009Q1) 0.8328* 0.0644* 0.0587*
Japan (1995Q3-2009Q1) 0.8858* 2.0676 3.1254
United states (1986Q1-2009Q1) 1.0939* 1.1140 0.7777*
ALL 71% 42% 57%
Notes: the benchmark model has the form: and the Candidate
model: , where
and H is the forecasting period in quarters.
We are ending the section with the forecasts of GDP and three conclusions,
which summarize all the above. First, we showed that the real stock returns have a
great deal of predictive content and can be used to forecast the GDP growth even
when the forecasting horizon increased. Second, the term spread and the short rate are
good predictors only for a short period ahead since they lost their forecasting power
when the horizon got longer. Figure 1 following confirms the above conclusions,
showing that only the stock returns do retain their predictive power in quite high
levels for longer forecasting horizons.

Finally, the short rate is a better predictor than the term spread to forecast the
GDP growth. Moreover, the first differences of the short rate have performed better
predictability than the levels of the short rate.
FIGURE 1: PERCENTAGE OF COUNTRIES THAT HAVE MSFEs LESS THAN ONE, GDP GROWTH
NOTE: THE HORIZONTAL AXES PRESENTS THE CANDIDATE PREDICTORS
7.2.2 INDUSTRIAL PRODUCTION
In this part, we present the results for the industrial production. The methodology
that we applied is the same with that for the GDP. We (a) used two forms for the IP
like we did for the GDP and (b) checked the predictive ability of the term spread, the
short rate and the real stock returns for 1, 12 and 24 months ahead. We present all the
results on tables 15-19 (APPENDIX).
The research for the real stock return, as the candidate variable, found that this
could be a good predictor of the Industrial Production for a forecasting horizon of one
month. The model including these outperformed the AR benchmark in Canada,
Germany, Italy, Japan and the UK, but not in France and United States. For a
forecasting horizon of twelve months (one year ahead) the stock return failed to retain
its predictive content in high levels. The relative MSFEs in this case are less than one
only in Japan and the UK. Similar results we observed when the forecasting horizon
71% 71% 71%
57%
42% 42%
57%
28% 28%
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
REAL STOCK RETURNS TERM SPREAD SHORT RATE
H=1
H=4
H=8

increased to twenty four months (two years ahead). The index beat the AR model only
in Germany and Japan. Thus, the percentage of the countries with MSFEs less than
one starts with 71% for h=1, falls to 28% for h=12 and stays at this low level for
h=24. Stock and Watson (2003), who examined candidate predictors in the same
countries with our research, found results for the link between real stock returns and
the Industrial Production very close to ours. Specifically, for the second period of
their research (1985-1999), which is more relative to our work than the other period
they checked (1971-1984), they found for h=12 that the index beat the benchmark
only in one country (Japan). Moreover, the values of the MSFEs are also close to our
values; for Japan they found MSFEs equal to 0.98, for Canada 1.18, for Germany
1.12. Table 15 demonstrates our results for all countries and for all forecasting
horizons.
TABLE 15: OUT-OF-SAMPLE MEAN SQUARE FORECAST ERRORS ,INDUSTRIAL PRODUCTION
H= 1 12 24
Canada (1996M01-2009M05) 0.9804* 1.0758 2.7313
France (1988M01-2008M12) 1.0581 1.0190 1.0039
Germany (1990M07-2009M08) 0.9983* 1.0265 0.9996*
Italy (1992M02-2008M12) 0.9871* 1.3492 1.0241
Japan (1986M10-2009M05) 0.8378* 0.8733* 0.9827*
United kingdom (1998M01-2009M08) 0.9963* 0.9964* 1.0000
United states (1986M01-2009M03) 1.1363 1.4265 1.0066
ALL 71% 28% 28%
Notes: The benchmark model has the form: and the Candidate model:
where and H is
the forecasting period in months.
For the term spread the results are quite different from the results of the real stock
return. For the precision the out-of sample results are similar to the in-sample results
(table 4). We met good results only in 3 countries for a forecasting period of one
month (Italy, Japan and United States). The results became worse when the h got
bigger; for h=12 the term spread beat the AR benchmark in two countries (Japan and
UK) and for h=24 again only in these two countries the relative MSFEs is less than
one. Obviously, the term spread is not the best indicator to predict the Industrial
production. Table 16 (APPENDIX) summarises all the above for the term spread. If
we check again the Stock and Watson’s paper their results do not agree with our
results. Specifically, they found a strong link between the term spread and the
Industrial Production in four instead of two countries, where we did (France,
Germany, Japan and UK).

On the other side the short rate is quite better indicator than the term spread,
because when this variable was involved in the candidate model we met better results.
Nevertheless, the results of the short rate are not significantly different from the
results of the term spread for a forecasting period of one month ahead. Specifically,
the forecasting ability of the model with the short rate increased and the relative
MSFEs became less than one in four countries out of seven (France, Italy, Japan and
the United Kingdom) instead of three out of seven in the case of the model with the
term spread. For forecasting period of twelve months the short rate beat the AR
benchmark in four countries again (Germany, Japan, UK and USA) and for twenty
four months in Canada, Japan and the United States. Thus, if we include the short
rate in the model, with the term spread, we notice that the percentage of countries that
have MSFEs less than one became 57% for h=1, 42% for h=12 and 42% again for
h=24. Andrew Ang, Monica Piazzesi and Min Wei (2006), also, showed that the
short rate achieved to increase the predictability of the model.
The figure 2 shows all the results (percentage) for the term spread, short rate and
real stock returns.
FIGURE 2: PERCENTAGE OF COUNTRIES THAT HAVE MSFEs LESS THAN ONE, INDUSTRIAL PRODUCTION
NOTE: THE HORIZONTAL AXES PRESENTS THE CANDIDATE PREDICTORS
71%
42%
57%
28% 28%
57%
28% 28%
42%
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
REAL STOCK RETURNS TERM SPREAD SHORT RATE
H=1
H=4
H=8

Forecasting Economic Activity using Asset Prices

Recommended

Recommended

More Related Content

What's hot

What's hot (18)

Viewers also liked

Viewers also liked (20)

Similar to Forecasting Economic Activity using Asset Prices

Similar to Forecasting Economic Activity using Asset Prices (20)

Recently uploaded

Recently uploaded (20)

Forecasting Economic Activity using Asset Prices