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 (R

S):

.

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 ytk

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%


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



Discussion

In this part we present some unofficial conclusions about our results with out-of

sample method. The general conclusions of our work will be presented in the last

section of this dissertation.

Generally, and without looking one by one at the countries of the research we can

notice that the previous researchers noted similar things to us about the predictability

of the term spread. Gikas Hardouvelis and Arturo Estrella (1991), Joseph Haubrich

and Ann Domborsky (1996), Michael Dtsey (1998), Arturo Estrella and Frederic

Mishkin and also Arturo Estrella, Anthony Rodrigues and Sebastian Schich (2003)

and finally Stock and Watson (2003), they all said that the term spread has some

predictive content but it is not a reliable indicator, since their forecasting power does

not remain stable over time. For the short rate, we can say that it is a better indicator

than the term spread; the work of Andrew Ang , Monica Piazzesi and Min Wei (2006)

confirmed this conclusion. Finally, our work found that the real stock returns are the

best indicators to predict the output growth and this could be confirmed even if

someone used monthly or quarterly data. Binswanger (2000) and Mauro (2000) found

similar results



8. CONCLUSIONS

This part, which is the last section of our dissertation, presents all the conclusions of

our study. From both the in-sample and the out-of sample statistics we lead to four

main conclusions.

First, although the most common and most simple econometric method to

identify whether a candidate variable is a useful tool to forecast another variable is the

in-sample statistics, like the Granger causality test, using this may not prove reliable

to do so. This occurs because variables, which showed they could be reliable future

predictors with in-sample statistics, lost their forecasting power when out-of-sample

statistics were applied. Thus, we can notice that the in-sample statistics provide no

guarantee that two variables have stable predictive relation.

Second, the forecasting power of the indicators seems to lessen when the

forecasting horizon increases. The out-of sample statistics showed that the term

spread and the short rate were good predictors for h=1, but their predictability became

quite smaller when the forecasting horizon is (4) four and even smaller when it is (8)

eight. We observed the same thing when the real stock returns were used to forecast

the IP. Only for the GDP growth the real stock returns can be useful predictors

independent of the forecasting period.

Third, we saw that one indicator which is an appropriate predictor of Industrial

Production or GDP growth for one country, perhaps does not predict good for the

other countries as well. 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. This conclusion is a problem for

those, who want to forecast, because they do not know a priori which indicator is

good for example for Germany or the UK.

Fourth, if we check our candidate variables more thoroughly we can obtain

some results for their predictability. The stock returns and the short rate give the

impression that they are the best predictors for the GDP growth. However, we

conclude that generally the real stock returns are the best indicators for GDP, because

their power is bigger when the forecasting period increases than that of the short rate.

The term spread seems to be a good indicator only for one quarter ahead. Between the

short rate and the term spread we can notice that when the former is included in a

model with the latter the forecasting ability of this model improves in most of the

countries independent of the forecasting horizon. For the Industrial Production we

think that no variable can be useful to predict it for a forecasting horizon bigger than

one month or one quarter ahead; our results showed that their predictive content fell to



very low levels for predictive horizons of 12 and 24 months. We can only say that the

stock returns show quite a better predictability for the Industrial Production for the

forecasting period of one month and the short rate for twelve and twenty four months.

Moreover, we found that the term spread is the worst variable to make forecasts for

the Industrial Production.



APPENDIX

TABLES

TABLE 8: Granger causality tests ( Ho: Short rate 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 3.06638 2.46869 7.45852 0.99440 1.76213 2.71371 4.97730

Prob. 0.02956* 0.03545* 0.00828** 0.39945 0.14263 0.002235** 0.00030**

Lags 3 5 1 3 4 5 5

AIC -15.17173 -16.16270 -18.15553 -17.42060 -16.18149 -14.47036 -15.57837

Adj

R-squared

0.152722 0.364287 0.085109 0.140835 0.309223 0.073332 0.199104


sample). We present only the price of the Akaike criteria of the appropriate model that we estimated.


TABLE 11B: OUT-OF-SAMPLE MEAN SQUARE FORECAST ERRORS ,REAL GDP GROWTH

H= 1 4 8

Canada (1985Q1-2009Q1) 1.2810 5.1817 4.6137

France (1990Q1-2009Q1) 0.4421* 0.4150* 0.1446*

Germany (2001Q1-2007Q2) 1.5427 - -

Italy (1991Q1-2009Q1) 1.4236 1.9096 2.2193

Japan (1995Q3-2009Q1) 1.7041 1.5937 0.2610*


United states (1986Q1-2009Q1) 1.0187 1.2525 1.4981

ALL 28% 28% 42%

Notes: the benchmark model has the form: and the candidate model

is:

,

where

, H is the forecasting period in quarters and the short

rate is used as levels. The data for the Germany is not enough to make reliable forecasts for 4 and 8

quarters ahead.




H= 1 4 8

Canada (1985Q1-2009Q1) 0.9302* 2.6757 3.0739

France (1990Q1-2009Q1) 0.7879* 0.8260* 2.0991

Germany (2001Q1-2007Q2) 2.2059 4.0456 -

Italy (1991Q1-2009Q1) 0.8323* 1.6210 4.0112

Japan (1995Q3-2009Q1) 0.5244* 0.4766* 0.4531*


United states (1986Q1-2009Q1) 1.0833 3.1274 1.3618

ALL 71% 42% 28%


model is:

, where

and H is the forecasting period in quarters. The data for the Germany is not

enough to make reliable forecasts for 8 quarters ahead.

TABLE 14A:OUT-OF-SAMPLE MEAN SQUARE FORECAST ERRORS ,REAL GDP GROWTH

H= 1 4 8

Canada (1985Q1-2009Q1) 0.8903* 3.5199 1.5083

France (1990Q1-2009Q1) 0.4509* 0.3747* 1.9477

Germany (2001Q1-2007Q2)(1) 1.2328 - -

Italy (1991Q1-2009Q1) 0.5815* 0.3231* 0.0238*

Japan (1995Q3-2009Q1) 0.2322* 0.2365* 0.1781*

United kingdom (1988Q1-2009Q2) 0.7917* 1.1417 1.5881

United states (1986Q1-2009Q1) 1.0199 1.6913 2.1036

ALL 71% 42% 28%


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.



TABLE 16: OUT-OF-SAMPLE MEAN SQUARE FORECAST ERRORS ,INDUSTRIAL PRODUCTION

H= 1 12 24

Canada (1996M01-2009M05) 1.1193 1.2174 1.7077 France (1988M01-2008M12) 1.0186 1.0454 1.0050

Germany (1990M07-2009M08) 1.0092 1.0100 1.0000 Italy (1992M02-2008M12) 0.9886* 1.5550 1.0291 Japan (1986M10-2009M05) 0.7393* 0.7219* 0.9592*

United kingdom (1988M01-2009M08) 1.3653 1.0049 1.0035

United states (1986M01-2009M03) 0.8823* 0.7680* 0.9953* ALL 42% 28% 28%


model:

, where

and H is the forecasting period in months.

TABLE 14B: OUT-OF-SAMPLE MEAN SQUARE FORECAST ERRORS ,REAL GDP GROWTH

H= 1 4 8

Canada (1985Q1-2009Q1) 0.9350* 4.1527 5.2723

France (1990Q1-2009Q1) 0.4509* 0.3570* 0.1158*

Germany (2001Q1-2007Q2) 5.2328 - -

Italy (1991Q1-2009Q1) 1.3866 1.7457 2.5033

Japan (1995Q3-2009Q1) 1.5907 1.4117 0.2970*


United states (1986Q1-2009Q1) 1.1463 2.2361 4.8659

ALL 42% 28% 42%


model:

,

where

, H is the forecasting period in quarters and the short rate is

used as levels. The data for the Germany is not enough to make reliable forecasts for 4 and 8

quarters ahead.



TABLE 17A: OUT-OF-SAMPLE MEAN SQUARE FORECAST ERRORS ,INDUSTRIAL PRODUCTION

H= 1 12 24

Canada (1996M01-2009M05) 1.1121 1.6151 0.8540* France (1988M01-2008M12) 0.8523* 1.0050 1.0042 Germany (1990M07-2009M08) 1.3322 0.9602* 1.0016 Italy (1992M02-2008M12) 0.8265* 1.3500 1.0214 Japan (1986M10-2009M05) 0.7099* 0.7519* 0.9849* United kingdom (1988M01-2009M08) 0.9149* 0.9972* 1.0099 United states (1986M01-2009M03) 1.8765 0.6709* 0.9989*

ALL 57% 57% 42%

Notes: the benchmark model has the form: and the candidate model is:

, where

, H is the forecasting period in months and short rate is used as

first differences.

TABLE 17B: OUT-OF-SAMPLE MEAN SQUARE FORECAST ERRORS ,INDUSTRIAL PRODUCTION

H= 1 12 24 Canada (1996M01-2009M05) 1.0821 1.2122 3.7357 France (1988M01-2008M12) 0.9901* 1.2711 1.0038

Germany (1990M07-2009M08) 1.1798 0.9739* 1.0027 Italy (1992M02-2008M12) 0.9538* 1.7154 1.0419

Japan (1986M10-2009M05) 0.5473* 0.6081* 2.2023

United kingdom (1988M01-2009M08) 0.8761* 0.9926* 1.0016 United states (1986M01-2009M03) 1.7475 0.6950* 0.9947*

ALL 57% 57% 14%

Notes: the benchmark model has the form: and the candidate model is:

, where

, H is the forecasting period in months and the short rate is used as

levels.



TABLE 18 OUT-OF-SAMPLE MEAN SQUARE FORECAST ERRORS ,INDUSTRIAL PRODUCTION

H= 1 12 24

Canada (1996M01-2009M05) 0.9768* 1.5768 2.5678 France (1988M01-2008M12) 1.0689 1.3546 1.0043

Germany (1990M07-2009M08) 0.9989* 1.0728 0.9435*

Italy (1992M02-2008M12) 0.9941* 1.2978 1.0456 Japan (1986M10-2009M05) 0.9978* 0.8987* 0.9897*

United kingdom (1998M01-2009M08) 0.8023* 0.9998* 1.0005 United states (1986M01-2009M03) 1.4377 1.4867 1.0039

ALL 71% 28% 28%

Notes: The benchmark model has the form: and the Candidate model:

where

and H is the

forecasting period in months.

TABLE 19 OUT-OF-SAMPLE MEAN SQUARE FORECAST ERRORS ,INDUSTRIAL PRODUCTION

H= 1 12 24

Canada (1996M01-2009M05) 1.2345 1.3765 1.7954 France (1988M01-2008M12) 1.0567 1.0445 1.0896

Germany (1990M07-2009M08) 1.0456 1.0167 1.0001 Italy (1992M02-2008M12) 0.9738* 1.3456 1.0243

Japan (1986M10-2009M05) 0.8542* 0.7577* 0.9567*

United kingdom (1988M01-2009M08) 1.1596 1.0078 1.0036 United states (1986M01-2009M03) 0.8790* 0.8680* 0.9998*

ALL 42% 28% 28%


model:

, where

and H is the forecasting period in months.

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Education

Forecasting Economic Activity using Asset Prices