Utilizing financial market information in forecasting real g

Utilizing ?nancial market information in forecasting real growth,in ?ation and real exchange rate

Juha Junttila a ,Marko Korhonen b,?

a

Department of Economics,University of Oulu,PO Box 4600,FIN-90014,University of Oulu,Finland b Department of Economics,University of Turku,Assistentinkatu 7,FIN-20014Turku,Finland

a r t i c l e i n f o a

b s t r a

c t

Article history:Received 24June 2009Received in revised form 31March 2010Accepted 15June 2010Available online 24July 2010In this paper we build an open economy extension of the Gordon (1962)valuation model that

suggests a simple forecasting system for three macroeconomic variables;the real growth,

in ?ation and real exchange rate.All the forecasting equations in our system utilize current

?nancial market information in the form of pidend yields and short-term interest rate.Our

empirical results indicate that these simple forms of ?nancial market information are relevant

for forecasting the time-varying underlying trends in the macroeconomic data for the U.K.,

Eurozone and Japan,when treating the U.S.as the world market.

?2010Elsevier Inc.All rights reserved.JEL classi ?cation:G15

G28

Keywords:

Stock market

Forecasting

Macroeconomy

Exchange rates

Parities

1.Introduction

The recent downturn in economic activity has again intensi ?ed research on the connections between the ?nancial market and macroeconomic performance.It is clear that even though the aggregate stock market indexes like the S&P 500for the U.S.market and S&P 350for the Euro market have experienced a strong positive long-run (e.g.,5-year)trend for decades,even fairly short-term (e.g.,from 3to 6months)periods of decreasing stock market indexes are always worrying for the ?nancial market practitioners and policy makers,in view of their potential real economy effects.In the current situation,although during the most recent months the stock markets globally have experienced some kind of recovery,the overall,‘?nal ’medium-and long-term macroeconomic effects of the experienced almost 2-year slack in some parts of the global ?nancial system are yet to be seen.

Stock and Watson (2003)lay a good ground for the empirical analysis of the role of ?nancial market prices and/or returns in forecasting macro economy.1The basic idea in almost all the analyses in this area 2is the fact that asset prices are forward-looking,and they form a class International Review of Economics and Finance 20(2011)281–301

?Corresponding author.Tel.:+35823335404;fax:+35823335893.

E-mail address:mjkorho@utu.?(M.Korhonen).

1See also Domian and Louton (1997)and Black,Fraser and Groenewold (2003)for the previous analyses on the relationships between the stock market returns and the real economy.

2Based on their own studies and a huge number of studies by other researchers Stock and Watson (2003)give an extensive review on the possibilities of the sets of different kinds of ?nancial market and other economic indicators that might have a role to play in forecasting especially the values of economic growth and in ?ation.However,in this paper we want to focus primarily on the role of simple stock market information.Another comprehensive review on these issues is provided by Cochrane (2006)in his collection of some of the most essential articles on our theme.Other recent papers focusing especially on real growth and in ?ation forecasting in the U.S.and Euro area are for example Banerjee and Marcellino (2006)and Marcellino,Stock and Watson (2003).See also Heilemann and Stekler (2007)and the other articles in the special issue of the International Journal of Forecasting (2007/2)for the discussion on current directions of research trying to resolve the problems (both theoretical and empirical)in macroeconomic

forecasting.

1059-0560/$–see front matter ?2010Elsevier Inc.All rights reserved.

doi:

10.1016/j.iref.2010.06.006Contents lists available at ScienceDirect

International Review of Economics and Finance

j o ur n a l h o m e p a ge :ww w.e l s ev i e r.c o m/l o c a t e /i re f

282J.Junttila,M.Korhonen/International Review of Economics and Finance20(2011)281–301

of potentially useful predictors of future values of macroeconomic indicators like output growth and in?ation.Stock&Watson also argue that actually the role of asset prices in forecasting future aggregate economic conditions is basically rooted in some fairly simple foundational macroeconomic concepts.Among these are the theory by Irving Fisher stating that the nominal interest rate is comprised of real interest rate plus expected in?ation,and the hypothesis that stock prices re?ect the expected present discounted value of stock market fundamentals,e.g.,future earnings or pidends.3However,the general?nding from the studies on macro forecasting using several types of?nancial data sets is that it seems to be the case that some data forecast some macro variables in some countries for some time periods, but the sets of relevant forecasting?nancial data collections vary a lot between countries and time periods(see Stock and Watson(2003)).

Put it more precisely,for example Guo(2002)?rst replicated the Campbell,Lettau,Malkiel and Xu(2001)result for the U.S data,that in the period of1963:Q1–1997:Q4the excess stock market returns were statistically insigni?cant in predicting GDP growth if stock market variance was also included to the forecasting equation.However,when he extended the data sample to cover the period of1947:Q2–2000:4,he found that the excess returns actually drove out the variance in forecasting output growth.On the other hand,for the case of in?ation forecasting,Goodhart and Hofmann(2000)added the changes in share prices and(nominal)exchange rate to the in?ation forecasting equation,which also included the real GDP growth,broad money growth,short-term nominal interest rate,and changes in the house prices,all these with appropriate numbers of lags. The regression analysis was conducted using semi-annual and quarterly data for eleven countries,and the sample period varied from the largest of1966:Q1–1998:Q3(for the U.S.)to the smallest of1982:Q1–1998:Q3(for Canada).The overall result was that the asset market variables(changes in share prices and nominal exchange rate)were not very useful in out-of-sample forecasting compared to the more traditional‘leading variables’of in?ation,like the change in the amount of broad money.

None of the above mentioned studies attempt to derive a forecasting system based on similar long-run arbitrage conditions that we use.Our theoretical framework is based on a set of simple stock and currency market arbitrage conditions added to the standard equilibrium conditions for the nominal and real interest rates(Fisher parity and Euler equation),so we are not attempting to derive a fully speci?ed general equilibrium model for a dynamic aggregate economy.However,based on these already simple long-run equilibrium conditions we are able to derive a three-equation system for forecasting real growth,in?ation and real exchange rate,that seems to work in out-of-sample forecasting exercises clearly better than e.g.the simple structural time series models for real growth and in?ation forecasting utilized in many of the papers mentioned above.

One of the main contributions of our system model is that it yields also a forecasting equation for the real exchange rate,which is one of the most important macroeconomic variables due to e.g.its role in describing the international competitiveness of real economies.Previously, for example Ehrmann,Fratzscher and Rigobon(2005)analyzed the degree of?nancial transmission between money,bond,equity and currency markets between the United States and the Euro area.They found strong international spillover effects,both within asset classes as well as across?nancial markets.They also reported that the direct transmission of?nancial shocks within asset classes is strengthened through indirect spillovers via other asset prices.These results call for a better understanding of international cross-market?nancial linkages, which so far has been missing in the literature.Phylaktis and Ravazzolo(2005)used a data set of a group of Paci?c Basin countries over1980–1998and analyzed it with cointegration and VAR models.They found an evidence of positive correlation between foreign exchange and stock markets and that the U.S.stock market acted as a conduit through which the foreign exchange and the local stock markets are linked.

For the part of the exchange rate vs.stock market discussion perhaps the most intriguing recent paper for our analysis is the one by Hau and Rey(2004).They introduce three main hypotheses for this relationship,based on the portfolio rebalancing effects presented by Kouri (1982)and Branson and Henderson(1985).According to their?rst hypothesis foreign equity market appreciations relative to the home equity market induce a portfolio rebalancing effect in the form of a home investor's reductions of foreign equity holdings for the purpose of reducing her exchange rate risk exposure.This results in foreign equity out?ows and a home currency appreciation.Their second hypothesis states that if the foreign currency appreciates,it increases the home currency share of assets in the foreign market and the higher overall foreign exchange rate risk exposure for the home residents may induce foreign equity market out?ows,and the foreign out?ows should produce negative foreign equity excess returns,when returns are measured in local currency.The third hypothesis states that the equity-?ow innovations change the demand for currency balances and for equity.Foreign equity market in?ows appreciate the foreign currency relative to home currency and induce excess returns in the foreign equity.All these hypotheses gain support from their empirical analysis using monthly portfolio?ow data for the period of January1990–September2003from France,Germany,Japan, Switzerland,and U.K.,and treating the U.S.as the home country.However,the low-frequency nature of the portfolio?ow data and the inclusion of two price variables(exchange rate and the stock price(s))in the VAR representations of the data appear inconsistent with any particular causal ordering,so the direction of causality between the two markets remains more or less an unsolved question.

This paper contributes to both‘branches’of macro forecasting and of?nancial market connections to the currency market literature. We propose a model which includes many of the insights from the above papers in a somewhat compact way.We start from basic macroeconomic equilibrium conditions mentioned,but not formally introduced/analyzed,also in Stock and Watson(2003).However, we extend their work to an open economy context,and arrive?nally at a prediction model consisting of three simple equations for real economic activity,in?ation and real exchange rate.In the empirical analysis we are especially interested in our model's ability to extract the underlying time-varying long-run trends in the forecasts of the aggregate macro data based on simple,but noisy contemporaneous observations from the stock markets.

The rest of the paper proceeds as follows.In Section2we derive our forecasting model.In Section3we describe the data used in the empirical analysis and in Section4we report the results from our empirical analysis based on some standard time series analytical tools. Finally,Section5gives conclusions and discussion.

3For an early practical implementation of this latter idea,see Mitchell and Burns(1938).

2.Forecasting model based on simple ?nancial market information

The main idea of our model is to be able to extract prevailing macroeconomic expectations purely from ?nancial market data,where some simple long-run equilibrium conditions have a strong role to play.The starting point in the analysis is the traditional Gordon (1962)growth model that gives the fundamental stock market pricing equation as

P S t =D t t ?g e t ?πe t ;e1a Twherethecurrent(time t )valueofequity(stockprice)isdenotedby P t S ,and i t isthenominalinterestrateattime t ,D t isthepidendrealized

attime t ,g t e istheexpectedgrowthrateoftheeconomyattime t ,re ?ectingthegrowthpossibilitiesoffuturerealyieldsonstockinvestments,

and πt e is theexpected in ?ation rate at time t .Put it simply,Eq.(1a)states that in equilibrium the current stock price should be a discounted value of the expected future pidend conditional on the available information at time t .When compared to the more conventional text-book presentations of this fundamental pricing equation,we actually decompose the required rate of return k t in two time-varying parts,namely the expected growth in pidends mimicked by the real growth rate of aggregate economy,g t e ,and the real required rate of return

from alternative investment targets,given by the risk-free real ex ante rate of interest,i t ?πt e .

4Note that because Eq.(1a)actually involves expectations on more than one variable,it basically gives a dynamic relationship

between the current stock price and the explicit,D t ,and implicit,(i.e.the risks in g t e and πt e ),fundamentals which affect it right from the

beginning.At this point we do not want to formalize the model in terms of any certain expectation horizons (like daily,monthly or lower frequencies),but wish to keep the representation as general as possible.Eq.(1a)can equally well be written in terms of the pidend yield,d t =D t /P t S ,that is,

d t =i t ?g

e t ?πe t :e1b TIn the spirit o

f Stock and Watson (2003),we next introduce the ?rst,very familiar macroeconomic equilibrium conditions for the nominal and real interest rate,i.e.,the Fisher (1930)equation

i t =r e t +πe t ;

e2Tand the Euler equation 5

r e t =ρ+λg e t ;e3Tasbehaviorallong-runequilibriumconditions,andnotjustaccountingidentities,tothemodel.Inadditiontopreviouslyde ?nedvariables,r t e is here the real (ex ante)interest rate,ρis the rate of time preference,and λis the inverse of the inter-temporal elasticity of substitution.

Moving towards an open economy extension of this single-country representation involves the use of some additional basic long-run equilibrium 2e09ec1dfc4ffe473368ab61ing a simple two-country setting,we ?rst rewrite the Fisher equation given in Eq.(2)for each country in the form

i t =r e t +E t ΔP t +1

i ?t =r e *t +E t ΔP ?t +1;e4T

where we use the expectations (E )one-period ahead only for notational convenience.Star (*)now indicates the foreign country variables.Naturally,in terms of investor behavior,the expectations horizon is subjective,and basically directly related to the length of the holding period of the investor's asset portfolio or inpidual assets,but in return calculations based on continuous compounding (that is,continuous trading),expected values for the very next period are the interesting ones for the investor in every period.Hence,we do not ?x the investment horizon either.Eq.(4)gives the nominal interest rate in each country as the sum of ex ante real interest rate and expected in ?ation,that is,for example for the home country πt e =E t P t +1?P t =E t ΔP t +1and here P t +1and P t refer now to the log values of the Consumer Price Index (CPI).

The relative purchasing power parity (PPP)introduces a long-run goods market condition in the form of differences in the country-speci ?c in ?ation rates to the model,yielding for the goods markets between the two countries an equilibrium condition

E t ΔS t +1=E t ΔP t +1?E t ΔP ?t +1+E t Δq t +1e5Twhere in addition to previously de ?ned variables E t q t +1is the expected change in the log of real exchange rate at time t ,and E t S t +1is the expected change in the log of nominal exchange rate at time t ,measured in domestic currency value per unit of foreign currency (the U.S.dollar in our analysis).

The ?nancial market equilibrium conditions (1a –4)and the goods market condition (5)are connected through the uncovered interest parity (UIP)condition,indicating that in an overall long-run equilibrium the current difference between the nominal interest rates in the two countries should equal the expected change in the exchange rate,i.e.,

i t ?i ?t =E t ΔS t +1:

e6T4

See Appendix for a more thorough discussion and derivation of Eq.(1a).5Our speci ?cation of Euler equation follows Romer's (2006,p.54–56)presentation for household behavior,assuming that the household consumption growth is most strongly connected to the expectations on future aggregate economic activity (see also the introduction in Cochrane (2006)).283

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Finally,because the main point in our paper is the macroeconomic forecasting ability of the relevant ?nancial market variables,for our forecasting purposes in addition to trying to forecast the future real growth of the economy,we want to view the analysis in terms of expected changes in the price variables (goods prices and the exchange rate),too.Assuming an overall equilibrium in all the markets analyzed here re ?ects now replacing the nominal interest rate difference from UIP to the left-hand side of Eq.(5),which gives us

i t ?i ?t =E t ΔP t +1?E t ΔP ?t +1+E t Δq t +1:

e7T

On the other hand,from the Fisher equations for both countries we get E t ΔP t +1=i t ?r t e and E t ΔP t +1*=i t *?r t e *.

Placing the Fisher equations now in Eq.(7)gives us the equation i t ?i ?t =i t ?r e t ?i ?t ?r e *t +E t Δq t +1that is,

E t Δq t +1=r e t ?r e

*t ;which can be written using the levels of real exchange rate as q t =E t q t +1?r e t ?r e *t :e8T

Hence,the testable equations for our analysis will for the part of the exchange rate variable be based on Eq.(8),stating that in the long-run equilibrium based on the PPP and UIP conditions the expected real exchange rate can be expressed as the sum of current real exchange rate and the real interest rate difference.In other words,the current real exchange rate is expected real exchange rate minus the difference between the domestic and foreign (ex ante)real interest rates.Most of the literature on PPP (already since Dornbusch (1976)),has stated that the real interest rate difference and the current real exchange rate move in opposite directions,indicating a negative correlation between them.However,in many later empirical tests in this framework it has been assumed that expectations about the future real exchange rate are constant (see e.g.Rogoff (1996)).This would indicate that the PPP holds,so in what follows,we stick to this basic assumption.

Hence,assume that the relative PPP as a long-run hypothesis holds,so the expectations on real exchange rate could be denoted to be constant (E t q t +1=q ˉ=α).If we collect all the relevant equations for the equilibrium values of asset prices in our model together,we have for both countries a stock market fundamentals Eq.(i),that is based on collecting the equilibrium conditions stated in Eqs.(1b)and

(3)together and rearranging,and based on Eqs.(2)and (3)a ‘Taylor-rule type ’interest rate Eq.(ii),and ?nally,Eq.(iii)for the real exchange rate in the two-country context,that is based on Eq.(8),and assuming there that the PPP holds as a long-run equilibrium condition.Hence,the total system of equations is comprised of

d t =ρ?1?λeTg

e t ;

ei Ti t =ρ+λg e t +πe t ;and

eii Tq t =α?r e t ?r e *t eiii T

We can see that the country-speci ?c Euler equation is the central building block for the ?rst two equations,and using Euler

equations for both countries (namely,that r t e =ρ+λg t e and r t e *=ρ+λg t e *),Eq.(iii)in the above system comes into form 6q t =α?λg e t ?g e *t ;

e9Tand solving them for the main interesting variables,i.e.the variables concerning expected values ?rst from Eqs.(i)and (ii)yields

g e t =

ρ1?λ?d t

1?λ

πe t =i t ?ρ1?λ+λd t 1?λ:Finally,by using the obtained country-wise real growth equilibrium equations,g e t =ρ1?λ?d t 1?λand g e *t =ρ1?λ?d ?t 1?λ,and hence,noting that the pidend yields in the different stock markets are allowed to deviate from each other,from Eq.(9)we get the third

?nal equation for our system of equations linking the pure ?nancial market information to the development of macro economy.This is an equilibrium condition for the currency market in terms of differences in the pidend yields between foreign and domestic markets ,that is

q t =α?λd ?t ?d t 1?λ :6Here we make use of an assumption on average investors'behavior that in both countries the rate of time preference and the inter-temporal elasticity of substitution are the same and constant,so the differences in the real rates of interest are here supposed to come basically from the differences in the growth rates of real economies.284J.Junttila,M.Korhonen /International Review of Economics and Finance 20(2011)281–301

Now we can see that our ?nal total forecasting system (i.e.,for expected macro values)of equations is comprised of

i Tg e t =ρ?d t

ii Tπe

t =i t ?ρ+λd t iii Tq t =α?λd ?t ?d t 1?λ :e10T

We propose that this simple system of three equations is able to give the predictions on expected real growth and in ?ation and ?nally,also for the contemporaneous values for real exchange rate,assuming that the PPP holds as a valid long-run arbitrage condition.Notice that in the empirical part we analyze this system under the perfect foresight assumption,so we assume that in the long-run equilibrium the expected future values correspond to the actual future values for real growth and in ?ation based on our system.

When compared for example to the paper by Engel and West (2005),which is often quoted as the modern cornerstone of modeling the behavior of exchange rates in view of the present-value models,there are some key differences in our analysis.They also use the present-value approach,but more directly applied to the determination of exchange rate,whereas our present-value equation is connected to the valuation of shares of common stocks.Moreover,Engel and West show analytically that the exchange rate as an asset price follows a random walk process if (at least one of)the fundamentals determining it is/are integrated of order 1,and most importantly,the discount factor for discounting it/them in the valuation equation is almost one.Furthermore,based on these theoretical ideas they are actually able to show empirically that in the data on quarterly bilateral exchange rates from 1974–2001for the dollar versus the currencies of the six other Group of Seven countries there was Granger causality from the exchange rates to the fundamentals.Hence,even though our derivation of the ?nal forecasting system is based on somewhat different main idea,we have to take into account the possibility of this reverse causality,too.Furthermore,we are actually able to derive a somewhat different type of fundamentals equation for the exchange rate,because Engel &West model the behavior of nominal exchange rate based on the traditional monetary model fundamentals,whereas we derive a fundamental equation for the real exchange rate,that uses only the stock market information,i.e.,the relative pidend yield as the key fundamental.

3.Data and descriptive statistics

Our empirical data consist of monthly observations from the U.K.,Japan,Eurozone and the U.S.The sample period varies for each country depending on the availability of the data.For the U.K.and Japan the sample period is 1978:9–2007:1and for Eurozone 1979:1–2007:1,but pided in two sub-samples so that from the period of 1979:1–1990:12we use only the German data,and from the latter period the available aggregate Eurozone data.In our analysis the U.S.represents the foreign country,i.e.the world market,against which all the relevant variables,e.g.,the exchange rates and pidend yield spreads are calculated.Most of the other data are obtained from the IMF's International Financial Statistics (IFS)and OECD Main Economic Indicators databases,but the pidend yield data are from Datastream.7When measured in levels,we convert all data but interest rates and pidend yields to log values,so growth of a certain variable is measured by log difference.We use seasonally adjusted industrial production indexes to describe real economic activity.Nominal interest rates are the 3-month money market rates.

In addition to the German/Eurozone sub-sampling we have also pided the data from the U.K.and Japan in different sub-samples for the purposes of controlling some obvious structural changes in these economies during the analyzed period.For the U.K.we have two sub-samples of approximately same size,i.e.,?rst the period 1978:9–1992:8,and second,a sub-sample starting from 1992:9,when the U.K.stepped out from the European Exchange Rate Mechanism (ERM).Among other things,this decision amounted to a period of high speculation in the foreign exchange market in general,so the U.K.stepping out from the ERM in September 1992was an obvious choice for our sub-sampling point.For the Japanese data,the ?rst sub-sample is the period 1978:9–1998:12covering a somewhat ‘normal ’period of business cycles in the Japanese economy,but in addition,we analyze also the whole sample period (1978:9–2007:1)that covers the liquidity trap period approximately after 1999,too.

For preliminary graphical inspection we provide the ?gures on pair-wise comparisons of the macro and ?nancial market variables in our ?nal system of Eq.(10).Due to the space limitations we give only the ?gures for the U.K.data in Fig.1as an example,but ?gures for all the other countries are naturally available upon request.

From Fig.1we see that at ?rst glance the role of ‘raw ’?nancial market return data either in terms of the domestic pidend yield and nominal interest rate (and spreads in pidend yields)in forecasting the macro variables is not easy to extract,due to the noisy nature of the ?nancial data.However,applying the Hodrick and Prescott (1997)?lter to the raw data revealed clearly that already based on purely visual inspection our system of equations might have a role to play in macro forecasting.It would seem that the stock market information has the strongest correlation,at least in terms of the contemporaneous values,with in ?ation and real exchange rate,7In Datastream the pidend yield is calculated as d t =100∑n N =1D t N t ∑n N =1P S t N t 0

B B B @1

C C C A ,where d t is the aggregate pidend yield on day t (and we use the values for the last trading day in each month),

D t is the pidend per share on day t ,N t is the number of shares in issue on day t ,P t S is the unadjusted share price on day t ,and n is the number of constituents in the index.The useful data on pidend yields for our purposes are calculated for the shares quoted only in the domestic market of each of the analyzed countries,and these series are available from the Datastream.285

J.Junttila,M.Korhonen /International Review of Economics and Finance 20(2011)281–301

286J.Junttila,M.Korhonen/International Review of Economics and Finance20(2011)281–301

Fig.1.Pair-wise comparisons of the time series of the contemporaneous values of the macro variables and the?nancial market variables based on the system of Eq.(10)in the text.Data for the U.K.All data are in%-values except the real exchange rate which is in log levels;DIPUK=real growth(annualized change in the log of industrial production index),DIVUK=pidend yield,DPUK=in?ation(annualized change in the log of Consumer Price Index),I3UK=the3-month nominal interest rate,RERUK=real exchange rate,and DDIVUK=the pidend yield spread(foreign(U.S.)minus domestic(U.K)yield).Left panels are for the raw time series data and right panels for the time-varying trends extracted from the raw data using a Hodrick and Prescott(1997)?lter with a lambda value1600.

plotted in the two middle panels (for in ?ation)and in the last panel (for real exchange rate).In addition to the U.K.data this preliminary conclusion emerged very strongly also from the visual inspection of the data from Germany,Eurozone and Japan,too.

From our descriptive statistics in Table 1we are able to see that the time series on the main interesting variables for our analysis,i.e.,the macro variables (growth in the real economic activity,measured by changes in the industrial production,in ?ation and the real exchange rate)are quite volatile.The raw (i.e.un ?ltered )data on pidend yields and pidend yield spreads are very persistent,and actually,we cannot reject the null of unit roots in the data generating processes (DGP)of these ?nancial market variables.8Furthermore,the coef ?cients for the ?rst order serial correlation in Table 1would seem to imply that some of the macro variables are stationary already in levels,whereas the ?nancial market variables (including the short-term nominal interest rate)clearly are not.Hence,for example for the decision on whether to use the variables of our model in levels or in differences in the empirical analysis is not clear-cut at all based on the preliminary data analysis.

Encouraged by these preliminary visual ?ndings and descriptive statistics we next proceed to a more fundamental empirical analysis,and especially to the analysis of the forecasting power of ?nancial market information.We start this from pair-wise Granger causality tests conducted equation by equation for the variables in the three inpidual equations in system (10).4.Forecasting power of ?nancial market

Obviously,because the unit root tests implied that some of the variables in our system of Eq.(10)might be non-stationary,but together theymightformsomekindofstationarylong-runequilibriumrelationships(thatevenmightbe ‘structural ’inviewofourproposedlong-run equilibrium relationships),we had to take into account the possibility of cointegration,and hence,error correction representations of the data,too.Resultsforthispartarenotreportedhere,butthemainconclusionfromthatanalysisisthatespeciallyforforecastingexercisesitwas not possible to ?nd any kind of theoretically and empirically relevant (structural and stable)vector error correction representation for the whole systemofEq.(10).Hence,we proceedtowardsother typesofdynamic representationsofour forecasting systemandthe natural next step in our empirical analysis were the Granger causality tests for the variables in each of the three equations in the system separately.

Resultsfromthe Grangercausality testsstrengthen theprevious ?ndingthatthe ?nancial marketvariablesin theinpidual equationsof system (10)are stronglyconnectedtothecorrespondingmacrovariables,andfurthermore,thatthe relationshipishighly dynamic,because causality seems simultaneous in most cases.This implies strong feedback relations between the ?nancial market and macro data.Put it in otherwords,atthe5%risklevelonlyin16casesoutofthetotalof70pair-wiseteststheF-statisticsindicatethattherewouldnotseemtobeany causal connections between the analyzed ?nancial and macro variables.More precisely,especially for in ?ation and real exchange rate data,the feedback relation between the stock market and macro variables seems to have been valid for the analyzed sample periods.

For example in Japan during the liquidity trap period,i.e.,since the end of 1990s,the stock market information captured by the spread between domestic and foreign pidend yields seems to have been strongly connected to the behavior of real exchange rate and vice versa.Also in ?ation seems to have been connected to stock market information and nominal interest rate,despite the

8

Results from the unit root tests based on the augmented Dickey –Fuller and KPSS-tests (with constant,but no trend)are available from the authors upon request.The main interesting results were that in addition to the real exchange rate series,all the pidend yield series and the pidend yield spreads (i.e.,the differences between foreign and domestic pidend yields)were non-stationary for every country and all sample periods.Results for the macro variables were more mixed,but differenced values of all the analyzed variables seemed to behave like stationary variables for every sample and country.

Table 1

Descriptive statistics.Variable

U.K.(sample

1978:9–1992:8)

U.K.(sample 1992:9–2007:1)Germany (sample 1979:1–1990:12)Eurozone (sample

1991:1–2007:1)

Japan (sample 1978:9–1998:12)Japan (sample

1978:9–2007:1)

U.S.

(sample 1978:9–2007:1)Mean

ρ1Mean ρ1Mean ρ1Mean ρ1Mean ρ1Mean ρ1Mean ρ1

g t .91

(17.98)?.29.80(9.69)?.30 4.14(16.18)?.42 1.45(10.02)?.35 2.62(16.57)?.35 1.98(16.41)?.33 2.43(7.53)?.24πt 7.22(7.83).33 2.58(4.37).05.67(.79).49 2.04(3.91)?.03 1.95(6.40).09 1.27(5.78).12 3.93(4.13).57q t ?.42(.16).98?.42(.14).98.75(.20).99?.13(.12).98 5.05(.32).99 4.97(.31).99––d t 4.94(.76).93 3.32(.55).97 2.81(.79).98 2.45(.52).97 1.03(.47).99.99(.41).99 3.19(1.45).99i t 11.46(2.16).94 5.22(1.02).98 6.48(2.33).99 4.78(2.33).99 4.92(2.87).98 3.57(3.24).997.13(3.71).98d t *?d t

?.62(.70)

.94

?1.53(.30)

.93

1.66(.53)

.89

?.54(.49)

.97

2.62(1.03)

.99

2.03(1.27)

.99

–

–

Variables in the table are as follows:g t is the growth rate of real economy,measured by the log difference of the industrial production index (seasonally adjusted),πt is the annualized in ?ation rate,based on the Consumer Price Index (CPI),q t =S t +P t *?P t is the (log)of real exchange rate,based on adding the (log of)nominal spot exchange rate S t (end-of-period domestic currency price/U.S.dollar)to the difference in the foreign (P*)and domestic (P )log CPI-price levels (hence,a higher

value implies depreciation of the nominal value of domestic currency),d t and d t

?are the domestic and foreign (i.e.,the U.S.yield in the spread calculation)pidend yields,respectively,and ?nally,i t is the nominal short-tem (3-month)interest rate.The numbers in parentheses under the mean values are standard deviations,and ρ1denotes the ?rst order autocorrelation coef ?cient.All the growth measures are given as annualized percentage values.

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observed very low levels of both the nominal interest rate and in ?ation especially at the end of our data period.On the other hand,stock market information would not seem to have any dynamic connections to the real economic growth in Japan or the U.K.(at least after the U.K.stepping out from the ERM),but in the Euro area,and also in the data for the German market,real growth would seem to have had a connection to the stock market performance.In addition,there have clearly emerged strong causal relations from the stock market to in ?ation in every country and for every sample period.

The Granger causality test results form a strong basis for our next step especially for the part of the currency market,because it seems to be the case that the pidend yield spread Granger causes the real exchange rate at least for the Japanese data,but also for the data from the U.K.before the ERM step out,and for the whole U.K.data sample,too.Also in the German data sample the spread would seem to have causal connection to the real exchange rate,but not in the Eurozone data.However,the strong dynamic connection between the stock market(s)and currency market shows up in the causality from the real exchange rate to the pidend yield spread in every country and every sample period (Table 2).

Next we move towards the main part of our empirical analysis,which is the out-of-sample forecasting performance of our simple model.We will report all the rest of our results based on the following type of forecasting exercise.We utilize a

Table 2

Bivariate Granger causality test results.Null hypothesis U.K.(sample 1978:9–2007:1)U.K.(sample 1978:9–1992:8)U.K.(sample 1992:9–2007:1)Germany (sample 1979:1–1990:12)Eurozone (sample 1991:1–2007:1)Japan (sample 1978:9–2007:1)Japan (sample 1978:9–1998:12)d t fails to cause g t 1.57(.10) 1.37(.18).92(.53) 1.72(.08) 1.09(.37).89(.55) 1.05(.41)g t fails to cause d t .64(.81) 3.12(b .001).66(.79) 3.74(b .001) 5.84(b .001).18(.99).14(.99)d t fails to cause πt 6.83(b .001) 2.26(.01) 2.50(.004) 4.44(b .001) 2.22(.01) 2.18(.01) 1.90(.04)πt fails to cause d t 49.02(b .001)19.08(b .001).20(.99)17.96(b .001) 4.11(b .001)12.71(b .001)12.50(b .001)i t fails to cause πt 9.15(b .001) 3.28(b .001) 2.23(.01) 3.55(b .001) 1.16(.31) 6.70(b .001) 4.44(b .001)πt fails to cause i t 66.49(b .001)23.50(b .001) 3.66(b .001)34.26(b .001)21.48(b .001)71.59(b .001)30.88(b .001)i t fails to cause d t 48.54(b .001) 6.90(b .001) 1.87(.04)11.68(b .001) 2.43(.01)8.36(b .001)7.80(b .001)d t fails to cause i t

57.52(b .001)7.34(b .001).81(.64)9.28(b .001) 2.91(.001) 6.62(b .001)7.38(b .001)d t *?d t fails to cause q t 7.94(b .001) 6.15(b .001) 1.54(.12)14.65(b .001) 1.10(.36)45.33(b .001)33.31(b .001)q t fails to cause d t *?d t

7.01

(b .001)

4.92

(b .001)

4.71(b .001)

10.08

(b .001)

10.84

(b .001)

48.67(b .001)

28.88

(b .001)

The reported Granger causality F-test statistics are computed based on 12lags.The numbers in parentheses are p -values for the null of no causality.See the notations for variables below Table 1.

Table 3

Out-of-sample forecast error statistics for the U.K.;Hodrick –Prescott ?ltered forecasts.

g;real growth π;in ?ation rate q:real exchange rate RMSFE of AR-X against AR (%)

D –M for AR-X vs.AR

RMSFE of AR-X against VAR (%)

D –M for AR-X vs.VAR

RMSFE of AR-X against AR (%)D –M for AR-X vs.AR

RMSFE of AR-X against VAR (%)D-M for AR-X vs.VAR

RMFSE of AR-X against AR (%)D –M for AR-X vs.AR

RMSFE of AR-X against VAR (%)D –M for AR-X vs.VAR

Period 1985:8–2007:1forecast horizon 159.40?5.46???55.39?6.69???

49.73?5.19???41.55?5.59???102.99.46106.15.87351.08?6.45???69.86?5.27???49.50?5.00???50.34?4.23???132.42?3.75BBB 143.04?4.64BBB 670.99?4.47???82.16?3.31???55.40?4.28???55.24?3.31???91.14?1.35?93.91?.881273.83?4.66???81.77?3.29???95.53?1.2480.89?3.29???78.21?2.85???76.79?2.89???24100.86?.1091.58?1.46?

136.70

?2.16BBB

120.69

?1.46B

207.47

?4.15BBB 179.93

?3.33BBB

Period 1985:8–1992:8forecast horizon 147.74?6.01???35.51?10.55???71.82?2.26??54.99?3.46???87.88?2.90???89.23?2.76???350.79?6.03???55.91?7.92???74.35?2.03??68.03?2.14??90.30?.5889.07?.69665.52?5.44???76.00?4.95???83.28?1.2674.43?1.55?72.01?2.20??69.04?2.44???1262.55?8.60???81.71?4.91???122.32?1.16115.56?.6765.50?2.84???62.30?3.07???24

81.16?2.26??72.57

?8.89???

175.02

?3.14BBB

154.86

?2.48BBB

171.22

?2.25BB

141.87

?1.48B

Period 1992:9–2007:1forecast horizon 174.65?2.14??104.31?.42

17.11?5.37???16.52?4.83???140.00?6.91BBB 158.33?9.46BBB 353.15?3.48???108.25?.6413.76?5.15???17.42?4.39???150.00?5.67BBB 175.22?7.78BBB 678.25?1.75??90.26?.9116.44?5.06???20.11?4.40???105.36?.93115.45?2.64BBB 1287.31?1.0481.87?1.61?27.17?4.62???27.27?4.39???96.44?.6599.39?.1124145.07 2.59BB 136.42

?2.18BB 67.56

?2.10??

59.42

?2.66??

285.36

?6.50BBB

295.61

?6.64BBB

We report the relative mean squared forecast error statistics against the H –P-?ltered future values (in %)in the ?rst and third columns for each macro variable;values below 100indicate that the AR-X model containing ?nancial variables is better than the benchmark model (either an AR(2)-representation for the variable in question,or a VAR(2)-system for the vector of all the three macro variables).D –M refers to the Diebold and Mariano (1995)-test statistics for the comparison of the AR-X model to the benchmark models;***,**and *refer to the cases where the AR-X is better than the benchmark at 1,5or 10%signi ?cance levels,respectively,whereas BBB,BB,or B to the cases where the corresponding benchmark model is better,respectively.

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rolling regression approach with a 5-year moving estimation window in our forecasting analysis.9Due to the observed possibility of unit roots in the DGP of some of the variables each inpidual forecasting equation in system (10)is estimated based on an AR-X-type (i.e.,an autoregressive model with additional explanatory variables)dynamic representation with 2lags of all the variables in system (10).10In other words,our out-of-sample forecasts are based on regression equations of the following form:

i Tg t =αg 0+αg 1g t ?1+αg 2g t ?2+βg 0d t +βg 1d t ?1+βg 2d t ?2+εg

t

ii Tπt =απ0+απ1πt ?1+απ2πt ?2+βπ0d t +βπ1d t ?1+βπ2d t ?2+δπ0i t +δπ1i t ?1+δπ2i t ?2+επt iii T

q t =αq 0+αq 1q t ?1+αq 2q t ?2+γq 0d ?t ?d t eT+γq 1d ?t ?1?d t ?1eT+γq 2d ?t ?2?d t ?2eT+εq t ;

e11T

Table 4

Out-of-sample forecast error statistics for Germany and the Euro zone;Hodrick –Prescott ?ltered forecasts.

g;real growth π;in ?ation rate q:real exchange rate RMSFE of AR-X

against AR (%)

D –M for AR-X vs.AR

RMSFE of AR-X against VAR (%)

D –M for AR-X vs.VAR

RMSFE of AR-X against AR (%)D –M for AR-X vs.AR

RMSFE of AR-X against VAR (%)D –M for AR-X vs.VAR

RMSFE of AR-X against AR (%)D –M for AR-X vs.AR

RMSFE of AR-X against VAR (%)D –M for AR-X vs.VAR

Germany 1985:8–1990:12forecast horizon 1107.46?.4446.06?4.32???

38.55?4.26???38.00?3.88???97.64?.28103.50?.343169.52?3.82BBB 99.60?.0317.99?5.70???17.86?5.03???152.23?3.57BBB 182.69?3.67BBB 6161.98?2.72BBB 79.19

?1.2816.27?5.93???17.08?6.73???101.32?.13103.99?.3012228.26?3.62BBB

93.57?.4319.32?5.47???22.13?9.69???94.55?.7596.63?.3824301.03?2.82BBB 126.33?1.0822.72

?5.01???40.75

?14.13???

175.22

?4.67BBB 288.65

?6.44BBB

Euro zone 1998:1–2007:11forecast horizon 1114.30?.9868.57?2.86???180.95?3.91BBB 107.61?.57282.20?8.81BBB 141.16?2.50BBB 3119.78?1.1776.22?1.78??130.76?1.51BB 76.47?1.77BB 270.76?7.71BBB 261.29?5.96BBB 6162.57?2.82BBB 95.38?.64142.04?1.74BB 91.65?.55132.23?2.72BBB 143.07?3.30BBB 12221.09?4.21BBB 114.62?.62148.98?1.86BB 104.39?.24148.79?4.09BBB 157.51?4.75BBB 24258.58?6.30BBB 118.38?.86

99.47

?.03

91.15?.44616.47

?7.11BBB

622.07

?7.25BBB

For the notations see Table 3.

Table 5

Out-of-sample forecast error statistics for Japan;Hodrick –Prescott ?ltered forecasts.

g;real growth π;in ?ation rate q:real exchange rate RMSFE of AR-X against AR (%)

D –M for AR-X vs.AR

RMSFE of AR-X against VAR (%)

D –M for AR-X vs.VAR

RMSFE of AR-X against AR (%)D –M for AR-X vs.AR

RMSFE of AR-X against VAR (%)D –M for AR-X vs.VAR

RMSFE of AR-X against AR (%)D –M for AR-X vs.AR

RMSFE of AR-X against VAR (%)D –M for AR-X vs.VAR

Period 1985:8–2007:1forecast horizon 180.31?1.80??70.87?3.19???

43.17?6.80???61.72?4.37???200.00?5.47BBB 195.65?5.26BBB 373.56?2.52???81.98?2.00??61.48?4.38???66.37?4.05’???229.75?5.18BBB 238.20?5.44BBB 6102.85?.2688.06?1.33?85.16?1.1886.84?1.13124.78?1.44B 126.20?1.51B 12135.03?2.83BBB 103.28

?.3385.88?1.34?67.56?4.14???80.10?2.26??81.63?2.09??24223.46?7.20BBB 150.94?3.97BBB 102.09

?.2155.20

?6.05???

54.81

?3.01???62.02

?2.57???

Period 1985:8–1998:12forecast horizon

166.24?2.96???59.37?4.24???27.17?9.07???46.31?5.47???92.00?.3095.92?.20342.40?4.68???51.08?4.26???37.74?6.55???45.80?5.37???129.37?1.93BB 136.79?2.48BB 672.50?2.17??62.73?3.49???39.71?6.47???44.28?6.17???51.28?6.88???52.19?6.76???12102.48?.1574.76

?2.19??60.00?3.61???48.65?5.97???48.66?9.22???49.69?9.11???24178.67?3.81BBB 108.50?.61

86.75

?1.18

45.66

?7.07???

22.87?5.56???26.25?5.12???

For the notations see Table 3.

9

The ?ve-year moving window was utilized in all the out-of-sample forecasting exercises for the inpidual equations in system (10)and also for the

comparison benchmark models based on the fact that many ?nancial market practitioners use the previous 60months data in their forecasting and performance analyses (see also Grif ?n (2002),for example).The rolling ?ve-year estimation procedure uses the ?rst 60observations as the starting sample,and the ?rst 1-,3-,6-,12-,and 24-month out-of-sample forecasts are formed based on these parameter estimates.Then,one observation is added to the end of sample for each variable,whereas the ?rst observation from the beginning is dropped out,keeping the sample size the same 60as before.This procedure is repeated in a loop until all the observations are utilized,so for example the last longest horizon,i.e.,the 24-month out-of-sample forecasts (for January 2007in the cases of whole sample data)on the macro variables are always based on actual data utilizing the January 2005observations as the last data point for the estimation of parameter estimates.10

Two lags were selected to be optimal based on the Schwarz information criteria obtained from testing for various lag structures also in the VAR representations of the macro variables'vector (g t ,πt ,q t )and the ?nding of unit roots in some of the analyzed macro time series in the whole data set.

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where in addition to the contemporaneous and one-and two-period lagged values of all the variables in system (10)(notations given in Section 2)parameters αi j ,βi j ,δi j and γi j are the regression coef ?cients (i=0,1,2,and j =g ,πor q )and εt j denote the error terms in the inpidual regression equations for each of the macro variables.The parameter estimates and out-of-sample forecasts were obtained from a 5-year rolling regression approach and the forecasting scheme described above for each inpidual equation separately in our system of Eq.(11)

.}

Fig.2.Pair-wise comparisons of the time-varying trends in the out-of-sample forecasts of macroeconomy.Results for the U.K.at 3-and 24-month forecast horizons.In the left-hand are the forecasts from AR(2)and VAR(2)benchmark models with the actual future values,and in the right-hand are the forecasts from AR-X-type estimation for the inpidual equations of system (11)given in the text and the actual future values.For comparison the left-and right-hand panels use the same scale pair-wise.In both panels the Hodrick –Prescott ?ltered forecasts (with a lambda value 1600)and actual values are plotted.HPARDIPF#UK,HPARDPF#UK,and HPARRERF#UK refer to the forecast values for real growth,in ?ation and real exchange rate,respectively,from the AR(2)-model;HPVARDIPF#UK,HPVARDPF#UK,and HPVARRERF#UK to the corresponding forecast values from the VAR(2)-model.HPARXDIPF#UK,HPARXDPF#UK,and HPARXRERF#UK are the corresponding forecast values from the AR-X-type model based on system (11)in the text,and #refers to the forecast horizon.HPDIPUK,HPDPUK and HPRERUK are the (?ltered)actual future values of real growth,in ?ation and real exchange rate.

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Analogously to Stock and Watson (2001)and many other similar types of ‘forecasting horse races ’,when analyzing the system of Eq.(11)the most natural benchmark models for the comparison of our forecasts are the AR and VAR models.An AR-model for each inpidual macro variable is obtained basically by restricting the coef ?cient values on the ‘additional ’?nancial market information,i.e.,on d t and the lags of it in the ?rst equation of (11),both on d t ,i t and their lags in the second,and on (d t *?d t )and the lags of it in the third equation to zero in each equation 2e09ec1dfc4ffe473368ab61ing these zero restrictions for the whole system we obtain the VAR representation for the system of analyzed macro variables.Both AR and VAR models (and naturally again with lag length 2)were used as the benchmark models for the calculation of the forecast performance statistics in Tables 3–5

.Fig.2(continued ).

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Before presenting forecast statistics we take a look at the ?gures on forecasts,and again,due to the space limitations give only some illustrative examples.Now we give the ?gures from every country (treating always the U.S.as the world market)and for every macro variable,but only for two forecast horizons,i.e.for the 3-month horizon representing the short-term,and the 24-month horizon for the long-term forecasts.Results for all the other forecast horizons are again naturally available upon request.For comparison we plot the ?gures of forecasts based on our benchmark models,that is,the AR(2)-and VAR(2)-representations and the actual future values of the macro variables in the left-hand panels,whereas the forecasts based on the AR-X-type estimation of the inpidual equations in system (11)compared to actual future values are in the right-hand

panels.Fig.3.Pair-wise comparisons of the time-varying trends in the out-of-sample forecasts of macroeconomy.Results for Germany at 3-and 24-month forecast horizons.In the left-hand panel the forecasts from AR(2)and VAR(2)benchmark models together with the actual future values are plotted,and in the right-hand panel are the forecasts from AR-X-type estimation for the inpidual equations of system (11)given in the text and the actual future values.For comparison the left-and right-hand panels use the same scale pair-wise.In both panels the Hodrick –Prescott ?ltered forecasts (with a lambda value 1600)and actual values are plotted.HPARDIPF#GER,HPARDPF#GER,and HPARRERF#GER refer to the forecast values for real growth,in ?ation and real exchange rate,respectively,from the AR(2)-model;HPVARDIPF#GER,HPVARDPF#GER,and HPVARRERF#GER to the corresponding forecast values from the VAR(2)-model.HPARXDIPF#GER,HPARXDPF#GER,and HPARXRERF#GER are the corresponding forecast values from the AR-X-type model based on system (11)in the text,and #refers to the forecast horizon.HPDIPGER,HPDPGER and HPRERGER are the (?ltered)actual future values of real growth,in ?ation and real exchange rate.

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Because the main interest in our forecasting exercise is in attempting to extract the potential of our model in forecasting the underlying,time-varying trends in the future values of the macroeconomy,in Figs.2–5we give the corresponding graphs for the Hodrick –Prescott ?ltered forecasts and future values of the macro variables.11When viewing the ?gures for the ‘raw ’(i.e.,un ?ltered 12)data it was obvious that due to the observed strong noise also in the actual forecast values based on our model

containing

Fig.3(continued ).

11In other words,the H –P ?ltering procedure was applied after obtaining the out-of sample forecast values based on the system of Eq.(11),so the actual estimation and forecasting procedure itself utilizes always the ‘raw ’data,and the obtained series of forecasts are ?ltered and compared to the actual (?ltered)future values of the macro variables after this.

12Due to the space limitations none of the ?gures and tables for the un ?ltered data are reported here but they are all available from the authors upon request.293

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?nancial data the ?ltered time series of forecasts reported here in Figs.2–5enable a more fundamental comparison of the different forecasting models in terms of their ability to extract the underlying long-run trends in the future values of the macro data.

A common and strikingly strong overall message from all Figs.2–5is that the ?nancial market information based on system

(10)is highly relevant for forecasting real growth and in ?ation especially for the shorter-term 2e09ec1dfc4ffe473368ab61pared to the German and Eurozone data,for the more volatile U.K.and Japanese data on industrial production and in ?ation the additional information introduced in the form of these ?nancial market variables seems to be very important in forecasting the time-varying trends in

the Fig.4.Pair-wise comparisons of the time-varying trends in the out-of-sample forecasts of macroeconomy.Results for the Eurozone at 3-and 24-month forecast horizons.In the left-hand panel the forecasts from AR(2)and VAR(2)benchmark models together with the actual future values are plotted,and in the right-hand panel are the forecasts from AR-X-type estimation for the inpidual equations of system (11)given in the text and the actual future values.For comparison the left-and right-hand panels use the same scale pair-wise.In both panels the Hodrick –Prescott ?ltered forecasts (with a lambda value 1600)and actual values are plotted.HPARDIPF#EURO,HPARDPF#EURO,and HPARRERF#EURO refer to the forecast values for real growth,in ?ation and real exchange rate,respectively,from the AR(2)-model;HPVARDIPF#EURO,HPVARDPF#EURO,and HPVARRERF#EURO to the corresponding forecast values from the VAR(2)-model.HPARXDIPF#EURO,HPARXDPF#EURO,and HPARXRERF#EURO are the corresponding forecast values from the AR-X-type model based on system (11)in the text,and #refers to the forecast horizon.HPDIPEURO HPDPEURO and HPREREURO are the (?ltered)actual future values of real growth,in ?ation and real exchange rate.

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macro economy.Also in the longest,i.e.,2-year forecast horizon the ?nancial market information clearly helps in forecasting especially the future in ?ation.13When compared to the good forecasting power for real growth and in ?ation during the era of German data,the time-varying trends in the future values of both the Eurozone industrial production and in ?ation are perhaps not so well revealed in the short-and long-term horizons.In Japan the added ?nancial information clearly improves the forecasting power of simple AR and VAR models especially for the sample prior to the time period of liquidity trap,but the ?nancial information seems to have a strong role to play in forecasting time-varying trends of future industrial production also in the whole sample data for Japan both at short and long

horizons.

Fig.4(continued ).

13In view of the basic idea in the Taylor-rule for the role of short-term nominal interest rate this is not surprising,but based on the statistical signi ?cance of the time-varying regression coef ?cients on the contemporaneous and lagged values of domestic pidend yield the stock market information was also relevant in the in ?ation equations in many cases.Naturally,thestatisticalsigni ?canceofaninpidualregressorincreasesthemoreparsimoniousisthemodel,sostatisticallythemostsigni ?cantparameterestimateswere obtainedfortheAR-representations,butinouranalysiswewanttostressmorethepossibleroleofadditional,?nancialmarketinformationinout-of-sampleforecastingterms,so the statistical signi ?cance of each inpidual regressor was not so high on the agenda in this paper right from the beginning.295

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For Japanese data also the pidend yield spread against the U.S.market would seem to be a highly relevant information variable in forecasting the time-varying trends in the future values of the real exchange rate.Based on visual inspection the equation for forecasting future real exchange rate would not seem to be clearly better in the case of added ?nancial market information in the form of pidend yield spreads for the analyzed European countries.

Our ?nal conclusions on forecast accuracy are based on out-of-sample forecast error statistics given in Tables 3–5.We report the relative mean squared forecast error (RMSFE)values from our model compared to both the benchmark

models Fig.5.Pair-wise comparisons of the time-varying trends in the out-of-sample forecasts of macroeconomy.Results for Japan at 3-and 24-month forecast horizons.In the left-hand panel the forecasts from AR(2)and VAR(2)benchmark models together with the actual future values are plotted,and in the right-hand panel are the forecasts from AR-X-type estimation for the inpidual equations of system (11)given in the text and the actual future values.For comparison the left-and right-hand panels use the same scale pair-wise.In both panels the Hodrick –Prescott ?ltered forecasts (with a lambda value 1600)and actual values are plotted.HPARDIPF#JAP,HPARDPF#JAP,and HPARRERF#JAP refer to the forecast values for real growth,in ?ation and real exchange rate,respectively,from the AR(2)-model;HPVARDIPF#JAP,HPVARDPF#JAP,and HPVARRERF#JAP to the corresponding forecast values from the VAR(2)-model.HPARXDIPF#JAP,HPARXDPF#JAP,and HPARXRERF#JAP are the corresponding forecast values from the AR-X-type model based on system (11)in the text,and #refers to the forecast horizon.HPDIPJAP,HPDPJAP and HPRERJAP are the (?ltered)actual future values of real growth,in ?ation and real exchange rate,and #refers to the forecast horizon.

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together with the Diebold and Mariano (1995)test statistics 14for each country and all the analyzed out-of-sample forecast horizons of 1,3,6,12,and 24months.Again,to be able to analyze the models'real ability to extract the underlying

time-varying

Fig.5(continued ).

14The Diebold –Mariano (D –M)test is used to compare the accuracy of two forecasts.The D –M tests whether the predictions of a given model,A ,are signi ?cantly more accurate,in terms of loss function g (?),than those of the competing model,B .The test aims to test the null hypothesis of equality of expected forecast accuracy against the alternative of different forecasting ability across models.The null hypothesis of the test can be written as d t ;h =E g e A t ;h ?g e B t ;h

h i =0,where e t ,h refers to the forecasting error of model i =(A or B )when performing h -steps ahead forecasts.The D –M-test uses the autocorrelation corrected sample mean of d t ,h in order to test the above null hypothesis.If n observations and forecasts are available,the test statistic is S =V ∧P d

àá???O P d ,where V ∧P d =1n γ∧0+2∑h ?1k =1γ∧k "#and γ∧k =1n ∑n t =k +1d t ?P d d t ?k ?P d .Under the null hypothesis of equal forecast accuracy,S is asymptotically normally distributed.297

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trends we discuss and report here only the results for the?ltered time series,and the results for the un?ltered data are available upon request.

The forecast comparison statistics enforce our preliminary conclusions from visual analysis.The out-of-sample forecasts computed for real growth and in?ation detect well the time-varying underlying trends in both the data for the U.K.(in Table3)and Japan(in Table5),and the common factor in this?nding seems to be the ability of our system to detect especially the changes in time-varying underlying trends of macro economy.When compared to Germany and the Eurozone,both the U.K.and Japan experienced perhaps even stronger turbulence in the?nancial markets and macro economy during the analyzed time periods,15and for these turbulent times the role of?nancial market information seems to have been important when forecasting future macro economy.

Based on the results reported in Table3,prior to the step out from the ERM the AR-X-model containing the stock market information forecasts the time-varying trends in real growth extremely well for all forecast horizons compared to both the AR and VAR benchmarks,and for the short-term(1to6-month)horizons it is better than at least the AR benchmark also in the most recent data.On the other hand,especially for the data after the U.K.abandoned the ERM the?nancial market data on nominal interest rate and pidend yield have a strong role to play in forecasting in?ation rate at all horizons,even though the shorter horizon forecasts from the AR-X model were more accurate also in the data prior to the ERM step out.Furthermore,for this earlier sample period the pidend yield spread seems to have had a strong role in forecasting the future values of real exchange rate in the U.K.for the money market horizons,but this stock market information would not seem to be so relevant in the most recent data for the U.K.

The‘worst’results in terms of the forecast accuracy are obtained for the German and Eurozone data.From Table4we see that our AR-X-type forecasting model is able to‘beat’the benchmark models only for forecasting in?ation in the German data. However,when noting that this period of data in the German era was characterized by very low and stable in?ation rate,but somewhat high and volatile short-term nominal interest rate,16one might be tempted to draw a conclusion that in the in?ation forecast equation the role of pidend yield is actually dominated by the role of nominal interest rate in terms of aggressive(and effective)monetary policy directed towards controlling expectations of future in?ation.Especially for the Eurozone data our forecasting system containing?nancial market information would seem to be somewhat irrelevant when compared to the benchmark AR and VAR representations.However,these?ndings are perhaps not surprising already based on viewing the?gures on actual and Hodrick–Prescott?ltered values of the macro variables both for the German and Eurozone eras(see Figs.3and4).As we see,the macro time series are by far the smoothest for these two eras so the number of possible change points in the underlying time-varying trends is also the smallest in these cases.Hence,already based on visual a priori reasoning the highly noisy?nancial market information might not have any role in forecasting these smoothly behaving macro time series.This is also the main result obtained from the empirical out-of-sample analysis for the German and Eurozone data.

For the Japanese data the results speak even more uniformly for the inclusion of the?nancial market data to the macro forecasting systems than for the U.K.data.Especially prior to the liquidity trap period the AR-X-model containing the stock market information forecasts the time-varying trends both in real growth and in?ation very well for all forecast horizons compared to both the AR and VAR benchmarks.For the part of real exchange rate we obtain the strongest results of all the analyzed countries in Japanese data.For all except the3-month horizon the pidend yield spread against the U.S market seems to be able to forecast the time-varying trends in future values of real exchange rate,and more speci?cally,according to the RMSFE and D–M statistics the longest term,i.e.2years ahead,forecasts seem even to be the most accurate ones.

To put it all together,the main novel?nding in our paper seems to be the fact that the stock market pidend yield is a relevant information variable for forecasting the future values of macro economy,at least for real economic growth and in?ation,especially during turbulent time periods.For the pidend yield's role as an information variable this is something new compared to the previous?ndings that speak for the ability of the pidend yield(or the pidend–-price ratio)to mimic the expected(or unexpected) stock returns,17but not actually the future values of macro economy.The?nancial markets'ability to forecast the time-varying underlying trends even in the longer horizon(like2years ahead)macro values is obvious using the derived system of equations based on some simple long-run equilibrium conditions both for the macro economy and?nancial markets,especially for periods of frequent changes in the time-varying trends of macro economy.

5.Conclusions

In this paper we have derived a system of forecasting equations rooted in fundamental long-run equilibrium relationships both for the macro economy and?nancial markets.The?nal form for our system of equations consists of a forecasting equation for real growth,in?ation,and the real exchange rate.The main explanatory variables are the domestic pidend yield for real growth,the nominal interest rate and the domestic pidend yield for in?ation,and the pidend yield spread against the world market for the real exchange rate.

The empirical results from the U.K.,Germany,Eurozone and Japan,treating the U.S.as the world market,show that the stock market pidend yield is a relevant information variable for forecasting the future values of the macro economy.The forecasting

15See also the descriptive statistics of the data in Table1.

16In our data the sample mean of German in?ation rate is0.67%per annum,and the standard deviation is0.79,whereas the sample mean of the German3-month nominal interest rate is6.48per annum,and standard deviation is2.33.

17Early contributions on this?nding are Campbell(1991)and Campbell and Ammer(1993),and for more recent evidence,see for example Bekaert,Harvey and Lundblad(2007)and Campbell and Yogo(2006).Also in the so-called Economic Tracking Portfolio(ETP)approach(see Lamont(2001)for more details)the role of pidend yield is more of an instrumental variable,i.e.,to serve as an instrument to expected stock market returns.

power shows up especially during turbulent time periods both in the macro economy and ?nancial markets.This is a new result compared to many other studies regarding the role of pidend yield as an informative variable.Previous studies have suggested that the pidend –price ratio is more able to approximate the expected (or unexpected)stock returns,but our results are favorable for using the pidend yield as an actual forecasting variable for future macro economy.Furthermore,when using our system of equations the ?nancial markets'ability to forecast the time-varying underlying trends even in the longer horizon (like 2years ahead)macro values is obvious,especially during periods of frequent changes in the time-varying trends of the future values of the macro economy.Hence,according to our results,the inclusion of stock market performance data in some form or the other would seem to be highly recommendable when building even small scale macroeconomic forecasting systems.

All our equations,estimation procedures etc.are based on linear speci ?cations,so the somewhat mixed ?ndings especially on the forecasting ability of the pidend yield spread for future values of real exchange rate might call for more advanced empirical and theoretical analyses,which might for example reveal nonlinearities in the actual data and/or in the relationships between the analyzed ?nancial market and macroeconomic variables.However,because the forecast ability for real economic activity and in ?ation seems somewhat strong already based on simple linear techniques,the various possibilities for applying nonlinear tools will be left to future work.

Acknowledgements

An earlier version of this paper was titled ‘An augmented Gordon model for forecasting macroeconomic variables ’and we thank Louis K.C.Chan,Juha Tarkka,and Mikko Puhakka for their comments and suggestions for that version,and the more recent modi ?cations of it.In addition to the comments from the anonymous referees,comments from the seminar and conference participants at University of Turku,University of Oulu,FSER annual meeting 2008in Jyv?skyl?,ESEM2008conference in Milan,and the MMF2008meeting in London were all very useful for the current version of this paper.We are also grateful for the ?nancial support from the OKO-Bank of Finland and the Yrj?Jahnsson Foundation,and for the hospitality of the Bank of Finland Research Department during his ancient visit to the Bank in 2001,which,in addition to some other research papers,launched also this research project.Finally,thanks to Juha Joenv??r?and Jukka Pakola for their help with some data issues.

Appendix

The usual starting point when applying the Gordon (1962)growth model in the stock market analysis is some version of equation P S t =E t P S t +1+D t +1 =1+k eT;eA1Twhere k is the agents'discount rate for future utility (assumed constant in the static version),P t S is the current price of equity share,and D t +1is the pidend accruing to the ownership of the equity share during the holding period.Hence,in equilibrium the current stock price should be the discounted value of the expected future pidend and future price conditional on the available information at time t .We may derive an asset pricing formula from Eq.(A1)by recursive substitution,yielding for the ?rst round

P S t =E t D t +1+E t +1D t +2+P S t +2 =1+k eTh i =1+k eT:eA2TUpdating Eq.(A1)again i times,substituting for each P t +i S from this recursive operation into Eq.(A2)and using the law of iterated expectations E t (E t +1(D t +2))=E t (D t +2)with an in ?nite number of substitutions,we are able to ?nd that the current price on the asset is the expected value of all future pidends,i.e.,

P f t =∑∞i =11=1+k eT? i E t D t +i àá:eA3T

In Eq.(A3)superscript f now refers to the market fundamentals price.Eq.(A3)is often referred to as the so-called rational

valuation formula (RVF)for the stock price.18In deriving this formula we have imposed the terminal or transversality condition lim i →∞

E P S t +i àá=1+k eTi h i =0;implying that the pricing Eq.(A3)has a ?nite number of possible solutions.Due to the obvious role of the expectations on future pidends and the discount factor in the rational valuation formula a natural question that arises from this equation concerns the role of economic factors,i.e.,state variables that might have effects on either or both of these two main components of the return generating process of common stocks in general.This is the part where we address the role of expectations about future economic growth and in ?ation,i.e.macroeconomic activity.More speci ?cally,we want to allow both for time-varying discount factor (k t )and time-varying pidends in our analysis,where time-variation is mainly based on expectations regarding real economic variables.

The simplest model for time-variation in pidends is the AR(1)model,i.e.

D t +1=1+g eTD t +w t +1;

eA4T18See also Cuthbertson and Nitzsche (2005),where details on applying RVF in other than stock markets,too,are given.299

J.Junttila,M.Korhonen /International Review of Economics and Finance 20(2011)281–301

where g is the (constant)growth rate of pidends,and w t +1is the white noise term.In this case,expected pidend growth is

g =E t D t +1?D t t

;and the optimal forecasts of future pidends may be found by leading (A4)and by repeated substitution as

E t D t +i =1+g eTi D t :

eA5T

Substituting now the forecast of future pidends from (A5)in the RVF gives

P t =∑∞i =11+g eTi D t 1+k eTi ;and after some simple algebra we obtain the Gordon growth model now in the form

P t =1+g eTD t with k ?g eTN 0:

If for example g =0.02,and k =0.06,the price-pidend ratio (i.e.,inverse of the pidend yield utilized in the main text)is 25.5,and if agents suddenly revise their expectations of g or k ,prices will move substantially.Assuming that for example g falls to 0.01,ceteris paribus,the new price –pidend ratio would be 14.4,implying a dramatic ‘crash ’in equity price of 43.5%.

For our application also the notion that rational investors might require a different expected return in each future period in order to hold a stock portfolio is important.Therefore,the expected one-period total return on stocks E t R t +1=

E t P S t +1?P S t +E t D t +1P S t should equal the required rate of return k t +1for her,implying that also the required rate of return is time-varying.Repeating again the previous steps,involving also forward substitutions now gives

P S t =E t 1+k t +1àá?1D t +1+1+k t +1àá?11+k t +2àá?1D t +2+…+…1+k t +N ?1àá?11+k t +N àá?1D t +N +P S t +N h i ;

which can be written in a more compact form as

P S t =E t ∑∞j =1∏j i =11+k t +i àá?1"

#D t +j "

#≡E t ∑∞

j =11+k t ;t +j ?1D t +j :eA6T

Put it in other words,the main message is now that the current stock price depends both on expectations of future discount rates and pidends .However,the severe problem in (A6)is that it is more or less ‘non-operational ’as a pricing equation,because it contains unobservableexpectationterms,andlike CuthbertsonandNitzsche(2005)argue,inappliedworkweusuallywouldneedsomeancillary tractable hypotheses about investors'forecasts of pidends and the discount rate to move towards empirical analysis.

Our innovation for this part is that,when our aim is to provide evidence on the forecasting power of ?nancial market information for future macro economy we should not even try to develop for example AR-type forecasting models for pidends or the equilibrium rate of return.We argue that in this case it is enough to note that when ?nancial market participants make their investment decisions over time,they have some kind of rational expectation forecasts,i.e.,expectations about the development of macro economy in the future in mind,and these expectations affect both the expected pidends and expected returns,so it must be the case that the current stock market price and/or return information mirrors these expectations in some way.Hence,in this case it is enough to formalize the basic Gordon growth model in the form given in the main text,i.e.,

P S t =D t i t ?g e t ?πe t

;that basically factorizes the discount factor (k t )described above in two components,i.e.the expected real growth of the economy

(g t e ),mimicking the potential growth rate of future pidends,and the (ex ante)real rate of interest (i t ?πt e ),at least partly

capturing the role of time-varying expected returns.In this paper we aim to utilize this long-run equilibrium version of the Gordon model as the starting formulation for our open economy extension.

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