Predicting European Union Recessions in the Euro Era 欧盟

Predicting European Union Recessions in the Euro Era:The Yield Curve as a Forecasting Tool of Economic ActivityDionisios Chionis &Periklis Gogas &Ioannis PragidisPublished online:12November 2009#International Atlantic Economic Society 2009Abstract Several studies have established the predictive power of the yield curve for the U.S.and various European countries.In this paper we use data from the European Union (EU15),from 1994:Q1to 2008:Q3.We use the European Central Bank ’s euro area yield spreads to predict European real GDP deviations from the long-run trend.We also augment the models tested with non monetary policy variables:the unemployment and a composite European stock price index.The methodology employed is a probit model of the inverse cumulative distribution function of the standard distribution using several formal forecasting and goodness of fit evaluation tests.The results show that the yield curve augmented with the composite stock index has significant forecasting power in terms of the EU15real output.Keywords Forecasting .Yield spread .Recession .Probit .Term structure .Monetary policy .Real growth JEL E43.E44.E52.C53IntroductionThe yield curve,measuring the difference between short and long term interest rates,has been at the center of recession forecasting.The theoretical justification of this line of work is that since short term interest rates are instruments of monetary policy,and long term interest rates reflect market ’s expectations on future economic conditions,the difference between short and longer term interest rates may contain useful information to policy makers and other individuals for the corresponding timeInt Adv Econ Res (2010)16:1–10DOI 10.1007/s11294-009-9247-2D.Chionis :P.Gogas (*):I.PragidisDepartment of International Economic Relations and Development,Democritus University of Thrace,Komotini 69100,Greecee-mail:pgkogkas@ierd.duth.gr2 D.Chionis et al. frame.Furthermore,when the yield curve is upward slopping during recessions,it indicates that there are expectations for future economic upturn.On the other hand, just before recessions,the yield curve flattens or even inverts.There are two major branches of empirical work in this area:first,simple OLS estimation where researchers try to predict future economic activity and second,probit models are used to forecast upcoming recessions.The main objective of these two classes of papers is to accommodate the fluctuations of future economic activity taking into account the information that is included in the yield curve and is independent of the exercised monetary policy.According to the influential paper in this line of research by Estrella and Mishkin(1997),the short end of the yield curve can be affected by the European Central Bank or the Federal Reserve or any other central bank,but the long end will be determined by many other considerations,including long term expectations of inflation and future real economic activity.In their paper,after taking into account monetary policy conducted in four major European countries(France, Germany,Italy and the U.K),Estrella and Mishkin(1997)show that the term structure spread has significant predictive power for both real activity and inflation. Bonser-Neal and Morley(1997),after examining eleven developed economies, found that the yield spread is a good predictive instrument for future economic activity.In the same vein,Venetis et al.(2003)reached the same conclusions,as did Hamilton and Kim(2002).On the other hand,Kim and Limpaphayom(1997)tested Japan and found evidence that the expected short term interest rate is the only source of predictability for Japan,and not the term premium.Ang et al.(2006),after modeling regressor endogeneity and using data for the period1952to2001, conclude that the short term interest rate has more predictive power than any term spread.They confirm their finding by forecasting GDP out of sample.There is also a class of papers that uses probit models to forecast recessions.Wright(2006),using as explanatory variables the Federal Reserve funds rate and the term spread, forecasts recessions six quarters ahead for the U.S.economy.Chauvet and Potter (2001)propose out-of-sample forecasting using standard probabilities and“hitting probabilities”of recession that take into account the length of the business cycle phases.They found that standard probit specification that does not consider the presence of autocorrelated errors and that has time varying parameters due to existence of multiple breakpoints tends to over-predict recession results.In their paper,Estrella et al.(2003)use recent econometric techniques for break-testing to examine whether the empirical relationships are in fact stable.They find that models that predict real activity are somewhat more stable than those that predict inflation, and that binary models are more stable than continuous models.Feitosa and Tabak (2007),for the case of Brazil,find that the spread possesses information which is not totally explained by the monetary policy.This paper,following the line of previous works using probit models, concentrates on the predictive power of the yield spread in the context of the European Union.To the best of our knowledge,no such analysis has yet been done for the E.U.Furthermore,as a dependent variable,we use the business cycle instead of the commonly used GDP,and a recession in this paper is defined as a deviation of the business cycle below the trend.We also employ other explanatory variables as well,such as the rate of unemployment and a European composite stock index,in an effort to improve the predictive power of the model.Predicting European Union Recessions in the Euro Era3 The rest of the paper is organized as follows.In the next section,we describe the data used.We then discuss the methodology and present the empirical results,and finally,in the last section we draw the conclusions for this study.The DataWe measure economic activity within the European Union in terms of the EU15 GDP which is comprised of the15countries that participated in the Union before the enlargement of May1,2004.The data for the EU15group are quarterly GDP from the OECD data base.They are seasonally adjusted for the period1994:Q1to2008: Q3.We restrict the analysis to this period as data availability and consistency issues arise for earlier data.Before taking the natural logarithm of the GDP series we apply the OECD seasonally adjusted GDP deflator with2000as the base year and we get the EU15seasonally adjusted real GDP.The aim of the paper is to predict deviations of real output from the long term trend and especially the probability that the GDP of a particular quarter will be below the long run trend.For this reason,we first decompose the EU15seasonally adjusted real GDP to the trend and cyclical component employing the Hodrick-Prescott(1997)filter(HP).The HP filter is commonly used in the area of real business cycles.It produces a smooth non-linear trend which is affected more from the long-term fluctuations rather than the short-term ones.The filter’s contribution is to distinguish an observed shock into a component that causes permanent effects and a component that has transitory effects on the economy.Furthermore,we address the issue described in the literature—possible bias of the cycle obtained by the HP filter—by investigating the robustness of the results to alternative decompositions of the GDP time-series.In doing so,we first produce the cyclical component of the EU GDP using alternative specifications for the HPλparameter i.e.λ=1,000,1,600and2,200.As it is evident from Fig.3in the appendix and the construction of the dependent variable dummy for the probit model employed below,the cyclical component is not affected by the alternative values used forλ.Next,we also employ the Baxter and King(1995)filter(BK)and extract the cycle using alternatively six and twelve leads/lags.The extracted cyclical components are presented in Fig.4of the appendix.As the qualitative results of the extracted cyclical components are quite similar to the ones obtained by the HP filter and since the Baxter and King(1995)leads/lags leave us with much fewer observations1for the estimation of the probit models we continue the analysis with the cycles produced by the standard HP filter withλ=1600.Having extracted the cyclical component of the EU15real GDP as it is depicted in Fig.1,we then construct the business cycle dummy variable(BS)that takes the value one whenever the cycle is negative implying that the GDP is below trend and the value zero elsewhere.It is important to be noted here that for the purposes of this paper we define recessions as the negative deviations of GDP from the long term trend.In other words,our aim is to use the yield spread information and other explanatory variables in order to forecast negative values for the cyclical component of the 1The usable sample reduces from59observations using the HP filter to47and35using the BK with6 and12leads/lags.quarterly EU15seasonally adjusted real GDP as it is extracted employing the Hodrick-Prescott (1997)filter.The explanatory variables we use are various yield spreads,the EU15unemployment rate and the stock indices of the London,Frankfurt,and Paris stock exchanges.All interest rates used in calculating the yield spreads are extracted from the ECB statistics and are the interest rates for the euro area government benchmark bonds with maturities for the long term rates of 1,2,5and 10years,and for the short term rates with maturities of one and three months.The EU15unemployment rate is obtained from the Eurostat database.Finally,the composite stock index is produced as an average of the three major European stock exchanges —London,Frankfurt,and Paris —using the FTSE-100,DAX,and CAC-40indices,respectively.We employ these three indices in the calculation of the composite stock index for the euro area as combined they comprise the vast majority of volume of trades in the euro zone and they also appear to influence the rest of the exchanges as well.The stock data are obtained from Six Telekurs.In Table 1,we present a statistical summary of all the explanatory variables.Methodology and Empirical ResultsWe consider 48alternative models for probit regressions forecasting a quarterly GDP cycle below trend at some point within the next h quarters:prob BS t ¼1ðÞ¼Φe a 0þe a 1i LR ;t Ài Ài SR ;t Ài ÀÁÂÃ;i ¼1;...;h ð1Þwhere BS t is the dummy variable that takes the value one every time the cyclicalcomponent of the GDP is negative implying a below-trend GDP,and zero elsewhere.Φ(∙)denotes the standard normal cumulative distribution function,i LR ;t Ài Ài SR ;t Ài ÀÁrepresents the spread between the long and short run interest rates with i =1,...,6.For the long run interest rates we use four rates alternatively,the 1,2,5and 10year rates,while for the short run rates we use two alternatives,the one and three monthsFig.1The extracted cyclical component of the EU15GDP4D.Chionis et al.maturities.Finally,e a 0and e a 1are the estimated parameters.Thus,Eq.(1)is estimated for all combinations of the short with the long run interest rates and forecast windows from one to six quarters ahead,a total of 48probit regressions.The estimated coefficient of the spread e a 1,is statistically significant at probabilities p <.01only for the one year/one month,two years/one month,one year/three months and two years/three months spreads and at forecast window i =2quarters and for the one year/one month spread at forecast window i =3quarters.As the main purpose of this paper is the prediction of GDP fluctuations below the long run trend,we formally compare the above five models in terms of their forecasting ability by calculating the root mean squared error (RMSE),mean absolute error (MAE),and the mean absolute percent error (MAPE)statistics.These statistics are calculated using the following formulas:RMSE ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1F X F f ¼1e 2t þfv u u t MAE ¼1F X F f ¼1e t þf MAPE ¼1F X F f ¼1e t þf ;t y t þfwhere e t þf ¼y t þf Ày *t þf ,and y t +f is the actual value of the series at period t +f ,y *t þfis the forecast for y t +f and F is the forecast window.These statistics are summarized in Table 2.We see that model 4,the one constructed with the spread of the 1year interest rate minus the three month interest rate,and at forecast window of twoTable 1Descriptive statistics for the explanatory variables1-month 3-month 1-year2-year 5-year 10-year Unemployment Stock Index Mean 3.95 4.02 4.16 4.14 4.67 5.308.974512.62Median 3.96 3.95 4.11 4.08 4.40 4.818.764651.22Maximum 7.077.297.737.768.669.3210.796788.52Minimum 2.06 2.05 2.15 2.21 2.66 3.26 6.972291.02Std.Dev. 1.42 1.46 1.47 1.43 1.48 1.59 1.201370.90Skewness 0.520.510.610.87 1.13 1.120.20−0.06Kurtosis 2.49 2.47 2.76 3.33 3.68 3.25 1.65 1.85Jarque-Bera 3.26 3.25 3.757.7613.6312.54 4.84 3.30Probability 0.200.200.150.020.000.000.090.19Sum 233.21237.45245.72244.54275.72312.52529.33 2.66E +05Sum Sq.Dev.117.11122.84125.75118.21127.02146.9383.76 1.09E +08Observations5959595959595959Predicting European Union Recessions in the Euro Era 5quarters,outperforms,in terms of forecasting efficiency,all four of the other models and all three for forecasting criteria.Moreover,we report in the last column of Table 2the McFadden R 2for each model,and this is maximized for the model employing the 1year interest rate minus the three month interest rate and at forecast window of two quarters.The value of 0.1422for the McFadden R 2is considered a satisfactory fit as this statistic tends to be smaller than standard R 2.Thus,for the rest of the paper we employ this model for the purposes of estimating the probability that the real GDP will be bellow trend.Next,in an effort to examine whether other variables from the real economy can add any informational content to the forecasts of GDP,we estimate the following probit regressions:prob BS t ¼1ðÞ¼Φe a 0þe a 1i LR ;t Ài Ài SR ;t Ài ÀÁþe a u u t Ài ÂÃð2Þprob BS t ¼1ðÞ¼Φe a 0þe a 1i LR ;t Ài Ài SR ;t Ài ÀÁþea s s t Ài ÂÃ;ð3Þwhere u t is the unemployment rate in the EU15area,s t is the stock market compositeindex,i =1,…,6and e a u ,e a s are their estimated coefficients.As we can see in Table 3,the unemployment as an explanatory variable is not statistically significant at all estimated forecast windows -from u t −1to u t −6-and probabilities of 0.10or 0.05.From Table 4we see that the inclusion of the stock index as an explanatory variableTable 2Forecasting model selection criteria Predicting Spread Forecasting Criteria ModelLong Term Rate Short Term Rate Forecast Window RMSEMAEMAPEMcFadden R 21One Year One Month 2quarters 0.45490.414520.93950.13342One Year One Month 3quarters 0.46860.436922.10790.09853Two Years One Month 2quarters 0.46350.426621.42230.11594One Year Three Month 2quarters 0.4533*0.4100*20.8120*0.1422*5Two YearsThree Month2quarters0.46520.430221.61840.1092An asterisk denotes the selected model by each criterionTable 3Probit estimation with unemployment as an explanatory variable Variable Coefficient Std.Error z-Statistic Prob.u t −10.1800.156 1.1500.250u t −20.1520.1530.9940.320u t −30.1040.1520.6830.495u t −40.0180.1530.1190.905u t −5−0.0460.156−0.2920.770u t −6−0.1200.159−0.7540.4516D.Chionis et al.is statistically significant at all forecast windows for probability 0.10and all but three and four forecast windows at the 5%probability.Thus,we then compare the forecasting power of the previously selected model 4,the one constructed with the spread of the 1year interest rate minus the three month interest rate and at forecast window of two quarters and the same spread and lag structure with the inclusion of the stock index variable.The forecasting error statistics of the two compared models are presented in Table 5along with the McFadden R 2.According to all four statistics,the model with the stock index variable is selected in terms of forecasting accuracy and goodness of fit.In Fig.2,we graph the forecasted probability of a recession using the best fit model already selected along with the EU15seasonally adjusted real GDP cyclical component.As it can be seen in Fig.2,the predictive power of the estimated model in terms of the forecasted probabilities of EU15GDP deviations from the trend is very high.It seems that the yield spread between the 1year and the three month euro area government benchmark bonds,augmented by the composite stock index and a forecast window of two quarters ahead,is a very good predictor of the cyclical behavior of GDP in terms of its deviations from the long run trend.In Table 6,we provide the Andrews and Hosmer-Lemeshow tests of goodness of fit grouped in four quartiles of risk.According to the goodness of fit evaluation criteria,our selected model provides a very good fit and the χ2statistics reported at the bottom of Table 6for the Hosmer-Lemeshow and Andrews tests are 0.009and 0.001respectively.Table 4Probit estimation with the stock index as an explanatory variable Variable Coefficient Std.Error z-Statistic Prob.s t −1−0.000320.000−2.1520.031*s t −2−0.000280.000−2.0000.046*s t −3−0.000250.000−1.8580.063s t −4−0.000220.000−1.7110.087s t −5−0.000270.000−2.0040.045*s t −6−0.000260.000−1.9770.048*An asterisk denotes significance at the 5%levelTable 5Forecasting model selection criteria Predicting Spread Forecasting Criteria Long Term Rate Short Term Rate Forecast Window Stock Index RMSEMAEMAPEMcFadden R 2One Year Three Month 2quarters no 0.45330.410020.81200.1422One YearThree Month2quartersyes0.4372*0.3800*19.3203*0.1921*An asterisk denotes the selected model by each criterionPredicting European Union Recessions in the Euro Era78 D.Chionis et al.Fig.2GDP cyclical component and forecasted probabilityConclusionsIn this paper,we have used several probit models to examine the power of the yield spread between various long term and short term maturities of euro area benchmark bonds in predicting deviations of real output from the long run trend. Our results show that the yield spread of relatively short term interest rates dominates in terms of forecasting efficiency the yield spread of longer term interest rates.Moreover,we have included in the estimation models both the EU15unemployment rate and a composite stock index of the London,Frankfurt and Paris stock exchanges in an effort to investigate whether other than monetary policy variables can add any forecasting power to the yield spread.The results, after the formal evaluation of the forecasting ability of the different yield spreads and in different forecast horizons show that the best model is the one employing the spread between relatively short term interest rates,the one year and the three months euro area benchmark bond rates with a forecast horizon equal to two Table6Goodness-of-fit evaluation for binary specificationQuantile of Risk Dep=0Dep=1Total H-L Low High Actual Expect Actual Expect Obs Value10.050.251411.720 2.2814 2.72 20.260.5059.0910 5.9115 4.66 30.500.705 5.6498.36140.12 40.720.935 2.921012.0815 1.83Total2929.37292928.6271589.34254 H-L Statistic9.34Prob.Chi-Sq(2)0.009Andrews Statistic19.25Prob.Chi-Sq(4)0.001quarters ahead.These results come in line with the findings of Ang et al.(2006)that short rates have more predictive power than any term spread.The inclusion of unemployment in the best yield spread model was not statistically significant at any forecast horizons.The composite stock index on the other hand was statistically significant,and according to the formal forecasting evaluation tests,it improved the ability of the model to predict GDP fluctuations in the euro area significantly.Overall,the final model used for forecasting appears very efficient to forecast deviations of real output from the long run trend according to the standard formal goodness of fit tests employed.The results of course generate obvious policy implications.The policymaker can use the information provided by the yield spread and the stock markets today in order to estimate the probability of obtaining a below-trend real output two quarters ahead.A shrinking yield spread or in other words a yield curve with a diminishing slope in the short rates domain may be the signal for an upcoming below-trend real output.Thus,the policymaker who is concerned with stable growth and targets small fluctuations of real GDP —especially downwards —can use this information and loosen monetary policy in an effort to reduce short-term interest rates (directly affected by monetary policy),increase the spread,and lower the probability of a below-trend real GDP two quarters ahead.In this manner,successful intervention in the term structure of interest rates could shorten the below-trend cycle and/or make the fluctuation milder.Acknowledgements The authors would like to thank the participants at the 67th International Atlantic Economic Conference in Rome,Italy 11–14March 2009,and especially the organizer of the session “Topics in Macroeconomics ”,Prof.Nicholas Apergis for helpful comments that improved the original draft of the paper.We also thank an anonymous reviewer for constructive comments on the first draft of the paper.Appendix-.04-.03-.02-.01.00.01.02.03Fig.3Hodrick-Prescott cyclical component sensitivity to λPredicting European Union Recessions in the Euro Era 9ReferencesAng,A.,Piazzesi,M.,&Wei,M.(2006).What does the yield curve tell us about GDP?Journal ofEconometrics,131,1–2.March –April,359–403.Baxter,M.,&King,R.G.(1995).Measuring business cycles.approximate band-pass filters for economictime series.NBER Working Paper Series ,No.5022,February.Bonser-Neal,C.,&Morley,T.R.(1997).Does the yield spread predict real economic activity?Amulticountry analysis.Economic Review ,Federal Reserve Bank of Kansas City,Third Quarter,37–53.Chauvet,M.,&Potter S.(2001).Forecasting recessions using the yield curve.Staff Reports ,FederalReserve Bank of New York,134,August.Estrella,A.,&Mishkin,F.S.(1997).The predictive power of the term structure of interest rates in Europeand the United States:implications for the European Central Bank.European Economic Review,41(7),1375–1401.Estrella,A.,Rodrigues,A.P.,&Schich,S.(2003).How stable is the predictive power of the yield curve?Evidence from Germany and the United States.The Review of Economics and Statistics,85(3),629–644.Feitosa,M.A.,&Tabak,B.N.(2007).Predictability of economic activity using yield spreads:the case ofBrazil.Anais do XXXV Encontro Nacional de Economia [Proceedings of the 35th Brazilian Economics Meeting],029.Hamilton,J.D.,&Kim,D.H.(2002).A reexamination of the predictability of economic activity using theyield spread.Journal of Money,Credit and Banking,34(2),340–60.Hodrick,R.,&Prescott,E.P.(1997).Postwar business cycles:an empirical investigation.Journal ofMoney,Credit,and Banking,29(1),1–16.Kim,A.,&Limpaphayom,P.(1997).The effect of economic regimes on the relation between termstructure and real activity in Japan.Journal of Economics and Business,49(4),379–392.Venetis,I.A.,Paya,I.,&Peel,D.A.(2003).Re examination of the predictability of economic activityusing the yield spread:a non linear approach.International Review of Economics and Finance,12(2),187–206.Wright,J.(2006),The yield curve and predicting recessions.Finance and Economics Discussion Series ,Federal Reserve Board,2006–7,February.-.03-.02-.01.00.01.02.0319941996199820002002200420062008Fig.4Baxter-King cyclical component sensitivity to lead/lag specification10D.Chionis et al.Copyright of International Advances in Economic Research is the property of Springer Science & Business Media B.V. and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use.。