Predicting European Union Recessions in the Euro Era:The Yield Curve as a Forecasting Toolof Economic Activity

Dionisios Chionis & Periklis Gogas & Ioannis Pragidis

Published online: 12 November 2009# International Atlantic Economic Society 2009

Abstract Several studies have established the predictive power of the yield curvefor the U.S. and various European countries. In this paper we use data from theEuropean Union (EU15), from 1994:Q1 to 2008:Q3. We use the European CentralBank’s euro area yield spreads to predict European real GDP deviations from thelong-run trend. We also augment the models tested with non monetary policyvariables: the unemployment and a composite European stock price index. Themethodology employed is a probit model of the inverse cumulative distributionfunction of the standard distribution using several formal forecasting and goodnessof fit evaluation tests. The results show that the yield curve augmented with thecomposite stock index has significant forecasting power in terms of the EU15 realoutput.

Keywords Forecasting . Yield spread . Recession . Probit . Term structure . Monetarypolicy . Real growth

JEL E43 . E44 . E52 . C53

Introduction

The yield curve, measuring the difference between short and long term interest rates,has been at the center of recession forecasting. The theoretical justification of thisline 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 economicconditions, the difference between short and longer term interest rates may containuseful information to policy makers and other individuals for the corresponding time

Int Adv Econ Res (2010) 16:1–10DOI 10.1007/s11294-009-9247-2

D. Chionis : P. Gogas (*) : I. PragidisDepartment of International Economic Relations and Development, Democritus University of Thrace,Komotini 69100, Greecee-mail: pgkogkas@ierd.duth.gr

frame. Furthermore, when the yield curve is upward slopping during recessions, itindicates 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 majorbranches of empirical work in this area: first, simple OLS estimation whereresearchers try to predict future economic activity and second, probit models areused to forecast upcoming recessions. The main objective of these two classes ofpapers is to accommodate the fluctuations of future economic activity taking intoaccount the information that is included in the yield curve and is independent of theexercised monetary policy. According to the influential paper in this line of researchby Estrella and Mishkin (1997), the short end of the yield curve can be affected bythe European Central Bank or the Federal Reserve or any other central bank, but thelong end will be determined by many other considerations, including long termexpectations of inflation and future real economic activity. In their paper, after takinginto account monetary policy conducted in four major European countries (France,Germany, Italy and the U.K), Estrella and Mishkin (1997) show that the termstructure 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 economicactivity. In the same vein, Venetis et al. (2003) reached the same conclusions, as didHamilton and Kim (2002). On the other hand, Kim and Limpaphayom (1997) testedJapan and found evidence that the expected short term interest rate is the only sourceof predictability for Japan, and not the term premium. Ang et al. (2006), aftermodeling regressor endogeneity and using data for the period 1952 to 2001,conclude that the short term interest rate has more predictive power than any termspread. They confirm their finding by forecasting GDP out of sample. There is also aclass of papers that uses probit models to forecast recessions. Wright (2006), usingas 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 “hittingprobabilities” of recession that take into account the length of the business cyclephases. They found that standard probit specification that does not consider thepresence of autocorrelated errors and that has time varying parameters due toexistence of multiple breakpoints tends to over-predict recession results. In theirpaper, Estrella et al. (2003) use recent econometric techniques for break-testing toexamine whether the empirical relationships are in fact stable. They find that modelsthat 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 nottotally 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 theEuropean Union. To the best of our knowledge, no such analysis has yet been donefor the E.U. Furthermore, as a dependent variable, we use the business cycle insteadof the commonly used GDP, and a recession in this paper is defined as a deviation ofthe business cycle below the trend. We also employ other explanatory variables aswell, such as the rate of unemployment and a European composite stock index, in aneffort to improve the predictive power of the model.

2 D. Chionis et al.

The rest of the paper is organized as follows. In the next section, we describe thedata used. We then discuss the methodology and present the empirical results, andfinally, in the last section we draw the conclusions for this study.

The Data

We measure economic activity within the European Union in terms of the EU15GDP which is comprised of the 15 countries that participated in the Union before theenlargement of May 1, 2004. The data for the EU15 group are quarterly GDP fromthe OECD data base. They are seasonally adjusted for the period 1994:Q1 to 2008:Q3. We restrict the analysis to this period as data availability and consistency issuesarise for earlier data. Before taking the natural logarithm of the GDP series we applythe OECD seasonally adjusted GDP deflator with 2000 as the base year and we getthe EU15 seasonally adjusted real GDP. The aim of the paper is to predict deviationsof real output from the long term trend and especially the probability that the GDP ofa particular quarter will be below the long run trend. For this reason, we firstdecompose the EU15 seasonally adjusted real GDP to the trend and cyclicalcomponent employing the Hodrick-Prescott (1997) filter (HP). The HP filter iscommonly used in the area of real business cycles. It produces a smooth non-lineartrend 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 acomponent that causes permanent effects and a component that has transitory effectson the economy. Furthermore, we address the issue described in the literature—possible bias of the cycle obtained by the HP filter—by investigating the robustnessof the results to alternative decompositions of the GDP time-series. In doing so, wefirst produce the cyclical component of the EU GDP using alternative specificationsfor the HP λ parameter i.e. λ=1,000, 1,600 and 2,200. As it is evident from Fig. 3 inthe appendix and the construction of the dependent variable dummy for the probitmodel employed below, the cyclical component is not affected by the alternativevalues used for λ. Next, we also employ the Baxter and King (1995) filter (BK) andextract the cycle using alternatively six and twelve leads/lags. The extracted cyclicalcomponents are presented in Fig. 4 of the appendix. As the qualitative results of theextracted cyclical components are quite similar to the ones obtained by the HP filterand since the Baxter and King (1995) leads/lags leave us with much fewerobservations1 for the estimation of the probit models we continue the analysis withthe cycles produced by the standard HP filter with λ=1600. Having extracted thecyclical component of the EU15 real GDP as it is depicted in Fig. 1, we thenconstruct the business cycle dummy variable (BS) that takes the value one wheneverthe cycle is negative implying that the GDP is below trend and the value zeroelsewhere. It is important to be noted here that for the purposes of this paper wedefine recessions as the negative deviations of GDP from the long term trend. Inother words, our aim is to use the yield spread information and other explanatoryvariables in order to forecast negative values for the cyclical component of the

1 The usable sample reduces from 59 observations using the HP filter to 47 and 35 using the BK with 6and 12 leads/lags.

Predicting European Union Recessions in the Euro Era 3

quarterly EU15 seasonally adjusted real GDP as it is extracted employing theHodrick-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 stockexchanges. All interest rates used in calculating the yield spreads are extracted fromthe ECB statistics and are the interest rates for the euro area government benchmarkbonds with maturities for the long term rates of 1, 2, 5 and 10 years, and for the shortterm rates with maturities of one and three months. The EU15 unemployment rate isobtained from the Eurostat database. Finally, the composite stock index is producedas an average of the three major European stock exchanges—London, Frankfurt, andParis—using the FTSE-100, DAX, and CAC-40 indices, respectively. We employthese three indices in the calculation of the composite stock index for the euro areaas combined they comprise the vast majority of volume of trades in the euro zoneand they also appear to influence the rest of the exchanges as well. The stock dataare obtained from Six Telekurs. In Table 1, we present a statistical summary of allthe explanatory variables.

Methodology and Empirical Results

We consider 48 alternative models for probit regressions forecasting a quarterly GDPcycle below trend at some point within the next h quarters:

prob BSt ¼ 1ð Þ ¼ Φ ea0 þ ea1 iLR;t�i � iSR;t�i

� �� �; i ¼ 1; . . . ; h ð1Þ

where BSt 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, iLR;t�i � iSR;t�i

� �represents the spread between the long and short run interest rates with i = 1,...,6. Forthe long run interest rates we use four rates alternatively, the 1, 2, 5 and 10 yearrates, while for the short run rates we use two alternatives, the one and three months

-.020

-.015

-.010

-.005

.000

.005

.010

.015

.020

1994 1996 1998 2000 2002 2004 2006 2008

Fig. 1 The extracted cyclical component of the EU15 GDP

4 D. Chionis et al.

maturities. Finally, ea0 and ea1 are the estimated parameters. Thus, Eq. (1) is estimatedfor all combinations of the short with the long run interest rates and forecastwindows from one to six quarters ahead, a total of 48 probit regressions. Theestimated coefficient of the spread ea1, is statistically significant at probabilitiesp<.01 only for the one year/one month, two years/one month, one year/three monthsand two years/three months spreads and at forecast window i = 2 quarters and for theone year/one month spread at forecast window i = 3 quarters. As the main purpose ofthis paper is the prediction of GDP fluctuations below the long run trend, weformally compare the above five models in terms of their forecasting ability bycalculating the root mean squared error (RMSE), mean absolute error (MAE), andthe mean absolute percent error (MAPE) statistics. These statistics are calculatedusing the following formulas:

RMSE ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1

F

XFf¼1

e2tþf

vuut

MAE ¼ 1

F

XFf¼1

etþf

�� ��

MAPE ¼ 1

F

XFf¼1

etþf ;t

ytþf

��������

where etþf ¼ ytþf � y*tþf , and yt+f is the actual value of the series at period t+f, y*tþfis the forecast for yt+f and F is the forecast window. These statistics are summarizedin Table 2. We see that model 4, the one constructed with the spread of the 1 yearinterest rate minus the three month interest rate, and at forecast window of two

Table 1 Descriptive statistics for the explanatory variables

1-month 3-month 1-year 2-year 5-year 10-year Unemployment Stock Index

Mean 3.95 4.02 4.16 4.14 4.67 5.30 8.97 4512.62

Median 3.96 3.95 4.11 4.08 4.40 4.81 8.76 4651.22

Maximum 7.07 7.29 7.73 7.76 8.66 9.32 10.79 6788.52

Minimum 2.06 2.05 2.15 2.21 2.66 3.26 6.97 2291.02

Std. Dev. 1.42 1.46 1.47 1.43 1.48 1.59 1.20 1370.90

Skewness 0.52 0.51 0.61 0.87 1.13 1.12 0.20 −0.06Kurtosis 2.49 2.47 2.76 3.33 3.68 3.25 1.65 1.85

Jarque-Bera 3.26 3.25 3.75 7.76 13.63 12.54 4.84 3.30

Probability 0.20 0.20 0.15 0.02 0.00 0.00 0.09 0.19

Sum 233.21 237.45 245.72 244.54 275.72 312.52 529.33 2.66E + 05

Sum Sq. Dev. 117.11 122.84 125.75 118.21 127.02 146.93 83.76 1.09E + 08

Observations 59 59 59 59 59 59 59 59

Predicting European Union Recessions in the Euro Era 5

quarters, outperforms, in terms of forecasting efficiency, all four of the other modelsand all three for forecasting criteria. Moreover, we report in the last column ofTable 2 the McFadden R2 for each model, and this is maximized for the modelemploying the 1 year interest rate minus the three month interest rate and at forecastwindow of two quarters. The value of 0.1422 for the McFadden R2 is considered asatisfactory fit as this statistic tends to be smaller than standard R2. Thus, for the restof the paper we employ this model for the purposes of estimating the probability thatthe real GDP will be bellow trend. Next, in an effort to examine whether othervariables from the real economy can add any informational content to the forecastsof GDP, we estimate the following probit regressions:

prob BSt ¼ 1ð Þ ¼ Φ ea0 þ ea1 iLR;t�i � iSR;t�i

� �þ eauut�i

� � ð2Þ

prob BSt ¼ 1ð Þ ¼ Φ ea0 þ ea1 iLR;t�i � iSR;t�i

� �þ easst�i

� �; ð3Þ

where ut is the unemployment rate in the EU15 area, st is the stock market compositeindex, i = 1, …, 6 and eau, eas are their estimated coefficients. As we can see inTable 3, the unemployment as an explanatory variable is not statistically significantat all estimated forecast windows -from ut−1 to ut−6- and probabilities of 0.10 or 0.05.From Table 4 we see that the inclusion of the stock index as an explanatory variable

Table 2 Forecasting model selection criteria

Predicting Spread Forecasting Criteria

Model Long TermRate

Short TermRate

ForecastWindow

RMSE MAE MAPE McFadden R2

1 One Year One Month 2 quarters 0.4549 0.4145 20.9395 0.1334

2 One Year One Month 3 quarters 0.4686 0.4369 22.1079 0.0985

3 Two Years One Month 2 quarters 0.4635 0.4266 21.4223 0.1159

4 One Year Three Month 2 quarters 0.4533* 0.4100* 20.8120* 0.1422*

5 Two Years Three Month 2 quarters 0.4652 0.4302 21.6184 0.1092

An asterisk denotes the selected model by each criterion

Table 3 Probit estimation with unemployment as an explanatory variable

Variable Coefficient Std. Error z-Statistic Prob.

ut−1 0.180 0.156 1.150 0.250

ut−2 0.152 0.153 0.994 0.320

ut−3 0.104 0.152 0.683 0.495

ut−4 0.018 0.153 0.119 0.905

ut−5 −0.046 0.156 −0.292 0.770

ut−6 −0.120 0.159 −0.754 0.451

6 D. Chionis et al.

is statistically significant at all forecast windows for probability 0.10 and all butthree and four forecast windows at the 5% probability. Thus, we then compare theforecasting power of the previously selected model 4, the one constructed with thespread of the 1 year interest rate minus the three month interest rate and at forecastwindow of two quarters and the same spread and lag structure with the inclusion ofthe stock index variable. The forecasting error statistics of the two compared modelsare presented in Table 5 along with the McFadden R2. According to all four statistics,the model with the stock index variable is selected in terms of forecasting accuracyand goodness of fit. In Fig. 2, we graph the forecasted probability of a recessionusing the best fit model already selected along with the EU15 seasonally adjustedreal GDP cyclical component. As it can be seen in Fig. 2, the predictive power of theestimated model in terms of the forecasted probabilities of EU15 GDP deviationsfrom the trend is very high. It seems that the yield spread between the 1 year and thethree month euro area government benchmark bonds, augmented by the compositestock index and a forecast window of two quarters ahead, is a very good predictor ofthe cyclical behavior of GDP in terms of its deviations from the long run trend. InTable 6, we provide the Andrews and Hosmer-Lemeshow tests of goodness of fitgrouped in four quartiles of risk. According to the goodness of fit evaluation criteria,our selected model provides a very good fit and the χ2 statistics reported at thebottom of Table 6 for the Hosmer-Lemeshow and Andrews tests are 0.009 and 0.001respectively.

Table 4 Probit estimation with the stock index as an explanatory variable

Variable Coefficient Std. Error z-Statistic Prob.

st−1 −0.00032 0.000 −2.152 0.031*

st−2 −0.00028 0.000 −2.000 0.046*

st−3 −0.00025 0.000 −1.858 0.063

st−4 −0.00022 0.000 −1.711 0.087

st−5 −0.00027 0.000 −2.004 0.045*

st−6 −0.00026 0.000 −1.977 0.048*

An asterisk denotes significance at the 5% level

Table 5 Forecasting model selection criteria

Predicting Spread Forecasting Criteria

Long TermRate

Short TermRate

ForecastWindow

StockIndex

RMSE MAE MAPE McFaddenR2

One Year Three Month 2 quarters no 0.4533 0.4100 20.8120 0.1422

One Year Three Month 2 quarters yes 0.4372* 0.3800* 19.3203* 0.1921*

An asterisk denotes the selected model by each criterion

Predicting European Union Recessions in the Euro Era 7

Conclusions

In this paper, we have used several probit models to examine the power of theyield spread between various long term and short term maturities of euro areabenchmark bonds in predicting deviations of real output from the long run trend.Our results show that the yield spread of relatively short term interest ratesdominates in terms of forecasting efficiency the yield spread of longer terminterest rates. Moreover, we have included in the estimation models both theEU15 unemployment rate and a composite stock index of the London, Frankfurtand Paris stock exchanges in an effort to investigate whether other than monetarypolicy variables can add any forecasting power to the yield spread. The results,after the formal evaluation of the forecasting ability of the different yield spreadsand in different forecast horizons show that the best model is the one employingthe spread between relatively short term interest rates, the one year and the threemonths euro area benchmark bond rates with a forecast horizon equal to two

0.0

0.2

0.4

0.6

0.8

1.0

-.02

-.01

.00

.01

.02

1994 1996 1998 2000 2002 2004 2006 2008

GDP Cycle Probability

Fig. 2 GDP cyclical component and forecasted probability

Table 6 Goodness-of-fit evaluation for binary specification

Quantile of Risk Dep = 0 Dep = 1 Total H-L

Low High Actual Expect Actual Expect Obs Value

1 0.05 0.25 14 11.72 0 2.28 14 2.72

2 0.26 0.50 5 9.09 10 5.91 15 4.66

3 0.50 0.70 5 5.64 9 8.36 14 0.12

4 0.72 0.93 5 2.92 10 12.08 15 1.83

Total 29 29.3729 29 28.6271 58 9.34254

H-L Statistic 9.34 Prob. Chi-Sq(2) 0.009

Andrews Statistic 19.25 Prob. Chi-Sq(4) 0.001

8 D. Chionis et al.

quarters 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 ofunemployment in the best yield spread model was not statistically significant atany forecast horizons. The composite stock index on the other hand wasstatistically significant, and according to the formal forecasting evaluation tests,it improved the ability of the model to predict GDP fluctuations in the euro areasignificantly. Overall, the final model used for forecasting appears very efficient toforecast deviations of real output from the long run trend according to the standardformal goodness of fit tests employed. The results of course generate obviouspolicy implications. The policymaker can use the information provided by theyield spread and the stock markets today in order to estimate the probability ofobtaining a below-trend real output two quarters ahead. A shrinking yield spread orin other words a yield curve with a diminishing slope in the short rates domain maybe the signal for an upcoming below-trend real output. Thus, the policymaker whois concerned with stable growth and targets small fluctuations of real GDP—especially downwards—can use this information and loosen monetary policy in aneffort 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 quartersahead. In this manner, successful intervention in the term structure of interest ratescould shorten the below-trend cycle and/or make the fluctuation milder.

Acknowledgements The authors would like to thank the participants at the 67th International AtlanticEconomic Conference in Rome, Italy 11–14 March 2009, and especially the organizer of the session“Topics in Macroeconomics”, Prof. Nicholas Apergis for helpful comments that improved the originaldraft of the paper. We also thank an anonymous reviewer for constructive comments on the first draft ofthe paper.

Appendix

-.04

-.03

-.02

-.01

.00

.01

.02

.03

1994 1996 1998 2000 2002 2004 2006 2008

GDPC_HP1000GDPC_HP1600GDPC_HP2200

Fig. 3 Hodrick-Prescott cyclical component sensitivity to λ

Predicting European Union Recessions in the Euro Era 9

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-.03

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-.01

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1994 1996 1998 2000 2002 2004 2006 2008

BK12BK6

Fig. 4 Baxter-King cyclical component sensitivity to lead/lag specification

10 D. Chionis et al.