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©TechMind Research, Canada 93 | P a g e

International Journal of Management Excellence

Volume __ No.__ Month Year

Yield spread as a leading indicator of

Tunisian industrial production

BEN ALI TAREK

Higher Institute of Business Administration, University of Gafsa, Tunisia

Tarek.benal@yahoo.fr

Abstract- Can the yield spread, which has been found to predict with surprising accuracy the movement of key

macroeconomic variables of developed countries, also predict such variables for an emerging country. This paper is an

attempt to answer empirically this question for the Tunisian economy. It also examines international financial linkages and

how the euro area yield curve helps to predict domestic macro financial variables. Although the phenomenon has been

widely examined in developed market economies, similar studies are virtually absent in the case of emerging economies. In

part, this is because in developing economies with administrated interest rates, the yield curve has been either completely

absent or not market determined and thus did not form a suitable test case. In the Tunisian financial market, there has been

considerable improvement in terms of volumes, variety of instruments, numbers of participants and dissemination of

information, and a yield curve particularly in case of government securities started emerging since 2000.

In our study, two approaches are implemented. The first one, widely used, consists in regressing the growth rate of the

coincident indicator on the leading indicator. In the second one, we examine the usefulness of the yield spread in

predicting whether or not the economy will be in recession in the future. So, in that particular case we use a Probit model.

For both approaches we use the in-sample forecasting ability as well as the out-of-sample accuracy of the outcomes.

The results are somewhat tentative but consistent with the similar studies conducted in case of other countries. Findings of

the study provide evidence that the yield curve could be considered as a leading indicator of real growth or recessions in

Tunisian context, and consequently may be useful for both to private investors and to policy makes for forecasting

purposes and, perhaps more importantly to understand the ongoing process of international financial integration.

Key words- yield spread; in-sample forecasting; out-of-sample forecasting; economic growth; recessions; leading

indicator; predictive content; linear regression; probit model.

1. Introduction

There is a significant amount of empirical evidence to

suggest that the asset prices are forwardlooking and,

consequently, constitute a class of potentially useful

predictor of macroeconomic variables

1

. The literature on

forecasting using asset prices has identified in particular

the yield spread. It’s the difference between long-term and

short-term interest rates. While there has been evidence of

association between yield spreads and real economic

activity in every case of developed economies,

predictability varies across the countries. It has been

suggested that country-wise variations in the predictive

power is on account of the differences in regulatory

regimes among the economies. Although the phenomenon

has been widely examined in developed economies,

similar studies are virtually absent in the case of emerging

1

For a recent review of the extensive literature on the historical and

international performance of asset prices as leading indicators, see for

example Stock and Watson (2003b): they provided a survey of 66

previous papers on this subject.

economies. In part, this is because in developing

economies with administrated interest rates, the yield

curve has been either completely absent or not market

determined and thus did not form a suitable test case.

After having granted the necessity of a financial

deepening, development of domestic debt security markets

in these economies in the very recent years reflects their

efforts to self-insure against ‘sudden stops’ and reversals

in international capital flows following the string of crises

of the 1990s (IMF 2006). From a macroeconomic

perspective indeed, domestic debt markets were seen by

policy makers in emerging countries as an alternative

source of financing to cushion against lost access to

external funding. Moreover, from a microeconomic

perspective, deeper domestic debt markets were expected

to help widen the menu of instruments available to address

currency and maturity mismatches, which reduces risks of

financial crises. For all these reasons, local authorities

have engaged in deliberate efforts to develop domestic

debt markets. Until 1986, the Tunisian financial system

was characterised by a highly regulated regime, which has

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International Journal of Management Excellence

Volume 2 No. 1 October 2013

since been gradually liberalized. By the mid-1990s, there

has been considerable improvement in terms of volumes,

variety of instruments, number of participants and

dissemination of information, and a yield curve

particularly in case of government securities started

emerging since 2000.

The present paper is an attempt to test the relationship

between the yield spreads and real economic activity in

Tunisian context. It is organized as follows: section I

explains the economic rationale behind observed

association between the yield spread and real economic

activity. Section II presents a survey of the literature on the

phenomenon under study. Section III sets out the empirical

results of our exercise conducted on the Tunisian economy

when we evaluate the explanatory power of several

different combinations of yield spreads, based on the long

rates of five and ten years, and the short rates of one year,

three months and one month, in their ability to explain

cumulative growth of real industrial production. We

compare also the explanatory power of the domestic

spreads with the one of foreign spread. Section V

concludes this study.

2. Yield spread as predictor of real economic

activity: theoretical rationale

According to Peel and Taylor (1998), it is a “stylised fact”

that the slope of the yield curve can be used as a leading

indicator of future economic activity. Therefore, this

section will not devote much time to reviewing the

relevant theoretical reasons that explain the observed

relationship between the yield spread and real economic

activity. There are at least three main reasons that explain

the relationship between the slope of the yield curve and

real economic growth and thus explain why the yield curve

might contain information about future growth or

recessions. In general, this relationship is positive and,

essentially, reflects the expectations of financial market

participants regarding future economic growth. A positive

spread between long-term and short-term interest rates (a

steepening of the yield curve) is associated with an

increase in real economy activity, while a negative spread

(a flattening of the yield curve) is associated with a decline

in real activity.

The first reason stems from the expectations hypothesis of

the term structure of interest rates. This hypothesis states

that long-term interest rates reflect the expected path of

future short-term interest rates. In particular, it claims that,

for any choice of holding period, investors do not expect to

realise different returns from holding bonds of different

maturity dates. The long-term rates can be considered a

weighted average of expected future short-term rates. An

anticipation of a recession implies an expectation of

decline of future interest rates that is translated in a

decrease of long-term interest rates. These expected

reductions in interest rates may stem from countercyclical

monetary policy designed to stimulate the economy

2

. In

addition, they may reflect low rate of returns during

recessions, explainable, among other factors, by credit

market conditions

3

and by lower expectation of inflation.

Indeed, the slope of the yield curve is calculated on

nominal interest rates

4

and therefore embodies a term

representing expected inflation. Since recessions are

generally associated with low inflation rates, assuming for

example that a downward Phillips-curve relationship

holds, this can play a role in explaining the expectation of

low rate of returns during recessions. Alternatively, if

market participants anticipate an economic boom and

future higher rates of return to investment, then expected

future short rates exceed the current short rate, and the

yield on long-term bonds should rise relative to short-term

yields according to the expectations hypothesis.

Another reason which explains the above relationship is

related to the effects of monetary policy. For example,

when monetary policy is tightened, short-term interest

rates rise; long-term rates also typically rise but usually by

less than the current short rate, leading to a

downwardsloping term structure. The monetary

contraction can eventually reduce spending in sensitive

sectors of the economy, causing economic growth to slow

and, thus, the probability of a recession to increase.

Estrella and Mishkin (1997) show that the monetary policy

is an important determinant of term structure spread

5

. In

particular, they observe that the credibility of the central

bank affects the extent of the flattening of the yield curve

in response to an increase in the central bank rate.

The third reason is given by Harvey (1988) and Hu (1993)

and it is based on the maximisation of the intertemporal

consumer choices. The central assumption is that

consumers prefer a stable level of income rather than very

2

Haubrich and Dombrosky (1996) call this the « policy anticipations

hypotheses ».

3

The authors show also that the monetary policy is not the only

determinant of the term structure spread. In fact, there is a significant

predictive power for both real activity and inflation. They demonstrate by

an empirical analysis that the yield curve has significant predictive power

for real activity and inflation in both the United States and Europe. See

Estrella and Mishkin (1997) for further details. Estrella (1997) presents

also a theoretical rational expectations model that shows how the

monetary policy is likely to be a key determinant of the relationship

between the term structure of interest rates and future real output and

inflation.

4

Although the theoretical linkage expressed in economic models is

between the real term structure and future economic activity, it’s the

relationship of the nominal term structure with economic activity that has

been engaged the attention of empirical researchers for the simple reason

that nominal term structure is so readily observable whereas the

computation of the real term structure requires the estimation of inflation

expectations of market participants. These expectations are not directly

observable. In this case, Plosser and Rouwenhorst (1994) pointed out that

one would expect the nominal term structure to forecast real activity

better if the term structure of expected inflation is flat and stable over

time rather than sloped and variable.

5

But as Dueker (1997) explains, this is depends on their assessment of

the size and duration of the recession’s effect on short-term interest rates.

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Volume 2 No. 1 October 2013

high income during expansion and very low income during

slowdowns. In a simple model where the default-free bond

is the only financial security available, if the consumers

expect a reduction of their income - a recession - they

prefer to save and buy long-term bonds in order to get

payoffs in the slowdown. By doing that they increase the

demand for long-term bond and that leads to a decrease of

the corresponding yield. Further, to finance the purchase of

the long-term bonds, a consumer may sell short-term

bonds whose yields will increase. As a result, when a

recession is expected, the yields curve flattens or inverts.

3. Survey of literature

Fama, as early as in 1986 and later Stambaugh in 1988

mentioned that term structure appears to predict real

economic activity though these were not supported by any

detailed statistical analysis

6

. The presented graphs show

that rise and fall in forward rates precedes economic

upswing and recession respectively. Since then a

significant amount of empirical evidence has been

conducted to test the existence of relationship between

yield spread and real economic activity. The literature on

term spreads uses different measures of yield spread

7

. The

adage that an inverted yield curve signals a recession was

formalized empirically, by a number of researchers in the

late 1980s, including Laurent (1988, 1989), Campbell

Harvey (1988, 1989), Stock and Watson (1989), Chen

(1991), and Estrella and Hardouvelis (1991). These studies

mainly focused on using the term spread to predict output

growth (or in the case of Harvey 1988, consumption

growth) using U.S. data. Of these studies, Estrella and

Hardouvelis (1991) provided the most comprehensive

documentation of the strong (in-sample) predictive content

of the spread for output, including its ability to predict a

binary recession indicator in probit regressions. This early

work focused on bivariate relations, with the exception of

Stock and Watson (1989), who used in-sample statistics

for bivariate and multivariate regressions to identify the

term spread and a default spread. Notably, when placed

within a multivariate model, the predictive content of the

term spread can change if monetary policy changes or the

composition of economic shocks changes (Smets and

Tsatsaronis 1997). Movements in expected future interest

6

According to A. Estrella (2005), the analysis of the behaviour of interest

rates of different maturities over the business cycle back at least to

Mitchell (1913), Kesel (1965) and Butler (1978).

7

Research on the United States business cycle has relied mostly on

interest rates for U.S Treasury securities. One reason is convenience: data

for maturities are available continuously for a long period. Another

reason is that the pricing of these securities is not subject to significant

credit risk premiums that, at least in principle, may change with maturity

and over time. For similar reasons, studies of other countries tend to use

data on national government debt securities. Rates on coupon bonds and

notes are most easily accessible, but researchers in many countries have

also produced zero-coupon rates, witch may directly matched with the

timing of forecasts. Some analysts have also used, at short-term rates, the

leading rates of the central bank or others rates of many market.

rates might not account for all the predictive power of the

term spread. For example, Hamilton and Kim (2002)

suggested that the term premium has important predictive

content for output as well.

For the studies which forecast recessions rather than a

quantitative measure of real output growth, Estrella and

Hardouvelis (1991) and Estrella and Mishkin (1998)

documented that the yield curve slope significantly

outperforms other indicators in predicting recessions,

particularly with horizon beyond one quarter. This forecast

is done estimating a probit model. Dueker (1997) confirms

this result using a modified probit model which includes a

lagged dependent variable. Built on these works, many

papers, on the one hand, give empirical results on the fact

that these evidences are present also in the major countries

of the European Union and, on the other hand, they try to

improve or change the model used to forecast recessions.

These papers include Bernard and Gerlach (1998), which

provide a cross-country evidence on the usefulness of the

term spreads in predicting the probability of recessions

within eight quarters ahead. Estrella and Mishkin (1997)

focus on a sample of major European economies (France,

Germany, Italy and the United Kingdom). Sédillot (2001)

provides an empirical evidence for France, Germany and

the U. S. Ahrens (2002) evaluates the informational

content of the term structure as a predictor of recession in

eight OECD countries. Stock and Watson (2003b) examine

the behaviour of various leading indicators before and

during the U.S. recession that began in March 2001.

Harvey (1991), Hu (1993), Davis and Henry (1994),

Plosser and Rouwenhorst (1994), Bonser-Neal and Morley

(1997), Kozicki (1997), Campbell (1999), Estrella and

Mishkin (1997), and Estrella, Rodrigues, and Schich

(2003), Moneta (2003), and Mehl (2006) generally

conclude that the term spread has predictive content for

real output growth in major OECD economies. Estrella,

Rodrigues, and Schich (2003) use in-sample break tests to

assess coefficient stability of the forecasting relations and

typically fail to reject the null hypothesis of stability in the

cases in which the term spread has the greatest estimated

predictive content (mainly long horizon regressions).

Additionally, Bernard and Gerlach (1998) and Estrella,

Rodrigues, and Schich (2003) provide cross-country

evidence on term spreads as predictors of a binary

recession indicator for seven OECD countries. Unlike

most of these papers, Plosser and Rouwenhorst (1994)

considered multiple regressions that include the level and

change of interest rates and concluded that, given the

spread, the short rate has little predictive content for output

in almost all the economies they consider.

These studies typically used in-sample statistics and data

sets that start in 1970 or later. Three exceptions to this

generally sanguine view are Davis and Fagan (1997),

Smets and Tsatsaronis (1997) and Stock and Watson

(2003a). Using a pseudo out-of-sample forecasting design,

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Volume 2 No. 1 October 2013

Davis and Fagan (1997) find evidence of sub-sample

instability and report disappointing pseudo out-ofsample

forecasting performance across nine EU economies. Smets

and Tsatsaronis (1997) find instability in the yield curve–

output relation in the 1990s in the United States and

Germany.

Our paper follows the path of these studies with the aim of

examining the forecasting ability of the yield spread in

predicting growth and recession in the Tunisian context.

The main object of our contribution is to carry out this

investigation at different segments of the yield curve and

testing therefore which specific spread is the best predictor

of industrial production in the Tunisian economy.

4. Data description

Yield data used for the study were derived from the series

of annualised yields of different maturity Treasury bonds

and money-market interest rates compiled at daily intervals

by the Central bank of Tunisia. The sample period is from

month 1, 2001 to month 9, 2006. From the daily yield

series, a series of month-end yields were extracted and

these month-end yields were averaged to drive a series of

monthly yields. The term spreads were computed from

monthly yield series. The purpose of transformation the

yield data to monthly series is to match the frequency of

Industrial production data which are available at monthly

intervals. In this article, the term spread

8

at time t, St, is the

observed difference between a selected long term-yield

YLt and a selected short-term yield SYt : St = LYt − SYt .

We consider the following list of spreads

9

:

S1 = LY1 − SY1 where : LY1 is the annualised

yield of ten year and SY1 is the annualised yield

of one year;

8

Observe that the difference

tt YSYL

is proportional to the

difference between the forward rate calculated from YLt et YSt ,

t

f

,

and YSt. The forward rate is defined as in Shiller, Campbell and

Schoenholtz (1983):

)( sL

tstL

tDD YSDYLD

f

, where DL is the duration of the bond

with L as maturity and DS is the duration of the

bond with S as maturity. The difference

tt YSf

is the correct

measure of the slope of the yield curve, but it is proportional to

).()/( : ttsLLtttt SYLYDDDSYfSYLY

9

Since we subject our data to linear regression analysis we need to carry

out tests for stationarity because it has been well established that non-

stationarity data can produce spurious results. These tests are carried by

means of augmented Dickey-Fuller tests. The results indicates that all

spreads are integrated of order zero and there is no reason to be concerned

about the danger of obtaining spurious results on account of non-

stationarity in the regression analysis to follow.

S2 = LY2 − SY2 where : LY2 is the annualised

yield of five year and SY2 is the annualised yield

of one month;

S3 = LY3 − SY3 where : LY3 is the annualised

yield of ten year and SY3 is the annualised yield

of one month;

S4 = LY4 − SY4 where : LY4 is the annualised

yield of ten year and SY4 is the annualised yield of

five year;

SF = LYF − SYF where: LYF is the annualised

yield of five year and SYF is the annualised yield

of three month.

5. Methodology

The basic methodology used for testing forecasting power

is the linear regression model and the probit model. For the

linear model, measures of economic growth (Index of

Industrial Production, IIP) are regressed on the spread and

it takes the following form:

ttktt SG

.

,

Where

ktt

G,

is the annualised percentage continuously

compounded growth of IIP over k months, and it’s defined

as

tktktt IIPIIPkG log(log)/1200(

,

.

kt

IIP

denotes the level of IIP during the month t + k and IIPt

denotes the level of IIP during the month t.

Regressions are carried out to test the explanatory power

of the yield spread in respect of industrial production

growth over a k months ahead. Our approach to evaluate

the explanatory power of the models is to use all available

observations for estimating the regression model and to

examine the statistical significance of the regression

coefficients and the within sample explanatory power of

the models considered

10

.

For the second type of regression

11

, we use a probit model

in which the variable being predicted is a dummy variable

Rt where Rt=1 if the economy is in recession in period t

and Rt = 0 otherwise. The probability of recession at time

10

An econometric problem that arises whenever the cumulative growth of

several months is forecasted in a time

series regression of this nature where the overlap of observations is

created is the autocorrelation of the regression error terms. When the

cumulative growth of k months is forecasted, the regression errors tend to

follow a moving average process of k-1. This results in inconsistent

estimates of the standard errors of the regression coefficients. A well-

known solution for this problem is to correct the variance-covariance

matrix for serial correlation up to order k-1 adopting the Newey and West

(1987) method. We have followed this procedure in all our regressions

involving insample forecasting estimates.

11

These two types of models may be compared in two dimensions:

accuracy and robustness. But there is evidence that the most accurate

binary models perform about as well as the linear regression (Estrella

2005).

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Volume 2 No. 1 October 2013

t, with a forecast horizon of k periods is given by the

following equation:

)()1Pr( 10 ktt XccR

Where

(.)

is the cumulative standard density function,

and X is the set of explanatory variables used to forecast

the recessions.

6. Results and interpretations

6.1. The linear regression estimates

In measuring the term spread, the long term yield can be

selected from several alternative long term maturity yields

and likewise the short term yield can be chosen from

several alternative short yields available to us in the data

set. As forecasting tools, how do these different yield

spreads perform? Is there an optimal choice of spread that

would perform best for a particular forecasting horizon and

for a particular beginning point in the period of activity

forecasted? To answer these questions we examine the

predictive power based on several alternative measures of

yield spreads. Thus, Equation (1) is estimated for each

spread over the 2001: M1 – 2006: M9 time period and the

results of estimates are presented in tables 1, 2, 3, 4 and 5

in appendix.

We first examine the question of whether the choice

between the yields of one and three months matters in the

computation of the spread by comparing, in charts 1, the

explanatory powers of the following regressions:

tktt

tktt

SG

SG

3,

1,

The

2

R

from the regression equation measures the

proportion of the variation in real industrial production

growth that is explained by the yield spread. At shorter

horizons ( k ≤ 4months ahead) the one year yield does as

better as the one month yield since their R-bar squares for

these months are nearly the same. Given the shorter yield

we now examine which of the longer yields are more

effective by selecting in turn the five year and the ten year

for computing the yield spread:

tktt

tktt

SG

SG

3,

2,

In the same way, we compare the predictive powers of the

two equations (system 4) for horizons which exceed 6

months ahead. By comparing the explanatory powers

(Charts 1), the spread S3 is more effective than the S2. The

pattern in explanatory power suggests that explanatory

power improves when the maturity period of the long term

bond corresponds more closely with the forecasting

horizon.

Financial markets have become increasingly integrated

internationally and the nature of this integration and the

transmission channels are not always well understood. A

growing strand of literature has attempted to analyse

international financial spillovers

12

but has largely ignored

the slope of the yield curve. To this level the yield curve in

the euro area can be expected to have some predictive

content for growth in Tunisian economy. It can further be

expected to convey better information on the future impact

of common shocks, given that euro area debt security

markets are more liquid than emerging economy ones.

Last, the euro has an important role in the exchange rate

policy of our economy. This magnifies the pass-through

from euro area policy interest rates to our domestic interest

rates. In turn, this contributes to potential co-movements

between the slope of the yield curve in the euro area and

the Tunisian domestic slope of the yield curve. And

indeed, recent evidence from Frankel et al. (2004) and

Shambaugh (2004) suggest that countries that have a

pegged exchange rate follow base country interest rates

more than countries that have a float, in particular when

they have lifted capital controls. In other words, having

fixed exchange rates forces countries to follow the

monetary policy of the base country.

Against this background, we investigate the usefulness of

the French slope of the yield curve as a predictor of

domestic growth over k months ahead. To compare the

explanatory power of foreign spread and domestic spread

and test for the existence of international financial

linkages

13

, we estimate the following system of equation:

tktt

tFktt

SG

SG

3,

,

12

For example, Plosser and Rouwenhorst (1994), using time series

techniques, find evidence that the US slope of the yield curve helps

predict growth in both Germany and the U.K. (and vice versa)

significantly. Bernard and Gerlach (1998), using probit estimation, find

that the slope of the yield curve in the US and Germany helps predict

recessions in other G7 countries, the UK and Japan, in particular,

significantly. Those earlier contributions have two main features,

however. First, they have ignored inflation altogether. Second, and more

importantly, they have focused on a small number of industrial

economies. Yet, when it comes to the slope of the yield curve,

international financial linkages are also pronounced for emerging

economies. Their small economic size makes the US or the euro area a

possible determinant of their domestic inflation and growth.

13

This predictive content may stem from ( i ) the larger economic size of

the French comparatively to Tunisian one, which makes it an important

component of foreign demand; (ii) the deeper French debt security

market, which leads to a greater ability of its yield curve to convey

information on the future impact of common shocks; and (iii) the

prominent role played by the EURO in the exchange rate policy of

domestic economy, which magnifies interest rate pass-through.

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The explanatory powers relative to the first equation of this

system are always higher than ones relative to the second

equation. By considering all spreads, the French one has

in-sample forecasting an important information content for

future k months ahead (k=18, 24, 30, 36 and 40) and,

relatively to the international sector, it can be considered

as a good leading indicator for Tunisian activity. In order

to judge the overall performance of the forecasting

equation, Charts 1 and 2 plot the R-bar squares values

from estimating the forecasting equation 1 using the

industrial production growth as the measure of the change

in real economic activity. The

),4,3,2,1(

2FiRSi

from

the estimation of equation 1 range from -1.54 to 17.3

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International Journal of Management Excellence

Volume 2 No. 1 October 2013

percent for i = 1, from -3.1 to 6.5 percent for i = 2 , from -

5.54 to 30 percent for i = 3 , from -3.5 to 24 percent for i =

4 and from -1 to 14 percent for i = F. Thus the explanatory

power d epends on yield spread considered and in general

it increases with the lengthening of the forecast horizon.

For the spread S3 , for example, the proportion of variation

in future real activity explained by this leading indicator is

beyond 15% for forecasting horizon exceeds seven

months, but less than 5% for very short-term forecasting

horizon. This note is valid for the remaining spreads but

the best leading indicators, following

2

R

, are S1 and S3.

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While the

2

R

provides an indicator of the explanatory

power of the spreads for real IP growth, the coefficient

from equation 1 measures how much real IP growth

changes following a onepercentage point change in the

yield spread. A positive

would imply a positive

relationship between the current yield curve and future

economic growth. That is, the larger the spread is between

long-term and short-term interest rates, the stronger real

growth will be in the future. The yield spreads are found to

have information content for future industrial production

growth. Moreover, the response of industrial production

growth is often positive, in line with expectations (i.e. a

steepening of the yield curve is associated with higher

expected growth). This is not always the case, however, as

suggested by the results for the spread S4 and in some

instances, estimated coefficients are unstable, switching

sign across forecast horizons.

Charts 3 and 4 provide estimates of

1

for the k months

ahead forecasts for each spread. The coefficient

is

positive in all estimation with the exception of that relative

to S4 (for very short forecasting horizon). The statistical

significance of

is indicated by a solid bar. For the

spread S2, the solid bar also show that this leading

indicator is a significant predictor of real economic growth

in 75% observations related to forecasting horizon ranges.

The charts 3 and 4 show that the numbers of observations

for witch the yield spreads are statistically significant

predictor of future industrial production growth increase

with the forecast horizon. In particular, the spreads S2 and

S3 are being significant since k = 6 and remain until k =

40.

Estimates of the

’s themselves from the equation 1

provide an indication of the economic significance of the

yield curve as a predictor of future real economic growth.

In particular, the coefficient

measures the change in

industrial production growth for a given one-percentage

point change in the yield spread.

For the yield spread S3, for example, the chart 8 chows

that a one-percentage-point increase in yield spread today

is associated with an annualized 3.74-percentage-point

increase in growth over the next six months, an annualized

4-percentage-point increase in growth over the seven

months, an annualized 3.85-percentage-point increase in

growth over the next eight months, an annualized 3.65-

percentage-point increase in growth over the next nine

months and an annualized 3.11-percentage-point increase

in growth over the next ten months. Hence a widening of

the yield spread would imply an increase in industrial

production growth. For example, if real economic growth

in the Tunisian industrial production was 3 percent, a

widening of S3 by one percent point would imply an

increase in industrial production to 6 percent (2 + 1×4, 02)

over the next seven months.

Together the results indicate that while the yield spread

does help explain future real IP growth for many spreads,

the strength of the predictive power varies by explanatory

variable. The explanatory power of the yield spread is

highest in the case of S1 and S3 and lowest for others

spreads (Each bar represents the beta coefficients from the

regression of future real industrial production growth on

the corresponding yield spread. Statistical significance is

indicated by a shaded bar. Source: see appendix and

author's calculations).

6.2. The probit model estimates

A somewhat different approach involves the prediction of

whether or not the economy will be in a recession K

months ahead. This type of exercise abstracts from the

actual magnitude of economic activity by focusing on the

simple binary indicator variable. Although this forecast is

in some sense less precise, the requirements on predictive

power are in another sense less demanding and may

increase the potential accuracy of the more limited

forecast. Empirically, we would like to construct a model

that translates the steepness of the yield curve at the

present time into a likelihood of a recession some time in

the future. Thus, we need to identify three components: a

measure of steepness, a definition of recession, and a

model that connects the two.

The approach we employ is a probit model equation,

which uses the normal distribution to convert the value of

a measure of yield spread steepness into a probability of

recession k months ahead. Following Estrella and

Hardouvelis (1991) and Estrella and Mishkin (1998), we

study the ability of the slope of the yield curve to predict

recessions in the Tunisian context. First, we estimate a

probit model to obtain a probability of recession in the

Tunisian economy between 1 and 7 months ahead. Then,

we improve the probit model using the modification

proposed by Dueker (1997). In order to analyse the

predictive informative content in different segments of the

yield curve we use five yield curve spreads as explanatory

variables. We plug, therefore, in the right side of the

equation (2) all the spreads listed in the first panel of Table

1 and we estimate the model

14

.

Defining what is a recession is fundamental for

constructing the binary time series t R. The National

Bureau of Economic Research (NBER) officially dates the

beginnings and ends of US recessions and it defines a

recession as “a significant decline in activity spread across

the economy, lasting more than a few months, visible in

industrial production, employment, real income and

wholesale ret ail trade”.

14

The model is estimated using a non-linear method (the Newton-

Raphson).

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Another issue is raised in analysing the goodness of fit. In

the classical regression model, the coefficient of

determination R2 is used as a measure of the explanatory

power of the regression model. It can range in value

between 0 and 1, with a value close to 1 indicating a good

fit. In this kind of model it is no more likely to yield a R2

close to 1

15

. To avoid this problem we use the measure of

fit proposed by Estrella (1998). It is a pseudo-R2 in which

the log-likelihood of an unconstrained model, Lu , is

compared with the log-likelihood of a nested model, Lc

16

c

Ln

cu LL )/2(

2)/(1R-pseudo

A last potential problem stems from the serially correlation

of the errors. Since the forecast horizons are overlapped,

the prediction errors are in general autocorrelated. Thus,

we correct this problem using the Newey-West (1987)

15

See, for example, Estrella , A.[1998]

16

The constrained model comes from a model with c1, in equation (1), is

equal to zero. The log-likelihood in the case of the probit model is given

by

)Pr(ln)1()1(Prln ktttktt

ttXRRXRRL

technique and presenting thus t-statistics calculating using

robust errors adjusted for the autocorrelation problem.

Table 1 (panel 1) presents the Pseudo-R2 calculated after

the estimation of a probit model using the different spreads

as explanatory variable and with lags ranging from 1 to 7

months. The highest pseudo-R2 is obtained with the

estimation of a probit model considering as predictor the

spread S3. In particular, the lag which presents the best fit

is k = 6.

In this case, the pseudo-R2 is 0.169 and the t- This result is

significant at the 5 percent level, and if we make a

comparison with the pseudo - R2 of the other spreads we

can draw the conclusion that the best recession predictor is

the spread S3 lagged six months. statistic is -2.585

17

.

Indeed, some other spreads have also a significant measure

of fit at 5 and 10 percent. The highest pseudo-R2 is

obtained with the estimation of a probit model considering

17

A value of 0:169 seems low if it is interpreted as an R2 , but also in

other empirical studies, the pseudo-R2 is not very large. For example,

Estrella and Mishkin (1998) yielded on U.S. data a value of 0:296 using

as predictor the spread 10-year minus 3-month lagged four quarters and

Frank Sédillot (2001) yielded on France data a value of 0.17 using the

same definition of spread lagged six months.

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as predictor the spread S3. In particular, the lag which

presents the best fit is k = 6. In this case, the pseudo-R2 is

0.169 and the t-statistic is -2.585. This result is significant

at the 5 percent level, and if we make a comparison with

the pseudo - R2 of the other spreads we can draw the

conclusion that the best recession predictor is the spread S3

lagged six months. Indeed, some other spreads have also a

significant measure of fit at 5 and 10 percent.

As explained above, the probit model allows us to estimate

the probabilities that the economy will be in recession in a

given month on the basis of the interest rate spread

observed some months before. Figure 6 presents an

example of these probabilities using the domestic spread

S3 lagged 6 months and the foreign spread SF lagged 2

months.

Ideally, the probability should be one in the recession

months (which are shaded in the figure) and zero

otherwise. This chart shows that the estimated probability

increases in the recession periods and remains low in the

non-recession months.

6.3. Probit model with a lagged dependent

variable

One of the main assumptions of the probit model is that the

random shocks are independent, identically distributed

normal random variables with zero mean. In this kind of

model the errors are generally autocorrelated. In traditional

time series approach we deal with this problem using an

autoregressive moving average filter. Here, since the

shocks are unobservable this technique is not more

available. Therefore, we adopt the solution proposed by

Dueker (1997) and Stock and Watson (2003b) to remove

the serial correlation by adding a lag of Rt (the indicator

variable of the state of the economy). Therefore, we allow

the model to use information contained in the

autocorrelation structure of the dependent variable to form

predictions. The probit equation with a lagged dependent

variable becomes:

)()1Pr( 210 ktktt RcXccR

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Table 2 presents the results of the estimations of this

model using respectively as explanatory variable the

spread S1, S2, S3 and SF and with lags ranging from one

to six . The pseudo-R2 is now calculated in the same

manner as explained above with the exception that we can

have three different specifications. The unrestricted model

Lu is calculated using also the lag of Rt. The restricted

model Lc can come from a model with both c1 and c2 are

equal to zero, with only c2 is equal to zero or with only c1

is equal to zero.

In the first specification (first row of Table 2), the

restricted model is the same as the simple probit model and

therefore, it possible to compare this pseudo - R2 with the

value obtained estimating the simple probit model. Now,

the pseudo-R2 is 0:236 for S3 and the best recession

predictor was obtained with the spread S3 lagged six

months

18

. However, this measure is sensible to the fact that

we add another explanatory variable making thus the

comparison not really meaningful. In the second

specification (first row in Table 2), we test for the

informational content provided by the lagged dependent

18

For this case, the McFadden R-squared indicates the same result as the

pseudo-R2. This is valid for the remaining spreads.

variable in addition to the information embodied in the

spread

The measure of fit is significant for the most leading

spread at one to six months forecast horizon, in particular

for S3 (with k=6), suggesting that the lagged dependent

variable provides also important information. In the last

and most interesting case (last specification in first row of

table 2), we test for the information content which goes

beyond the information already contained in the

autoregressive structure of the binary time series. The lag

which presents the best fit is still k = 6 and the value of the

pseudo-R2 is 0.099, proving a good informative content of

the spread.

The estimated probabilities of recession obtained from

running this model give us the same pace of probability’s

curve indicating that in recession months there is an

important likelihood of future decline in industrial activity.

Considering in-sample forecasting, it seems that the use of

a lagged dependent variable helps to forecast historically

recessions in the Tunisian economy.

Therefore, a probit model modified with the insertion of a

lagged dependent variable appears somewhat preferable

than the standard probit model. One disadvantage with in-

©TechMind Research, Canada 104 | P a g e

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sample forecasts is that they allow the forecast to depend

on data which were not available at the time of the

forecast. As a result, the empirical results of the previous

section may provide a misleading indication of the true

ability of the yield curve to forecast real activity. By

contrast, an out-of-sample forecast uses only information

available to market participants at the time of the forecast.

Moreover, an in-sample forecast can always be improved

by adding a new explanatory variable, but that can lead to

an over fitting problem. To avoid a possible misleading

indication of the true ability of the term spread to forecast

a recession it is important to carry out an exercise of out-

of-sample forecasting. Specifically, forecasts for each

period are based on an estimate of equation (2) and (7)

using only data up to the previous period. For example, the

forecast for 2005:M1 is estimated using coefficients from

the regression estimated over the 2001:M1 to 2004:M12

period.

The quality of the out-of-sample forecast is evaluated

using the Root Mean Squared Error (RMSE) statistic. The

RMSE provides an estimate of the out-of-sample forecast

error, and hence measures the accuracy of the forecast. The

low the RMSE, the better the forecast. In evaluating the

out-of-sample forecast power of the yield spreads, the

RMSE from each yield spread forecast is compared with

the RMSE of alternative forecasts of industrial production

activity. Indeed, one advantage of the RMSE measure is

that, for a given country, it can be compared across

different forecasting models. In this section, the out-of-

sample predictive power of the yield spreads model is

compared with that of two alternative forecasting models

aver range horizon. In the first alternative, equation (2) is

used ( called m1). In the second one, equation (7) is

implemented (called m2), and in the third case we use a

benchmark equation which is simply the identical equation

(2) without the indicator variable and where past changes

in t R are used to predict future changes.

To determine the relative forecast performance of the three

models, the yield spread model, the lagged model and the

combined yield spread plus lagged model were estimated

across six forecast horizons and their relative out-of-

sample RMSE’s were compared for the three spreads: S1,

S3 and SF.. Relatively to the two models (m1 and m2), we

have three sets of RMSE for every horizon of forecasting.

Thereafter, we return the RMSE of the equation m1 to the

RMSE of the equation m3 and the RMSE of the equation

m2 in the RMSE of the equation m3. If the report is lower

to the unit, then the model m1 brings information in

relation to the model m3

19

. The same reasoning makes

itself for the model m2. Tables 6, 7 and 8 show the results

of these model comparisons (m1 and m2).

19

The relative RMSE compares the performance of a candidate forecast

to a benchmark forecast, where both are computed using the pseudo out-

of-sample methodology. See for example Stock and Watson (2001).

For the equation (7) in witch S3 is the leading indicator,

the model m1 outperforms the model m2 in 19 out of 30

cases and m2 outperforms m1 only 11 out of 30 cases.

Otherwise, there are 10 out of 30 cases where the relative

RMSE related to m1 is less than one. Whereas, there are

only 7 out of 30 cases in witch the relative RMSE related

to m2 is less than one. By considering the case of spread 2,

the model m1 outperforms the model m2 in 19 out of 30

cases and m2 outperforms m1 only 11 out of 30 cases. In

relation to m3, there are 73% cases where the relative

RMSE related to m1 and that related to m2 are less than

one and consequently the spread S1 is better than S2 as

regard to the out-of-sample forecasting based in equation

(7). Lastly, for the spread SF, the model m1 outperforms in

all cases the model m2 and in each case of out-of-sample

estimates, their relative RMSE are all less than one,

suggesting that SF dominate the others two spreads

concerning this criterion of robustness’ dimension.

7. Summary and conclusion

This article has provided evidence on the ability of mainly

Tunisian yield spreads to predict future real economic

activity. Several interesting and important results were

identified witch are broadly consistent with the results of

previous studies, but are also more comprehensive in that

they evaluate the predictive power of yield spread across

multiple segments of the Tunisian yield curve. The results

indicate the considering yield spreads are economically

significant predictor of economic activity. Explanatory

power begins to increase beyond five months for the

spreads ten year minus one month and ten year minus one

year, indicating that these two domestic spreads are the

best leading indicators for Tunisian industrial production.

In examining international financial linkages, the paper has

also assessed the ability of the slope of the French yield

curve to help predict growth in domestic activity. It has

found that the French spread five year minus three month

has information content in particular for long forecasting

horizon.

The empirical results of this study also show, in sample

estimates, that the strength of the relationship between the

yield spreads and future economic growth varies across the

different examined spreads. The predictive power is

strongest in the case of spread ten years minus one month

and in the case of French spread. Concerning the first

spread, it consistently explains, in average, roughly 15

percent of the variation in future industrial production for

forecasting horizon exceeding 6 month ahead. For the

second spread, it explains 14 percent of the variation in

future industrial production for forecasting horizon with 30

month ahead.

Considering the out-of sample forecasts, the results of this

paper show that the best predictor of recession is the

spread between 10-year and 1-month interest rates.

Therefore, this specific yield spread can be useful for

©TechMind Research, Canada 105 | P a g e

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Volume 2 No. 1 October 2013

economic and monetary policy purposes. To arrive to this

conclusion we used two non-liner model specifications to

forecast the probability of a recession in the Tunisian

economy. These are the standard probit model proposed by

Estrella and Mishkin (1998) and the modified probit model

with the addition of a lagged dependent variable proposed

by Dueker (1997). We found that the use of a lagged

dependent variable helps to forecast historically recessions

in domestic context. Specific attention was paid on the

accuracy of the forecast. We carried out an exercise of out-

of-sample forecasting to investigate the out-of-sample

performance of the probit models. The simple probit model

(with the spread 10-year minus 1-month as explanatory

variable) gives the best result at 6 months forecast horizon

and performs better than the remaining spreads. With the

addition of the lagged dependent variable in the probit

model (with same spread) the forecasting ability improves

significantly and beat the results related to a simple probit

model. The different results carried out show that the

spread 10-year minus 1-month could have provide useful

information both to private investors and to policy Makers.

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Volume 2 No. 1 October 2013

Appendix

Table 1: Predicting future change in Industrial Production using the yield Spread S1

Sample: Monthly, 2001M1 to 2006M9

Spread S1

k

(Months

ahead)

c1

c2

2

R

SEE

NOBS

1

0.028561

-0.326443

-0,01536

0.339292

67

(0.368452)

(-0.069924)

2

-0.005065

1.634079

-0,012631

0.155654

66

(-0.106411)

(0.534829)

3

-0.021254

2.533809

-0,004951

0.126886

65

(-0.521641)

(0.929559)

4

-0.008172

1.636745

-0,007111

0.090275

64

(-0.242405)

(0.738618)

5

-0.031451

2.967716

0,037973

0.065686

63

(-1.089138)

(1.629789)***

6

-0.041377

3.614858

0,08757

0.056728

62

(-1.811085)

(2.522006)*

7

-0.040329

3.597536

0,128601

0.047081

61

(-2.526773)

(3.821367)*

8

-0.035004

3.206183

0,15598

0.038087

60

(-2.666530)*

(4.075803)*

9

-0.033001

3.113668

0,126452

0.041569

59

(-2.838866)

(4.239253)*

10

-0.025297

2.590052

0,131807

0.034067

58

(-2.404132)

(3.883054)*

11

-0.021775

2.360778

0,11641

0.033316

57

(-2.065799)

(3.567261)*

12

-0.020789

2.305020

0,110936

0.033573

56

1.930094

(3.711107)*

18

-0.007439

1.524122

0,10694

0.023573

50

(-0.745732)

(2.844720)*

24

0.000836

1.050934

0,10534

0.017080

44

(0.103163)

(2.642508)*

30

0.009425

0.633171

0,071212

0.012749

43

(1.527080)

(2.180401)

36

0.011251

0.536042

0,141903

0.007915

32

2.732678)

(2.240930)*

40

0.007151

2.073985

0,172986

0.009095

28

(0.846952)

(2.748280)*

Notes: for this table and the following four ones, in parentheses are t-statistic after correction by

method of Newe and West (1987) of standard errors that take into account the moving average

created by the overlapping of forecasting horizons as well as conditional heteroskedasticity. Nobs.

denotes the number of monthly observations.

2

R

is the coefficient of determination adjusted for degrees of freedom, and SEE represents the

corrected regression standard error.

*,** and *** significantly different respectively at 5%, 10% and 20%.

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Volume 2 No. 1 October 2013

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International Journal of Management Excellence

Volume 2 No. 1 October 2013

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International Journal of Management Excellence

Volume 2 No. 1 October 2013

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International Journal of Management Excellence

Volume 2 No. 1 October 2013