lantz frederick

7/30/2019 Lantz Frederick

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Multiple structural break change and energy forecasts : application to

diesel cars equipment in France

Jean-Pierre Indjehagopian1, Frdric Lantz

2, Elodie Sentenac-Chemin

3

Summary :

Diesel oil consumption rapidly growths in Europe during the last decades up to 202 million of

tons in 2008. This increase is mainly attributed to the growing transport needs by trucks and to

the switch between gasoline and diesel cars. Nowadays most of the passenger cars sales are diesel

cars. This increasing share of diesel engine for passenger cars could be associated to the evolution

of the household income, the spread between gasoline and gas oil price, and to the performance

of the diesel engine with a lowest fuel consumption.In this context, we have built an econometric cointegration model in order to establish a long term

equilibrium between le diesel car share and the GDP, the price spread and the engine fuel

consumption in France. We use quarterly data from 1985-Q1 to 2008-Q3.

The classical Chow test and cusum tests point out several structural break dates over the sample.

When we carry out the unit root test with structural break, some of these dates are significant.

Consequently, we apply the Bai and Perron (1998, 2003) procedures to test for multiple break

points and the recent Kerjrival and Perron (2008) developments for cointegration models. We

compare the different test procedures and we establish a long term equilibrium for the diesel car

share with a decreasing impact of the price spread and an increasing effect engine performance.

We analyze the consequences of these structural breaks on the long term energy demand forecast

in the case of diesel oil.

Introduction

The consumption of fuel for road transport (for passengers and goods) in Europe amounted to 180million tonnes (Mt) in 1985, of which 60% was petrol and 40% diesel. Twenty yearslater, this consumption exceeded 270 Mt, but the proportion had reversed, with 60% ofconsumption being diesel and 40% petrol. This reversal of the situation took place in everycountry in Western Europe, beginning in the mid-1980s for passenger vehicles, but with very

different situations from one country to another, because of the fiscal context and differingperceptions of the environmental characteristics of diesel. As a consequence, France is one ofthe countries with the largest market share going to diesel in Europe. Today, over 70% of carssold have diesel engines.

Diesel was chiefly for commercial use at the beginning (for example, in taxis) but step bystep has moved into the fleet of private cars. Its popularity is due to several factors. Firstof all, the price differential between petrol and diesel, largely due to different tax rates,helped this kind of engine to enter the fleet. Subsequently, performance comparisonsdemonstrate that the distances covered in a diesel car are greatly superior to those possiblein a petrol car. Furthermore, environmental considerations have incited people tochoose vehicles with lower emissions levels, and diesel cars, being more economical on

1 Essec Business School, Av. Bernard Hirsch Hirsch, F-95021 Cergy-Pontoise cedex2

IFP- School, 228, av. Napolon Bonaparte F-92852 Rueil-Malmaison cedex3 IFP-Energies Nouvelles, 1 & 4 av. de bois prau, F-92852 Rueil-Malmaison cedex

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fuel, emit less pollution than petrol cars. Finally, while diesel vehicle purchases lostmomentum in the mid-1990s, new diesel engine technologies helped sales take off oncemore, especially particle filters and the adoption, in the mid-price range of engines, of high-pressure direct injection, which enables better performance.

The principal topic of this paper is the analysis of the structural breaks in the proportion ofdiesel vehicles in France. We perform an econometric estimation of the penetration of dieselas a function of various factors such as the price differential between petrol and diesel, thedifferential in fuel consumption between these two engine types, and the revenue, by means ofquarterly figures and drawing on a sample beginning in the 1st quarter of 1985 and ending in the 3rdquarter of 2008. The estimation of this model raises statistical difficulties (e.g. the non-significant nature of the coefficients, auto-correlation, and instability of the coefficients) andproblems with the economic interpretation of the coefficients. Temporal stability tests leadto the detection of several dates for structural breaks, which correspond to majorchanges in vehicle acquisition choices. The use of multiple structural break tests suggestedbyBai and Perron (1998, 2003) enables identification of these breaks.

The paper is organised in the following way: in Section 1, we develop an empirical analysis of theswitch to diesel in the French car fleet; in Section 2, we explain the procedures for theeconometric tests for stationarity with structural breaks that apply to our work. In fact, the standardtests for a unit root (e.g.Augmented Dickey-Fuller - ADF, Phillips-Perron - PP) may induce us toreject wrongly the idea that the series are stationary because of a structural break. It istherefore necessary to carry out tests for structural breaks on the series and on the long-termrelationship. Subsequently, in Section 3, we apply this methodology to the penetration of dieselin France. Finally, the lessons drawn from this analysis are presented in Section 5, as muchfrom an economic point of view on the penetration of new technology into the automotivefield, as from a methodological point of view on the use of econometric methods tocarry out this type of analysis.

1. Economic analysis of the switch to diesel in the French car fleet

Within Europe, the diesel engine has spread rapidly through the car fleet. Figure 1 shows therate of penetration of diesel vehicles in new vehicle sales in the five largest European markets France, United Kingdom, Italy, Germany and Spain. Nowadays, the diesel car sales stand for

around 46% of the total sales in Europe (around 70% in France) and they represent one half ofthe car fleet

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Figure 1: Proportions of diesel engines in new cars in the main European car markets:

Source: French Motor Manufacturers Association (CCFA)

We can see from this that the proportion has risen greatly since the 1990s. This switch to dieselwas initiated by France from the mid-1980s onwards, very rapidly followed by Spain. Today,

these proportions exceed 70%. The switch to diesel in the German and Italian fleets began before

that in France, at the beginning of the 1980s, but ran out of steam and dropped until the start of

the 1990s. Subsequently we can once again observe an increasing switch to diesel in these fleets,

with the sales of diesel vehicles now attaining between 48% and 58% of total new vehicleregistrations. Finally, in the United Kingdom, diesel had a tougher time making

its mark, with a leap at the beginning of the 1990s, followed by a drop, with arebound after 2000. The proportion of diesel engines has thus reached around

40% today. These disparities within Europe depend on several factors, in particular thefiscal treatment of fuel and the perception of environmental performances, which

may be different between one country and another.Within Europe, France is a very interesting case. We have seen how it was thiscountry that initiated the strong rise in the proportion of diesel engines. Inaddition, it has currently attained the highest proportion of diesel vehicle sales inEurope. The diesel engine option was chiefly developed at the beginning of the1980s, through the inclusion of this new technology in mid-range and entry-levelvehicles, the commonest range in France. The first diesel cars appeared earlier,

before 1980, but were mainly reserved for business use.The proliferation of diesel vehicles in the French fleet was very rapid. The share ofdiesel engines among new registrations was 9.9% in 1980, rising to around 70% in 2009,with 1.6 million diesel vehicles sold in that year.

The spread of vehicles with diesel engines in the French fleet followed three clearlydefined phases :- A phase of powerful growth in new diesel car numbers in the fleet from 1985 to 1995- A phase of stagnation between 1995 and 2000

0.00

0.10

0.20

0.30

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France

Germany

United Kingdom

Italy

Spain

0.80

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0.60

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0.10

0.00

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- A phase of further but slower growth from the beginning of the 2000s

Thus, several effects would seem to have had an impact on new diesel vehicleregistrations in and consequently on the penetration of diesel in the French car fleet. First

of all, rising standards of living have an impact on diesel vehicle purchases, as they aremore expensive than petrol cars. Subsequently fuel prices play a significant role, inparticular, the price differential. Thus, when the price of petrol rises, consumers maywish to exchange their petrol vehicles for diesel cars, which cost more to buy but whoserunning costs are lower. Finally, technological progress has an impact on new vehiclepurchases through the influence on fuel consumption. In fact, diesel engines are moreefficient than petrol engines, as they consume 30% less fuel on average (Pinchon, 2004).The factor that has the greatest influence is the gap between diesel and petrol fuelconsumption figures. When this gap increases, people turn to diesel cars.

The price differential corresponds to the difference between the prices of petrol and ofdiesel. To understand the way it changes, it is necessary to specify the main componentsthat constitute the price paid by the end consumer ex-refinery price, distribution costsand margin, excise duty and value added tax which applies to the whole cost.The price differential grows from the beginning of the period until the 1990s, thendecreases until 2008. While at the beginning of this period, the ex-refinery price ofdiesel and the taxes on it are lower than the same prices and taxes on petrol, a slightreduction of the difference in excise duty may be observed subsequently. But the effectabove all derives from the rise in the ex-refinery price of diesel (linked to the rise inthe share of medium-weight distillates in the demand for petroleum products and toimproved product specifications), amplified by the effect of VAT, thus explaining the

reduced price differential between petrol and diesel.The change in the fuel consumption differential, for its part, may be divided into threephases. The differential first rises until 1990, then decreases between 1990 and 2000,and finally rises again towards the end of the period. Diesel technology was efficient atthe beginning; subsequently major progress was made on petrol engines instead; and, atthe end of the 1990s, the installation of high-pressure direct injection engines in mid-priced cars resulted in great reductions in the fuel consumption of diesel cars. This hashad a definite effect on the rise in demand for new diesel cars from the beginning of the2000s.

The evolution of the economic activity (economic recession, car purchase subsidies andenvironmental policy) should give some explanations to the slowdown in demand for newdiesel cars in the mid-1990s. Car scrapping allowances between 1994 and 1995 favouredthe purchase of petrol vehicles. Effectively the latter, being less expensive than dieselcars, were in direct competition with second-hand vehicles. Finally, governmentpronouncements at the end of the decade on the poor environmental performances ofdiesel cars, especially because of particle emissions, contributed to the decline in dieselvehicles sales.

Thus, the various effects together characterise the modifications in consumer behaviour,which seem to presage multiple structural breaks in the long term balance existing between the

proportion of diesel vehicles and its principal determinants. We shall therefore seek to identifyand explain these breaks, then to estimate the long-term relationship. To this end, we make useof the diesel vehicle proportion data (denoted by TXD in the subsequent models), which is theratio of diesel vehicles sold to the total of all petrol and diesel vehicles. These data on newvehicles are drawn from theINSEEdatabases. We subsequently use data on gross domestic

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product (GDP) drawn from the same source. These are expressed in constant euros, with abase of 100 in the year 2000. The fuel consumption data are, for their part, drawn from thedatabases of the French Department of Energy and Raw Materials-Ministry of Industry(DGEMP), only concern new vehicles, and are expressed as litres per 100 kilometres. The most

recent data on this topic are provided by the French Environment and Energy ManagementAgency (ADEME). The fuel consumption differential is therefore calculated as the differencebetween the fuel consumption of petrol vehicles and that of diesel vehicles (designated DIChereafter). The data on petrol and diesel prices are drawn from the DGEMP databases, inparticular the Pegase database. They are in constants euros per litre. As several grades of petrolexist, the petrol price is calculated as a sum of the prices of the various grades weighted by theirsales figures, themselves drawn from the statistical records of the French Professional PetroleumCommittee (CPDP). The price differential is calculated by subtraction of the diesel price fromthat of petrol, including taxes (denoted byDIP in the following models).

2. Methodology

The search for long-term equilibrium relationships between different variables is generallybased on the co-integration techniques suggested byJohansen (1988) or on the use of the modelfromEngle and Granger (1987) when only a single relationship has to be tested. Nevertheless,interpretation of the standardAugmented Dickey-Fuller (ADF) and Phillips-Perron (PP) tests on theresidual values of the co-integration model and on the observed series, leading to non-rejectionof a unit root, is difficult when the sample under consideration incorporates economic events

that may cause structural changes.To deal with this problem, Perron (1994, 1997), Perron and Vogelsang (1992, 1998),Zivot andAndrews (1992) have proposed the introduction into the Dickey-Fullerregression an indicatorvariable specifying the existence of a structural break. Using a similar approach, Gregoryand Hansen (1996) modified theEngle and Grangermodel so as to enable a structural change in thelong-term relationship. These tests also include a procedure for detecting the date of the break,should this be unknown.The interaction between the structural breaks and the analysis of the unit root that we have justmentioned has given rise to numerous publications. Structural changes at known or unknown datesin the context of a co-integration analysis based on vectorial auto-regressive (VAR) modelshave been studied in particular byJohansen and Nielsen (1993), Quintos (1998) and Saikkonen and

Ltkepohl (2000). The more general problem of estimating linear models with multiplestructural changes, which concerns us more closely, was studied byBai and Perron (1998).The analysis of the relationship which exists between the proportion of diesel vehicles, the fuelprice differential, the fuel consumption differential between petrol and diesel and nationalincome, in France, provides us with an application of the various test and econometricestimation methodologies in the presence of structural breaks.

In our modelling context, the proportion of diesel vehicles should be affected by structural breaksin the trend, with respect to the integration of new technologies into the fleet and the changes ofhabits that the development of diesel has triggered. Thus, structural break detection testssuccessively carry out tests for unit root, first on the series and then on the co-integrationmodels. Because several breaks could occur, tests for multiple breaks have been considered.

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2.1 Tests for unit root and tests of co-integration with a single

structural break

In their approach, Perron and Vogelsang (1992), Perron (1994, 1997) andZivot and Andrews (1992)develop a procedure to test the null hypothesis that the time series ( )tY , with [ ]Tt ,1 , ischaracterised by the presence of a unit root and a possibly null constant with a structuralbreak occurring at time TB, (1 < TB


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kmT

aSCR

km

aSCRSCR

kmTkmF

)1(

0

))1(,(

+

=+ (1)

where kand Tare the number of variables and the number of observations respectively, SCR0

designates the sum of the squares of the residuals of the model estimated over the T

observations, and SCRa is obtained by summing the SCR over each of the sub-periods.

Ninomiya (1977) suggested systematic use ofChows test to determine the number of structuralchanges as well as the dates associated with them. This test, also known as the step by step Chowtest " conforms to the following methodology: (i) Calculate the Fisher statistic for formula (1)denoted by F(Tm) for all possible sub-periods , (ii) Find the largest significant F(Tm) statistic,

denoted by SupF(Tm)=Max(F(Tm)). Then, the structural break date is at Tm, (iii) Divide the

sample from Tm and repeat steps (i) and (ii) on the two sub-samples.

Bai and Perron use this procedure for cases of multiple structural breaks in a linear model with

unknown dates. The starting point for the analysis is a linear regression model with m structural

breaks and therefore m+1 regimes:

Y t = x + z t j + u t

with t = Tj-1+ 1,..., Tj ; j = 1, ..., m + 1

whereytis the variable being explained,

and where the explanatory variables are spread out betweenx andz. The vectorxt is the columnvector of the explanatory variables at time t whose effects are invariant with time, in such a way

that the vectorx 't is a line vector. The vectorztis the column vector of the explanatory variables attime t whose effects vary over time, in such a way that the vector z't is a line vector. The

coefficients and j are associated with the explanatory variablesx'tand z't respectively. Theerror term is denoted by ut.

In matrix form, the model may be expressed as:

UZXY ++=

where:

)',...,();,...,(

;)''...,','(;)',...,(;)',...,(;)',...,(

111

121111

1 iiTTim

mTTT

zzZZZdiagZ

uuUxxXyyY

++

+

==

====

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The structural break dates T1 to Tm are unknown, and in line with Bai and Perron, we have

adopted the convention T0 = 0 and Tm+1 = T. The procedure for sequential tests suggested by Bai

and Perron consists of estimating the coefficients of this equation as well as the structuralbreakpoints in the sample ofTobservations.

The hypotheses on the possible values of the structural break dates are as follows: each datemust be asymptotically distinct and delimited by an interval in the sample. Thus, the authorspostulate i = Ti/T(with i = 1, ..., m). This ratio will depend on the minimum size that may beallocated to each sub-period.

So, for m partitions in the sample, we obtain an estimator of the ordinary least squares ofand of the j terms. Subsequently, we can calculate the sum of the squares of the residuals on

the whole sample, having taken account of the break dates T1 to Tm, which we denote by ST(T1,..., Tm). Finally, the estimations of the regression parameters obtained are those associated with theestimated partition T1, ..., Tm.

The estimation of the structural breakpoints is as follows:

(T,...,Tm) = arg min (T1 ,...,Tm) ST (T,...,Tm)

For , the authors suggest a series of tests for structural breaks.

a. Test 1: No structural break against a fixed number of breaks, or test for SupF

In the first test, the null hypothesis (H0) is the absence of a structural break, i.e. m=0, againstthe alternative hypothesis (Ha) of an unknown number of breaks, i.e. m=k. The null hypothesiscorresponds to the estimation of the model over the full sample whereas the alternative hypothesiscorresponds to the estimation of the coefficients on each sub-sample of dimension Ti = i T. Thefractions of sample i are such that:

( ){ }= + 1,,;,..., 111 KiiK

where is a positive number close to 0.

For each partition (T1, ..., Tk), we calculate the following Fisher statistic:

( )( )K

XKT

SSR

RRZMZRR

kq

pqkTqF

'''')1();,...,(

11

1

+=

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where p represents the number of variant regressors, q the number of invariant regressors, whileSSRkis the sum of the squares of the residues corresponding to the alternative model (Ha).

R is the equality matrix of the coefficients over each of the sub-periods and MXis defined as:')'( 1XXXXIM

X

=

The test is then based upon one statistic:

SupFT(k,q) = sup (. . . , K) FT(1 , . . . , K;q) .

The distribution of the critical values ofSupFTdepends on the number of structural breaks k, on thenumber of variant regressors q and on . The tables of critical values were obtained bysimulation. (Bai and Perron 1998, page 58for the table of critical values with = 0.05.

In a recent article, Kejriwal and Perron (2008) broach the problem of multiple structural breaks

in a co-integration model. In this context, the value ofconsidered is higher (= 0.15) andthe distribution of the critical values depends on the order of integration of the regressors, on thepresence or absence of a trend in the long-term equilibrium relationship, and also on thenumber of structural breaks.

b. Test 2: The Double Maximum test

In a second test procedure, Bai and Perron test the null hypothesis (H0) that there is nostructural break against the alternative hypothesis (Ha) of an unknown number m of structuralbreaks limited by parM. This test, called the double maximum test by the authors, amounts tochoosing the number of structural breaks which maximises the Fisherstatistic that corresponds to

the highest Fisherstatistic. Thus we have:

=),(

11

1

,..1

);,...(supmax),...,,,(maxm

qFaaaqMFDmm

MmmT

where (a1,..., a m) is a set of weights defined a priori. If we consider that they are all equal to 1, thetest takes the following form:

=),( 11 ,..1

);,...(supmax

),(maxm

qFqMFUDmMmT

Bai and Perron (1998) also propose a definition of the weights am based on the critical values

of the test SupFT (k, q) = sup(1,k)FT ( 1,..., A K ; q) .

c. Test 3: The test ofl against l+1 structural breaks, SEQ(l/l+1)

In a third test procedure, Bai and Perron investigate the relevance of an l+1th structuralbreak, knowing that l have already been considered. They thus test the null hypothesis (H0) of lbreaks against the alternative hypothesis (Ha) ofl+1 breaks. We start with a sample in which

l breaks have been identified and denote by T1, ... ,Tl the estimated sub-samples, thus minimisingthe sum of the squares of the residuals. We therefore seek to determine whether a structural

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break may be detected in one of the sub-samples, thus leading to the l+1th break. To this end, weuse the test statistic FT (l+ 1 /l), defined as:

( ) ( ) /,...,,,,...,infmin,...,)/1( 11111 ,

=+ +

liiTli

lTT TTTTSTTSllFi

where )()(; 111, += iiiiiii TTTTTT

where is the parameter defining the sample share. The critical values of this sequential test for anumber of structural breaks l, a number of variables q and =0.05 are given byBai and Perron(1998)

The implementation of the sequential tests leads to the following procedure. First, we seek toidentify one structural break. If the Fisher statistic associated with this break is greaterthan the critical value, we select this break and deduce from the test the correspondingestimated break date. Next, with the sample split into two sub-periods, we test for the presenceof a possible additional break. If the Fisher statistic is greater than the critical value for each ofthe two sub-samples, the date corresponding to the higher value represents the secondbreakpoint. The procedure is repeated in this way until no further break date appears to besignificant.

3. Empirical results

The objective of our modelling approach is to test the existence of a long-termrelationship between the diesel vehicle proportion in the vehicle sales (TXD) and thefactors that influence it: national income (GDP), price differential (DIP), and fuelconsumption differential (DIC). The variables GDP, DIP, and DIC are logarithmic. Theeconometric tests are performed during the time t = 1985Q1, ..., 2008Q3. The whole set of testswas carried out using the EViews 7 and WinRats 7.2 software packages.

3.1 Unit root tests

We test for the existence of a unit root on the full sample 1985Q1 to 2008Q3, by means of two

tests: Augmented Dickey-Fuller (AD) and Phillips-Perron (PP), whose results are shown in

Table 1.


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Table 1: ADF and PP tests for unit root on the level and first difference variablesADF PPVariables Model

t-Student k t-Student Q

TXD c,tc

none

-2.10-0.80

1.86

44

4

-2.64-0.68

2.07

114

14

TXD c,t

c

none

-4.24***

-4.27***

-3.39***

3

3

3

-13.4***

-13.5***

-12.2***

6

6

1

log(GDP) c,t

c

none

-2.54

-1.07

3.02

2

2

2

-2.14

-1.14

7.18

6

6

6

log(GDP) c,t

c

none

-3.89**

-3.83***

-2.25**

1

1

1

-6.2***

-6.1***

-3.22***

5

5

5

log(DIP) c,tc

none

-1.25-0.36

0.71

22

2

-2.58-2.07

0.61

2122

34

log(DIP) c,t

c

none

-9.06***

-11***

-11***

2

1

1

-17.9***

-11***

-10.6***

29

44

48

log(DIC) c,t

c

none

-1.73

-1.95

-0.66

5

5

1

0.01

-0.91

-0.28

6

6

6

log(DIC) c,tc

none

-2.88-2.79*

-2.8***

00

0

-3.1-2.99*

-3***

33

3

a- The drift k is chosen so that perturbations in the ADF regression are not autocorrelatedb-The drift parameter q appearing in the Newey-West estimator is chosen so that perturbations in the ADF regression are not auto-correlated at times t and t-qc- The critical values are drawn from McKinnons table (1996) for rejection of H0=stationarityd- ***,**,* indicate the level of significance associated with the 1%, 5%, and 10% thresholds respectively

Thus, the test for unit root indicates that the series all exhibit first-order integration I(1).

Nevertheless, theADFand PP tests may be suspect when the sample under analysis includesmajor events (introduction of technical developments, fuel tax changes, car scrappingallowances, etc.), which are likely to create structural breaks in the series. In order to verify thisand so take account of possible changes in regime, we go on to carry out Perron (1997) tests forunit root with structural break. In Table 2, we present the results of these tests.


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Table 2: Perron 1997 tests for stationarity with structural break

TXD log(GDP) log(DIP) log(DIC)

t(alpha) -6.9*** -3.81 -3.92 -2.87Model A

date 1994Q4 2003Q2 2004Q1 1996Q1

t(alpha) -6.67*** -3.95 -4.76 -7.43***Model B

date 1994Q4 2003Q2 2000Q3 1999Q1

t(alpha) -3.94 -3.47 -3.91 -3.22Model C

date 2001Q2 2008Q1 2000Q3 2008Q1

a- The critical values are drawn from Perrons table (1997) for rejecting H0=stationarityb- ***,**,* indicate the level of significance associated with the 1%, 5%, and 10% thresholds respectively

Thus the diesel vehicle proportion series presents a structural break in the fourth quarter of1994, where we in fact observe a drop in demand for diesel vehicles, due to the slowdown ineconomic growth. The logarithm of the fuel consumption differential also shows a trend break inthe first quarter of 1999. This year represents the spread of direct injection engines to mid-and entry-level cars. In addition, a new technological feature was introduced to dieselvehicles from that year: the particle filter. This fuelled the enthusiasm for the diesel engine,which has lower consumption than petrol, and for which one of the major objections from theenvironmental point of view (particulate emissions) was then resolved.

3.2 Co-integration tests

Dealing with time series implies testing for the existence of co-integration between thediesel vehicle proportion and its main factors. We therefore apply the Johansen (1988) testsshowing the results in Table 3.

Table 3: Cointegration test

H0: Rank = r Eigenvalues Trace statistics max statistics

r = 0 0.28 57.47** 30.81**

r 1 0.17 26.66 17.93

r 2 0.06 8.73 6.05

r 3 0.03 2.68 9.16

a- ** indicates the level of significance associated with the 5% thresholdb- The critical values are tabulated in McKinnon-Haug-Michelis (1999)

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TheJohansen test indicates that we cannot reject the hypothesis of a co-integration relationship

between the variables. In Appendix 1, we present the co-integration relationship. Estimatingthis nevertheless raises many problems. On the one hand, from a statistical point of view, thesigns of the residuals alternate between positive and negative values over fairly long sub-periods, which may be characteristic of temporal instability. On the other hand, from aneconomic point of view, the estimated coefficients of log(DIP) and log(DIC) are not of theexpected sign and/or are not significant. Thus, we evoke the existence of an equilibriumrelationship between the diesel vehicle proportion and its various explanatory variables, butwhich seems to be subject to different regimes.Having highlighted the presence of structural breaks in the TXCand log(DIC) series, the causes

of these may be the existence of structural changes in the long-term relationship. In order to

detect these changes, we perform a series of tests on the equilibrium relationship.First of all, we estimate the econometric model :

TXC= + log(GDP) +log(DIP) + log(DIC) +t

and then we apply the co-integration tests thanks to the Engle and Grangers two-stageprocedure (which is justified since we only have a single co-integration relationship). We thenapply theBrown, Durbin and Evans (1975) tests on the recursive residuals (CUSUM squared).On the co-integration relationship, we perform Gregory and Hansen tests for a singlestructural break. Finally, we apply theBai and Perron (1998, 2003) tests.

3.3 Detection of structural changes

In the initial stage, we apply the CUSUM squared test, which enables identification of twostructural breaks in the whole sample, in the first quarter of 1990, and then in the first quarterof 2000. We then go on to apply the test suggested by Gregory and Hansen (1996), whichallows identification of a single structural break with unknown date. The results are presentedin the following table 4.

Table 4 Results of Gregory and Hansen tests

Date of break

Model C -6.04** 1995Q4

Model C/T -4.73 1996Q4

Model C/S -5.48 1995Q3

a- ** indicates the level of significance associated with the 5% threshold

b- The critical values are as tabulated by Gregory and Hansen (1996)

These tests indicate a change of level in the co-integration relationship around the date 1995Q3. Inaddition, they show the existence of a drift, although we had not detected one in the co-integrationrelationship. This may therefore be suspect and synonymous with the existence of multiples

T- stat


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structural breaks in the co-integration relationship. We then go on to test for the existence ofmultiple changes thanks to Bai and Perron tests.As we have seen, the Bai and Perron (1998, 2003) tests are recent tests that enable characterisationof multiple structural breaks in the long-term relationship, where the number of breaks, as well as

the dates at which they appear, is unknown. Tests for unit root with structural break have indicatedthat, out of all the exogenous variables, only the fuel consumption differential (log(DIC)) actuallypossessed a break. Thus, we only modify this one variable. The two others, log(GDP) andlog(DIP), are considered as invariant over time. In addition, we suppose that the constant variesaccording to the different regimes. We test for the maximum number of possible structural breaksthrough these tests, i.e. M=5. This assumes that the variable is equal to 0.15, signifying that theaverage distance between two break dates is at least 0.15*T "time steps", where T represents thesample on which we are testing for the existence of a break. Table 5 below shows the results of theSupF tests (no break versus m breaks) and the SEQ.

Table 5: Results of Bai and Perron (1998, 2003) tests:

Specificationsqf= 1 qb = 2 = 0.15

Tests of SupF: H0=0 Ha=m

SupFT(1)

22.06***

SupFT(2) SupFT(3)

28.77*** 377.21***

Tests of SupF: H0=l Ha=l+1

SEQT(1/0)

22.06***

SEQT(2/1) SEQT(3/2)

16.90** 5.75

Number of breaks chosen, with dates

Two breaks: 1995Q4

2001Q1

a- ***,**,* indicate that the coefficients are significant at 1%, 5%, and 10% respectivelyb- For the SupF test, the critical values are drawn from Perrons table (2008) Category a, Case 4, for

rejection of H0=No breakc- For the SEQ test, the critical values come from Perrons table (2008) Category a, Case 4, for

rejection of H0=l break

The initial interest is in determining the number of structural breaks. Thus, the SupFtest, whose null hypothesis corresponds to the non-existence of a break as opposed to mruptures, is significant, at a risk of 1%, for M in the range from 1 to 3. Thus, we wouldalways prefer one or more breaks rather than no break at all. We therefore conclude that atleast one break exists. The sequential procedure of the test for l breaks against l+1 breaksshows that SEQT(2/1) is significant to 5%. Thus, the number of breaks in the co-integrationrelationship, determined by this test, is 2.The second interest lies in determining the dates of the structural breaks. These seem to haveoccurred in 1995Q4 and 2001Q1. The first date corresponds to the slowdown in demand

for new diesel vehicles, on the one hand because in the mid-1990s, the rate of economicgrowth dropped in France, and on the other hand because during those years, the pricedifferential between petrol and diesel fuels decreased with the rise in taxes on diesel fuel, andenvironmental concerns came to the fore, as particle emissions were considered to be veryrisky for human health. The mid-1990s thus marked a structural break in the rise of the diesel

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vehicle proportion. The second date, the first quarter of 2001, is a more specific effect oftechnology, that of fuel consumption. Thus, at the beginning of the 2000s, there was agrowing gap between the fuel consumption of a new petrol vehicle and that of a newdiesel vehicle, with the consumption of the latter dropping more quickly than that of a petrol

car.The results of the tests ofBai and Perron are consistent with the results of the tests for unitroot with structural break. Thus, the break observed in the endogenous variable of dieselvehicle proportion brings with it a change in the co-integration relationship at the break pointin 1995Q4, which corresponds to the final date of the first sub-sample. Similarly, the break inthe series of the logarithm of fuel consumption differential causes variation in the relationship, towithin a few quarters, in 2001Q1.

3.4 Model estimation taking account of structural changes

The estimation of the long term equilibrium between the diesel proportion in the car sales (TXC)and its determinants is carried out in a VAR approach and, then, in a univariate approach (Engle &Granger).

In the VAR approach, we substitute the variable log(DIC) by log(DIC)xDU01Q1 where DU01Q1is a dummy variable (DU01Q1(t)=0 until 2000Q4, then DU01Q1=1); consequently, this newvariable is set to 0 until 2000Q4 and is equal to log(DIC) after. Furthermore, we allow a trend inthe con-integrating equation. From the cointegration Johansen test we could not reject thehypothesis of one long term equilibrium between the variables (Table 6).

Table 6: Cointegration Test with modified variable

H0: Rank = r Eigenvalues Trace statistics max statistics

r = 0 0.363 71.997*** 41.973***

r 1 0.184 30.024** 19.023

r 2 0.097 11.002 9.564

r 30.015 1.4371 1.437

Thus, we estimate the long term equilibrium with the modified variablelog(DIC)xDU01Q1. All the coefficient are significant and could be interpreted from aneconomic point of view : both an increase of the price differential and an increase ofthe consumption differential have a positive influence on the diesel proportion TXC(Table 7). Subsequently, the residual variance of the Vector Error Correction Model(with structural break on the long term equilibrium) is strongly reduced.

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Table 7 Normalized coefficients of the long term co-integration relationship with

modified variableTXC Log(GDP) Log(DIP) Log(DIC)*DU01Q1

1.000000 -0.951066 -0.367260 -0.457158

(0.10272)*** (0.07374)*** (0.12609)***( ): Standard deviations*** significance of the coefficients at 1%

In the second apporach, the estimation of the co-integration relationship by means of theordinary least squares must take account of the various structural breaks identified by the tests.Thus, we estimate the diesel vehicle proportion as a function of national income, of the pricedifferential in fuels, and of the fuel consumption differential. The tests for breaks in the serieshave shown that it would seem that there was a change in trend in the development of the dieselvehicle proportion in France, in 1995Q4, as well as a break in the fuel consumption differential in

1999Q1, due to technological progress which stimulated sales of diesel cars. The tests formultiple structural breaks show that there are two breaks in the co-integration relationship,caused by changes in the variables. All these elements are therefore taken into account in themodelling process to get as close as possible to the observed data. The results are therefore asfollows:

StatisticsT:()

2.187

97.0

101*)log(08.0

)log(05.0)log(34.1495*01.01.35

2

)2.2(

)11.4()4.16()1.16()2.16(

==

=

+++

++=

DWn

R

dummiesQDUDIC

DIPGDPQDUTXD

Estimation period: 1985Q1 to 2008Q3.

As before, all the coefficients are significant and, in addition, they have the expected signs.Two structural breaks were integrated into the modelling process. Thus, the constant in themodel allows for a change in regime in the mid-1990s, and the variable log(DIC) allows for achange at the beginning of the 2000s. We tested two by two for equality between the coefficients

of DU95Q4 and (1-DU95Q4), and log(DIC)*DU01Q1 and log(DIC)*(1-DU01Q1). In bothcases, the Wald test indicates that equality of the coefficients is rejected; thus, the change ofregime hypothesis is accepted.The fuel price differential, defined as the petrol price minus the diesel price, has a positive effecton the demand for diesel vehicles. The existence of a pump price difference would seem tofavour a switch to diesel. The price difference represents a psychological phenomenon forconsumers, who feel that they have done their sums right in terms of usage cost (Prieto, 2005).However, it is chiefly the tax differential that explains the price differential. Thus, it was at atime when this was high that the effect on the penetration of diesel was significant.The difference of consumption between petrol and diesel car has a positive effect on thesecond pat of the sample: since the mid-1980s, the diesel engine has profited from numerous

technological advances, in particular at the end of the 1990s, when high-pressure directinjection was adopted for mid-priced models.

22

StatisticsT:()

95

97.0

101*)log(08.0

)log(05.0)log(34.1495*01.01.35

2

)2.2(

)11.4()4.16()1.16()2.16(

=

=

+++

++=

n

R

dummiesQDUDIC

DIPPIBQDUTXD


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Conclusion

Some methodological issues for the econometric tests and some economic issues for the

choice of car engine (and consequently automotive fuel consumption) raise from thisstudy.

Some spurious results could raise from classical tests when structural break could occur(which is the case for the diesel car in our analysis). The unit root test of Perron (1989),the cointegration tests of Gregory et Hansen (1996) and, more recently, the tests of Bai &Perron (1998, 2003) and Kejriwal & Perron (2008) point out such structural break. In ourmodelling approach, the dates of the structural breaks have an economic interpretationand a long term equilibrium is estimated taking into account these structural break dates(with significant coefficients, which was not the case in the first approach)

The switch to diesel in the French car fleet is an interesting case of the spread of atechnological advance. Empirical analysis and subsequent econometric modelling bring outthe fact that this change did not take place in a smooth fashion, but with structural breaks.Until the mid-1980s, diesel engines spread from the top of the range towards the mid-point of therange of cars on offer from manufacturers, thus allowing this technology to be adopted by alarge number of motorists. The econometric study of the determining factors in the switch todiesel that we have carried out is thus focused on the period from 1985 to 2008. In thismodelling process, we analysed the relationship between the diesel vehicle proportion, the

GDP, the fuel price differential and the fuel consumption differential.The chief lessons to be drawn from this econometric modelling process are as follows:- The switch to diesel in the car fleet is characterised by smooth progression until the mid-1990s;this point was marked by the impact of the price differential between petrol and diesel;- A powerful structural break is subsequently observed, which can be explained both by areduction in the fuel price differential and by announcements on vehicle emission standards;- Finally, the development of the high pressure direct injection engine enabled large reductions infuel consumption figures at the beginning of the 2000s, which explains the zest for dieselvehicles in the final sub-period.

References:

Bai J., RL. Lumsdaine, JH. Stock (1998). Testing for and dating common breaks inmultivariate time series. Review of Economic Studies, vol. 65.

Bai J., P. Perron (1998). Estimating and testing linear models with multiple structural changes.Econometrica, vol. 66.

Bai J., P. Perron (2003). Computation and analysis of multiple structural change models.Journal of Applied Econometrics, vol. 18.

Brown RL, J. Durbin, JM. Evans (1975). Techniques for testing the constancy of regression

relations over time (with discussion). Journal of the Royal Statistical Society B, vol. 22.Chow G. (1960). Tests of equality between sets of coefficients in two linear regressions.Econometrica, vol. 28 (3).

Dickey D., Fuller W.(1979). Distribution of the estimators for autoregressive time serieswith a unit root. Journal of the American Statistical Association, vol. 74

Engle R., Granger W.(1987). Cointegration and error correction: representation, estimation


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and testing. Econometrica, vol. 55.Gregory A., Hansen B. (1996). Residual-based tests for cointegration in models with regime

shifts. Journal of Econometrics, vol. 70Indjehagopian J.P., F. Lantz, V. Simon (2000). Dynamics of heating oil market prices in

Europe. Energy Economics vol. 2 (2).Johansen S., (1988). Statistical analysis of cointegration vectors. Journal of EconomicDynamics and Control, vol. 12.

Johansen S. , B. Nielsen (1993), Asymptotics for cointegration rank tests in the presence ofintervention. Manuscript, University of Copenhagen.

Kejriwal M., P. Perron (2008). The limit distribution of the estimates in cointegratedregression models with multiple structural changes. Journal of Econometrics, vol. 146.

Kwiatkowski D., P. Phillips, P. Schmidt, Y. Shin (1992). Testing the null hypothesis ofstationarity against the alternative of a unit root. Journal of Econometrics, vol. 54

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Perron P.(2006). Dealing with structural breaks.Palgrave Handbook of Econometrics.Perron P. , TJ. Vogelsang (1992). Nonstationarity and level shifts with an application to

purchasing power parity. Journal of Business and Economic Statistics, vol. 10Perron P. , TJ. Vogelsang (1998). Additional Tests for a Unit Root Allowing the Possibility of

Breaks in the Trend Function. International Economic Review, vol. 39.Phillips P., P. Perron (1988). Testing for a unit root in time series regression. Biometrika, vol.

75Pinchon P. (2004). Futures evolutions des motorisations dans lautomobile. Revue de

lEnergie.Prieto M. (2005). L'effet de l'offre et des anticipations sur les choix de consommation: la

demande de vhicules particuliers neufs en France. Economie et Socit, vol. 39Quintos C. (1998). Stability tests in error correction models. Journal of Econometrics, vol. 82

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Appendix : Co-integration relationship between the diesel proportion sales and itsdeterminants

In this appendix, we present the long-term normalised equilibrium relationship between thevariables TXD, log(GDP), log(DIP) and log(DIC). The Johansen test for co-integration ispresented in Table 3. From this test, we could not reject the existence of a long termrelationship. Nevertheless, some coefficients are non significant (price and consumptiondifferentials) and the residuals have different patterns according to sub-periods as displayed inthe residual plot (figure A1).

Table A1 Normalized coefficients of the long term co-integration relationship

TXC Log(GDP) Log(DIP) Log(DIC) constant

1.000000 -1.415697 -0.113457 -0.085184 36.81461

(0.25256)*** (0.10755) (0.10635) (6.61715)***

( ): Standard deviations*** significance of the coefficients at 1%

Figure A1 - Graph of the residuals

lantz frederick

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