TRANSPORTATION

THE MALAYSIAN GOVERNMENT’S
ROAD ACCIDENT DEATH REDUCTION TARGETFOR YEAR 2010
LAW, T.H.

RADIN UMAR, R.S.

WONG, S.V.

Road Safety Research Center
Universiti Putra Malaysia
Serdang, Malaysia

Professor, Road Safety Research Center
Universiti Putra Malaysia
Serdang, Malaysia

Mechanical and Manufacturing Department
Universiti Putra Malaysia
Serdang, Malaysia(Received June 17, 2004)
Objective: This paper makes a projection of the vehicle ownership rate to the year 2010 and to use this projection to predict road accident
deaths in year 2010. The projection served as an indicator for the Malaysian government to achieve a 4 road accident deaths per 10,000 vehicles
safety target in year 2010.
Method: The study included the prediction of vehicle ownership and the analysis of past trends in the road accident death rate. Gompertz
growth model was used to project vehicle ownership and the prediction of road accident death rate was done using Autoregressive Integrated Moving
Average (ARIMA) model with transfer noise function.
Results and Conclusions: The Gompertz model predicted that vehicle ownership would be equal to 0.4409 by the year 2010. The road accident death rate is projected to decrease to 4.22 in year 2010, at an average decline rate of 2.14% per annum. This result suggests that a minimum
2.18% reduction per annum is required to achieve the national target in year 2010.
Key Words: Road safety target, Autoregressive Integrated Moving Average (ARIMA), Gompertz growth model, Vehicle ownership rate, Transfer noisefunction

1. INTRODUCTION
In the year 1996, the Malaysian government established a 5-year national road safety target to reduce roadaccident deaths by 30% by the year 20001. During the 5year period, several road safety initiatives from national
to community levels were initiated. A series of intervention programs on strategic issues, such as lack ofconspicuity and protection, speeding, bad driving behavior and unsafe road conditions, were proposed. An integrated safety program was introduced to both prevent andreduce future traffic accidents, as well as to reduce injuries during and after accidents. Strategies were categorized into: (a) accident prevention and reduction, (b)injury control and (c) post injury reduction. Targeted televised motorcycle safety campaigns, more stringent traffic legislation, national accident blackspot programs, roadsafety auditing, construction of new motorcycle lanes andbetter protection for motorcyclists were among the integral components of this comprehensive approach.
By 2001, the concerted efforts resulted an 11%,
10.7% and 29% decrease in the number of deaths, serious and slight injuries, respectively, in spite of a dramaticincrease in vehicle ownership in the same period2. The

42 • IATSS RESEARCH Vol.29 No.1, 2005

road accident death rate dropped from 6.2 deaths per
10,000 vehicles in year 1999 to 5.6 deaths per 10,000 vehicles in year 2001. However the nation’s safety performance is still far behind world-class standard, which is
below 3 deaths per 10,000 vehicles. Hence, in year 2001,
the Malaysian government adopted a new national roadsafety target of 4 road accident deaths per 10,000 vehicles
by year 2010.
This paper makes a projection of the vehicle ownership rate to the year 2010 and to use this projection topredict the road accident death in 2010. This was undertaken using an Autoregressive Integrated Moving Average(ARIMA) model with transfer noise function, developed
to project road accident deaths in year 2010. The projection takes into account changes in population and the vehicle ownership rate. The relationship between death rate
and population, vehicle ownership rate, are described utilizing transfer noise function in ARIMA analysis. Prior
to road accident death rate projection, the prediction ofvehicle ownership rate using the Gompertz growth model
was done separately. The projection may be served as anindicator for the Malaysian Government to achieve the 4road accident deaths per 10,000 vehicles safety target inyear 2010.

THE MALAYSIAN GOVERNMENT’S ROAD ACCIDENT DEATH REDUCTION TARGET FOR YEAR 2010

2. QUANTIFIED ROAD SAFETY TARGETS:
OTHER COUNTRIES' EXPERIENCEOf all modes of transport, transport by road is themost dangerous and most costly in terms of human lives.
Although extensive efforts has been made in many countries in reducing both risk and the absolute number of accidents, the present number of accidents is still far too
high in most countries. Improved road safety is achievable if suitable safety targets in respect to time frame, as
well as ambitiousness are adopted3. This is supported by
Elvik4, who pointed that the best performance in roadsafety was achieved by countries with highly ambitious
quantified targets.
The European Union countries with the best roadsafety records, such as Sweden, the United Kingdom andthe Netherlands, were the first to set quantified targets
to reduce the number of victims to derive maximum benefit from potential improvements in road safety from increased knowledge, accumulated experience and technicalprogress. It is broadly accepted that targeted road safety
programs are more beneficial in terms of effectiveness ofaction, the rational use of public resources and reductionsin the number of people killed and injured than non-targeted programs.
In 1997, Sweden adopted an ambitious road safety
program to aim to achieve zero deaths and serious injuries on the road for the country as a whole. The program
addresses all areas in which local authorities and companies have a leading role to play. Systematic improvements to the road network have been undertaken to reduce
the severity of accidents, and incentives have been provided in conjunction with the private sector, to reduce thedemand for road transport and thus the exposure of road
users to risk.
Australia has adopted a national target to achieve a
40% reduction in the number of fatalities per 100,000
population, from 9.3 in 1999 to no more than 5.6 in 2010.
A series of two-year Action Plans was developed to monitor the road safety program and a review with recommendations for a new Action Plan is required. This target
provides a framework for coordinating the road safety initiatives of the federal, state, territory and local governments and of others capable of influencing road safety
outcomes.

LAW, T.H., RADIN UMAR, R.S., WONG, S.V.

3. THE VEHICLE OWNERSHIP MODEL
Growth in vehicle ownership is often seen as an inevitable outcome of increasing per-capita Gross Domestic Product (GDP)5. In this study the Gompertz growthmodel, proposed by Dargay and Gately6 is used to describe the growth of vehicle ownership as a function of
per-capita GDP. The main advantage of this equationis that its asymmetric sigmoidal nature can fit a vehicle
growth curve well. It was proven to be highly effectivein generating the growth curve and for relating the impact of variables on different vehicle ownership growthphases. Of particular significance is that the Gompertz
growth function allows a slow vehicle ownership growthin the lowest per-capita GDP level, followed by an increasing rate of growth as per-capita GDP rises, andfinally reaches a saturating level. The vehicle ownershipmodel is expressed by:
Vt = θ (γ exp(α exp(β GDP))) + (1 − θ )Vt −1(1)where Vt is the rate of vehicle ownership at time t, θ isthe adjustment of vehicle ownership and per-capita GDP
growth (0<θ <1), and γ is the asymptotic vehicle ownership as t increases indefinitely. Parameters α and β are
curvature parameters. Analogously, the parameter α determines the value of Gompertz growth function at percapita GDP is equal to zero and the parameter β plays arole in determining the per-capita GDP value at vehicle
ownership saturation level. The smaller the value of β,
the greater the per-capita GDP at saturation level.
Long-run elasticity of the vehicle per population
ratio with respect to per-capita GDP varies with economic
performance. Long-run per-capita GDP elasticity is presented as,τ LR = αβ .GDP.e β .GDP

(2)

Fitting of data for the Gompertz growth model was
performed by the Marquardt-Lebenberg algorithm7. The
algorithm calculates the regression coefficient α, β, γ andθ. The goodness of fit was checked by the estimation of
the regression coefficient, coefficient of determinant (RSquare) and the associated p-values for the model parameters.

IATSS RESEARCH Vol.29 No.1, 2005 •43

TRANSPORTATION

4. ROAD ACCIDENT DEATH RATEPROJECTION MODEL
Many statistical methods are available to explain
accident-related variables, such as log-linear model, generalized linear model and multiple-linear model. Dataobserved over time usually have strong correlations
among neighboring observations. Therefore the ordinary
methods are not appropriate for this analysis because
these methods assume that the observations over time are
independent8.
In light of the problem associated with ordinary
methods, several researchers have turned to the ARIMA
model as a means to better predict accident variables. The
ARIMA model is a useful statistical method for analyzing longitudinal data with a correlation a1mong neighboring observations. This method has proven to be very
useful in the analysis of multivariate time series9-11.
In ARIMA analysis, there are two simple components for representing the behavior of observed time series processes, namely the autoregressive (AR) andmoving average (MA) models. The AR model is used todescribe a time series in which the current observation
depends on its preceding values, whereas the moving average (MA) model is used to describe a time series process as a linear function of current and previous random
errors. It is possible that a time series model will consistof a mixture of AR and MA components. In this case theseries are said to be computed by an autoregressive moving average process of order (p,q), where p and q are theorders of the AR and MA components, respectively. The
selection strategy for such models was developed and selected by the Box and Jenkins method 12. A general
ARIMA model can be written as:
Bd Nt =

θ ( B)a t
φ ( B)(3)

where at is assumed to have white noise, B is the backshiftoperator, N represents stochastic part, d is the order ofregular differencing needed to achieve time series
stationarity, and other parameters in the model are defined
as follows:θ q ( B) = 1 − θ 1 − θ 2 B 2 − ... − θ q B q(4)

φ P ( B) = 1 − φ1 − φ 2 B 2 − ... − φ P B P(5)ky t = α + ρ y t −1 + β t + ∑ φ i ∆ yt −i + ε t

(6)

i =1

where t is a time trend, yt represents the road accident
death rate, ∆ yt-i is the lagged change in road accident
death rate, and εt is a white noise error term. Null hypothesis ρ=0 versus alternative hypothesis ρ<0 was tested.
Failure to reject the null hypothesis is evidence that theseries yt is non-stationary.
At the identification stage, the appropriate AR andMA parameters are found by examining autocorrelation
function (ACF) and partial autocorrelation function(PACF) of the time series. Autocorrelation and partial
autocorrelation analyses were conducted on the stationary time series. Autocorrelation measures the unconditional relationship of values between time lags, while
partial autocorrelation measures the conditional relationship between series observations. Based on the characteristics of ACF and PACF, a variety of possible ARIMA
models was established for the road accident death ratein the first stage, and then estimated in the second stage.
In contrast to the ARIMA model, which describe
the behavior of single time series, ARIMA model withtransfer noise function model can represent more complex systems which are able to connect one series not onlywith its own past values, but also with past and present
values of other, related time series. In this study, ARIMA
with transfer noise function was used to assess the effectof vehicle ownership and population on altering the trendof the road accident death rate (per 10,000 vehicles). The
general form of the transfer function ARIMA model comprises a part relating to the transfer function and a part
relating to the error terms, is defined as:

Yt = v1 ( B ) x1t + v 2 ( B ) x 2 t + N t

where φ1…φp are autoregressive (AR) parameters, θ 1…θ q
are moving average (MA) parameters.

44 • IATSS RESEARCH Vol.29 No.1, 2005

ARIMA model development consists of a threestage iterative process, which consists of identification,model parameters estimation, and diagnostic checkingof the residuals of the fitted model13. In the process ofidentification, the first step is to determine whether thetime series is stationary or not stationary. If the series indicates nonstationarity, the time series is first converted
to a stationary series by appropriate transformative anddifferencing operations. TheDickey and Fuller test14 wasused to examine the time series data staionarity. The Augmented Dickey-Fuller regression is given as follows:(7)

where Yt is the road accident death rate, xit is the explanatory variable (x1t represents population number; x2t represents vehicle ownership) and N t is the stochastic

THE MALAYSIAN GOVERNMENT’S ROAD ACCIDENT DEATH REDUCTION TARGET FOR YEAR 2010

component assumed to follow a general ARIMA structure. In equation (7), vi (B) is the transfer noise function
determining the nature of the influence of the backward
shift operator. Specifically vi (B) can be expressed as:
v i ( B ) = [ω ( B ) / δ ( B )]B b

ω 1 ( B) B b
ω ( B) B b
θ ( B)
x1t + 2x2 t +atδ 1 ( B)
δ 2 ( B)φ ( B)

Per-capita GDP and population projection figures
were obtained from Malaysia Third Outline Perspective
Plan 2001–201016. Per-capital GDP and population were
expected to grow at 2.3% and 7.5% per annum between
2000–2010, respectively.

(8)

where the numerator can be expanded to ω(B) = (ω0 –ω1B – … – ωs Bs ), the denominator can be expanded toδ (B) = (1 – δ 1B – … – δ r Br ), “s”, “r” and b represent
the orders of the polynomials and the degree of seasonality, respectively. Combining equation (3) and (7) yields:
Yt =LAW, T.H., RADIN UMAR, R.S., WONG, S.V.

(9)

The identification of a transfer function ARIMA
model was accomplished by calculating the sample crosscorrelation function (rxy(k)) at various lags, k, and thencomparing it to theoretical impulse response functions ofdifferent orders in order to obtain some idea of the delay
parameter b and the orders r and s of the operators in thetransfer noise function between an output and an input
series. In the modeling effort presented in this paper, themodel error term was estimated using the least square estimation method15, in which the least square function is
calculated via non-linear least-squares iterations.
Diagnostic check is needed to determine the bestmodel among the tentative ‘adequate’ models. A number of criteria for model comparisons have been proposed.
The diagnostic tools used include the statistical significance of the parameters, the Box-Ljung (Q) statistic and
the Akaike information criterion (AIC). The best model
should have the lowest AIC value, a statistically insignificant Q statistic at a lag of about one-quarter of thesample size. After carrying out the complete identification, estimation and diagnostic iterative scheme of BoxJenkins, the final ARIMA model can be used forpredictions of the future road accident death rate (per10,000 vehicles).

5. DATA
Registered vehicle number data from 1976 to 2001
were taken from the Malaysia Traffic Police annual statistics2 while the per-capita Gross Domestic Product(GDP) and population data were obtained from the Central Bank of Malaysia.

6. RESULTS AND DISCUSSIONS
6.1

Projections of vehicle ownership
Projection of vehicle ownership rate was made on
the basis of the Gompertz growth model of vehicle ownership described above and assumptions concerning population and per-capita GDP growth. Fitted parameters for
all the growth models are shown in Table 1.
Table 1 Estimated parameters of vehicle ownership
model
Parameter

Parameter Definitionθ

Speed of adjustment

Coefficient
0.2671γ

Saturation level

0.9621βShape or curvature of the function

90.8862

αShape or curvature of the function

2.2921R-square0.9612(Significant level, p< 0.05)

The estimated Gompertz growth model for vehicle
ownership was significant at a significance level of 0.05.
The Gompertz growth model yielded the best fit to data,
as shown by the high R2 value (0.9612). Based on theGompertz growth equation, the adjustment parameter, θ,
is estimated to be 0.267, indicating that 26.7% of the total response could be attributed to per-capita GDPchanges in that particular year. The estimated saturationlevel is 0.96 vehicles per population and vehicle ownership saturation occurs when per-capita GDP reaches 0.066
million annually (Figure 1).
Value β determines the maximum per-capita GDP
elasticity level. The smaller the β, the greater the percapita GDP required to reach saturation level. In thisanalysis β is equal to 90.8862 and maximum per-capita
GDP elasticity is estimated to occur when per-capita GDP
is 0.014 million (Figure 2).
The GDP is assumed to increase by 2.2% per year
for the entire forecast period16. The resulting projections
yield an estimate of 0.4409 vehicles per capital in year
2010 (Table 2). The estimated relationship between vehicle ownership and per-capita GDP is illustrated in Figure 3.
IATSS RESEARCH Vol.29 No.1, 2005 •45

TRANSPORTATION

1
0.9
Vehicle per population

0.8
0.7
Estimated Saturate
Level

0.6
0.5
0.4
0.3
0.2
0.1
0
0.000

0.010

0.020

0.030

0.040

0.050

0.060

0.070

0.080

Per-capita Gross Domestic Product (million)

Fig.1 Estimated vehicle ownership function

Income elasticity of vehicle
per population

0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1

08
4
0.

07
8
0.

0.
07
2

6

6
0.
06

0.
0

05
4
0.

0.
04
8

04
2
0.

36
0.
0

0.
03

4

8

0.
02

0.
01

01
2
0.

0.
0

06

0

Per-capital Gross Domestic Product (million)

Fig. 2 Estimated per-capita Gross Domestic Product elasticity for vehicle ownership

Table 2 Projection of vehicle ownership, 2001–2010
Projection Year

Per-capita GDP

Vehicle per population

2001

0.01570.4603

2002

0.01490.48562003

0.0142

0.49852004

0.01350.50232005

0.01290.49982006

0.0122

0.49262007

0.0117

0.4822

2008

0.01110.46962009

0.01050.45562010

0.01000.440946 • IATSS RESEARCH Vol.29 No.1, 2005

6.2

Projection of road accident death per 10,000 vehicles
The results of the Augmented Dickey Fuller (ADF)
stationarity test are summarized in Table 3. The ADF test
statistic is compared with the critical values from the
Dickey-Fuller distribution with a trend at the 5% significance level. Since the absolute value of ADF statistics
for road accident deaths series are more than the criticalvalue of 2.86. Thus, the null hypothesis of the ADF test
is rejected. This result reveals that the road accident death
series is stationary.

LAW, T.H., RADIN UMAR, R.S., WONG, S.V.

0.6
ActualPredicted

0.5
0.4
0.3
0.2
0.1

09
20

07
20

05
20

03
20

01
20

99
19

97
19

95
19

93
19

19

91

89
19

87
19

85
19

83
19

81
19

19

19

79

0

77

Vehicle ownership per population

THE MALAYSIAN GOVERNMENT’S ROAD ACCIDENT DEATH REDUCTION TARGET FOR YEAR 2010

Year

Fig. 3 Vehicle ownership estimation and projection, 1976–2010

Table 3 Result of Augmented Dickey Fuller (ADF) testfor road accident death rate
VariableRoad accident death

ADF statistic

5% Critical value–4.123–2.86

From the plots in Figure 4, the autocorrelation function appears to be dying down exponentially, while thepartial autocorrelation function cuts off to zero after lag
1, thus suggesting a Moving Average MA(1) model.
The cross-correlation plot between input and output series shows a positive correlation at lag 0 (Figures
5 and 6). This result implies that the road accident death
rate increases with the growth in population and vehicle
ownership. Based on the above autocorrelation and partial autocorrelation functions observation, the ARIMA
model with transfer noise function is established as follows:

Yt = 3.0332 + 2.0694 × 10 −8 X 1t + 1.8825 X 2t +A diagnostic check was performed using Q-statistic, which tests for the non-randomness of the residual
autocorrelations. The model had insignificant Q-statistics
at the 10% level, implying that the residual autocorrelations
are independent. Hence, it may be inferred that the residual autocorrelations are not significantly different fromzero. The Box-Ljung analysis implies that the model isadequate. This is further enhanced by the lowest AIC
value and the model parameters are significant at 10%
significant level (Table 4).
The road accident death rate is projected to decrease
to 4.22 in 2010, at an average decline rate of 2.14% perannum (Figure 7). This result suggests that to achieve a
new national target of 4 deaths per 10,000 vehicles, thedecline rate has to be 2.18% per annum.

1.0

1.0

0.5

0.5

0.0

0.0

-0.5

-0.5

-1.0

Nt
(10)
(1 − 0.4288 B)-1.0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Fig. 4 Partial autocorrelation (left) and autocorrelation (right) functions of road accident death rate
IATSS RESEARCH Vol.29 No.1, 2005 •47

TRANSPORTATION

1.0

1.0

0.5

0.5

0.0

0.0

-0.5

-0.5

-1.0

-1.0
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

Fig. 5 Cross-correlation functions of the pre-whitening
time series between road accident death rate
and population series

Fig. 6 Cross-correlation functions of the pre-whitening
time series between road accident death rate
and vehicle ownership series

Table 4 Estimation for the model of annual road accident death rate
Conditional Least Squares Estimation
Parameter

Estimate

Std Error

T-value

Lag

Constant

3.03320.137622.05

0Moving Average (1)–0.4288

0.2336–1.84

12.0694 × 10–8

1.4733 × 10–8

1.40

0

1.88250.55423.40

0Prob Q(6)=0.869

Prob Q(12) = 0.897

Prob Q(18) =0.435

Population
Vehicle Ownership
Q-Statistic(Significant level, p< 0.10)

18.00

ActualAccident Death Rate(per 10,000 vehicles)

16.00

Prediction

14.00
12.00
10.00
8.00
6.00
4.00

7
19
99
20
01
20
03
20
05
20
07
20
09

95

19
9

19

9

1
19
93

19
9

19
8

87
19

85
19

1
19
83

19
8

79
19

19
7

7

2.00

Year

Fig. 7 Road accident death per 10,000 vehicles estimation and projection, 1976–201048 • IATSS RESEARCH Vol.29 No.1, 2005

THE MALAYSIAN GOVERNMENT’S ROAD ACCIDENT DEATH REDUCTION TARGET FOR YEAR 2010

7. CONCLUSION
This paper provides the numerical context for recommendations for the reduction target of the road accident death rate for the year 2010 that was announced in
the Malaysian Road Safety Council annual meeting in
2002. The research included the prediction of vehicle
ownership and the analysis of past trends in the road accident death rate. Projections of the road accident death
rate were undertaken for 2010 taking into account the assumption of per-capita GDP, vehicle ownership andpopulation growth.
The Gompertz model predicted that the vehicle
ownership per population would be equal to 0.4409 by
the year 2010 while the ARIMA model with transfer
noise function reveals that a minimum 2.18% reduction
per annum is required to achieve the national target inyear 2010.

LAW, T.H., RADIN UMAR, R.S., WONG, S.V.

Planning Unit, Malaysia. (2001).

ACKNOWLEDGEMENTS
The authors would like to express their gratitude to the Ministry of Transport of Malaysia for providing the financial support
for this project. They also wish to acknowledge the central bankof Malaysia and Police headquarter’s contribution to this researchby providing the data.

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