An Analysis of Urban Road Traffic Safety in Stockholm - The use of aggregate time-series models with the TRIO programme

Grran B. Tegn~r Business Manager, M Pol Sc, TRANSEK Consultants

Vesna M. Loncar Lucassi, Project Manager M Sc CE, TRANSEK Consultants

1. THE DRAG MODEL APPROACH FOR STOCKHOLM 1970 - 1995

The DRAG-philosophy aims at creating an enhanced understanding of two aspects of mobility: the demand for road usage, and the complex interactions affecting road accidents. The notion is based on a three step approach, risk exposure, accident rate and its severity. A data base has been created for the County of Stockholm with a broad spectrum of explanatory variables, such as socio-economic factors, laws and regulations, road and public transport data, vehicle fleet data, climate data and other related information aiming at explaining the development of road traffic and road accidents ex post. A special statistical programme package, called TRIO 1 has been used in the analysis.

The demand model is estimated on aggregate time series data for the whole area (in this case Stockholm County). The idea is to explain both traffic volumes (vehicle kilometres, vkms) and road accidents by a wide spectrum of explanatory variables by exploiting the vast variation in the monthly data set. This technique is called DRAG and stands for: "Demand for Road use, Accidents and their GraviO/" , and is developed by professor Marc Gaudry at the Transport research Centre at the University of Montreal in Canada.

In our application of the DRAG approach in the Stockholm region, the following time series models have been carried out on a monthly basis for the period 1970 - 1995: • an EXPOSURE model of total road mileage (vehicle kilometres) for petrol

passenger cars ® a FREQUENCY model of total number of road accidents with personal injuries and

deaths

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a SEVERITY model of the: number of light injuries per road accident number of severe injuries per road accident

- number of fatal deaths per road accident.

Analogous DRAG-models have been carried out in Canada, Germany and are being developed in France and Norway 2.

. T H E D E M A N D F O R R O A D U S E I N S T O C K H O L M C O U N T Y 1 9 7 0 - 1 9 9 5

2 .1 T h e m o d e l

In TRIO a demand model function is specified as follows: :

Y'~-l-flo+flk~'~('x~?l')+u I

where yt po Pk

~.kresp~. y the

and

= the dependent variable for month t = the constant term = the estimated regression coefficient = the independent variable xk:s value for month t = the so-called lambda-parameters for the independent variable xk and for

dependent y-variable, i.e. a scale factor also estimated on the data set and which transforms the model or to a certain mathematical form. As a special case, when lambda is = I, you get a linear model, and iflambda is = O, you get a logarithmic model. This transformation is called "Box- Cox" transformation.

I u, = v,f(Z,) v', v, =

where z, Ut Vt

= a vector of heteroskedastic variables = the error term (the residual vector) depending on the heteroskedasticity = the error term (the residual vector) which is assumed to be dependent in

the auto-correlation &the model

and finally Pl = the so-called auto-regressive (time lag) parameters, which are also

estimated and carries information about the time lag in the model. 0~t = the third stage vector of residuals

2.2 Overall transport trends in Stockholm county 1970 - 1995

The rapid development of car traffic in the Stockholm County during the last 35 years can not be explained by any single factor. Rather, there is a wide range of factors, which contribute to this augmentation. In Figure 1 some key factors of importance to car traffic growth is presented in percent change between 1970 and 1995: Public transport supply has almost doubled and increased even more than road traffic vehicle-kilometres. But public transport demand has only increased by 13 percent over the last 25 years. Real petrol prices has increased slightly more than public transport fares, 46 compared to 43 percent. The car park, measured as cars in use, is in 1995 more than 50 percent larger than in 1970.

The Stockholm county population is 16 percent larger after 25 years, i.e. some 250,000 more inhabitants; employment went up by 185,000 person from 1970 to 1990, but has declined by 115,000 persons between 1990 and 1994 due to the economic recession.

On the other side, the length of the state road network, has only expanded by one percent, i.e. it is of almost the same length as in 1970. Most new road links have replaced older ones.

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2.3 D R A G - m o d e l Results - Es t imated Elasticit ies

Table 1 summarises the model results in terms of average elasticities:

Table 1 20factors explain car traffic growth 1970 - 1995

No Dependent variable: Vehicle-kms per month Explanatory variables

Economic activities 1 Employment (days) + I. 107 2 Retail sales per employed in constant prices + 0.267 3 Leisure activity (holidays per working day) + 0.211 4 Holiday "per so" + 0.554 5 Population per employed -0.433 6 No of tourists per vehicle km - 0.102

The Car p a r k 7 No of cars in use per employed + 0.536 8 No of cars in use per employed (squared) - 0.255

Prices & public t ransport 9 Peal petrol price - 0.280 10 Public transport improvements- dummy (- 0.047)

Average elasticity 1970 - 1995

Road network & restrictions 11 New road links + 0.262 12 Parking restrictions in Inner city (+ 0.046) 13 Temporary speed limits (-0.022) 14 Petrol rationing, jan -74 - 0.098

Climate and calendar data 15 Average temperature per month + 0.057 16 No of snow days per month - 0.029 17 Share of day/night 06-24 with darkness - 0.168

18 No of work-days per month + 0.632 19 No of other days per month (+0.0201)

Special events 20 The Kuwait war dummy

Lambda 1- value for activity- and price variables Lambda 2- value for variable no 7 Auto regressive term: Rho: t-I Auto regressive term: Rho: t-2 Auto regressive term: Rho: t-12 Percentage explained b~' the model- R 2

t-value

(4.72) (7.64) (4.23) (4.41) (2.09) (3.98)

(2.11) (-2.7O)

(-3.92) (-0.72)

(3.78) (0.80) (-0.93) (-2.98)

(5.27) (-3.39)

-0.051 0.532 1.507 0.272 4).264

0.129

96.5 %

(-7.30) (6.12) (0.43)

(-1.04) (7.58) (0.43) (+4.18) (-4.79)

(-i.80)

Note! Elasticities within parenthesis are not significant at the 90 % confidence level.

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In the Table 1 above the Demand for Road use model for the period 1970 - 1995 for Stockholm county is presented in terms of average elasticities, with respect to the number of vehicle-kilometres per month, which is the dependent variable.

The vehicle-kms are calculated through petrol sales records per month, and adjusted for the fuel-efflciency of the car fleet, but also for the average monthly temperature. As temperature becomes lower than 8 centigrade (Celsius) fuel consumption increases per kilometre, and even more as temperature falls beyond the freezing point.

The 20 factors of the model explain 96.5 percent of the total variation in traffic production (vkms) during the last 25 year period.

Economic activities The 'locomotive" among the explanatory variables is the employment variable. A 10 percent increase in the number of employed is estimated to enhance the number of vehicle-kms by 15 percent. Increased employment produces higher personal income, which in turn leads to higher car ownership and this governs much of the activities in the urban area, such as private consumption and leisure activities. A one percent population growth, without any increase in employment, on the other hand, reduces car traffic by 0,4 percent. To summarise, employed persons use the car, while others use public transport or the walk/bike mode.

The demand for transport is a derived demand. The demand for all those activities creates the demand for mobility, not income per se. That is why we have not inserted an household or personal income variable, but measured the demand via five activity variables.

As real retail sales increases by 10 percent, road traffic increases by 2,7 percent, according to the time-series model. This indicator measures the effect of shopping trips on total road traffic demand. The corresponding elasticity of 0,27 for Stockholm could be compared to a very similar result obtained in both Quebec and in Germany. In Quebec, Canada the corresponding elasticity has been calculated to 0,25 and in Germany to 0,24; thus, these findings are highly consistent to each other 3.

2.4 Comparison between estimated and actual road traffic demand

The performance of the vehicle-km-model is shown below, where the observed and the model estimated traffic production (vkms) are compared on a yearly basis:

The overall correspondence between observed and estimated vehicle kilometres is quite good. For a single year the deviations between model and reality varies between 0 and 3 percent, with some very few exceptions:

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• in 1973 the model underestimates the observed road mileage by 6,5 percent; * in 1989 the model underestimates the observed road mileage by 5,2 percent

In both cases the time period could be characterised by an exceptional increase in road traffic over the past years.

.

3.1

ROAD ACCIDENT EXPOSURES AND SEVERITY IN S T O C K H O L M COUNTY 1970 - 1995

Accident trends in Stockholm county 1970 - 1995

The number of police-reported road traffic accidents has shown a variation around 2,000 to 2,800 accidents per annum, and the total amount has only declined by 1 percent during the last 25 year period. The number of fatal deaths and injured persons has been reduced by 3 percent in the same period. However, the severity of road traffic accidents has changed dramatically - the number of fatal deaths has gone down from some 150 persons to 50 persons, i.e. a reduction by 65 percent in 25 years.

The number of severely injured persons has changed from some 900 persons in 1970 to 450 persons in 1995. On the other side, the number of light injuries has increased from approximately 2,600 to 3,000 persons or by 18 percent. The overall accident pattern is shown in figure 2.

3.2 The Accident exposure model results

A comparison between the observed number of personal road accidents and the estimated number obtained from the time-series model is illustrated in Figure 3.

As could be seen from Figure 3 the correspondence between observed and estimated number of involved victims in road accidents is very good.

3.3 Various explanatory factors contribution to the number of accidents

We have identified 30 various factors that contribute to explain the monthly variations in the number of road accidents with personal injuries or deaths. In the table below the most important factors are presented:

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Table 2. Factors with an important impact on the number o f personal accidents

Factors with an important impact on the Average elasticity 1970 - Average elasticity 1970 - number of personal accidents 1995 with respect to the 1995 with respect to the

total number of accidents 4 number of fatal death Road traffic vehicle-kilometres Use of safety belts Number of employed per veh.km Number of remarks per inspected car Share of daylight hours per day Medical consumption (no of recipes/person) New road links

+1,8 -1,8 -0,5 -1,2 +0,4 -0,9 +0,4 +0,4 -0,3 -0,9 +0,3 +0,8 +0,1 -0,25

The elasticities indicate how much a certain accident type changes at a 1 percent change in the explanatory variable.

Our results indicate that the number of road accidents in an urbanised area like the Stockholm region increases much more than proportional to the amount of road traffic (elasticity: +1,8). Maybe it is explained by a rapid growth in the number of potential conflicts as the number of total vehicle-kilometres increases. The number of fatal deaths seems to be reduced, probably due to reduced speeds.

The quality of the vehicle fleet - measured here in terms of the number of remarks per inspected car - also indicate an important factor that influences both number of accidents and the severity of the accidents.

Medical consumption - measures as the number of sold recipes per person and month - seems to have a major impact on road traffic accidents, according to our findings. If supported by micro-studies, this result indicate an important factor to be dealt with in order to reduce road accidents and their severity.

An interesting result is also the impact of new road links in Stockholm county during the last 25 years. Both the number of severely injured as well as the number of fatal deaths has been reduced by 25 percent as an estimated effect of some 35 new road links during the 25 year period.

An impressive amount of various traffic safety measures have been implemented during the last 25 years in Sweden (and elsewhere). One such example is the use of traffic safety belts. A 10 percent increase in the use of safety belts is estimated to lead to a reduction in the number of road accidents with personal victims by 5 percent and a

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reduction in the number of fatal deaths by 12 percent, according to the tlme-series model for Stockholm.

A summary of the contribution from various explanatory factors to the number of road accidents with personal victims in Stockholm county 1970 - 1995 is presented in Figure 4.

To sum up, one could argue that all the traffic safety measures that have been implemented during the last quarter of the century have been necessary to balance the expected increase in the number of accidents caused by an increase in road trzffic volumes at the same time period. This is also dearly illustrated in figure 3.4 above, where the magnitude of two factors exactly even out (- 54 %, +54 %). The better vehicle fleet quality has contributed to a decrease in the accident rate, but the car occupancy factor seems to have had a major negative impact on accidents (that variable ought to be viewed with great care).

The road infrastructure is shown to have a slight positive impact, in terms of a minor accident reduction; however, the major impact is a substantial decrease in the number of severely injured and in the number of fatal deaths.

NOTES

TRIO zs a statlsfi=I prograram e package for multiple regression model esttmataon of dependent variables oft.he types: level, share and probability. TRIO has bee=l dev¢lopad by Prof Mare Gauch~ at the Centre de Recherche s ~ le~ Trar~sport~ (C.R.T.) at University of Montreal in Carmda.

2 So~ce I: "Appllsadon of Economcth~ Modal DRAG-2 to Rc~d Travel Demand in Quebec" Proceedings of the Canadhn M ulddlsclpRnazy Road Safety Confcamc~

VIII, Jtme 14-] 6, 1993, So~katoork Saslczt cbewan. By M. Gaud~, C,R.T., Ur, Jv. of Montreal, Quebec, F.FoLmdc¢ and R. Shn ~d, Soci~d de l'assur~,~cc aut~mobg¢ du

Quebec; Some= 2: "A!~zcgat¢ Time-Series Gasokae ~ d Models; Rc~cw of the Llttemtwe ~d N~v Evldmcc for West Germany", by Uldeh C, H. Blum,

- Gcrtmud Fc~s trod Marc Gauthy, Tmnspotladon Rcs~'ch A, VOI, 22A, NO 2. pp 75-88, 198~,

Som'ce: "Applicauon of Econometric MOde] DRAG-2 to Road Travel D~'mond m Quebec ~, M. Guuci~, F. Fomtmie¢ and R. Ska~d, p~c~dings o f the CanadJo~

M u l 6 ~ p l l n ~ * Road Safety Con fc~nc¢, Jm~e 14-16,1993, SaskatooP, Saskatcehwon

4 NB: Matcd,"J damage~ not included

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BIBLIOGRAPHY

Gaudry, M., Fournier, F. and Simard, R. (1993) Application of Econometric Model DRAG-2 to Road Travel Demand in Quebec, Proceedings of the Canadian Multidisciplinary Road Safety Conference VIII, June 14-16, 1993, Saskatoon, Saskatchewan.

Blum, U.C.M., Foos, G. and Gaudry, M. (1988) Aggregate Time-Series Gasoline Demand Models: Review of the Litterature and New Evidence for West Germany, Transportation Research A. Vol. 22A, No 2, pp 75-88, 1988.

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Figure 1 Overall transport trends in Stockholm County - some key factors

Tourists

Trucks in use

Public Ira nspo~t pbce-krr~s

Road traffic produc~on

Cars in use

Real petrol pdce

Real pdvate consumptioNcap

Real pdce montHy pass P.T,

Car ownership

Real retail sales

Popula~on

Public transport tdps

Employment

State road network lenght

0% 20%

~ .~. ~,,~,~;~',.~x~z~/~:.,,~ ~ 46%

-..~.'..,~,..~.,...:.~ .< ~ 44%

~ ~ ~ ~ ~ ~.~, ," "-'~ ~'# ~'~ ~.~,I 43%

30% L.

17%

13%

11%

40% 60% 80% 100% 120% 140% 160% 180%

141

Figure 2. Number o f injured and fatal deaths in traffic accidents in Stockholm county 1970 - 1995

1 N u m b e r o f i ~ u r e d a n d f a t a l d e a t h s i n t r a f f i c accidents in S tockho lm c o u n t y |

1970-1995 /

1970 1972 1974 1976 1978 1989 1982 1984 1986 1986 19~0 1992

I OFatatdeaths Ig Severely injuries [3Lightinjuries I

L 1994

Figure 3. Estimated and observed number o f personal accidents in Stockholm county 1970 - 1995

Estimated and observed number of personalaccidents Stockholm county 1970 -1995

3 000

2 500

2 000

1 500

I 000

500

0

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Figure 4. Contributions from various factors to the number o f road accidents with personal victims in

Stockholm county 1970 - 1995 .

Contribution from various factors to the number of road accidents I with personal victims in Stockholm county 1970 - 1995 /

Traffic safety measures

O~her favors

Road infraWucture

Car Remarks & occupancy

Road traffic vel~ms

-17%

-60% -40% -20%

-1%

~ 2 o ~

0% 20% 40% E0%

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