The DRAG model in Québec

(Demande Routière, Accidents et Gravité)

Robert SimardSociété de l’assurance automobile du Québec

Paris, May 30, 2007

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Plan of the presentationPlan of the presentation

History of the model in QuébecHistory of the model in Québec Administrative aspects Administrative aspects Dependent variablesDependent variables Independent variablesIndependent variables Examples of resultsExamples of results ForecastingForecasting Usefulness of the results at the SAAQUsefulness of the results at the SAAQ

– SAAQ: Société de l’Assurance Automobile du QuébecSAAQ: Société de l’Assurance Automobile du Québec

Future Future

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History of the model in QuébecHistory of the model in Québec

It all began in 1982It all began in 1982 Professor Gaudry suggested to the leaders of the SAAQ Professor Gaudry suggested to the leaders of the SAAQ

the development of an econometric model that would the development of an econometric model that would – identify the factors affecting the number of crashes and victims identify the factors affecting the number of crashes and victims – estimate the impact of these factors: elasticityestimate the impact of these factors: elasticity

The report of Professor Gaudry was published in 1984The report of Professor Gaudry was published in 1984

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History of the model in QuébecHistory of the model in Québec(continued)(continued)

A couple of years later, in 1989, the leaders of the A couple of years later, in 1989, the leaders of the SAAQ agreed with Professor Gaudry to:SAAQ agreed with Professor Gaudry to:– Implement the DRAG model for the province of Implement the DRAG model for the province of

Québec at the SAAQQuébec at the SAAQ– Train 2 of the SAAQ staff, so that they would become Train 2 of the SAAQ staff, so that they would become

as familiar as possible with all the aspects of the as familiar as possible with all the aspects of the modelmodel

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Administrative aspects of the projectAdministrative aspects of the project

Duration:Duration:– The full development of the model at SAAQ spanned The full development of the model at SAAQ spanned

over a period of 9 years 1990-1999over a period of 9 years 1990-1999– The development took place on a part-time basisThe development took place on a part-time basis

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Administrative aspects of the projectAdministrative aspects of the project(continued)(continued)

8 reports have been published8 reports have been published

– 1: Estimate of the monthly amount of distance travelled (kilometres) in Québec and analysis of the 1: Estimate of the monthly amount of distance travelled (kilometres) in Québec and analysis of the number of victims (no econometrics), Oct. 1993number of victims (no econometrics), Oct. 1993

– 2: Methodological aspects of the model, March 19942: Methodological aspects of the model, March 1994

– 3: A econometric model developed for the monthly amount of distance travelled (kilometres) with gas 3: A econometric model developed for the monthly amount of distance travelled (kilometres) with gas (essentially by cars) and with diesel (essentially by trucks), August 1994(essentially by cars) and with diesel (essentially by trucks), August 1994

– 4: Main Model: A econometric model developed for the monthly number of crashes, their severity 4: Main Model: A econometric model developed for the monthly number of crashes, their severity and the number of victims, May 1995and the number of victims, May 1995

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Administrative aspects of the projectAdministrative aspects of the project(continued)(continued)

– 5: Synthesis of these results, Nov. 19955: Synthesis of these results, Nov. 1995

– 6: Updating of the distance travelled (kilometres) and the number of crashes and victims on a monthly 6: Updating of the distance travelled (kilometres) and the number of crashes and victims on a monthly basis, Feb. 1996basis, Feb. 1996

– 7: Updating of the model (see n.4) developed for the distance travelled (kilometres - gas and diesel) and 7: Updating of the model (see n.4) developed for the distance travelled (kilometres - gas and diesel) and the monthly number of crashes, their severity and the number of victims, Mar. 1997the monthly number of crashes, their severity and the number of victims, Mar. 1997

– 8: Forecasting for the monthly amount of distance travelled, the number of crashes and victims for the 8: Forecasting for the monthly amount of distance travelled, the number of crashes and victims for the period 1997-2004, based on data available at the end of 1996, June 1999period 1997-2004, based on data available at the end of 1996, June 1999

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Administrative aspects of the projectAdministrative aspects of the project(continued)(continued)

Other publications, mainlyOther publications, mainly– Conference at Saskatoon, Canada in 1993Conference at Saskatoon, Canada in 1993– Conference in Paris in 1998Conference in Paris in 1998– One chapter in the book "Structural Road Accident Models - The One chapter in the book "Structural Road Accident Models - The

International DRAG Family", edited by M. Gaudry and S. Lassarre, 2000International DRAG Family", edited by M. Gaudry and S. Lassarre, 2000

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Main characteristics of the DRAG model Main characteristics of the DRAG model developed in Québecdeveloped in Québec

Aggregated at the provincial level (all of Quebec)Aggregated at the provincial level (all of Quebec)– Population: 7.7 millions in 2006Population: 7.7 millions in 2006– Registered Vehicles: 5.4 millionsRegistered Vehicles: 5.4 millions– Licensed Drivers: 4.8 millions Licensed Drivers: 4.8 millions

Monthly dataMonthly data Period Period

– First time: 1957-1989 (397 obs.)First time: 1957-1989 (397 obs.)– Update: 1957-1993 (445 obs.)Update: 1957-1993 (445 obs.)– Forecasting: 1997-2004, based on 1957-1996Forecasting: 1997-2004, based on 1957-1996

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9 DEPENDENT VARIABLES9 DEPENDENT VARIABLES Distance travelled (kilometres)Distance travelled (kilometres)

– with gaswith gas– with dieselwith diesel

Number of crashesNumber of crashes– FatalFatal– Bodily injury Bodily injury – Property damage only (PDO)Property damage only (PDO)

SeveritySeverity– Mortality: n. of victims killed / n. of fatal crashesMortality: n. of victims killed / n. of fatal crashes– Morbidity: n. of victims injured / n. (fatal + b. i.) crashesMorbidity: n. of victims injured / n. (fatal + b. i.) crashes

Number of victimsNumber of victims– KilledKilled– InjuredInjured

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Annual number of victims killed in Québec 1957-2006

0

500

1000

1500

2000

2500

1957 1962 1967 1972 1977 1982 1987 1992 1997 2002

2 209 in 1973

610 in 2001

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INDEPENDENT VARIABLES: examplesINDEPENDENT VARIABLES: examples

Exposure (model on the number of crashes and victims):Exposure (model on the number of crashes and victims):– Distance travelled (kilometres)Distance travelled (kilometres)

PricesPrices– GasGas– Maintenance of vehiclesMaintenance of vehicles

Characteristics of automobilesCharacteristics of automobiles– Proportion of small carsProportion of small cars

MotorcyclistsMotorcyclists– Number of vehiclesNumber of vehicles– Laws:Laws:

» Mandatory wearing of safety helmet (July 1972)Mandatory wearing of safety helmet (July 1972)» Headlights 24 hours a day (July 1974)Headlights 24 hours a day (July 1974)

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INDEPENDENT VARIABLES: examplesINDEPENDENT VARIABLES: examples(continued)(continued)

Drivers:Drivers:– Proportion of young drivers: 16-24 years oldProportion of young drivers: 16-24 years old

Laws related to road safety (in general):Laws related to road safety (in general):– Demerit points system (March 1973)Demerit points system (March 1973)– Lowering of speed limit on main roads AND Lowering of speed limit on main roads AND

mandatory seat belt use (August 1976)mandatory seat belt use (August 1976)– New highway safety code (1982, 1987)New highway safety code (1982, 1987)

Laws related to alcohol and drivingLaws related to alcohol and driving– "0.08" (Dec. 1969) "0.08" (Dec. 1969) – Lowering drinking age from 21 to 18 (July 1971)Lowering drinking age from 21 to 18 (July 1971)– Increasing severity of Criminal Code related to Increasing severity of Criminal Code related to

alcohol and driving (Dec. 1985)alcohol and driving (Dec. 1985)

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INDEPENDENT VARIABLES: examplesINDEPENDENT VARIABLES: examples(continued)(continued)

Economics:Economics:– Ratio: number of unemployed / number of driversRatio: number of unemployed / number of drivers

Weather conditions:Weather conditions:– RainfallRainfall– SnowfallSnowfall– TemperatureTemperature– Hours of lightHours of light– Proportion of hours of sunshine / lightProportion of hours of sunshine / light

Crash reportingCrash reporting– Improvement of the reporting procedure (July 1962)Improvement of the reporting procedure (July 1962)– "Constat à l’amiable" joint report (June 1979)"Constat à l’amiable" joint report (June 1979)– New reporting: min. $500 vs $250 AND less New reporting: min. $500 vs $250 AND less

information for PDO crashes (Sept. 1988)information for PDO crashes (Sept. 1988)

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EXAMPLES OF RESULTS (1957-1993)EXAMPLES OF RESULTS (1957-1993)Effect of an increase of 10% for the following Effect of an increase of 10% for the following independent variables on the distance travelled independent variables on the distance travelled

(kilometres) with GAS(kilometres) with GAS

Price of gas to travel 1 km (taking into account inflation, Price of gas to travel 1 km (taking into account inflation, energy consumption and temperature):energy consumption and temperature):– Decrease of 4.6% (|student " t"| > 2) Decrease of 4.6% (|student " t"| > 2)

Number of vehicles (gas) / adultNumber of vehicles (gas) / adult– Increase of 11.1% (|student " t"| > 2)Increase of 11.1% (|student " t"| > 2)

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EXAMPLES OF RESULTS (1957-1993)EXAMPLES OF RESULTS (1957-1993)Effect of an increase of 10 % for the following Effect of an increase of 10 % for the following independent variables on the number of crashesindependent variables on the number of crashes

Total distance travelled (kilometres)Total distance travelled (kilometres)– PDO crashes: Increase of 6% (|student " t"| > 2 )PDO crashes: Increase of 6% (|student " t"| > 2 )– Bodily injury cr.: Increase of 7.8% (|student " t"| > 2)Bodily injury cr.: Increase of 7.8% (|student " t"| > 2)– Fatal cr.: Increase of 4.6% (1 < |student " t"| < 2)Fatal cr.: Increase of 4.6% (1 < |student " t"| < 2)

» Possibility of road congestion effect. If so, thenPossibility of road congestion effect. If so, then» KMKM11((λ=1):λ=1): Increase of 15.1% (|student " t"| Increase of 15.1% (|student " t"| > 2) WITH KM> 2) WITH KM22((λ=2): λ=2):

Decrease of 7.1% (|student Decrease of 7.1% (|student " t"|" t"| > 2)> 2)

Price of gas to travel 1 km (with inflation, energy and Price of gas to travel 1 km (with inflation, energy and temperature)temperature)– PDO crashes: Decrease of 0.2% (|student " t"| < 1)PDO crashes: Decrease of 0.2% (|student " t"| < 1)– Bodily injury crashes.: Decrease of 3.9% (|student " t"| > 2)Bodily injury crashes.: Decrease of 3.9% (|student " t"| > 2)– Fatal crashes.: Decrease of 4.4% (|student " t"| > 2)Fatal crashes.: Decrease of 4.4% (|student " t"| > 2)

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EXAMPLES OF RESULTS (1957-1993)EXAMPLES OF RESULTS (1957-1993)Effect of the following laws on the number of crashesEffect of the following laws on the number of crashes

Lowering of the speed limit on "main roads" from 100 to Lowering of the speed limit on "main roads" from 100 to 90 km/h (90 km/h (provincial roads, not divided 4-lane roadsprovincial roads, not divided 4-lane roads) and mandatory ) and mandatory seat belt use (August 1976)seat belt use (August 1976)– PDO crashes: Increase of 2% (|student " t"| < 1)PDO crashes: Increase of 2% (|student " t"| < 1)– Bodily injury crashes: Decrease of 9.4% (|student " t"| > 2)Bodily injury crashes: Decrease of 9.4% (|student " t"| > 2)– Fatal crashes: Decrease of 14.7% (|student " t"| > 2)Fatal crashes: Decrease of 14.7% (|student " t"| > 2)

Increasing severity of Criminal Code related to alcohol Increasing severity of Criminal Code related to alcohol and driving (Dec. 1985)and driving (Dec. 1985)– PDO crashes: Decrease of 4.4% (|student " t"| < 1)PDO crashes: Decrease of 4.4% (|student " t"| < 1)– Bodily injury cr.: Decrease of 15% (|student " t"| > 2)Bodily injury cr.: Decrease of 15% (|student " t"| > 2)– Fatal cr.: Decrease of 28.8% (|student " t"| > 2)Fatal cr.: Decrease of 28.8% (|student " t"| > 2)

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EXAMPLES OF RESULTSEXAMPLES OF RESULTS

FORECASTINGFORECASTING

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Examples of resultsExamples of resultsForecasting of the number of victims killedForecasting of the number of victims killed

in Quebec for 1997-2004 in Quebec for 1997-2004

0

200

400

600

800

1 000

1 200

1987 1989 1991 1993 1995 1997 1999 2001 2003

Observed

Forecasted

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Examples of resultsExamples of resultsNumber of victims killed in Quebec 1997-2004Number of victims killed in Quebec 1997-2004

Forecasted vs ObservedForecasted vs Observed

0

200

400

600

800

1 000

1 200

1987 1989 1991 1993 1995 1997 1999 2001 2003

Examples of results (continued)Examples of results (continued)Number of victims killed: 2004 vs 1996 Number of victims killed: 2004 vs 1996

Forecasted: Decrease of 18%Forecasted: Decrease of 18% Observed: Decrease of 25%Observed: Decrease of 25%

Examples of results (continued)Examples of results (continued)

Forecasting with different scenarios on Forecasting with different scenarios on independent variables independent variables

– Optimistic, pessimistic, …Optimistic, pessimistic, … Sensitivity analysis: change in only 1 variableSensitivity analysis: change in only 1 variable

– ExampleExample» Continuous variable: impact of 10% more of that variableContinuous variable: impact of 10% more of that variable

» Intervening variable: a particular law is not in force Intervening variable: a particular law is not in force during a given period of timeduring a given period of time

Usefulness of such a modelUsefulness of such a model

Estimated impact of a given factor on Estimated impact of a given factor on distance travelled, number of crashes and distance travelled, number of crashes and number of victims by severitynumber of victims by severity Each year: tool to better understand the Each year: tool to better understand the evolution of the number of crashes and victims evolution of the number of crashes and victims of each severityof each severity

–For instance: variation between 2005 and 2006 For instance: variation between 2005 and 2006

Usefulness of such a model: oUsefulness of such a model: other examplether exampleIncrease in the price of gas in Sept. 2005Increase in the price of gas in Sept. 2005

August: $1.058 ; September: $1.197 (max. of $1.364 ) ; October: $1.042August: $1.058 ; September: $1.197 (max. of $1.364 ) ; October: $1.042

Sales of gas: Sept. 2005 vs Sept. 2004Sales of gas: Sept. 2005 vs Sept. 2004– Decrease of 5.2% (as expected by the model)Decrease of 5.2% (as expected by the model)

Number of victimsNumber of victims– Even though the number of victims (killed, severely Even though the number of victims (killed, severely

injured or slightly injured) increased for all of 2005 injured or slightly injured) increased for all of 2005 compared to 2004, it decreased or slightly increased compared to 2004, it decreased or slightly increased in September 2005 (as expected by the model)in September 2005 (as expected by the model)

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Future: what could be done Future: what could be done

Update the model to include more than 10 yearsUpdate the model to include more than 10 years– That would also allow consideration of new variables, That would also allow consideration of new variables,

especially laws that have come into effect since then especially laws that have come into effect since then – Another very important point would be the possibility Another very important point would be the possibility

of taking into account the difference between the of taking into account the difference between the severely or slightly injured victimsseverely or slightly injured victims

» This information has been available since 1978 This information has been available since 1978

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Other possibilities Other possibilities

Build a model for a particular area Build a model for a particular area – Example: A very populated area like MontréalExample: A very populated area like Montréal

Build a model for a particular kind of road userBuild a model for a particular kind of road user– Example: Pedestrians, cyclists, motorcyclists …Example: Pedestrians, cyclists, motorcyclists …

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Thank you very much for Thank you very much for your attentionyour attention