Econometric models of road use, accidents, and road investment decisions

299 Pages·2007·4.72 MB·English

TØI report
457/1999

Econometric models of road use,
accidents, and road investment decisions

Lasse Fridstrøm

Volume II:

An econometric model of car ownership, road use, accidents, and
their severity (Essay 3)

Copyright @ Institute of Transport Economics, 1999

ISSN 0802-0175
ISBN 82-480-0121-0
Oslo, November 1999
Title: Econometric models of road use, accidents, Tittel: Econometric models of road use, accidents, and
and road investment decisions. Volume II road investment decisions. Volume II
Author(s): Lasse Fridstrøm Forfatter(e Lasse Fridstrøm
TØI report 457/1999 TØI rapport 457/1999
Oslo, 1999-11 Oslo: 1999-11
292 pages 292 sider
ISBN 82-480-0121-0 ISBN 82-480-0121-0
ISSN 0802-0175 ISSN 0802-0175
Financed by: Finansieringskilde
Research Council of Norway (formerly NTNF), Norges Forskningsråd (tidl NTNF), Transportøkonomisk
Institute of Transport Economics (TØI) institutt (TØI)
Project: 1523 Road use, accidents, and fuel Prosjekt: 1523 Vegtransport, ulykker og energi
consumption
Project manager: Lasse Fridstrøm Prosjektleder: Lasse Fridstrøm
Quality manager: Marika Kolbenstvedt Kvalitetsansvarli Marika Kolbenstvedt
Key Emneord:
Road accidents; car ownership; car use; regression Bilhold; vegtrafikk; ulykker; regresjonsmodell; elastisiteter
analysis; elasticities
Summary: Sammendrag:
Using a fairly large cross-section/time-series data Ved hjelp av en økonometrisk modell anslås hvordan de
base, covering all provinces of Norway and all månedlige trafikkulykkestallene i norske fylker avhenger av
months between January 1973 and December 1994, bl a folkemengde, inntekter, priser, rentenivå,
we estimate non-linear (Box-Cox) regression veginvesteringer og -vedlikehold, kollektivtrafikktilbud,
equations explaining aggregate car ownership, road dagslys, værforhold, bilbeltebestemmelser, alkohol-
use, seat belt use, accident frequency, and accident tilgjengelighet, rapporteringsrutiner, kalenderbegivenheter
severity. Explanatory variables used include road og geografiske forhold. Modellen forklarer også bilhold,
infrastructure, public transportation level-of-service bilbruk og bilbeltebruk. Faktorer som påvirker disse
and fares, population, income, fuel prices, vehicle størrelsene får indirekte også virkning for ulykkestallene.
prices, interest level, weather, daylight, seat belt Datamaterialet er månedlige tidsserier for alle norske fylker
legislation, access to alcohol, calendar effects, gjennom 22 år (1973-94). Modellen har fått navnet TRULS
reporting routines, and geographic characteristics. (TRafikk, ULykker og Skadegrad).
The econometric model has received the acronym
TRULS.
Language of report: English
The report can be ordered from: Rapporten kan bestilles fra:
Institute of Transport Economics, The library Transportøkonomisk institutt, Biblioteket
Gaustadalleen 21, NO 0349 Oslo, Norway Gaustadalleen 21, 0349 Oslo
Telephone [phone] - www.toi.no Telefon [phone] - www.toi.no
Copyright © Transportøkonomisk institutt, 1999
Denne publikasjonen er vernet i henhold til Åndsverkloven av 1961
Ved gjengivelse av materiale fra publikasjonen, må fullstendig kilde oppgis
An econometric model of car ownership,
road use, accidents, and their severity

Contents
Preface..............................................................................................................................................................1
Acknowledgements............................................................................................................................................3
Chapter 1: Introduction and overview...............................................................................................................7
1.1. Motivation................................................................................................................7
1.2. Scope........................................................................................................................7
1.3. Essay outline............................................................................................................8
Chapter 2: General perspective and methodology..........................................................................................11
2.1. A widened perspective on road accidents and safety.............................................11
2.2. TRULS – a model for road use, accidents and their severity................................12
2.2.1. The DRAG family of models.........................................................................12
2.2.2. The general structure of TRULS....................................................................12
2.3. Choosing the level of aggregation.........................................................................15
2.3.1. Errors of aggregation and disaggregation.......................................................15
2.3.2. Aggregate vs disaggregate demand modeling in transportation.....................17
2.3.3. The case for moderately aggregate accident models......................................19
2.3.4. An exogenous population of counties and months.........................................21
2.4. Econometric method..............................................................................................24
2.4.1. The issue of functional form...........................................................................24
2.4.2. The Box-Cox and Box-Tukey transformations..............................................24
2.4.3. The BC-GAUHESEQ method of estimation..................................................25
2.4.4. Elasticities......................................................................................................25
2.4.5. Dummies and quasi-dummies........................................................................26
2.4.6. A note on alternative methods of estimation..................................................28
Chapter 3: The relationship between road use, weather conditions, and fuel sales........................................31
3.1. Motivation..............................................................................................................31
3.2. Notation.................................................................................................................32
3.3. Relating traffic counts to fuel sales........................................................................33
3.4. An error theory for traffic counts...........................................................................38
3.5. Specifying the random disturbance term...............................................................40
3.6. Sample...................................................................................................................42
3.6.1. Traffic counts.................................................................................................42
3.6.2. Fuel sales statistics.........................................................................................42
3.6.3. Meteorology...................................................................................................44
3.7. Empirical results....................................................................................................44
3.7.1. Fuel sales........................................................................................................45
3.7.2. Weather..........................................................................................................45
3.7.3. Price variations...............................................................................................49
3.7.4. Calendar effects..............................................................................................50
3.7.5. Heteroskedasticity..........................................................................................52
3.8. Model extrapolation and evaluation.......................................................................53
Chapter 4: Aggregate car ownership and road use.........................................................................................61
4.1. Introduction............................................................................................................61
4.2. A partial adjustment model of aggregate, private car ownership...........................62
4.3. Models for overall and heavy vehicle road use......................................................64
4.4. Empirical results....................................................................................................65
4.4.1. Car ownership partial adjustment...................................................................65
4.4.2. Effect of car ownership on road use...............................................................67
4.4.3. Population.......................................................................................................67
4.4.4. Public transportation supply...........................................................................68
4.4.5. Income............................................................................................................68
4.4.6. Prices and taxes..............................................................................................72
4.4.7. Road infrastructure.........................................................................................82
4.4.8. Spatial differences in road supply..................................................................86
4.4.9. Weather and seasonality.................................................................................89
4.4.10. Calendar events............................................................................................92
4.4.11. Geographic characteristics............................................................................92
4.4.12. Heteroskedasticity........................................................................................94
4.4.13. Autocorrelation.............................................................................................96
4.5. Summary and discussion........................................................................................96
Chapter 5: Seat belt use...................................................................................................................................99
5.1. Motivation..............................................................................................................99
5.2. Seat belt use sample surveys and regulations......................................................100
5.3. A logit model of seat belt use..............................................................................100
5.4. Empirical results..................................................................................................104
5.5. Imputed seat belt use............................................................................................106
Chapter 6: Accidents and their severity.........................................................................................................109
6.1. Behavioral adaptation..........................................................................................109
6.1.1. Balder’s death – a mythical example............................................................109
6.1.2. The lulling effect – and its generalization....................................................110
6.1.3. Behavioral adaptation on the road................................................................113
6.1.4. A microeconomic perspective......................................................................116
6.1.5. Testing for risk compensation......................................................................125
6.2. Road accidents as an internal and external cost...................................................127
6.3. Random versus systematic variation in casualty counts......................................132
6.3.1. The Poisson process.....................................................................................135
6.3.2. The generalized Poisson distribution............................................................138
6.4. Testing for spurious correlation in casualty models............................................140
6.4.1. The overdispersion criterion.........................................................................140
6.4.2. Specialized goodness-of-fit measures for accident models..........................141
6.4.3. The casualty subset test................................................................................143
6.5. Accident model specification...............................................................................146
6.5.1. General.........................................................................................................146
6.5.2. Heteroskedasticity........................................................................................147
6.5.3. Autocorrelation.............................................................................................148
6.6. Severity model specification................................................................................148
6.6.1. General.........................................................................................................148
6.6.2. Heteroskedasticity........................................................................................148
6.6.3. Autocorrelation.............................................................................................148
6.7. Empirical results..................................................................................................149
6.7.1. Traffic volume and density...........................................................................150
6.7.2. Motorcycle exposure....................................................................................161
6.7.3. Public transportation supply.........................................................................162
6.7.4. Vehicle stock................................................................................................163
6.7.5. Seat belt and helmet use...............................................................................165
6.7.6. Population.....................................................................................................168
6.7.7. Road infrastructure.......................................................................................173
6.7.8. Road maintenance........................................................................................175
6.7.9. Daylight........................................................................................................177
6.7.10. Weather......................................................................................................179
6.7.11. Legislation and reporting routines..............................................................183
6.7.12. Access to alcohol........................................................................................185
6.7.13. Geographic characteristics..........................................................................190
6.7.14. Calendar and trend effects..........................................................................191
6.7.15. Autocorrelation...........................................................................................193
6.7.16. Explanatory power.....................................................................................193
Chapter 7: Synthesis......................................................................................................................................195
7.1. Calculating compound elasticities in a recursive model structure.......................195
7.2. Direct and indirect casualty effects......................................................................197
7.2.1. Exposure.......................................................................................................197
7.2.2. Road infrastructure.......................................................................................200
7.2.3. Road maintenance........................................................................................202
7.2.4. Population.....................................................................................................204
7.2.5. Income..........................................................................................................204
7.2.6. Prices and tax rates.......................................................................................206
7.2.7. Weather........................................................................................................207
7.2.8. Daylight........................................................................................................210
7.2.9. Seat belts.......................................................................................................211
7.2.10. Alcohol availability....................................................................................213
7.2.11. Calendar effects..........................................................................................216
7.2.12. Time trend..................................................................................................217
7.3. Suggestions for further research..........................................................................219
7.3.1. Methodological improvements.....................................................................219
7.3.2. Subject matter issues....................................................................................221
Literature.......................................................................................................................................................225

Appendix A: Estimating Box-Cox accident and severity models with Poisson disturbance variance...........237
Appendix B: Supplementary tables................................................................................................................245
Appendix C: Variable nomenclature.............................................................................................................289

Preface
The present volume contains the last part of the author’s dissertation for the dr. polit. degree
at the Institute of Economics of the University of Oslo.
In total, the dissertation consists of an introductory overview and three accompanying essays.
The first essay – entitled «The barely revealed preference behind road investment priorities»
and co-authored by Rune Elvik – has been published in Public Choice 92: 145-168 (1997).
The second essay – entitled «Measuring the contribution of randomness, exposure, weather,
and daylight to the variation in road accident counts» and co-authored by Jan Ifver, Siv Inge-
brigtsen, Risto Kulmala and Lars Krogsgård Thomsen – can be found in Accident Analysis
and Prevention 27: 1-20 (1995). This paper is based on the report «Explaining the variation
in road accident counts», by the same authors, issued by the Nordic Council of Ministers
(Nord 1993:35).
Both of these essays are reprinted, together with the introductory overview, in a separate Vol-
ume I (TØI report 456/1999).
The third essay – entitled «An econometric model of car ownership, road use, accidents, and
their severity» and printed in this Volume II – is by far the largest. Certain parts of this re-
search were presented at the 8th World Conference on Transport Research (WCTR) in Ant-
werpen in July 1998, at the 9th International Conference «Road Safety in Europe» in Ber-
gisch-Gladbach in September 1998, at the conference «The DRAG Approach to Road Safety
Modelling» in Paris in November 1998, at the «2nd European Road Research Conference» in
Brussels in June 1999, at the 10th International Conference «Traffic Safety on Two Conti-
nents» in Malmö in September 1999, in report 402/1998 from the Institute of Transport Eco-
nomics (TØI) (in Norwegian), and in a series of articles in the journal Samferdsel (issues 4
through 10, 1998 and 1-2, 1999 – also in Norwegian). Additional documentation is forthcom-
ing in the book «Structural Road Accident Models: The International DRAG family», edited
by Marc Gaudry and Sylvain Lassarre and published by Elsevier, and in the final report from
the COST 329 project («Models for traffic and safety development and interventions») of the
European Commission.

Oslo, November 1999
INSTITUTE OF TRANSPORT ECONOMICS

Knut Østmoe Marika Kolbenstvedt
Managing Director Head of Department

Copyright @ Institute of Transport Economics, 1999 1
2
Acknowledgements
The author is indebted to a large number of people and institutions for their help in complet-
ing the present analyses.
First and foremost, thanks are due my colleague Peter Christensen for his help in extracting
seemingly endless sets of specified casualty counts from the national register of road acci-
dents, and for his fruitful comments and advice at various stages of the research process.
Without Peter’s invaluable assistance from an early stage, it is doubtful if this thesis would
have ever seen the light.
I was also, in an early phase of the process, greatly helped by Per Christian Svae, who set up
and organized the first version of the database for essays 2 and 3, using the dBase IV format.
For our most constructive cooperation during the so-called MBAT project («Metode for Be-
skrivelse og Analyse av ulykkesTall»), which forms the basis for essay 2, I am indebted to my
Nordic partners Jan Ifver, Risto Kulmala and Lars Krogsgård Thomsen. Thanks are also due
to my Norwegian colleagues Siv Ingebrigtsen and Jan Erik Lindjord, who helped perform
certain parts of the statistical and numerical calculations for the MBAT project, to Tore
Vaaje, who initiated the project, and to the Nordic Council of Ministers, which financed it.
For the analysis underlying essay 1, I was helped by James Odeck and Toril Presttun of the
Norwegian Public Roads Administration in obtaining a data set on road investment priorities,
by Rune Elvik, Jan Erik Lindjord og Lasse Torgersen in «purging» and preparing the data for
analysis, and by Inger Spangen in interpreting and qualifying the results.
This doctoral dissertation would not have been possible without the financial support – which
is gratefully acknowledged – of the Royal Norwegian Council for Scientific and Industrial
Research (NTNF – now merged into the Research Council of Norway), of the Norwegian
Ministry of Transport and Communications, and of my employer – the Institute of Transport
Economics (TØI). For the support received through TØI I am indebted to each and every em-
ployee, who have accepted to cross-subsidize my research through a large number of years
and, on top of that, have offered continual encouragement and advice. Although no one is
forgotten, I especially want to thank Torkel Bjørnskau, Rune Elvik, Stein Fosser, Alf Glad,
Odd Larsen, Harald Minken, Arne Rideng, and Fridulv Sagberg, for their helpful hints and
assistance, Astrid Ødegaard Horrisland and Anne Marie Hvaal for their superb library ser-
vices, Svein Johansen and Jack van Domburg for their graphical and printing services, Lars
Hansson, Jurg Jacobsen, Tore Lien, Torbjørn Strand Rødvik, and Arne Skogli for their com-
puter support services, and Laila Aastorp Andersen, Jannicke Eble, Magel Helness, Trude
Rømming, and Unni Wettergreen for their secretarial assistance.
I am generally indebted to my colleagues at the Department of Safety and Environment for
our inspiring discussions and exchange of views and for their warm support in my apparently
never-ending pursuit of the dr. polit. degree. I am particularly grateful to my Head of Depart-
ment Marika Kolbenstvedt, who helped provide the resources and energy needed to give this
thesis its final touch.
Certain people outside my Institute have also contributed significantly to the realization of
this thesis. Morten Merg of the Road Traffic Information Council («Opplysningsrådet for
vegtrafikken») provided machine-readable data on the vehicle stock by county and year.
Bjørn Reusch and the Norwegian Petroleum Institute helped provide data on fuel sales by
Copyright @ Institute of Transport Economics, 1999 3
county and month. Finn Harald Amundsen, Kjell Johansen and Lars Bendik Johansen of the
Public Roads Administration were most helpful in making available a suitable data set on
traffic counts. I am generally grateful to a large number of helpful researchers and employees
in the Central Bureau of Statistics (now Statistics Norway), in the Norwegian Social Science
and Data Services (NSD), and in the Bank of Norway, who on various occasions have pro-
vided the necessary data input and background material for my analyses. I have learnt a lot
from the constructive comments and advice offered by Finn Jørgensen of the Bodø Graduate
School of Business, and from my cooperation, within the COST 329 action and the OECD
Scientific Expert Group RS6 on «Safety Theory, Models, and Research», with Sylvain Las-
sarre of the INRETS. I have also benefited greatly from the insights offered, through the
AFFORD project for the European Commission, by Erik Verhoef of the Free University of
Amsterdam.
Without the software support offered by Francine Dufort and the TRIO team at the Centre de
Recherche sur les Transports of the Université de Montréal my analyses would not have been
feasible.
Last, but not least, I wish to extend a warm thank you to my advisors Erik Biørn and Marc
Gaudry, for their untiring support, encouragement and advice, and for letting me partake of
their immense professional competence and patience.

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