Project Work (svolto) + paper - Costs and Benefits of an helmet law in Germany

OMITTED EFFECTS

In their analysis the authors deliberately omitted certain effects because

they were considered to be statistically insignificant or irrelevant to the

final result. heterogeneity of cyclists risk

These effects include, for example, the , the

that some cyclists compensate for the safety gain by riding faster and the

helmets are inefficient at certain speeds or when worn

fact that

incorrectly . 13

OMITTED EFFECTS – Literature review

Lei Kang, Akshay Vij, Alan Hubbard, David Shaw, «The unintended

, 2021,

impact of helmet use on bicyclists’ risk-taking behaviors »

Available online at: https://www.sciencedirect.com/science/article/abs/pii/S0022437521001122?via%3Dihub

Findings suggest, on average, that individuals which are more likely

to wear a helmet are 15.6% more likely to undertake a risky

overtaking maneuver.

In the light of the authors' findings, it seems necessary to update the

to take account of this side effect, which had

cost benefit analysis

not been considered. 14

CONCLUSIONS OF THE AUTHORS

The authors therefore conclude that, as far as the helmet law is

concerned, the benefits do not outweigh the costs.

Therefore, from a collective point of view, the law would be a waste of

resources. 15

WAHT WE DID

An to latest year before the pandemic (2019)

1. update of the data

A in order to compute the Benefit Cost Ratio

2. MATLAB model

A on MATLAB in order to observe the

3. Monte Carlo Simulation

probabilistic distribution of the project’s NPV

A in order to compare the results of this paper

4. literature review

with other similar scientific analysis 16

MATHEMATICAL MODEL: UNCHANGED PARAMETERS 17

MATHEMATICAL MODEL: PARAMETERS ASSOCIATED WITH DATA

FROM 2019 18

UPDATED PARAMETERS UNCHANGED PARAMETERS

- The distance cycled and the - Value of statistical life

number of cyclists - Speed of cycling, walking,

- The risk reduction value of travelling by car/public

helmets transport

- The fraction of injuries - Health gains from

reduced by helmets cycling/walking

- The external cost of

travelling by car

- The average cost of helmes 19

PROTECTION EFFECT

Helmet reduces the severity of injury in the event of an accident. The

benefit derived from the induced helmet use is [ ]

Nf

with

Statistical value for the protection provided by a helmet =

: 4,42 cent

(2,083 cent per km in 2012)

per km

Distance of helmeted cycling induced by the law =

: 29.215 millons km

with

Proportion of cyclists using helmets = 22,8% (13% in 2011)

Reduction of cycling if a helmet law is passed = 0,044 (as in the paper)

Distance cycled in Germany = 39.858 millions km (32.970 millions km in 2008)

20

EXPOSURE EFFECT

Some cyclists opt for walking or another mode of transport (bus or car) rather than

wearing and/or buying a helmet. These cyclists increase their safety by changing the

nature of exposure to risk related to the traffic mode used [ ]

Nn

with

distance of cycling substituted by walking, car and public transport = 1.344.600.000

km

distance walked instead of cycled = 254.460.000 km

distance travelled by car instead of cycled = 497.360.000 km

distance travelled by public transport instead of cycled = 115.670.000 km

using transport mode i (where i=bicycle, car, public transport, walk) induces costs

related to the number of accidents with fatalities ( we assume the costs are equal

)

to those in the paper 21

PURCHASE EFFECT

Cyclists who do not have a helmet have to buy one. Cost of helmets [ ]

Km

with

Opportunity costs of a helmet = (Ch_best+Ch_cheap/2)*(1-Sale_taxes) =

= (27.62 € in 2013)

20,90 €

Time to replacement of a helmet = (as in the paper)

5 years

Number of cyclists = (73,000,000 in 2013)

63.232.000

Proportion of cyclists using helmets = (13% in 2011)

22,8% 22

ENVIRONMENTAL EFFECT

From an environmental point of view, the substitution of cycling with motorized

Costs related to motorized transport (noise, pollution

transport is undesirable.

and global warming) [ ]

Ke with

Traveling by car induces external costs (Climate change, air pollution,

soil sealing and noise) = (0.0314 €/km in 2007)

0,15 €/km

distance travelled by car instead of cycling = 497.360.000 km 23

COMFORT EFFECT

Helmet may reduce the pleasure of cycling. Additional costs arise through the utility

losses caused by helmet wear (they are regarded as ‘‘uncool’’, they are also

incompatible with ‘‘big hair’’ , and they generally reduce air circulation) [ ]

Kg

with

Average utility losses due to helmet wear = (0,00625 €/km in 2012 )

0,0133 €/km

= 0,5 *

where Fraction of the benefits internalized (because social insurance covers

0,6

hospital costs) =

Statistical value for the protection provided by a helmet = 4,42 cent

(2,083 cent per km in 2012)

per km

Distance of helmeted cycling induced by the law = 29.215 millions km 24

HEALTH EFFECT

Cyclists that opt for another mode of transport will sacrifice the positive impact

of cycling on health. The monetary losses due to deteriorating health are [ ]

Kh

with

Statistical value of the health gains = (as in

1,05 € per additional km cycled

the paper)

Statistical value of the health gains = (as

2,50 € per additional km walked

in the paper)

The distance of cycling that is substituted induces monetary costs of

and only the distance that is walked improves health by 25

BENEFIT COST RATIO

BCR (2019) = 0,9894

BCR (2013) = 0,720

Since the BCR is still

less than 1, the results

of the paper are

confirmed even using

more recent data (even

though there is a

significant increase in

BCR).

Helmet law in Germany

is (still) a waste of

resources. 26

MONTE CARLO SIMULATION (Probabilistic sensitivity analysis)

1. We assumed we have uncertainty on these parameters: rr, q_head, VSL, Ch, r, ul

2. We defined the probability distributions:

for

Normal distribution rr, q_head, r, ul

→ in a interval for

Uniform distribution [a,b] VSL, Ch

→

3. We generated for each uncertain variable

N= 1000 realizations

4. We have than obtained a for the relevant

probability distribution performance

indicator (NPV)

We chose to observe the probabilistic distribution of the NPV instead of the BCR due to

the fact that the is a and therefore is sometime

BCR ratio misleading in this specific

analysis.

Indeed, the combination a very small number in the denominator with a big number in

the numerator (or viceversa) generates values that are exponentially high (or low). 27

MONTE CARLO SIMULATION - MATLAB Code 28

MATLAB SIMULATION - Histogram

Frequency distribution of NPV With a pretty the

large probability NPV

will be positive.

By introducing a range in which the

parameters can change, the result of the

as

paper is reversed, benefits appear to

be greater than costs in most cases.

Anyway, we have introduced variability for

only some of the parameters, so this is a

partial analysis. 29

LITERATURE REVIEW/1

Igor Radun, Jake Olivier, « Bicycle helmet law does not deter cyclists in

, 2018, Available online at:

Finland » https://www.sciencedirect.com/science/article/pii/S1369847818300810?via%3Dihub

- Data across three surveys suggest cycling has declined from before to after

Bike Helmet Law.

- In a 2004/2005 survey, however, only 0.063% (95% CI: 0.02–0.10%) of

responders identified helmet use as their most important obstacle to cycling.

It is therefore unlikely Bike Helmet Law is a causal factor in the downward

- trend in Finnish cycling. and

Lack of cycling infrastructure concerns for

(not strictly connected with the helmet use) are much more common

safety

reasons given. 30

LITERATURE REVIEW/2

Gary M. Ginsberg, Don S.Silverberg, « A Cost-Benefit Analysis of Legislation

, 1994, Available online at:

for Bicycle Safety Helmets in Israel » https://pubmed.ncbi.nlm.nih.gov/8154573/

- The cost of crash helmets (current retail price: $23.40) for Israel’s 833000 cyclists

would be $19.5 million. An additional $607000 would be required over 5 years for

health education purposes.

- Legislation for bicycle helmet use in Israel would, over a helmet's 5-year duration,

avoid approximately 57 deaths, 2544 fewer hospitalizations, 13355 emergency room

visits, 26634 ambulatory visits, and 832 and 115 fewer short-and long-term

rehabilitation cases (including children needing special education), respectively.

- The ($44.20 million) ($20.14 million) When

direct benefit to cost ratio is 2.19:1.

benefits from reductions in work absences are included

($7.55 million) , the benefit-

adding benefits from reductions in mortality

. After

cost ratio rises to 2.57:1

($8.94million), the total benefit-cost ratio to society rises to 3.01:1. 31

CONCLUSIONS AND FURTHER ANALYSIS/1

◦ In the paper we analyzed the authours cocluded that the Helmet

would be a (since the

Law in Germany waste of resources

is equal to )

BCR_2013 0,720

◦ On the other hand, , the

by updating the data to the 2019 BCR

and it almost reached the breakeven point

has increased

( )

BCR_2019 = 0,9894

◦ In addition, the value of the is to the initial

BCR very sensible

For example, Gary M. Ginsberg, Don S.Silverbergin

assumptions.

their paper, by making different assumptions, concluded that the

BCR in Israel was between 2.19 and 3.01. 32

CONCLUSIONS AND FURTHER ANALYSIS/2

◦ Furthermore, the literature in this field is making important

progress and is starting to evaluate in a different way some of

by the authors in the paper

the effects which have been omitted

we analyzed (i.e. The impact of helmet use on bicyclists’ risk-

taking behaviors)

◦ We can conclude that no universal and definitive answer can be

, but in the future it will be useful to repeat the cost benefit

given

analysis, taking into account the various differences between

countries in terms of infrastructure, citizens' habits, etc. 33

BIBLIOGRAPHY

◦ « Bicycle helmet law does not deter cyclists in Finland »

Igor Radun, Jake Olivier, ,

2018, Available online at:

https://www.sciencedirect.com/science/article/pii/S1369847818300810?via%3Dih

ub

◦ « A Cost-Benefit Analysis of Legislation for

Gary M. Ginsberg, Don S.Silverberg,

Bicycle Safety Helmets in Israel »

, 1994, Available Online at:

https://pubmed.ncbi.nlm.nih.gov/8154573/

◦ «The unintended impact of

Lei Kang, Akshay Vij, Alan Hubbard, David Shaw,

helmet use on bicyclists’ risk-taking behaviors »

, 2021, Available online at:

htt