Public Preferences for Hydrogen Buses: Comparing Interval Data, OLS and Quantile Regression Approaches

Abstract

We use a quantile regression (QR) approach to analyse contingent valuation estimates of public willingness to pay (WTP) for the air and noise pollution reductions associated with the introduction of hydrogen buses in London. QR results show that variables that were not significant in interval regression or ordinary least squares regression become significant at certain quantiles along the WTP distribution. In addition, the determinants of WTP at the lower tail of the distribution differ from those at the higher end of the distribution. Our findings illustrate the usefulness of quantile regression methods for analysing contingent valuation data, enhancing our understanding of the determinants of willingness to pay. Copyright Springer Science+Business Media, Inc. 2007

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Public Preferences for Hydrogen Buses: Comparing Interval Data, OLS and
Quantile Regression Approaches
Tanya O'Garra and Susana Mourato
1
Centre for Environmental Policy, Imperial College London,
Prince Consort Road, London SW7 2BP, United Kingdom
This article was published as: O’Garra, T. and Mourato, S. (2007) ‘Public
preferences for hydrogen buses: comparing interval data, OLS and quantile regression
approaches’, Environmental and Resource Economics, 36(4), 389-411
Abstract
We use a quantile regression approach to analyse contingent valuation estimates of
public willingness to pay for the air and noise pollution reductions associated with the
introduction of hydrogen buses in London. Quantile regression results show that
variables that were not significant in interval regression or ordinary least squares
regression become significant at certain quantiles along the willingness to pay
distribution. In addition, the determinants of willingness to pay at the lower tail of the
distribution differ from those at the higher end of the distribution. Our findings
Acknowledgements
We thank Roger Koenker, Peter Pearson, Paul Johnson, David Hart, two anonymous reviewers and the
editor for very helpful comments. We also thank Tiago Neves for his data from the ACCEPTH2
project, as well as Lisa Garrity, Simon Whitehouse, Matthias Altmann, Cornelia Grasel and Anne
Stevcevski for valuable collaboration in the design of the core questionnaire. Finally, we acknowledge
financial support from the European Union under the ACCEPTH2 project (Contract N° ENK5-CT-
2002-80653) and from the John Stanley Studentship (for Tanya O’Garra).
1 Corresponding author address: Centre for Environmental Policy, Imperial College London, Prince
Consort Road, London SW7 2BP, United Kingdom. Tel: +44 (0)207 594 9316; Fax: +44 (0)207 594
9334; E-mail: s.mourato@imperial.ac.uk

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illustrate the usefulness of quantile regression methods for analysing contingent
valuation data, enhancing our understanding of the determinants of willingness to pay.
Keywords: contingent valuation, interval data, quantile regression, OLS, hydrogen
1. INTRODUCTION
When introducing new environmental technologies, such as cleaner transport fuels
and vehicles, it is often necessary to value the associated environmental benefits. Due
to their public good nature, such benefits are typically non-priced. Hence, in order to
estimate their monetary value, researchers often use one of various non-market
valuation approaches, such as contingent valuation (CV). CV methods were
developed within environmental economics as a means to place an economic value on
environmental changes, which due to their public good nature, are not traded in the
market (Mitchell and Carson, 1989; Bateman et al., 2002). The method involves a
questionnaire in which respondents are presented with a hypothetical (or ‘contingent’)
market where the good or service in question can be traded. Respondents are then
typically asked for their willingness to pay (WTP) for a hypothetical change in the
level of provision of the good or service.
The validity of monetary values produced using CV is typically assessed by
regressing variables predicted by theory to be key determinants of preferences, on
WTP data, using parametric or semi-parametric regression models, such as ordinary
least squares (OLS) techniques, or maximum likelihood estimation (e.g. Tobit, Logit
and Interval Data models). These methods are typically dependent on a priori

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assumptions about the distribution of respondents’ WTP
2
. If the distribution is
incorrectly specified, such approaches may produce biased estimates (Crooker and
Herriges, 2004). Unfortunately, economic theory has little to say regarding the
appropriate distribution that should be used in regression analyses of WTP data
(Crooker and Herriges, 2004).
Furthermore, these approaches assume a homogenous influence of explanatory
variables on the dependent variable. This assumption could be problematic if the
impacts of the explanatory variables on WTP are inconsistent, or more complex than
assumed in the functional form. Indeed, there is a growing literature addressing
preference heterogeneity in valuation contexts (e.g. Morey et al, 2006; Milon and
Scrogin, 2006; Boxall and Adamowicz, 2002). In general, these studies find that
individuals tend to belong to different preference groups with different characteristics.
As indicated by Adamowicz and DeShazo (2006), ‘the failure to identify differences
in the preferences of individuals may both bias estimates of demand and forego the
opportunity to observe differences within the population at a higher resolution.’
Quantile regression (QR) techniques, developed by Koenker and Bassett (1978), are
an increasingly important tool used by researchers to estimate relationships between
variables along the entire length of the conditional distribution. In contrast with
classical regression techniques, such as OLS or maximum likelihood estimation (e.g.
Tobit, Logit, interval regression), which generally involve examining relationships
between variable means, the QR approach can provide a more complete statistical
picture of the relationships between variables. Moreover, QR is robust to the presence
2
There are exceptions, such as Li (1996), where semi-parametric models are applied to CV data without relying on distributional
assumptions.

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of outliers or skewed tails (Koenker and Hallock, 2001). This feature of QRs is likely
to be particularly useful in the context of contingent valuation studies, in which very
high willingness to pay bids (‘outliers’) or large numbers of small bids can frequently
occur. QR techniques can permit a more detailed assessment of the validity of the
values at the tails of the WTP distribution by separately identifying their determinants.
QR may also be used to identify non-linearities in the relationships between variables,
as well as threshold effects and other non-homogenous relationships.
Using data on WTP for hydrogen (H2) buses in London,
3
this paper aims to assess the
usefulness of QRs in identifying the determinants of WTP along the entire conditional
distribution. In order to assess the performance of this method for analysing CV data,
QR regression estimates are compared with results using an interval regression
estimator, and an ordinary least squares estimator. It is expected that the QR analysis
will complement these regressions, by highlighting the pattern of influences of the
explanatory variables along the distribution of WTP.
There are numerous policy-related purposes for using QR on CV data. For example,
there is an obvious interest in understanding whether the factors that affect benefits at
the highest quantiles are the same that influence benefits at the lower quantiles. If they
are not, then policy-makers might want to know who is benefiting most from a
particular policy, and in particular, whether the intended recipients of a policy are
those actually benefiting from it; QR allows us to do this by identifying the
3
This work forms part of the larger ACCEPTH2 project coordinated by the Centre for Environmental Policy at Imperial College
London. This is a EU-funded collaboration between 5 cities worldwide: London (UK), Munich (Germany), Luxemburg, Perth
(Western Australia) and Oakland (USA), and consists of a cross-continental comparative study of public acceptance of H2 fuel
cell buses, and an estimation of the economic value of their environmental benefits. This paper uses survey data on the
environmental benefits of H2 buses in London. Further information on the project is available from http://www.accepth2.com.

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determinants of WTP at the upper percentiles. In the context of this study, such
information may be used to assist in the development of appropriate policies or
projects associated with H2 buses in London. In addition, understanding what
variables drive higher WTP (and hence, higher benefits from introducing H2 transport
in London) can be useful for the development and design of information campaigns
and education materials associated with hydrogen. For example, an information
campaign based on variables that only drive low WTP values may not be as effective
as one that also focuses on variables driving higher values.
To the best of our knowledge, only one study to date (Belluzzo, 2004) has applied QR
to valuation data. Using dichotomous choice (DC) data on WTP for water resource
improvements in Brazil, Belluzzo (2004) finds that QR provides a more
comprehensive picture of the distributional impacts of different water management
policies, than standard logit-based analysis of DC data
4
. In particular, he notes
significant differences between the size and statistical significance of coefficients at
each of the tails of the distribution, suggesting that the ‘winners’ (at the right-hand
tail) and ‘losers’ (at the left-hand tail) of the water management policies may be
driven by very different factors.
The present paper complements this existing literature by applying QR analysis to
payment card economic valuation data. To the best of our knowledge QR has not been
applied to open-ended or payment card data, hence this represents a significant
contribution to the economic valuation literature.
4
For more information on analysis of DC data and application of the quantile regression approach to binary data see Bateman et
al (2002) and Kordas (2000), respectively.

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The rest of this paper is structured as follows. Section 2 describes the QR model.
Section 3 presents the background to the study and the CV study design. Section 4
contains descriptive statistics for WTP and other variables. In Section 5, the interval
data, OLS and quantile regression approaches are analysed and compared, and
explanatory factors at higher WTP quantiles are investigated. Section 6 concludes
with a discussion of the findings.
2. THE QUANTILE REGRESSION MODEL
Standard regression approaches to welfare analysis are based on the mean (or median)
of the conditional distribution of the dependent variable, in this case WTP. These
approaches, which include OLS, Tobit, Logit and interval data models, amongst
others, assume that impacts of the independent variables are homogenous along the
entire distribution of the dependent variable. However, this assumption may prove
inadequate if indeed the independent variables influence parameters other than the
mean (Koenker, 2003; Koenker and Bassett, 1978). Quantile regression methods
provide a mechanism for estimating relationships based on the range of quantiles
along the conditional distribution. In a willingness to pay setting, the QR model can
be written as (Koenker and Bassett, 1978):
WTPi = Xiβθ + ui,θ with Quantθ (WTPi│Xi)=Xiβθ (1)
where Xi is a vector of exogenous variables, βθ is the vector of parameters that are
being estimated, and ui,θ is the error term, for which no parametric distribution is
assumed. Quantθ (WTPi│Xi) denotes the θth regression quantile of WTPi given Xi. In

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order to estimate the θth regression quantile, where 0<θ<1, linear programming
methods are used to obtain a solution to the problem:
minbθ ∑ θ│WTPi − Xiβθ│ + ∑ (1− θ)│WTPi − Xiβθ│ (2)
i:WTPi≥Xiβ i:WTPi<Xiβ
where bθ is the estimate of βθ. The QR estimator therefore minimises the weighed sum
of the absolute value of the residuals. By varying θ, coefficients for any quantile along
the distribution of WTP can be estimated. The coefficients in a quantile regression can
be interpreted in a similar way to OLS coefficient estimates. For example, in a
regression of income on WTP, the coefficient on income at the 25th quantile (θ=0.25)
gives the marginal change in WTP given a marginal change in income, for
respondents in the bottom quarter of the conditional distribution of WTP.
QR has been used in economics to analyse returns to education (Bauer and Haisken-
DeNew, 2001), determinants of wages and wage inequality (Martins and Pereira,
2003) and income convergence in growth equations (Mello and Perrelli, 2003).
However, with the exception of the study by Belluzzo (2004), there appear to be no
other studies applying QR techniques in environmental economics in general and in
CV studies in particular. By applying QR methods to WTP for H2 buses in London,
this paper aims to add to the findings in Belluzzo (2004) by highlighting the added
value of using QR to analyse payment card data in addition to common techniques
such as OLS or maximum likelihood estimation to investigate determinants of WTP.

8
3. DATA
3.1 Background
Growing concerns about climate change and urban air quality have highlighted the
need to initiate a shift towards emissions-free transport fuels and technologies.
Hydrogen, currently one of the most promising lower carbon energy options for
transport, is being tested in three H2 fuel cell (FC) buses introduced in London in
December 2004 as part of the EU-wide Clean Urban Transport for Europe (CUTE)
demonstration project.
5
H2 FC buses provide several environmental benefits. Firstly,
the only by-product of hydrogen combustion is water vapour, thus potentially
reducing greenhouse gas emissions and local air pollution from buses at point of use.
Secondly, fuel cells (the electrochemical devices that run on hydrogen to power the
vehicle) are more efficient than current engines. Thirdly, H2 FC vehicles produce less
noise when running, thus reducing noise pollution.
As a secondary output, this paper also presents CV estimates of the environmental
benefits of H2 FC buses (namely reduction of emissions and noise pollution) to
London-based residents. Although there are a number of studies that estimate the
environmental benefits of alternative-fuel buses (e.g. Karlstrom, 2005; Schimek,
2001), these tend to use indirect damage-cost approaches to estimate environmental
benefits. To the best of our knowledge, this is the first (CV) study to directly estimate
WTP for the environmental benefits of alternative-fuel buses. Furthermore, the only
study to date that estimates the WTP for H2 FC vehicles was carried out by Mourato
et al (2004). Using the CV method, they estimated taxi driver’s WTP to drive H2 FC
5
For more information on the CUTE project see: www.fuelcellbusclub.com

9
taxis, and found that there was a positive WTP overall. Apart from this study, here
have been no other studies looking at WTP for H2 vehicles, and no studies reporting
economic values of the environmental benefits of H2 buses; hence this analysis
represents a significant contribution to the empirical transportation literature.
3.2 Contingent Valuation Study Design
A series of three focus groups and a pilot study were held during June 2003 to assist
in the design of the CV instrument. The valuation section of the questionnaire
contained neutral and balanced information on the advantages and disadvantages of
hydrogen as a fuel for transport, and a brief description of the CUTE hydrogen bus
project. Respondents were presented with the following scenario of large-scale
introduction of H2 buses in London: “Suppose that there was a proposal to substitute
the buses in the London transport system for hydrogen fuel cell buses. As I mentioned
earlier, these hydrogen buses would emit zero air pollution, be less noisy and more
efficient than conventional buses. However they would also be more costly to run”.
Respondents were then asked if they would support the introduction of H2 fuel cell
buses in London if that meant for a higher bus fare (participation question) and, if so,
how much they would be willing to pay extra bus fare per month, in order to support
the large-scale introduction of H2 buses in London. The elicitation format used was a
payment card. This involved asking respondents to choose a WTP value from a series
of seventeen amounts read out by the interviewer, starting at zero and increasing by
discrete amounts to a maximum of £50.

10
The questionnaire also established bus usage, attitudes towards existing buses in
London, perceptions, knowledge about and attitudes towards the development of
hydrogen as a fuel for transport. Attitudes were explored before and after giving
respondents information on hydrogen as a fuel for transport and the CUTE hydrogen
bus project. Finally, information was elicited on socio-economic characteristics and
general environmental attitudes, knowledge and behaviour.
Using telephone numbers generated randomly using Excel, a total of 531 telephone
interviews were carried out with paying bus users living within the Greater London
area. Of these interviews, 282 were carried out between July and September 2003, and
249 were carried out during July and August the following year, using the same
questionnaire. These data were pooled together for the present study
6
, and the time
difference controlled for in all regressions using the dummy variable EXPOST (where
0=surveys carried out in 2003; 1=surveys carried out in 2004). Just under 50% of all
calls made were answered and, of these, an average of 20% were completed the first
time around and 40% completed in total (including call-backs). The average interview
duration was 20 minutes.
4. RESULTS
4.1 Descriptive Statistics
This section briefly presents summary statistics for the variables that were used in the
regressions. Table 1 summarises key socio-economic characteristics of the sample of
6
A Chow test confirms that the OLS coefficients estimated for the separate sub-samples (expost=0 and expost=1) are not
significantly different (F-statistic 0.148, p-value=0.99).

11
paying bus users (n=531) and compares these to characteristics of the wider London
bus population (where available).
7
As figures show, the sample may be considered
representative of the London bus user population in terms of sex and age; in terms of
work status, the sample is biased towards higher levels employment and lower levels
of retirement. This is likely to have occurred as a result of the data collection process
which involved random telephone calls using numbers generated on Excel. It appears
that individuals at work were more willing to complete a questionnaire than
respondents who were contacted whilst at home. This could be found to bias results,
and hence generalisations of the un-weighted sample to the overall London bus user
population should be interpreted with caution.
8
. However, as this paper is intended
primarily as a methodological contribution, aggregation of results is not conducted
and therefore these potential biases are not considered a major issue for the present
study. Moreover, work status (where the sample was unrepresentative) was not found
to be a determinant of WTP in the models we used.
INSERT TABLE 1 ABOUT HERE
Just under two thirds of bus users (60.5%) used the bus at least once a week and 24%
used the bus less than once a month. This compares favourably with bus usage of the
general London bus user population, of which 64% use the bus more than once a
week and 20% use it less than once a month. Just over half (53%) of bus users had
7
Average income and education statistics have not been found for the London bus user population. In these cases, Table 1 reports
general London population characteristics. However, as there is no reason to assume that London bus users have the same
characteristics as the wider population, the data has not been weighted. Interpretation of the results should take this into account.
8
Average income of the survey sample is also significantly higher than average income of the London population although, as
noted in footnote 7, it is not possible to tell how well it represents the population of interest (London bus users).

12
some form of season pass (weekly, monthly or annual), whilst the rest (47%) tended
to buy single adult tickets or daily travel cards.
Respondents rated “fumes from buses” as the least favoured attribute of existing
London buses (just over half of all respondents rated this attribute as “poor” or “very
poor”), whereas bus fare was rated amongst the most favoured attributes (together
with number of bus stops). General environmental attitudes were fairly positive with
just over four fifths (81%) of respondents agreeing that: “Solving environmental
problems should be one of the top 3 priorities for public spending in London.”
Self-reported awareness about H2 vehicles was moderate, with just over half (54.8%)
of respondents claiming to have heard about them. The most common sources of
information cited were newspapers/ magazines and television. Notably, the level of
prior knowledge about H2 vehicles appears to be about 10% higher in the 2004 sub-
sample. Average income is also significantly higher in the 2004 sub-sample. These
sub-sample differences are not considered problematic for the current study, as
parameter values across sub-sample regressions were found to be stable, suggesting
that the data can be pooled (see footnote 6 for details).
4.2 Willingness to Pay Statistics
All respondents (n=531) were asked to indicate, using a payment card elicitation
format, how much they were willing to pay extra bus fare per month to support the
introduction of H2 FC buses in London. Table 2 summarises the responses given.

13
INSERT TABLE 2 ABOUT HERE
Overall, results indicate that most respondents (85%; n=449) are willing to pay some
extra bus fare to support the introduction of H2 buses in London.
9
Respondents who
had bid zero WTP were asked for their reasons in a follow-up question; results show
that 9.8% of the sample protested against the valuation scenario. Protests included:
“Bus fares are expensive as it is”, “I object to paying more bus fare”, “The
government should pay for this” and “I am a frequent user, it would be very
expensive”. This is a relatively low protest rate and these responses were removed
from further analysis.
Respondents who had indicated in the participation question that they would be
willing to pay extra to support the introduction of H2 FC buses in London, yet
subsequently gave a zero WTP in the payment question, were considered to have a
non-negative WTP lying in the interval 0<WTP<0.10 of the payment card. Interval
data models, such as those used in this paper (see Section 5.1), assume that the true
WTP lies somewhere between the stated value and the value above that. It is therefore
assumed, in this case, that these respondents (n=11) are willing to pay a little extra,
but not as much as 10 pence. Notably, valid zero WTP bids - those in which
respondents did not support the introduction of H2 buses in London and therefore said
no to the participation scenario - accounted for only 3.6% of the sample.
Figure 1 shows the distribution of WTP results (using mid-points of payment card
intervals). As can be observed the distribution is skewed to the right due to two large
9
At the time of the study, the price of a single bus ticket was 70 pence. In June 2005 it had risen to £1.

14
values of £70 and £100. Mean WTP (calculated using the mid-point of the payment
card intervals) was estimated at £7.32 extra monthly bus fare (protests excluded). The
mean is significantly different from the median value of £6 (at the 1% level). Removal
of the two outliers of £70 and £100 does not significantly affect the mean (WTP is
reduced by 29p to £7.03).
INSERT FIGURE 1 ABOUT HERE
In the following section we will explore the determinants of WTP, first using both an
interval data model and an OLS regression, to identify influences on the mean, and
subsequently using quantile regressions, to identify influences at different quantiles
along the WTP distribution. Table 3 presents the quantiles that shall be explored and
the corresponding WTP values at each quantile (calculated using the mid-points of the
payment card intervals)
10
. These WTP values have a simple interpretation: values at
the θth quantile are greater than θ% of the WTP values, and smaller than (1- θ%) of
the WTP values. For example, the WTP at the 0.90th quantile is £13.50; this WTP
value is greater than 90% of the data, and smaller than 10% of the data - or, 90% of
the data lies to the left of the distribution, and 10% lies to the right.
INSERT TABLE 3 ABOUT HERE
10
Mean WTP in different quantile groups was calculated in STATA, which uses a binomial method for obtaining confidence
intervals that makes no assumptions about the underlying distribution of the variable (in this case WTP).

15
5. ECONOMETRIC ANALYSIS
5.1 Comparing interval regression, OLS and QR Results
Payment card data may be analysed in a number of ways. Standard OLS regressions
can be used, treating the payment card values chosen by respondents as point
estimates of their WTP or, alternatively, using the midpoint of the interval between
the value chosen and the next value up in the card. On the other hand, the WTP data
elicited from a payment card is typically censored at zero, i.e. respondents are only
offered positive payment amounts. Hence, to account for the censored nature of the
data, Tobit models can be used as well (Halstead et al., 1991). Finally, payment card
data can also be treated as interval data. This is because the respondent’s maximum
WTP may lie anywhere between the value ticked on the payment card and the next
value up. For this reason, payment card data can be analysed using parametric interval
regression methods (Cameron and Huppert, 1989)
11
.
The choice of which model to use depends on several attributes of the data which may
be conflicting (Whitehead et al., 1995). On the one hand, the greater the number of
zero responses the greater the probability of bias if an OLS is used instead of a Tobit
specification (Maddala, 1999). On the other hand, the wider the WTP intervals the
greater the chance of bias if interval regression is not used (Cameron and Huppert,
1989). And relative to interval regression, the greater the ratio of point estimates to
interval estimates the greater chance of bias if Tobit is not used, and vice versa
(Whitehead et al., 1995).
11
The interval data model is a generalization of the Tobit model, i.e. a censored model where each interval is taken as being
censored on both sides.

16
In this paper, we analyse the determinants of mean WTP using an interval regression
model to take into account the interval nature of our data. The interval data model
states that the probability that the true WTP of a respondent, with characteristics Y,
lies in the interval [BIDL, BIDU] is given by

(BIDU | Y) -

(BIDL | Y), where WTP
is assumed to follow a distribution with a standard normal cumulative distribution
function (). The model is estimated using maximum likelihood estimation (for more
details on interval regression model see Cameron and Huppert, 1989).
For comparative purposes we also present the results of an OLS regression model,
with robust standard errors, using the mid-point of the stated WTP intervals. The
results from the OLS and interval models are not expected to be very different, given
the relatively narrow intervals in the payment card. Both models will then be
compared with the QR model described earlier. Inspection of the data advised against
adopting a Tobit model in our case. This is because use of the Tobit model is typically
advocated for WTP data sets with large numbers of zero bids (Halstead et al., 1991)
which is clearly not the case in our data (less than 4% of data were valid zero bids).
Both interval data and OLS regressions were computed using STATA 8.0 software.
Quantile regressions were computed using Roger Koenker’s “quantreg” package on
CRAN R-software
12
. Explanatory variables included in the regressions are presented
in Table 4, while Table 5 contains the regression results.
INSERT TABLE 4 ABOUT HERE
12
This software can be downloaded on http://www.r-project.org/.

17
INSERT TABLE 5 ABOUT HERE
Results in the first two columns of Table 5 indicate that interval data and OLS models
produce very similar results; as noted above, this was expected given the relatively
narrow intervals used in the payment card. As expected, mean WTP is significantly
and positively influenced by income in both models, and by agreement with the
statement “Solving environmental problems should be one of the top 3 priorities for
spending in London”. In addition, results indicate that WTP for H2 buses is positively
related to prior awareness about hydrogen vehicles. These are largely expected
influences on WTP. Overall, the OLS regression is found to have very low
explanatory power (only 8% of variance in WTP is explained by the socio-economic,
attitudinal and knowledge regressors). The interval model fares only marginally better
with a pseudo-R2 of 0.09
13
. A possible explanation lies in the relatively small size of
the WTP amounts we are trying to explain: as seen in Table 3, the median monthly
WTP is £6, which constitutes only a very small part of an individual’s monthly
expenditure (Garrod and Willis, 1999).
The last eight columns of Table 5 present results of the QR model. Inspection of the
QR results reveals some interesting findings. In particular, a number of variables that
were not identified as significant in the interval or OLS regressions now become
significant at particular quantiles of the WTP distribution. Specifically, gender,
education, bus use frequency, and date when survey was carried out (EXPOST), now
emerge as significant influences on WTP for H2 buses (although EXPOST is only
13
STATA does not compute an R2 or pseudo- R2 for the interval regression output; hence, we used the Long and Freese (2006)
“findit” utility command (installed from STATA website), which computes a number of goodness of fit tests. The goodness of fit
test reported in this paper is the McKelvey-Zavoina pseudo-R2 (STATA, 2006).

18
significant at the 10% level). So, for example, while interval regression results
indicated that bus use frequency did not significantly influence WTP for H2 FC buses,
QR estimates show that TRIPNOS is statistically significant (at the 1% level) at the
lower quantiles of the distribution. This suggests that those who travel more
frequently by bus are willing to pay a little more bus fare per month, but not a lot
more to support the introduction of H2 buses. Interestingly, all the variables that have
become significant in the QR are only significant at the tails of the distribution.
In general, QR results in Table 5 suggest that influences at the lower quantiles tend to
differ from those at the upper quantiles of the WTP distribution. Income, education,
bus usage, environmental attitude and date of survey are found to be significant
determinants at the lower quantiles of the distribution, whereas at the higher quantiles
(75th to 97.5th percentiles), the significant predictors include income, environmental
attitude, prior knowledge about hydrogen, as well as age, education and gender
(although these last three variables are only significant at the 10% level). This
suggests that – with the exception of income and environmental attitude, which have
significant effects at both ends of the distribution - there are indeed different drivers
for WTP depending on the magnitude of the amounts stated, which in turn implies
that the assumption of homogeneity in the influence of explanatory variables on WTP
may not always be appropriate in the analysis of CV data.
The only variable that is significant across the entire distribution – with the exception
of the 10th percentile – is ENVATT. Thus, generic environmental attitude (as implied
by agreement with the given statement) positively influences WTP regardless of the
amount stated. It is also worth noting that, with one exception, income is mostly

19
significant at the higher quantiles – as noted earlier, a possible explanation lies in the
relatively small size of the WTP amounts which constitute only a very small part of an
individual’s monthly expenditure (Garrod and Willis, 1999). Thus, it might be
expected that only higher WTP bids are constrained by respondents’ income levels.
It is also interesting to note that age, which is significant at the 5% level in both
interval data and OLS models, only becomes significant at the 97.5th percentile in the
QR model (in actual fact, age is significant between the 96th and 98th percentiles) -
this indicates that age is not a significant determinant of mean WTP, as would be
suggested by the interval data and OLS regression results, but rather, is only an
influence at the very highest WTP bids.
The performance of the QR models can be assessed using a weighted sum of absolute
residuals for each quantile (Koenker and Machado, 1999)
14
. In Table 5 this statistic is
denoted the pseudo-R2. Interpretation of the pseudo-R2 in the quantile regression is
similar to the interpretation of R2 in the OLS regression, except that in QR, the R2
values provide a local goodness of fit instead of a global goodness of fit (Baur et al,
2004). As results show, R2 values for different regression quantiles range between
0.04 and 0.17. These are acceptable values, given that they are only measuring local
fit. The strongest performance is found, perhaps as expected, at the 25th and 50th
percentiles; the weakest performance is found at the highest quantiles.
14
The QR output in R does not automatically provide ‘goodness of fit’ tests, such as R2 or Chi-2 (which are provided in other
packages such as STATA). In order to test for ‘goodness of fit’, one tests the performance of a restricted version of the model (in
this case, the restricted model had three of the variables removed) relative to the full model (using a Wald test as computed in
Bassett and Koenker (1982). The tests return an F-like statistic, from which the authors calculated the R2 values (see Dougherty,
2001 for details on how to calculate R2 from F-statistics).

20
Overall, these results suggest that relationships between variables can depend
significantly on the magnitude of the amount that people are prepared to pay for H2
buses, and standard modelling approaches such as interval data or OLS tend to
obscure such relationships. These results tentatively support findings in Morey et al
(2006) and Milon and Scrogin (2006) that individuals belong to different preference
groups. In this case, we might distinguish respondents who are strongly pro-H2 buses,
from respondents who are only weakly supportive of H2 buses.
The tendency of the effects of the explanatory variables to vary along the distribution
of WTP can clearly be detected graphically. Figure 2 illustrates the extent of this
variation, by presenting the effects of the explanatory variables (i.e. the coefficients)
on WTP at different quantiles along the entire length of the WTP distribution.
INSERT FIGURE 2 ABOUT HERE
From these plots, we can immediately observe the extent of information that is lost in
the interval data or OLS regressions. For example, in the plot for income, at lower
quantiles the impact of income on a respondent’s WTP is about half of that predicted
by the interval regression coefficient. However, at around the 70th percentile, the
coefficient increases steadily to about five times the value of the interval regression
coefficient at the 99th percentile, indicating that the influence of income on WTP
increases with the amount bid. Inspection of results in Table 5 indicates that the
coefficient on income is statistically significant between the 90th and 97.5th percentiles
(it is also significant at the 99th percentile, although results for this quantile are
unreported in the table), indicating that income has a much greater impact on WTP at

21
the highest quantiles. The results at the higher quantiles of the WTP distribution shall
be discussed in Section 5.2.
Another plot worthy of mention is that for AGE, which shows the QR coefficients
running almost parallel to the interval regression coefficient (at a value close to zero)
for the first half of the distribution, and then steadily decreasing from about the 70th
quantile. Notably, QR results in Table 5 indicate that age is only significant at the
very highest quantiles (between 96th and 98th percentiles). This suggests that the
interval regression coefficient is being dragged upwards by the shape of the
conditional distribution at the lower quantiles (up until the 70th percentile
approximately), even though age is not even significant at these quantiles. The plot for
prior awareness (H2KNOW) appears to have a similar pattern, such that the interval
regression coefficient is being dragged downwards by the shape of the distribution up
until the 60th percentile approximately, even though H2KNOW is not significant at
these quantiles.
Other interesting plots are those for TRIPNOS and ENVATT. These plots are
considered to particularly highlight the extent of information that is lost in standard
mean regression approaches, such as interval data or OLS models. For example, the
coefficient plot of TRIPNOS has an convex shape suggesting that the impact of bus
use frequency increases with the amount bid, and then decreases again to a negative
value at the 80th percentile (although it is not significant). The ENVATT plot, on the
hand, indicates that generic environmental attitude (indicated by agreement with the
statement “Solving environmental problems should be one of the top 3 priorities for
spending in London”) has an increasing influence on WTP along the conditional

22
distribution. The static interval regression (or OLS) coefficient obscures this
relationship between environmental attitude and WTP.
Tests on the equality of the slope coefficients can further highlight whether QR is
warranted for these data: if the slope coefficients at different quantiles are found not
to be statistically different, then this would imply that the effects of the regressors are
not different in different parts of the conditional distribution, and hence the
application of QR to this data would not be justified. Using tests presented in Koenker
and Bassett (1982), test statistics for the equality of a number of slopes at different
quantiles (10th, 25th, 50th, 75th, 90th and 95th) are reported for each of the slope
parameters. Results of a joint test for all parameters are also presented in the last
column, as well as results of a joint test for all parameters and all slope coefficients
(including the 92.5th and 97.5th percentiles)
15
. Results are presented in Table 6.
INSERT TABLE 6 ABOUT HERE
Results indicate that most of the parameters exhibit significantly different slope
coefficients in at least one of the reported tests. The effect of income on WTP, for
example, differs significantly between the 10th percentile and 90th percentile.
However, results also suggest that the effect of income is very similar in the rest of the
distribution. Test statistics for age, gender and RATEFUME indicate that the effect of
these parameters on WTP does not vary significantly along the distribution. Joint tests
15
The tests for slope coefficient equality in the “quantreg” package (R-software) return an F-like statistic. In order to avoid
confusion with t-statistics, which have been presented throughout the paper, we have opted to present the p-value for the F-
statistic, which is computed based on the numerator degrees of freedom equal to the rank of the null hypothesis, and the
denominator degrees of freedom taken to be the sample size minus the number of parameters of the maintained model (Koenker,
2006).

23
of equality, however, indicate that the null hypothesis is rejected along the entire
distribution. Overall, these test results confirm that a QR approach is indeed
warranted for the analysis of this data.
The following section will briefly address the influence of explanatory variables on
WTP at the extreme upper tail of the distribution.
5.2 Analysis of Higher Quantiles
Quantile regression may also be used to shed light on the validity of outlier bids in
CV studies. It is often the case that a certain number or percentage of these outlier
bids – usually on the right hand side of the distribution - are omitted from the analysis
(Bateman et al, 1995). Although commonly done in CV studies, such truncation
procedures are arbitrary, and have been criticised for potentially excluding
respondents who simply value the good in question very highly (Brouwer et al, 1999).
In a study of the effect of truncation procedures on the analysis of WTP data,
Bateman et al (1995) find that the truncation strategy used has a significant impact on
mean WTP estimates. They recommend that CV studies using open-ended data would
benefit from sensitivity analysis of several truncation strategies for estimating mean
WTP. It is suggested in the present paper that quantile regression may also provide an
additional method for assessing the (theoretical) validity of the outlier bids, and hence
identify whether, and how much, truncation is appropriate.
The last three columns in Table 5 shows the results of the QR analysis on the 92.5th,
95th and 97.5th percentiles, equivalent to mean WTP of about £25 (see Table 3).

24
Results indicate that at this extreme right tail of the distribution, income and
environmental attitude are highly significant determinants of WTP (and they have the
expected positive signs on the coefficients). In other words, income and
environmental attitude are strongly determining factors for large WTP bids, as might
be expected. This seems to indicate that truncation of WTP values at this level on the
basis that they are invalid would not be warranted. Thus these results might justify
retaining any values around the 97.5th percentile
16
.
Other influences at these quantiles include age, education and prior knowledge.
Again, these influences – although only significant at the 10% level – are largely
consistent with theoretical expectations.
6. DISCUSSION AND CONCLUSIONS
This study used a quantile regression approach to analyse WTP data from a CV study
of the benefits of air and noise pollution reductions arising from a scenario of large-
scale introduction of H2 fuel cell buses in London. Despite increasing applications in
areas such as labour economics, surprisingly, there appear to be very few economic
valuation studies (only Belluzzo, 2004) using this technique to analyse the
determinants of WTP along its distribution. It was hypothesized that QR analysis
might add value to the standard maximum likelihood interval regression, as well as
OLS regression approaches, as it allows the examination of relationships between
16
Analysis of the 99th percentile indicates that income and environmental attitude are still strong determinants of WTP in the
theoretically expected directions. Note that these results have not been reported in the main text because it was suggested by
Roger Koenker that the 0.99 quantile is rather extreme given the small sample size used in the present study. The 97.5th
percentile was considered the most appropriate higher quantile to report in the main text. Quantile regression results for the 99th
percentile are available upon request from the corresponding author.

25
variables along the entire length of the conditional distribution of the dependent
variable (Koenker, 2003). Furthermore, QR is robust to the presence of outliers or
skewed tails, which is typical of CV data (Mello and Perrelli, 2003). From a policy
perspective there is also an obvious interest in understanding if different variables
drive WTP differently along its distribution and, in particular, in finding out which
variables may influence the highest and the lowest benefit estimates.
Overall, it appears that there is a substantial added value in using QRs to analyse CV
data. QRs produced significant relationships with variables that were not significant in
the other models. This suggests that influences vary along the conditional distribution
of WTP, and do not solely affect mean values. Interestingly, most of the significant
influences detected by the QR seemed to occur at the tails of the WTP distribution. It
is often the case that outliers in CV studies are removed or WTP data are truncated at
certain higher quantiles; our results show that the arbitrary removal of such data may
inhibit a better understanding of the full range of responses.
Additionally, QR results highlighted the fact that influences at the lower quantiles
tend to differ from those at the upper quantiles of the WTP distribution. For example,
bus use frequency is a significant driver for lower WTP values, but it has no impact
on higher WTP values. The only variable that appears to be a significant driver for
WTP along the entire conditional distribution (except at the 10th percentile) is
environmental attitude. Furthermore, this impact of this variable on WTP increases as
the magnitude of the bids increases.

26
In the case of our study, these results have important implications for the design of
outreach campaigns intended to inform the public about hydrogen in general, and the
actual introduction of H2 buses in particular. If, as the QR results illustrate,
environmental attitudes are strong drivers along the entire conditional WTP
distribution, then information campaigns would preferably aim to raise awareness
about environmental issues. Furthermore, the significant influence of prior knowledge
(about hydrogen) at the higher quantiles suggests that such an information campaign
would be especially effective if it aimed to raise both environmental awareness, and
awareness about hydrogen transport.
Overall, this study shows that there appear to be substantial information gains to be
had by using QR techniques in addition to standard modelling techniques, such as
interval data and OLS models, for analysing contingent valuation data. Further work
is needed to assess the relevance of this finding in other contexts. Future studies might
also investigate the possibility of applying a QR type approach to the increasingly
popular choice modelling techniques, and to situations where one might expect a large
number of outliers (perhaps where donations are used), which together with a larger
sample sizes, might give additional insights on the meaningfulness of outliers in CV
studies.

27
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31
TABLES AND FIGURES
Table 1: Comparing socio-economic characteristics of London bus user sample
and bus user population
Sources: London Travel Report (TfL, 2002) and ONS (2004)
(a) Income/age taken as mid-interval of income/age categories.
(b) No bus user population data was available for this characteristic: general London population data
has been used instead (where available).
* Significantly different at 10% level, ** at 5% level, *** at 1% level
Table 2: Summary of responses to WTP elicitation question
Summary statistics
Number of respondents WTP>0
449
% respondents WTP>0
85.5
Number of respondents WTP=0
82
% respondents WTP=0
15.4
Number of respondents WTP=0 (protests)
52
% protests
9.8
Number respondents WTP=0 (valid zero bid)
19
% respondents WTP=0 (valid zero bid)
3.6
Number respondents: 0<WTP<0.1 (a)
11
% respondents: 0<WTP<0.1
2.1
(a) Respondents who had answered “yes” or “depends on increase” to the participation question
(see Appendix A.1) and then bid the lowest (zero) interval in the payment card, were considered
to have a WTP lying in the interval 0<WTP<0.1.
Variable
Levels
London Bus
User Sample
(n=531)
London Bus User
Population
(n=5,443m)
t-test
probability
Sex (% male)
43.9
42.0
0.87
Age (mean) (a)
37.0
37.8
0.12
Highest level of
education
(% respondents) (c)
Professional qualification
16.4
-
-
University degree
54.8
24.7 (b)
0.00 ***
Employment Status
(% respondents)
Self-employed
6.0
-
-
Employed (>30 hrs/wk)
67.6
44.5
0.00 ***
Employed (<30 hrs/wk)
8.9
13.5
0.00 ***
Retired
5.0
15.3
0.00 ***
Gross annual
household income
(mean £) (a)
£45,620
£38,376 (b)
0.00 ***
Car ownership (%
households owning car)
64.0
61.0 (b)
0.15

32
Table 3: WTP values at different quantiles of distribution
Quantiles
WTP at quantile (£)
95% confidence interval
Lower limit (£)
Lower limit (£)
0.10
0.75
0.35
1.50
0.25
2.50
2.50
3.50
0.50 (median)
6.00
6.00
6.00
0.75
9.00
6.00
11.00
0.90
13.50
11.00
17.50
0.925
17.50
13.50
22.50
0.95
22.50
17.50
22.50
0.975
27.50
22.5
45.00
Table 4: Explanatory variables
Variable
Description
YADJ
Income taken as mid interval of income levels (and divided by 10,000)
AGE
Respondent’s age
MALE
Dummy indicating 1=male/ 0=female
HIGHEREDUC
Dummy for university education: 1=yes/ 0=no
TRIPNOS
Bus use frequency (from 1-less than once a month to 6- over 14 times a
week)
RATEFUME
Attitude towards level of fumes produced by existing buses (from 1-very
poor to 5-very good)
H2KNOW
Dummy for knowledge about H2 vehicles: 1=yes/ 0=no
ENVATT
Attitude to statement: “Solving environmental problems should be one of the
top 3 priorities for public spending in London” (from 1-strongly disagree to
5-strongly agree)
EXPOST
Dummy indicating date respondent was interviewed: 0=summer 2003;
1=summer 2004

33
Table 5: Interval data, OLS and quantile regressions for WTP to support introduction of H2 buses in London (n=479)
* Significant at 10% level; ** significant at 5% level; *** significant at the 1% level
Figures in parentheses are t-statistics, which have been obtained by bootstrapping with 100 repetitions.
Variables
Interval
OLS
Quantile regression (quantiles)
0.10
0.25
0.50
0.75
0.90
0.925
0.95
0.975
YADJ
0.386
(2.88)
***
0.384
(2.89)
***
0.116
(1.31)
0.215
(2.76)
***
0.126
(1.40)
0.270
(1.40)
0.988
(1.80)
*
1.904
(2.71)
***
2.011
(2.87)
***
2.021
(2.48)
**
AGE
-0.043
(-1.97)
**
-0.044
(-1.99)
**
-0.018
(-1.40)
-0.011
(-0.59)
-0.007
(-0.45)
-0.049
(-1.50)
-0.126
(-1.61)
-0.123
(-1.47)
-0.150
(-1.52)
-0.260
(-1.93)
*
MALE
-0.360
(-0.43)
-0.354
(-0.41)
0.646
(1.77)
*
0.277
(0.66)
-0.063
(-0.14)
-0.728
(-0.87)
-3.356
(-1.69)
*
-2.941
(-1.21)
-0.606
(-0.21)
-1.503
(-0.30)
HIGHEDUC
0.488
(0.78)
0.511
(0.80)
-0.937
(-2.19)
**
-0.413
(-0.85)
-0.253
(-0.75)
0.129
(0.14)
0.371
(0.18)
2.523
(1.19)
3.013
(1.21)
6.196
(1.74)
*
TRIPNOS
0.809
(1.64)
0.808
(1.60)
0.703
(3.00)
***
1.504
(5.10)
***
0.358
(1.27)
0.524
(0.76)
-0.395
(-0.29)
0.411
(0.24)
0.615
(0.39)
0.650
(0.23)
RATEFUME
-0.447
(-0.55)
-0.428
(-0.52)
-0.347
(-0.98)
-0.553
(-1.31)
-0.495
(-1.50)
-0.454
(-0.53)
-0.942
(-0.44)
0.466
(0.18)
-1.226
(-0.42)
-2.719
(-0.62)
H2KNOW
1.595
(2.13)
**
1.580
(2.08)
**
0.146
(0.41)
-0.031
(-0.08)
0.438
(0.98)
2.368
(2.23)
**
3.538
(1.93)
*
2.306
(1.06)
2.713
(1.02)
8.366
(1.87)
*
ENVATT
1.531
(4.47)
***
1.554
(4.44)
***
0.272
(1.42)
0.792
(4.14)
***
0.991
(3.62)
***
1.087
(2.35)
**
2.841
(2.65)
***
3.042
(2.74)
***
3.510
(3.01)
***
4.517
(2.82)
***
EXPOST
1.122
(1.44)
1.149
(1.46)
-0.625
(-1.69)
*
-0.225
(-0.51)
0.355
(0.97)
0.219
(0.25)
2.943
(1.42)
3.513
(1.41)
2.631
(0.84)
3.237
(0.42)
Constant
-1.746
(-0.72)
-1.780
(-0.74)
-0.310
(-0.29)
-2.698
(-2.10)
**
0.585
(0.37)
3.025
(1.14)
3.095
(0.52)
-1.479
(-0.21)
-0.525
(-0.07)
0.748
(0.07)
Pseudo R2 /R2
0.09
0.08
0.08
0.16
0.17
0.08
0.08
0.08
0.05
0.04
Log-L
-1482.85
-
Chi2 (df)
31.46 (9)
***
-

34
Table 6: Tests for equality of coefficients across quantiles (F-statistic probability)
q10=q25
q25=q50
q50=q75
q75=q90
q10=q95
ALL
quantiles
YADJ
0.107
0.192
0.355
0.179
0.000***
0.000***
AGE
0.607
0.761
0.090*
0.162
0.106
0.327
MALE
0.240
0.311
0.337
0.093*
0.570
0.182
HIGHEDUC
0.090*
0.641
0.574
0.881
0.050**
0.180
TRIPNOS
0.000***
0.000***
0.713
0.395
0.954
0.000***
RATEFUME
0.480
0.856
0.950
0.743
0.709
0.985
H2KNOW
0.602
0.194
0.006***
0.453
0.399
0.096*
ENVATT
0.000***
0.285
0.780
0.014**
0.016**
0.000***
EXPOST
0.218
0.099*
0.854
0.080*
0.188
0.062*
ALL
parameters
0.000***
0.000***
0.082*
0.037**
0.000***
0.000***
* Rejects null hypothesis of equality between slope coefficients at 10% level; ** rejects null hypothesis
at 5% level; *** rejects null hypothesis at 1% level

35
Figure 1: Distribution of WTP extra bus fare per month to support introduction
of H2 buses in London
0
20
40
60
80
100
120
140
160
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
WTP extra bus fare per month (£)
Frequency

36
Figure 2: Plots of regression coefficients of explanatory variables at different
quantiles (the plots present QR coefficients for each explanatory variable in the
model, with their 90% confidence intervals (shaded area). The dashed line
indicates the interval regression coefficient.)
0.0 0.2 0.4 0.6 0.8 1.0
01234
yadj
o
ooooooo
oo
ooo
oooo
oo
ooooooooo
ooooooo
oo
ooooooooooooooooooooooooo
o
oo
ooooooooo
oooo
oo
o
oo
oo
ooo
oo
oo
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0.0 0.2 0.4 0.6 0.8 1.0
-0.4 -0.2 0.0
age
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0.0 0.2 0.4 0.6 0.8 1.0
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male
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0.0 0.2 0.4 0.6 0.8 1.0
-5 0 5 10
highereduc
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0.0 0.2 0.4 0.6 0.8 1.0
01234
yadj
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0.0 0.2 0.4 0.6 0.8 1.0
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age
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0.0 0.2 0.4 0.6 0.8 1.0
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male
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0.0 0.2 0.4 0.6 0.8 1.0
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highereduc
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0.0 0.2 0.4 0.6 0.8 1.0
01234
yadj
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0.0 0.2 0.4 0.6 0.8 1.0
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age
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0.0 0.2 0.4 0.6 0.8 1.0
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male
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0.0 0.2 0.4 0.6 0.8 1.0
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highereduc
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0.0 0.2 0.4 0.6 0.8 1.0
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tripnos
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0.0 0.2 0.4 0.6 0.8 1.0
0 5 10
h2know
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0.0 0.2 0.4 0.6 0.8 1.0
0 2 4 6
envatt1
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0.0 0.2 0.4 0.6 0.8 1.0
0 5 10
expost
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0.0 0.2 0.4 0.6 0.8 1.0
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age
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0.0 0.2 0.4 0.6 0.8 1.0
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male
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0.0 0.2 0.4 0.6 0.8 1.0
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highereduc
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0.0 0.2 0.4 0.6 0.8 1.0
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ratefumedummy
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0.0 0.2 0.4 0.6 0.8 1.0
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h2know
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0.0 0.2 0.4 0.6 0.8 1.0
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envatt1
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h2know
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envatt1
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expost
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h2know
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0.0 0.2 0.4 0.6 0.8 1.0
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envatt1
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expost
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0.0 0.2 0.4 0.6 0.8 1.0
01234
yadj
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0.0 0.2 0.4 0.6 0.8 1.0
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age
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male
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0.0 0.2 0.4 0.6 0.8 1.0
-5 0 5 10
highereduc
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