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Price and consumption misperception profiles: The role of information in the residential water sector

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Consumer misperceptions about key economic variables often hinder the effectiveness of management policies. When facing increasing block rates, water users might fail to identify the marginal price of their water use and guide themselves by information from their past total bill and water use amounts. This information might not be correctly perceived or remembered. By comparing them with actual bimonthly billing data from 1,465 households in Granada (Spain), we study the inaccuracy of users' recollections during an in-person survey that also asked them about their characteristics, environmental and conservation habits, and exposure to informational policies. A conditional mixed-process selection model is used to test the hypothesis that the degree of inaccuracy in the recollection of past water bill and consumption amounts is related to indicators of the costs and benefits of acquiring the relevant information. Then, a latent class model considers unobserved household heterogeneity to develop two classes of households, based on whether they recalled during the survey, and how accurately, past bill and consumption amounts and their probability of belonging to each class. We derive policy recommendations and show that knowledge of consumption and bill size is rather poor but that informational policies could improve consumer knowledge and the effectiveness of pricing policies. Finally, we identify which informational policies might be more effective and detect groups of consumers on which informational efforts should be focused.
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Price and consumption misperception profiles: The role of
information in the residential water sector
Mar´ıa ´
A. Garc´ıa-Vali˜nas
Oviedo Efficiency Group, Departamento de Economia
Universidad de Oviedo, Spain
Roberto Mart´ınez-Espi˜neira
Department of Economics
Memorial University of Newfoundland, Canada
Marta Su´arez-Varela Maci´a
Department of Structural and Development Economics
Universidad Aut´onoma de Madrid, Spain
Last revised: June 17, 2021
Abstract
Consumer misperceptions about key economic variables often hinder the effectiveness of
management policies. When facing increasing block rates, water users might fail to identify the
marginal price of their water use and guide themselves by information from their past total bill
and water use amounts. This information might not be correctly perceived or remembered.
By comparing them with actual bimonthly billing data from 1,465 households in Granada
(Spain), we study the inaccuracy of users’ recollections during an in-person survey that also
asked them about their characteristics, environmental and conservation habits, and exposure
to informational policies. A conditional mixed-process selection model is used to test the
hypothesis that the degree of inaccuracy in the recollection of past water bill and consumption
amounts is related to indicators of the costs and benefits of acquiring the relevant information.
Then, a latent class model considers unobserved household heterogeneity to develop two classes
of households, based on whether they recalled during the survey, and how accurately, past bill
and consumption amounts and their probability of belonging to each class. We derive policy
recommendations and show that knowledge of consumption and bill size is rather poor but
that informational policies could improve consumer knowledge and the effectiveness of pricing
policies. Finally, we identify which informational policies might be more effective and detect
groups of consumers on which informational efforts should be focused.
Keywords— Latent Class Model, Perception bias, Price perceptions, Pricing policies,
Water tariffs
Corresponding author: Department of Economics, Memorial University of Newfoundland, Canada Tel: 1-709-
864-3676 Fax: 1-902-867-3610. E-mail: rmartinezesp@mun.ca
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1 Introduction
Demand-side policies have long been considered a key issue in the management of natural resources,
due to their implications in economic, social, and environmental terms. Among others, economists,
biologists, and engineers have contributed to developing resource management strategies, with
special attention to fostering their efficient allocation or at least at promoting their conservation.
Regulations, education and information campaigns and, above all, pricing measures are demand-
side strategies that have been systematically applied.
Within the water sector, volumetric pricing is usually favoured by economists among demand-
side management tools, arguing that flat fees do not provide incentives to achieve an efficient or
equitable water allocation (Barraqu´e, 2020; Grafton et al., 2020a). However, apart from the avail-
ability of metering, it requires attention to the process of designing tariffs. Water tariff design is a
difficult process that involves multiple objectives, such as efficiency, equity, cost recovery, and en-
vironmental goals, especially at the residential level (OECD, 2010, 2003; Nauges and Whittington,
2017; Grafton et al., 2020b; Massarutto, 2020). Therefore, water tariffs usually display complex
structures, which combine fixed and variable components to try and achieve those objectives.
Water tariff design in the EU is supposed to, as established by the Water Framework Directive
(WFD) 2000/60/EC of the European Parliament and of the Council of 23 October 2000, ensure
“that water-pricing policies provide adequate incentives for users to use water resources efficiently”
(art. 9). Water tariffs must be sufficiently clear and simple to provide consumers with adequate
incentives to adjust their consumption (OECD, 2003, 2010). However, in Spain water tariffs are
extremely complex, because of institutional and governance factors (Calatrava et al., 2015; Garcia-
Vali˜nas, 2019) and this complexity might thwart the efforts of policymakers and itself distort the
final economic impact of water pricing policies. Moreover, and regardless of the complexity of
the tariffs, given the relatively small share of water budgets within household budgets, users are
unlikely to obtain full information about the incentives that the tariff is meant to convey. As a
result, decisions about water use might be inefficient, since they are not based on the main economic
criteria and water prices could then lose their power as a conservation instrument (Gaudin, 2006).
Under nonlinear pricing, knowledge about water consumption must be combined with informa-
tion about the water tariff, for users to respond to the marginal price of the water they consume.
It is difficult, however, to know the marginal price of the water being currently consumed. Apart
from being unable to know how much they are consuming that period, often users are unaware of
the tariff structure they confront, even if it is described in their bill (Martins and Moura e S´a, 2011;
Honey-Ros´es and Pareja, 2019). This is a problem both for researchers, who most often assume
no issues of tariff perception when, for example, estimating demand functions, and for managers,
since rate design policies assume that consumers make rational decisions in response to pricing. In
practice, it is unclear that consumers are aware of these prices. Therefore, consumers might simply
use information, however accurately perceived and recalled, from past bills or their typical bill to
guide their behaviour (Arbu´es et al., 2004; Wichman, 2014, 2017; Honey-Ros´es and Pareja, 2019).
Since information is a crucial ingredient in decision-making and in the design of effective tools
to manage water resources, this paper aims at analysing key informational issues about water
pricing in the residential sector. We study the degree of accuracy of users’ perceptions of the two
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key economic magnitudes involved in decision-making about resource use, comparing actual data
with the recollections of past water bills and consumption of residential water users in the city of
Granada, Spain. We explore the role of different informational aspects in explaining deviations
between actual values and perceptions, while detecting profiles of users that may respond differently
to informational policies. Our findings and methodological proposal could, therefore, be useful for
policymakers to identify which informational policies may be more effective to bridge the gap
between perceived and actual economic magnitudes and to identify target groups when designing
informational water policies (Attari, 2014).1Moreover, although our empirical implementation
focuses on the water sector, our results can also be applied to other related sectors that employ
pricing policies for the management of natural resources (such as energy/electricity).
We use a Conditional Mixed-Process (CMP) model to measure the degree of inaccuracy of
responders’ perceptions of their past water use and water bill amounts. However, our focus in
this paper is also on classifying households according to their readiness and ability to accurately
estimate such amounts. Therefore, we complement the analysis with a Latent Class Model (LCM)
that allows us to characterize what sort of households are relatively less successful at recalling the
information on their past bills. The ability to identify these type of households might help those
charged with fostering the correct perception of these two magnitudes to target those households,
making information policies more effective and efficient.
The CMP results are used to test the hypothesis that the degree of inaccuracy with which
households perceive or recall their water bill and consumption amounts is related to indicators of
their incentives to invest in acquiring the necessary information for accurate estimates. Because we
suspect that unobserved factors affect the two data generation processes involved, we use maximum
likelihood estimation, following the CMP approach, to model the selection process involved in
choosing to provide an estimate jointly with the degree of inaccuracy of that estimate.
Using information about how many estimates in total (either none, one, or two) of their past
water use and bill households provided during the survey and how inaccurately, we propose a LCM
that conceives two classes of households: best informed and worst informed. By thus classifying
the households, the LCM allows us to partially account for unobserved household heterogeneity
about their incentives to acquire and recall the relevant information. As a post estimation exercise,
we model posterior probabilities (the probabilities of belonging two each type of household), based
this time on observable characteristics, with particular attention to the effect of factors that could
conceivably be controlled by the policymaker and to how the effects of those policy controls would
depend on the values of observable characteristics of the households. That is, we acknowledge
that a host of unobservable factors prompt water users to pay more attention to their bills and
consumption but we attempt to identify observable measures that would help differentiate already-
informed users from those who might benefit from informational efforts aimed at strengthening
the link between water pricing and consumer responses. In sum, we propose to investigate to what
extent residential users know how much water they typically consume and how much it costs, what
kinds of information affects this knowledge, and what type of users are most likely to respond
measures intended to provide that information or facilitate its acquisition.
Section 2 presents a discussion of the previous literature on price perception and cognitive
biases. Section 3 describes the case study considered in the empirical analysis and includes a
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description of the dataset and definitions of the main variables. In Section 4, the econometric
techniques we use are briefly described and discussed, while Section 5 reports the main findings.
Finally, Section 6 summarizes the main conclusions and policy implications of this research.
2 Background & Literature Review
Consumer perception and responsiveness to price have long represented a concern for policymakers
seeking to achieve a sustainable use of natural resources. Microeconomic models are underpinned by
some basic principles, such as the expectation that consumers respond to price increases by reducing
the quantity demanded. As a first approximation, economic theory predicts that consumers respond
to marginal price. However, multiple deviations from this standard economic behavior leading to
misperceptions of key economic variables such as price or consumption have been found in related
literature (Nieswiadomy and Molina, 1989; de Bartolome, 1995; Nataraj and Hanemann, 2011;
Binet et al., 2014; Ito, 2014; P´erez-Urdiales et al., 2016; Brent and Ward, 2019).
Water is no exception when it comes to issues of misperception and misinformation. Indeed,
urban water rates represent a prime example of a situation in which the link between price and
quantity is obscured. Although most pricing policies are based on the assumption that consumers
enjoy perfect information about both the price and quantity consumed and are able to adjust their
behavior accordingly - that is, they assume perfect rationality -, this framework rarely holds in
practice. Both the assumption of complete knowledge of the relevant unit price of water and of the
knowledge of the level of consumption have been challenged (Binet et al., 2014; Wichman, 2017).
Cognitive costs have been shown to be an important factor in explaining diminished responses of
consumers to price, since most consumers find it complex to understand tariffs (Nieswiadomy and
Molina, 1989; de Bartolome, 1995). Even if consumers were assumed to perceive the actual marginal
price and adjust their behavior accordingly, the lack of information would still jeopardise the
effectiveness of pricing policies. Information deficiencies are a widespread problem; most consumers
usually report not knowing their consumption or the unit price, even the bill amount they pay
(Nieswiadomy and Molina, 1989; Nataraj and Hanemann, 2011; P´erez-Urdiales et al., 2016; Brent
and Ward, 2019). This suggests that pricing structures and payment mechanisms might be too
complex, making it more difficult to adopt rational price-quantity decisions (Brent and Ward,
2019). When prices and consumption are misperceived, suboptimal choices emerge that may cause
substantial losses in social welfare (Ito, 2014).
Identifying situations in which there is a lack of information and misperception of price and
consumption is crucial to improve economic efficiency. Lack of information is usually found at the
root of perception biases, that is, the gaps between consumers’ perceived price and consumption and
their actual values. In the absence of appropriate information, consumers tend to systematically
underestimate or overestimate their consumption, the price and the amount of bill paid (Binet
et al., 2014; Brent and Ward, 2019). Households are more likely to know their bill than their
marginal price or other price schedule details (Brent and Ward, 2019), so households may base
their decisions on incorrect price signals, obtained through simplified approximations to the actual
tariff they face.
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Ito (2014) found that households in South California reacted to the average price of electricity2
rather than the marginal price. Using an improved version of the model in the seminal contribution
by Shin (1985), who developed an empirical model to estimate a price perception parameter on
the electricity demand function, Binet et al. (2014)3analysed the perception of water prices by
users facing Increasing Block Rates (IBRs). They conducted a household survey in the French
overseas territory of R´eunion, finding that users underestimated the price of water and that lead
to overconsumption. Binet et al. (2014) also suggested that the actual water consumption units for
which households pay differ from the units on which consumers base their consumption decisions.
erez-Urdiales and Baerenklau (2019), in their analysis of the consequences of allocation-based
rates adoption in California, found that consumers react to the efficiency label (included in the
bill) rather than to the price structure, while Lott (2017) also noticed that non-transparent price
information led residential water users to inaccurate price perceptions.
In the same line, Attari (2014) asked respondents in a national-range survey in the US to
estimate their water consumption for 17 activities and compared these use perceptions with data
on actual consumption. Her results show that respondents underestimated their water consumption
and that deviations were especially large in the case of intensive water-use activities. Older and
male respondents showed more accurate perceptions of water use. However, no clear profiles
in terms of education level, previous experience with drought, or the adoption of water-efficient
appliances were detected. In their analysis of retail electricity sector in the Australian state of
Victoria, Byrne et al. (2018) observed that actual energy use was linked to perceptions about
energy consumption. Heavy energy users tended to underestimate, while light users tended to
overestimate their use. The authors designed a field experiment with information treatments
(based on peer-comparison information), finding that those treatments had asymmetric impacts
on energy use perceptions.
Finally, Brent and Ward (2019), one of the most extensive works on this topic in the water
sector, conducted a survey in Melbourne (Australia) to explore households’ perceptions of their
water bill, price structure, and water consumption. On the one hand, and based on the differences
between household’s perceptions and actual data provided by the water utility, Brent and Ward
(2019) found that households overestimated their water bill. On average, and focusing on water to-
tal bill and consumption, the deviations were not substantial. However, in terms of specific features
of the water tariff structure, households’ knowledge presented substantial shortcomings. Brent and
Ward (2019) found that households that used more water had more accurate information about
water bills and prices. Additionally, respondents over the age of 65 were more likely to have better
information about the marginal price of water and wastewater. Respondents’ confidence levels
were positively correlated with the probability of having more accurate information about water
prices. That result suggests that most households were aware of their actual level of information
about the price: “water costs are known unknowns”(Brent and Ward, 2019, p.2).
Brent and Ward (2019) also showed that consumers had poor information about the cost of
several water-using activities (irrigation; washing machine; shower; toilet). In this case, no clear
profiles of households getting accurate water cost estimates were detected. Brent and Ward (2019)
identified some slight positive impacts of respondents’ confidence in the estimates of the costs of
showers and toilet use and, in general, of respondents stating to have reacted to past price increases.
5
However, and surprisingly, respondents who stated to be motivated by money when using water
displayed worse cost estimates for most water-use activities.
A relatively limited number of studies (Attari, 2014; Binet et al., 2014; Brent and Ward, 2019)
have analysed in depth the degree of knowledge of water prices, bills, and consumption in the res-
idential water sector. Moreover, no clear profiles of households with different levels of information
have been revealed. One of the reasons is that this issue is informationally demanding, requiring
extensive surveys to properly address it. In order to contribute to fill this gap in the literature,
we study to what extent perceived values of consumption and bills deviate from actual values and
the role of different factors in explaining those deviations.
3 Empirical analysis
3.1 The context
Granada is a midsize city4located in Andalusia, Southern Spain, a region affected for years by pe-
riodic droughts and severe water stress (EEA, 2018). Water services are supplied by EMASAGRA,
a mixed ownership (51% publicly owned) corporation that supplies water services to 220,610 cus-
tomers the capital city of Granada and 14 other municipalities within that province. The next
sections provide details about the water tariff and features of the billing process in Granada.
3.1.1 Tariff structure.
Tables 1 (general tariff) and 2 (special tariff) summarize the residential water tariff used in Granada
in 2010.5Its two-part structure includes a fixed charge dependent on the size of the meter and
a variable charge, and an IBR variable component. Assuming the average household size in 2011
(INE, 2011) of 2.62 members per household, the first block captures a basic amount of water of
100 litres per person and day. Price increases substantially in the second block and beyond that
the degree of price escalation (Su´arez-Varela et al., 2015; Su´arez-Varela and Mart´ınez-Espi˜neira,
2018) becomes more moderate.
Apart from the fixed charges, this tariff schedule includes a volumetric charge (in C=/m3) for
water supply and sewerage and treatment services (based on a four-block structure), plus an
additional surcharge due to drought conditions (a two-block structure), so the integrated water
tariff effectively includes five increasing blocks.
Most Spanish cities (and Granada is no exception) apply special tariffs to specific user groups,
following different ad hoc eligibility criteria (Arbu´es and Garc´ıa-Vali˜nas, 2020). Table 2 shows
three different groups eligible for discounts off the general tariff. Low-income retirees, households
where all members are unemployed, and large families6are eligible for these social discounts. To
the extent that water consumption and household size are correlated (Arbu´es et al., 2010) the
application of IBRs adversely affects larger households, so the latter tariff is meant to partially
reverse negative distributional effects. The special discounts apply to the supply service charges
only. Most groups are eligible for a discount on the variable charge and retirees are eligible for
the discount to both the fixed and the variable charges. We note also that the discounts on the
variable charge affect only the first two blocks.
6
Block Supply Sewerage Treatment Drought Total
size (m3/month) (C=/m3) (C=/m3) (C=/m3) surcharge (C=/m3) (C=/m3)
>0-8 0.3895 0.2749 0.2834 0.0840 1.0318
>8-10 1.1401 0.4222 0.2902 0.0840 1.9365
>10-16 1.1401 0.4222 0.2902 0.1020 1.9545
>16-30 1.6020 0.5336 0.3035 0.1020 2.5411
>30 1.8980 0.5931 0.3206 0.1020 2.9137
Fixed charge (*) 2.3912 0.1610 0.0000 0.0000 2.5522
(C=/month)
Legend: (*) 13 mm. meter
Source: Own elaboration
Table 1: Residential water prices in Granada, 2010: General tariff.
Block Retirees Large-size Unemployed
size (m3/month) (C=/m3) families (C=/m3) families (C=/m3)
>0-8 0.1790 0.2391 0.1993
>8-16 0.5130 0.6841 0.8551
>16-30 1.6020 1.6020 1.6020
>30 1.8980 1.8980 1.8980
Fixed charge (*) 1.1956 2.3912 2.3912
(C=/month)
Legend: (*) 13 mm. meter size.
Source: Own elaboration
Table 2: Residential water prices for supply service in Granada, 2010: Special tariffs.
All these elements make water tariffs in Granada certainly quite complex. This complexity
goes against the simplicity principle (OECD, 2003, 2010) required to guarantee users’ awareness
of water price structure.
3.1.2 The bill
In order to illustrate the information displayed in Granada’s water bills, an English translation
of an anonymized 2010 sample bill (for a user with a 20 mm meter) is shown in Figure 5 in
Appendix D.
The charge for water consumption (measured in cubic metres per bimonthly billing period) is
displayed, as well as the consumption block in which the user falls. The unit price and the indirect
taxes are also itemized. The bill unfortunately also includes, as is often the case elsewhere in Spain
and in other countries, charges for services other than water supply (garbage collection, sanitation,
and sewage treatment). Therefore, although the total bill in the sample bill enclosed is 37.33 C=, only
14.08 C= of those correspond to the actual water bill. This means that, even if consumers do look
at the bill, they may find it difficult to decipher. Furthermore, the term E.D.A.R, quite a technical
term used by experts in the water sector to refer to wastewater treatment plant (W.W.T.P.) is
rather foreign to the lay person, further obscuring the identification of the total amount paid for
water.
Finally, the bill includes a brief reference to the official legislation regulating the tariffs and, at
7
the time of our survey, the supplier’s webpage also displayed a brief explanation of the water tariffs
and directed customers to consult the regulation published in the official provincial and regional
bulletins. The latter, however, might not be too easy to understand, since regulations and by-laws
are usually written in a quite technical legal jargon.
In sum, even users who read the bill might find it quite hard to understand. Moreover, most
Spanish users pay their water supplier through direct billing, thus not even having to check the
amount owed. In 2010 EMASAGRA started promoting the use of e-bills but customers received
paper bills. Indeed in 2011, the percentage of e-bills issued by the supplier (0.004%) was negligible
(EMASAGRA, 2011).7
3.2 Data and variables
Our database combines several sources of information. First, we use bimonthly data, provided
by EMASAGRA for a representative sample of urban households about their water consumption
and water tariffs during the period 2009-2011. In 2011, these same sampled households were
interviewed about, among others, issues such us their socioeconomic status, housing characteristics,
environmental and conservation habits, and exposure to water-saving information campaigns. The
key questions for our study were about the consumers’ recollection of their water use and water
bills from the year 2010 (Table 3).8
The survey was administered in person by a local polling company, to whom EMASAGRA
provided the sample customers’ addresses. A resident adult was instructed to individually answer
the questions but to provide answers about the socioeconomic characteristics (age, income, formal
education, gender, nationality, occupational status) of every member of the household. We would
not be able to know whether that is indeed the person who pays the bill, so we cannot control for
varying degrees of measurement error among the respondents.
The combination of these two data sources resulted in an unbalanced panel of 1,465 households.
However, although the data on actual consumption and bill amounts is available for all the billing
periods in the sample, we only have data on user-recalled values for the six bimonthly billing periods
in 2010, the year covered by the household survey. Moreover, although these values varied by billing
period, the rest of variables (e.g. socioeconomic, housing characteristics, and environmental and
conservation habits) are assumed constant throughout the year, which we do not think should pose
a problem, given the short period of time involved.
The dependent variables of the CMP models (which we describe in Section 4.1) used to capture
the level of perception biases about both the consumption level and the total bill were constructed in
two steps. A substantial proportion of households did not hazard a guess about their consumption,
87% of cases, or about their bill, 46% of cases, or neither 45% of cases.
Therefore, using the responses to the questions in Table 3 we first constructed two indicators
with value 1 if the respondent provided an estimate level of consumption (estimatedcons) or the bill
(estimatedbill) referring to any of the six sampled 2010 bimonthly billing periods and 0 otherwise
(if the respondent “did not answer/did not know” in all periods). In a second step, if any estimates
were provided, we measured, for each billing period, the proportional deviation in absolute terms
(pdit) between the actual (avit) and estimated (evit) values, as follows:9
8
Please, indicate your water consumption in 2010 (in m3):
Could you please tell us how much your water bills amounted to in 2010?
First Billing Period: Fourth Billing Period:
Second Billing Period: Fifth Billing Period:
Third Billing Period: Sixth Billing Period:
Table 3: Text of questions about consumption and bill amounts in 2010.
pdit =/(avit evit)//avit i= 1...N t = 1...6 (1)
where the values refer either to the consumption (pdcons abs) or to the bill (pdbill abs).
In order to ameliorate the undue influence of outliers, we eliminated observations whose values of
pdcons or pdbill fell beyond two standard deviations of their means. In the end we used information
from 1,378 households (7,157 observations) in the analysis.
The LCM (described in Section 4.2) uses one additional dependent variable to characterize
the degree of perception biases that residents in Granada exhibit. This ordinal variable with three
categories (estimatesinsurvey) attempts to capture the response patterns about water consumption
and bill perception captured by the survey (Table 3). Specifically, estimatesinsurvey takes the value
0 if respondents did not answer/did not know either question about their consumption or their bill
perception (both indicators estimatedcons and estimatedbill equal 0), the value 1 if they answered
only one of these two questions, and the value 2 if both questions were answered.
The figures in Table 4 show that, on average, consumers tend to underestimate their consump-
tion but overestimate their bill. However, the proportional gap between perception and actual
values seems to be much narrower in the case of consumption than in the case of the bill. We
tested for possible differences across seasons in the correlation between perceived and observed
values of consumption and bill amounts. Using several alternative definitions of the summer sea-
son, we did not find, though, significant seasonal differences in the degree of misperception.
Variable Mean Std. Dev. Min. Max. N
Perceived bimothly bill amount (C=) 42.8 15.78 0 186 3825
Perceived bimonthly consumption (m3) 13.56 13.55 0 150 948
Observed/registered bimonthly bill amount (C=) 24.51 13.85 5.35 97.63 7157
Observed/registered bimonthly consumption (m3) 16.08 9.32 1 63 7157
Table 4: Summary descriptives of actual and estimated consumption and bill.
The degree of inaccuracy in the estimation might also depend on the units shown in the bill
or the delay between the last bill and the survey. However, this should not pose a problem in our
study. The survey was conducted for all the households in 2011, within a short period. Since all
households in our sample were questioned about their 2010 bills, they all faced similar recollection
gaps. Moreover, all consumers in the sample received the same type, a hard copy, of the bill.
Only 13% of our respondents provided an estimate of consumption and 54% provided an esti-
mate of their bill, so most failed to provide an estimate of their consumption and almost half in the
case of their bill. When the information was provided, the mean values of overcons and overbill
9
illustrate the pattern of proportional deviations between observed (real) and perceived values of
both magnitudes. On average, when an estimate was provided, only 36% of households overesti-
mated their consumption (the rest underestimated it) but 88% of them overestimated their bill.
However, while on average consumers only underestimated consumption by about 1% (as shown by
the mean value of pdcons in Table 6), in the case of the bill the average deviation measured by the
mean value of pdbill (as also shown in Table 6) is -107%.10 That is, consumers on average thought
they paid more than twice as much as they did. This does not necessarily imply that households
are better at estimating their consumption than their bill. Indeed, the fact that most did not even
attempt to hazard a guess about their consumption suggests a severe lack of knowledge. But, for
the ones who did, the deviations are relatively small. On the other hand, households felt more
comfortable when estimating their bill but their deviations tend to be substantially larger. Table
5 shows more detailed statistics for the variables that measure the proportional deviations in con-
sumption and bill in absolute terms (that is, the size of the deviation between perceived and actual
values regardless of whether it corresponds to an over or an underestimation). The proportion of
households that offer an unbiased estimation of their bill is almost negligible.
Variable Obs Mean Std. Dev. P1 P10 P25 P50 P75
pdcons abs 948 0.51 0.58 0.00 0.05 0.15 0.38 0.71
pdbill abs 3825 1.14 0.88 0.02 0.18 0.45 0.94 1.61
Table 5: Detailed summary statistics for pdcons abs and pdbill abs.
The tenth percentile (P10 in the table) shows that deviations are non-zero even for the most
accurate 10% percent of households. Deviations are much more sizable as we consider the 25
percentile and beyond. Figure 1 shows the smoothed distribution of pdcons abs and pdbill abs
with vertical lines indicating selected percentiles.
Regarding the actual empirical model to be tested, we acknowledge that there is no explicit
underlying structural model that informs our model specification. However, our empirical strategy
implicitly assumes a theoretical relationship between the characteristics of the households and
their behavioral choices. Simply put, we assume that the degree of accuracy with which the
respondents recalled their past bills is given by their incentives to acquire the information (about
their tariff and their use) involved. Although this would be outside the scope of this contribution,
a theoretical model based on the maximization of the utility of household would account for both
the cost and benefit determinants of the decision about how much information to acquire. Our
objective does not include the testing of a theoretical model but rather the identification of key
empirical determinants of the level of misperception of water tariffs among households, based on
the information available from the responses to the household survey.
Appendix A contains further definitions of our variables and Table 6 displays descriptive statis-
tics for the variables in our models. As independent variables, we first consider socioeconomic
variables describing the household: satisfied with income takes the value 1 if the respondent states
that the household’s needs are met by its disposable income, and 0 otherwise; college indicates that
the first or second household member has a postsecondary degree; and ownership indicates that
the user of the dwelling is also the owner. Variable householdsize measures the number of mem-
10
0 .5 1 1.5
Density
0 1 2 3 4 5
Proportional deviation in estimate of use (absolute value)
kernel = epanechnikov, bandwidth = 0.0939
Kernel density estimate
0 .2 .4 .6
Density
0 1 2 3 4
Proportional deviation in estimate of bill (absolute value)
kernel = epanechnikov, bandwidth = 0.1485
Kernel density estimate
Figure 1: K-density plot for pdcons abs and pdbill abs with percentile 1, 10, 25, 50, 75, 90, and 99
indicators.
bers in the household, while we also consider the proportion of household members 18 or younger
(p age18 ) and 65 or older (p age65 ), as well as five of the six binary indicators of bimonthly billing
periods (bil ling period 1-billing period 5 ).
Additionally, we include indicators of environmental attitudes - whether the respondent declared
to be “very concerned” about the environment (enviro concern) - and behaviors. Following Stern
and Gardner (1981), we consider efficiency or “one-shot behaviors”(e.g. installation of resource-
saving technologies) and “curtailment behaviors” (involving daily habits). Our proxies for the
former include efficient apps, which indicates that the household owns both a water-efficient washer
and a water-efficient dishwasher. In terms of curtailment behaviors, respondents were asked in
which of a set of eight behaviors they engage in their daily lives. These include, for example,
waiting until the dishwasher and washer are full before running them, taking shorter showers, and
closing the tap while brushing teeth. With this information, we computed an index that measures
the proportion of behaviors adopted by the household, variable waterhabitindex.
11
Variable Label Obs. Mean Std. Dev. Min. Max.
avpdbill abs Average proportional misperception: bill (absolute value) 3825 1.14 0.74 0.03 3.98
avpdcons abs Average proportional misperception: use (absolute value) 948 0.51 0.41 0.02 3.27
bill not descriptive Bill is received at home but lacks sufficient detail 7133 0.10 0.30 0 1
bill not remembered Bill is received at home but not remembered by respondent 7133 0.36 0.48 0 1
clearbill Bill is received at home and sufficiently clear to respondent 7157 0.51 0.50 0 1
billing period 1 Billing period 1 7157 0.17 0.38 0 1
billing period 2 Billing period 2 7157 0.17 0.38 0 1
billing period 3 Billing period 3 7157 0.17 0.38 0 1
billing period 4 Billing period 4 7157 0.16 0.36 0 1
billing period 5 Billing period 5 7157 0.16 0.36 0 1
billing period 6 Billing period 6 7157 0.17 0.37 0 1
college College degree held by first or second household member 6990 0.68 0.47 0 1
consultedbill Consulted bill while responding to survey 7157 0.05 0.23 0 1
efficient apps Efficient washer and dishwasher 7157 0.25 0.44 0 1
enviro concern Environment is one of the respondent’s concerns 7157 0.79 0.40 0 1
estimatedbill Estimated bill 7157 0.54 0.50 0 1
estimatedcons Estimated use 7157 0.13 0.34 0 1
estimatesinsurvey Estimated use, bill, or both provided (0-2) 7157 0.67 0.67 0 2.00
hotshared Hot water partially billed communally 7134 0.52 0.50 0 1
householdsize Household size 7116 2.67 1.22 1 9.00
knowscampaign Knowledge of water saving campaign 7157 0.54 0.50 0 1
knowstariff Knowledge of the structure of the tariff 7157 0.34 0.47 0 1
knowsweb Knowledge of the water supplier’s webpage 7157 0.21 0.40 0 1
ownership Ownership of the dwelling held by user 7145 0.75 0.43 0 1
p age18 Proportion of family members 18 or younger 7116 0.06 0.15 0 1
p age65 Proportion of family members 65 or older 7116 0.34 0.43 0 1
pdbill Proportional divergence perceived vs. observed bill (proportion) 3825 -1.07 0.96 -4.24 1
pdbill abs Proportional deviation in estimate of bill (absolute value) 3825 1.14 0.88 0 4.24
pdcons Proportional divergence perceived vs. observed use (proportion) 948 0.01 0.78 -5.00 1
pdcons abs Proportional deviation in estimate of use (absolute value) 948 0.51 0.58 0 5.00
satisfied with income Satisfied with income 6812 0.89 0.31 0 1
waterhabitindex Water-saving habits index (0-1) 7157 0.57 0.18 0 1
Table 6: Summary descriptives.
12
Finally, variables related to the user’s informational profile are included: knowscampaign,
knowsweb, and knowstariff indicate that the user knows of any water saving campaign in the
previous five years, the water supplier’s webpage, and the correct tariff structure (volumetric, IBR,
flat rate, etc.). In Spain hot water is often billed as part of the contributions (akin to “condo
fees”) to one’s residents’ association (comunidad de vecinos), which may distort how households
receive information about consumption and prices. Variable hotshared indicates that hot water is
not individually billed.
In addition, when asked, after responding to the questions about perceptions of water use and
bill amounts, whether their bill was sufficiently detailed and informative, respondents could respond
“yes”, “no”, “I do not receive the bill at home”, or “I receive the bill, but do not remember it”.
With this information, we construct several variables: clearbill indicates that the respondent claims
that the bill is received at home and sufficiently detailed and informative (“yes” option), bill not -
descriptive if the household responded “no”, and bill not remembered, for the last option.11 Since
these variables would represent the perception by the respondent on whether the bill is detailed
enough, the obtained results could be interpreted as whether the household would need it to be
more detailed and informative to reduce their misperceptions. Our hypothesis here is that finding
the bill not descriptive will negatively affect the accuracy of the estimates, while the opposite
applies to clearbill. In addition, unfortunately we have no indicators of individual psychological
traits, particularly of whether respondents are conscientious or detail-oriented, which may affect
the households’ levels of information. However, with bill not remembered, we cautiously try to
proxy the lack of these traits.
Regarding the remaining information variables, consultedbill indicates that the respondent con-
sulted a bill to better respond to the survey. As explained before, the complexity of the bill may
make it difficult to understand. Therefore, this variable could allow us to disentangle whether
misperceptions are due to inattention to the bill (people do not pay them enough attention) or to
other causes, such as lack of information about the tariff (knowstariff ), an insufficiently detailed
bill (bill not descriptive ), or other information issues proxied by the rest of included variables. We
hypothesize that it may be a mix of both, and thus these variables may significantly affect the
accuracy of the recollections about the bill, but with differently-sized effects.
Therefore, the general type of hypotheses we tried to test involve the degree of accuracy of the
users’ perceptions about their water use and its cost, the type of information that affects it and,
finally, the type of user that would be more likely to respond improved levels of information.
The summary descriptives of the information variables (Table 6) show that about half of the
respondents considered their bill not sufficiently detailed and only around a third of respondents
reported knowing the type of tariff structure.12 As shown by the sample bill in Appendix D, the
tariff structure is not directly reported in the bill mailed to the users; it must be consulted on the
supplier’s website.
About half of the respondents remembered having received information about a water-saving
campaign but only around a fifth knew the supplier’s website. Just over half of the sample pays for
hot water through their residents’ community contributions. Since these fees include several items
and rarely provide detailed information about water use, we expected that they would reduce the
consumer’s information level. When it comes to ownership of the dwelling, we expected renters less
13
likely to gather enough detailed information, since their bill is most often sent to their landlords.
However, renters may end up being more informed, because they must ask their landlord every
month about their bill to reimburse it, forcing them to pay attention to it. Finally, only a very
small proportion of our sample of users consulted their water bill while responding to the survey.
4 Methodology
Our empirical analysis combines the use of two different techniques to study the degree of misper-
ception of water pricing variables. The first is a selection model of the degree of inaccuracy of the
recollection of the bill and consumption amount in the previous year (based on a CMP model).
The second is a LCM that classifies households according to how successfully the can recall the
information from those past water bills. In both cases, we took into account the intrahousehold
correlation by reporting standard errors corrected for clustering by household.
4.1 CMP models to address sample selection bias
At the outset, we suspected that our empirical exercise would be affected by the issue of sample
selection bias (Heckman, 1979). This is because the decision to provide an estimate of the amount of
water consumed or the size of the water bill would likely be affected by unobservable characteristics
of the respondent that would also affect the size of the misperception involved in these estimates.
The resulting bias would lead to incorrect inference about the effect of the observables in our
model. If the choice of providing an estimate were purely random, we would not need to worry
about sample selection bias. Similarly, if the decision to provide an estimate and the accuracy
of that estimate where related only through observables, we would be able to control for them,
avoiding the bias (Heckman, 1979; Vella, 1998).
In our case, the conventional sample selection model would be adapted, following Vella (1998)
into the form:
|pd|
it =x0
itβ+it ;i= 1...N t = 1...6 (2a)
estimated
i=z0
iγ+vi;i= 1...N t = 1...6 (2b)
estimatedi= 1 if estimated
i>0; di= 0 otherwise (2c)
|pd|it =|pd|
it ×di; (2d)
where |pd|
iis a latent endogenous variable reflecting each respondent’s underlying degree of
inability to accurately estimate their consumption and bill amount and whose observed counterpart
is |pd|i. The latent variable estimatedunderlies the observable indicator estimatei, which simply
indicates whether our primary dependent variable is observed, that is, that the respondent provided
an estimate (as indicated, more specifically, by our variables estimated cons and estimated bill ). N
denotes the entire sample, while only for a subsample of respondents is estimatedi= 1. The vectors
xiand zicontain exogenous variables; βand γare the vectors of the unknown parameters we are
14
looking to estimate, while iand viare zero-mean error terms for which we allow E[i|vi]6= 0.
Although exclusion restrictions are, in principle, not necessary for parametric estimation, we allow
for the possibility that the the vectors xiand zido not contain exactly the same variables.
We estimate this selection model using a maximum likelihood approach to estimating the two
main relationships shown in Equation 2 as a system, instead of using a two-step estimator, which
has potential efficiency gains (Roodman, 2011). A probit model is used to estimate the probability
that the respondent provides an estimate (the probability of selection) in the whole sample and a
linear regression is estimated for only those respondents who do provide one.
Our first analysis thus involves the estimation of this selection model using a conditional mixed
process (CMP), which allows to jointly estimate multiple dependent variables (estimatedcons and
estimatedbill, together with pdcons abs and pdbill abs, respectively) in order to account for the
likely correlation among the unobservable factors explaining the variability of those dependent
variables and, thus, correcting for the potential endogeneity in the modelled equations. This joint
estimation improves the efficiency of the whole set of estimates, if there is a substantial correlation
among the error terms of the equations in the system. Also, the null hypothesis of exogeneity (zero
correlation) can be tested.13
The highly flexible CMP technique relies on a simulated maximum likelihood method for evalu-
ating multivariate normal distribution functions based on the Geweke–Hajivassiliou–Keane (GHK)
algorithm B¨orsch-Supan et al. (1992); B¨orsch-Supan and Hajivassiliou (1993); Hajivassiliou and
Ruud (1994); Keane (1994).14 A good description of the command and method is given by Rood-
man (2011).
4.2 Latent Class Models
Our second analysis is based on the application of Latent Class Analysis15 in order for unobservable
factors to inform a distribution of consumers in terms of their level of awareness of water prices and
water use into a finite number of groups or “classes”.16 For each of these classes, different regression
models can be estimated, which makes it possible to control for heterogeneity in preferences and
constraints beyond what the information available through the observable data would. LCMs have
been applied in an increasing number of works in a variety of study areas (Deb and Trivedi, 2002;
Boter et al., 2005; d’Uva, 2005; Scarpa et al., 2005; Fernandez-Blanco et al., 2009; Ayyagari et al.,
2013; Grisol´ıa and Willis, 2012; Hensher and Greene, 2003; Shen et al., 2006; Shen, 2010; Hess
et al., 2011; Greene and Hensher, 2013; P´erez-Urdiales et al., 2016).
This approach involves two simultaneous steps: estimation of the main regression of interest and
estimation of the probability that each respondent household belongs to a specific class. Households
are allocated to each class according to how similar their unobservables are. In the extreme,
each household main behavioural function could be conceived as built using an individual set
of estimated coefficients: every class would contain only one household. That notion would be
practically intractable, as well as defeating the whole purpose of the notion of modelling. Instead,
the LCM approach aims at grouping households into the minimum number of classes consistent
with common household preferences P´erez-Urdiales et al. (2016).
The LCM approach is sometimes used to perform Latent Class Regression, whereby a finite
15
sample partition is motivated by the notion that different model specifications suit best different
segments of the population. However, we are not so interested on the heterogeneity of the effects of
certain factors on the misperceptions about water use and price across household types. We assume
instead that, from a policy perspective, it is more relevant to distinguish between households who
perceive their water use and bill more or less accurately and those who would benefit from a set
of measures aimed at improving that perception, as well as how most effectively to push a typical
household from the latter group to the former.
This is why we use a very simple LCM that groups households into classes, based on their
values of three dependent variables, estimatesinsurvey,avpdcons abs and avpdbill abs but, indeed,
no independent variables to explain the variability of their values within a class. What we are
interested in is which factors affect the probability of belonging to each class, so we include a set
of explanatory variables in the fractional Logit component of the analysis. Some of these variables
could be influenced exogenously, while some others would not be affected by policy but could be
observed with reasonably ease by those in charge of implementing that policy.
In general, the probability that household ibelongs to Class jcan be modelled as a function
of covariates assuming that the latent variable follows a multinomial probability that yields a
multinomial logit model:
πj =exp(γ0
jzi)
PJ
j=1(γ0
jzi), j = 1, ..., J (3)
where γiis a vector of parameters to be estimated and ziis a vector of observable characteristics.
One key consideration in the application of the LCM is the choice of the number of classes. The
usual approach involves estimating models with increasing numbers of classes in a stepwise fashion
and comparing the resulting information criterion measures. In our case, since our LCM has only
two classes, he multinomial logit model simplifies into a logit model (J= 2). Once the model is
estimated, we use the parameter estimates to compute the posterior probabilities of belonging to
each latent class using the fractional logit model.
5 Results and Discussion
5.1 CMP Models
Table 7 shows the results of the CMP models for the consumption and bill variables in two steps.
In both models, the first equation (reported in the first and third columns in the table), explaining
whether an estimate was provided or not, was estimated as a probit model, while the dependent
variable of the second equation (second and fourth columns), measuring the proportional size of
the deviation between the estimated and the actual value, was treated as continuous.
In order to identify the selection model,17 our selection equations contains one exclusion re-
striction: variable bill not remembered (the respondent received the bill but did not remember it
during the survey). We assume that failing to remember one’s bill should affect the first “hurdle”
or participation stage (deciding to offer an estimate of the consumption or bill amounts) but not
the main dependent variable (the accurate of the estimate). In fact, we find a strongly significant
negative effect of bill not remembered on the probability of offering an estimate of both consump-
16
Estimation of Consumption Estimation of Bill
estimatedcons pdcons abs estimatedbill pdbill abs
Bill is received at home but -0.223 0.149 -0.305∗∗ 0.131
lacks sufficient detail (0.222) (0.274) (0.021) (0.143)
Bill is received at home but not -0.521∗∗∗ -0.972∗∗∗
remembered by respondent (0.000) (0.000)
Billing period 1 -0.003 0.039 0.018 0.059
(0.874) (0.234) (0.265) (0.060)
Billing period 2 0.018 0.041 0.023 -0.014
(0.401) (0.271) (0.174) (0.623)
Billing period 3 0.004 0.013 0.026 -0.069∗∗
(0.860) (0.677) (0.125) (0.010)
Billing period 4 0.044∗∗ 0.058 0.035-0.076∗∗
(0.036) (0.212) (0.061) (0.012)
Billing period 5 0.014 0.307∗∗∗ -0.018 0.358∗∗∗
(0.563) (0.000) (0.322) (0.000)
College degree held by first or 0.2290.044 -0.200∗∗ 0.008
second household member (0.066) (0.561) (0.023) (0.897)
Consulted bill while responding 1.579∗∗∗ -0.2301.873∗∗∗ 0.050
to survey (0.000) (0.083) (0.000) (0.632)
Efficient washer and dishwasher 0.136 0.020 -0.146 -0.031
(0.293) (0.747) (0.160) (0.661)
Environment is one of the 0.450∗∗∗ 0.118 0.156 -0.155
respondent’s concerns (0.004) (0.221) (0.127) (0.064)
Hot water partially billed -0.010 -0.026 -0.1580.109
communally (0.931) (0.704) (0.053) (0.058)
Household size 0.022 0.061 -0.110∗∗∗ -0.086∗∗∗
(0.694) (0.179) (0.007) (0.006)
Knowledge of water saving -0.063 0.021 -0.169∗∗ -0.070
campaign (0.568) (0.715) (0.040) (0.226)
Knowledge of the structure of 0.532∗∗∗ -0.075 0.243∗∗∗ 0.093
the tariff (0.000) (0.283) (0.005) (0.130)
Knowledge of the water 0.326∗∗∗ 0.078 0.348∗∗∗ 0.036
supplier’s webpage (0.009) (0.265) (0.001) (0.621)
Ownership of the dwelling held 0.321∗∗ 0.096 0.133 -0.158∗∗
by user (0.034) (0.206) (0.203) (0.036)
Proportion of family members 18 -0.540 -0.276 0.149 0.265
or younger (0.224) (0.265) (0.605) (0.143)
Proportion of family members 65 0.236 0.124 -0.215-0.101
or older (0.117) (0.158) (0.067) (0.215)
Satisfied with income 0.154 -0.310-0.324∗∗ -0.001
(0.414) (0.080) (0.011) (0.994)
Water-saving habits index (0-1) 0.256 -0.406∗∗ -0.050 -0.059
(0.404) (0.035) (0.833) (0.732)
Observations 6631 6631
log-likelihood -2754 -8390
χ2 240 402
p-value 0.000 0.000
atanh(ρcons) 0.002
atanh(ρbill) -0.110
p-values in parentheses
p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01
Table 7: Results of the Conditional Mixed Process analyses.
17
tion and bill but, as shown by the separate OLS and CMP results in Table 11 (Appendix B) it
does not affect the magnitude of the misperceptions, thus constituting a valid exclusion restriction
(Cameron and Trivedi, 2005, p. 551). Additionally, in order to take into account the fact that each
individual respondent provided up to six estimates of their bill or consumption amount in 2010,
we estimated in all of our regressions standard errors corrected for clustering by respondent.
None of the two models returns a significant value of ρ,18 suggesting that there would be
significant endogeneity among the unobservable factors explaining the variability of the dependent
variables and, therefore, they should not be estimated separately. Specifically, the null hypothesis
of no correlation is not rejected in the case of consumption (the test statistic, χ20.00, results in a
p-value of 0.99) or in the case of the bill (with χ2equal to 1.29 and p-value 0.26).
The results in Table 7 suggest that the probability of providing an estimate about consumption
appears to be related to several factors.
We find college-educated respondents and those who said to be concerned about the environ-
ment (enviro concern) more likely to provide an estimate. As expected, knowing the tariffs and
knowing the supplier’s website make it more likely to provide an estimate of consumption. Having
consulted the bill before trying to recall past amounts also increases the probability of providing
an estimate, suggesting that users might have a faulty perception of their water use, not because
they do not understand their bill but because they may not pay enough attention to it.19 Having
hot water billed through the resident’s community (hotshared) does not seem to make a differ-
ence, though, while, as expected, homeowners are more likely to provide an estimate of their past
consumption.
The accuracy of the recollection of water use does not seem to be explained by informational
variables; only having consulted the bill during the survey appears, as expected, associated with
smaller deviations between perceived and actual consumption. Environmental variables also seem
to play a role, since individuals exhibiting more pro-environmental water-related habits provide
more accurate estimates.
The third and fourth columns in Table 7 show the results related to the size of the bill, which are
quite similar to those about consumption. Knowledge of the water tariff and the supplier’s website
predict higher probabilities of providing an estimate. Perceiving that the bill is not sufficiently
informative reduces this probability, while consulting the bill while being interviewed increases it.
These latter variable exerts the strongest influence.
Contrary to the case of the previous model, hotshared is significant in the case of the bill. That
is, having the hot water billed through a collective invoice jointly with other items reduces the
probability that households provide an estimate of the size of their bill and increases the size of the
deviations. This is consistent with our expectation that these households will have a more limited
awareness of their individual level of water consumption.
Regarding the socioeconomic and environmental variables, respondents who feel their income
covers their needs and are more educated provide an estimate of their water bill less frequently,
probably because it is less important within their budgets. Respondents in households with a
larger proportion of members older than 65 are less likely to provide a bill estimate. Concern
about the environment also tends to reduce the inaccuracy of recollections of the bill. Although
not significant at 10% level, the p-value of enviro concern is very close to 0.1 in the estimatedbill
18
equation, suggesting that this variable additionally affects the decision to provide estimates of past
bill amounts. Of course, this result should be taken with caution. Household size has a mixed
effect, since households with more members are less likely to provide an estimate but they provide
more accurate estimates when they do.
5.2 Latent Class Models
The results of the LCM (Table 10), together with the postestimation analysis summarized in
Tables 8 and 9, allow us to complement the ones from the CMP models. While the latter provide
key insights into how consumers may react to efforts to improve their level of information, the
former aim at characterizing groups of consumers, which, as explained above, we find it likely to
be the most relevant type of information for policy-makers.
Table 8 shows the comparison in terms of goodness of fit of the LCMs we applied to the data.
We achieved no convergence beyond two classes. However, we also judged from the outset that
there would likely be little gain in practical terms from trying to identify more than two classes
of water users. Conceivably, water suppliers and public agencies charged with improving users’
awareness of their own consumption and water tariffs would not find it necessary to isolate further
consumer types. Our results identify a class of households for whom the returns to informational
efforts would likely be non-existent or not needed, given their original high levels of awareness, and
a second class on which to concentrate informational efforts, because the latter would yield the
most returns.
Model log-likelihood AIC BIC
One class -1942 3897 3927
Two classes -1768 3588 3719
Table 8: Comparison of goodness of fit measures across latent class models.
Table 9 reports the predicted probability in the population of belonging to each class and
class-specific marginal means for each of the three variables modelled. The latent class marginal
probabilities in the general household population of belonging to each class are 0.44 for the first
class and 0.56 for the second class.
Marginal mean Class 1 Class 2
class membership 0.44 0.56
estimatesinsurvey = 0 0.00 0.77
estimatesinsurvey = 1 0.74 0.22
estimatesinsurvey = 2 0.26 0.01
avpdcons abs 0.46 2.46
avpdbill abs 1.16 1.10
Table 9: Class membership marginal probabilities and marginal means of dependent variables from
Latent Class Model across latent classes.
The first class would include households that appear better able to estimate their bill and con-
sumption levels. Our postestimation analysis predicts the marginal probability of their providing
19
Class 1 avpdcons abs avpdbill abs
Bill is received at home and sufficiently clear to respondent 2.076∗∗∗
(0.000)
College degree held by first or second household member -0.512∗∗
(0.017)
Consulted bill while responding to survey 4.663∗∗∗
(0.000)
Efficient washer and dishwasher -0.178
(0.451)
Environment is one of the respondent’s concerns 0.460
(0.110)
Hot water partially billed communally -0.210
(0.285)
Household size -0.239∗∗
(0.014)
Knowledge of water saving campaign -0.320
(0.108)
Knowledge of the structure of the tariff 0.635∗∗∗
(0.002)
Knowledge of the water supplier’s webpage 0.515∗∗
(0.033)
Ownership of the dwelling held by user 0.061
(0.808)
Proportion of family members 18 or younger 0.153
(0.824)
Proportion of family members 65 or older -0.294
(0.282)
Satisfied with income -0.463
(0.147)
Water-saving habits index (0-1) -0.593
(0.296)
Class 1 0.463∗∗∗ 1.160∗∗∗
(0.000) (0.000)
Class 2 2.458∗∗∗ 1.100∗∗∗
(0.000) (0.000)
Constant -0.141
(0.831)
Observations 1150
log-likelihood -1767.77
p-values in parentheses
LCM classifying households according to the number of estimates (about their consumption and their bill) they
provided and how they deviated from actual values. Class 2 is the benchmark of the Fractional Logit Model.
p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01
Table 10: Latent Class Models’ Fractional Logit results.
20
estimates for both consumption and bill as 0.26, while another healthy proportion of them, 0.74,
would be expected to provide one of the two estimates. Additionally, those providing an estimate
would be the most accurate between the two classes (as suggested by their expected values of
avpdcons abs and avpdbill abs ). However, this class of relatively well-informed customers would
be expected to be the smaller one, since the average probability of belonging to it is estimated as
only 0.44.
The second class of households would be expected to perform worse. Indeed, 0.77 is the expected
proportion of respondents in this class providing no estimate at all and, among those providing
them, the accuracy of their recollection of past water consumption would be much less: proportional
deviations would average 2.46 (about 5.3 times more than the first class). These deviations would,
however, be about the same but actually smaller on average in the case of the bill, as compared to
those in the first class. This second class would likely be larger, with a mean predicted probability
of class membership of 0.56. That is, our results suggest that most households are relatively
unaware of their water consumption levels and water bill amounts. However, the size difference
between classes suggested by the difference in average probability of class membership is not very
large.
The first column of Table 10 reports the untransformed estimated coefficients of a fractional
Logit model used to explain the probability of class membership for each household.20 These
estimates provide qualitative insights into how observable characteristics affect the predicted prob-
ability that a given household belongs to each class of user. They do not, however, provide
quantitative information, since, due to the nonlinearity of the model, the predicted probabilities
and the marginal21 effects of the covariates for individual households depend on the individual
values of all variables.
We are particularly interested in the determinants of class membership, since we consider that
knowledge of the effects of observable factors among these determinants would help those tasked
with fostering the level of awareness of water use and prices. Compared to the worse performers
(Class 2), better performers (Class 1) are more likely to know the tariffs and the supplier’s website,
as expected. Feeling that the bill is informative and clear enough (clearbill ) significantly increases
the probability of belonging to the latter. Having consulted the bill significantly affects class
membership although, of course, any claims about the policy relevance of this insight should be
taken with caution, since there may be unobservable factors that affect both the likelihood that
respondents had a bill handy to consult and felt the need to do it and the likelihood of estimating,
if at all, more or less correctly their past bill and consumption amounts.22
Furthermore, it is no surprise that the effect of consultedbill is positive, making the analysis of
its quantitative effect (again, subject to the caveats about its potential endogenous nature) that we
include in Section 5.3 relatively more interesting than the qualitative information extracted from
the untransformed coefficients in Table 10. The fact that such a simple gesture as consulting the
bill, at least during the survey, significantly increases the probability of belonging to the class of
“best performers” seems to support our hypothesis that misperceptions may be, to some extent,
driven by consumer inattention to the bills. However, some of the respondents still fail to provide
an answer and deviate substantially after consulting the bill. That implies that other interventions,
tackling other aspects such as complexity, providing detailed information and so on, would also be
21
necessary.
Regarding clearbill, our results also suggest that finding the bill sufficiently detailed and infor-
mative significantly increases the probability of belonging to the class of best performers. Although
any informational policies affecting this variable would seem to potentially be the most influential,
knowledge of the tariff and the suppliers’ website also increase the probability of belonging to
best performers. Education also seems to play a key role in determining class membership, the
significant coefficient of variable college suggests that higher levels of education are associated with
lower probabilities of belonging to Class 1.
5.3 Quantitative analysis of the drivers of class membership.
As explained above, the untransformed estimates of our fractional Logit model (Table 10) only
indicate the sign of the estimated effect on the probability of class membership of the independent
variables. Calculating quantitative effects requires a choice of type of household, defined by values
of each variable in the model, for which to calculate the effects. Often, marginal effects are reported
at the means of all explanatory variables, yielding the effects for a ‘typical’ household. In our case,
this strategy is complicated by the fact that the lion share of our dependent variables are binary
indicators. Therefore, first, we do not consider marginal effects but rather discrete effects of
changes from 0 to 1 in the explanatory variables. Second, it is not meaningful to conceive of a
representative household with mean values of all those binary indicators. Therefore, we calculate
discrete effects for each individual household in the sample and then average their discrete effects,
setting the values of all independent variables to their actual values for each case, except for the
variables explicitly mentioned in the comparative analysis shown.
The vertical axes of the plots in Figure 2, in this section, and Figures 3 and 4,in Appendix C,
show the evolution, for different combinations of values of several indicators, of the discrete effects
(on the probability of belonging to Class 1) of three selected explanatory variables. The horizontal
axes measure the values of three continuous demographic variables that can be potentially observ-
able and, therefore, used to target policies more effectively. Variable, householdsize (Table 2), for
example, measures information often available to city councils and conceivably to water suppliers,
while the age composition of a household (Appendix C) could be also found out.
Figure 2 shows how the effects on the probability of Class 1 vary with knowstariff,knowsweb
(left column) or ownership and hotshared (right columns) for the different values of householdsize
at which they are measured. We chose these indicators, again because they tend to be observable
and thus used to better tailor policies aimed at improving information. We note, however, that
the variables on whose quantitative effects we focus are consultedbill,clearbill, and enviro concern,
while the other variables provide values at which to calculate and report the effects of those main
variables of concern.
We restrict our quantitative analysis to the effects of three variables for reasons of economy of
space,23 because they proved generally influential throughout most of the analysis, and because
we see them as potentially amenable to be influenced by efforts to improve the households’ level
of information and environmental awareness.
The first row of Figure 2 shows the effects of consultedbill. We assume that a household’s
22
.3 .4 .5 .6 .7 .8
Effects on Pr(Class 1)
1 2 3 4 5 6 7 8 9 10
Household size
knowstariff=0, knowsweb=0 knowstariff=0, knowsweb=1
knowstariff=1, knowsweb=0 knowstariff=1, knowsweb=1
Average Marginal Effects of 1.consultedbill
.5 .6 .7
Effects on Predicted Probability (1.C)
1 2 3 4 5 6 7 8 9 10
Household size
ownership=0, hotshared=0 ownership=0, hotshared=1
ownership=1, hotshared=0 ownership=1, hotshared=1
Average Marginal Effects of 1.consultedbill
.1 .2 .3 .4 .5
Effects on Pr(Class 1)
1 2 3 4 5 6 7 8 9 10
Household size
knowstariff=0, knowsweb=0 knowstariff=0, knowsweb=1
knowstariff=1, knowsweb=0 knowstariff=1, knowsweb=1
Average Marginal Effects of 1.clearbill
.2 .25 .3 .35 .4 .45
Effects on Pr(Class 1)
1 2 3 4 5 6 7 8 9 10
Household size
ownership=0, hotshared=0 ownership=0, hotshared=1
ownership=1, hotshared=0 ownership=1, hotshared=1
Average Marginal Effects of 1.clearbill
.04.05.06.07.08.09
Effects on Pr(Class 1)
1 2 3 4 5 6 7 8 9 10
Household size
knowstariff=0, knowsweb=0 knowstariff=0, knowsweb=1
knowstariff=1, knowsweb=0 knowstariff=1, knowsweb=1
Average Marginal Effects of 1.enviro_concern
.04 .05 .06 .07 .08
Effects on Pr(Class 1)
1 2 3 4 5 6 7 8 9 10
Household size
ownership=0, hotshared=0 ownership=0, hotshared=1
ownership=1, hotshared=0 ownership=1, hotshared=1
Average Marginal Effects of 1.enviro_concern
Figure 2: Average marginal (discrete) effects of consultedbill,clearbill, and enviro concern on the
probabilities of belonging to Class 1 depending on combined values of knowstariff and knowsweb
or ownership and hotshared by householdsize.
23
frequent consulting of the bill would have a similar effect on their perception of their water con-
sumption and bill as the one we detected during our survey. This, again, assumes that the choice
to consult one’s bill is more due to exogenous than endogenous drivers. That is, we ignore that
the effect of consultedbill on the probability of providing estimates of water use and the water bill,
and how accurately, has to do with the fact itself that respondents looked up the water bill, not
with the fact that they were the sort of person who would look up their water bill. Of course, in a
real policy setting this endogeneity should be reconsidered: the observed effect of consulting water
bills might be caused both by doing that or by unobservable characteristics that would prompt a
respondent to consult their bill frequently.
Generally, consultedbill has a relatively strong effect on the probability of belonging to Class 1
households, quite capable of coming up with an estimated of their water use and their water bill
that is also relatively accurate. This effect is, unsurprisingly, much more substantial in the case
of households who admit not knowing what type of tariff structure they face (knowstariff =0) and
also for those who do not know the supplier’s website (knowswebsite=1). The weakest effect is
for households knowledgeable about both, although it is still substantial. Figure 2 also shows
how this average discrete effect increases with household size. However, depending on whether
the household knows about the tariff structure and the supplier’s website, the rate of increase is
different and, for the largest households, the effects end up being about the same regardless of the
values of knowstariff and knowsweb.
The second variable whose effects we consider is clearbill, which would be an obvious candidate
for a policy variable, since, in principle, there are many measures a supplier could implement to
improve the design of the water bill. The second row of Figure 2 shows that clearbill has a relatively
weaker effect in general than consultedbill but also in this case knowing the tariff structure and
the website make a difference. This result might be quite useful, since, as already mentioned, it
would be easy to ascertain which households have that knowledge. However, the effcet of clearbill
generally diverges rather than converge as the household size increases across the four combinations
of household types.
The third row of Figure 2 contains two plots showing the effect of variable enviro concern.
Although environmental concern seems to exert a weaker effect than the two variables previously
shown, we believe it is interesting to portray it, as environmental awareness is a variable amenable
to be influenced by policy makers at all levels of the administration and by utilities themselves. As
we can observe, the effect of environmental concern is higher in the case of households who admit
not knowing either the type of tariff (knowstariff =0) or the website (knowswebsite=0), as opposed
to the case of those that report knowing both, who show the weakest effect. However, it does not
seem to vary substantially across ownership and hotwater variables (right hand figure). Also, the
effect seems decreasing in household size, which points to interventions addressing environmental
awareness being more effective in small household rather than in sizable ones.
24
6 Conclusions
Accurate consumer perception of consumption, prices, and total paid amounts is at the core of
the effectiveness of demand-side policies designed to achieve a sustainable use of natural resources.
If consumers cannot obtain full information about the key economic variables involved in pricing
strategies, tariffs will likely fail to convey the necessary incentives to act as a conservation instru-
ment. In explaining how consumers’ perceptions of the key economic variables deviate from reality,
information has, not surprisingly, been shown to have a key role. Lack of information becomes,
therefore, a crucial aspect to be addressed in order to promote the effectiveness of those policies.
We explore the level of consumer knowledge about the two main variables involved in pricing
policies: consumption and bill amount, in order to explain how the level of information affects the
gap between consumers’ perception’ and real observed values.
We find that the level of knowledge of both consumption and bill amount is rather low. Most
respondents did not even feel confident enough about their level of information to attempt to
provide an estimate, which may be interpreted as an extreme case of perception bias. Moreover,
even when an estimate was provided, we find that deviations from actual values are very high.
In particular, we find that consumers tend, on average, to highly overestimate their bill (more
than double on average) while they underestimate their consumption. The analysis also reveals a
low average level of knowledge about the pricing structure and other informational variables such
as knowing the supplier’s website, finding that the bill is sufficiently detailed and informative, or
having heard of any water-saving campaigns taking place in the previous five years.
By applying CMP and LCM techniques we derive some further insights about which informa-
tional policies may be more effective to reduce consumers’ biases, as well as identifying groups of
consumers that display distinctive patterns with respect to those misperceptions. In particular,
we can differentiate two latent classes of consumers that could be labelled, according to their level
of perception bias, as “better performers” and “worse performers”. Characterizing those profiles
should be useful to help policymakers focus their efforts on those households in the latter class.
Our results have relevant policy implications, since they suggest that better informational poli-
cies could substantially improve the consumers’ response to and the effectiveness of pricing policies,
while allowing us to suggest effective interventions to increase it. First, we find that consulting
the bill before attempting to provide an estimate of consumption and bill is, unsurprisingly, one
of the best predictors of reduced perception biases. This suggests that misperceptions are largely
caused simply by lack of attention to the bills. Therefore, behavioral economics policies aiming at
promoting the careful reading of one’s bill (e.g. sending key facts about individual consumption,
tariffs, and bill by e-mail, SMS, or smart meter; or showing a banner when opening the website)
could prove very useful to increase consumer’s knowledge of consumption and prices. Second, we
find that another important factor in explaining misperceptions is the perceived lack of detail in the
issued bill. Better detailing the bills so that consumers find them more explanatory could, there-
fore, significantly improve awareness of the relevant economic variables in demand-side policies
while reducing the cognitive problems to understand them. The same applies to the knowledge of
tariffs themselves, which was found related to lower levels of misperception. These findings might
also contribute to the design of ‘nudging’ policies, suggesting that the combination of several in-
25
formative dimensions may have stronger impacts. Thus, pairing messages aimed to improve raise
environmental awareness with more detailed information on water tariffs could be a more effective
policy to manage residential water demand.
Knowledge of the supplier’s website also seems related to reduced levels of consumer mispercep-
tion. This suggests that fostering the use of modern and more instant channels of communication,
instead on relying only on traditional media (e.g. letters sent to households), could prove effec-
tive to increase consumer’s awareness. To increase consumers’ knowledge of the website, suppliers
could rely, for example, on usual marketing strategies such as conditioning the participation on a
lottery to signing on the provider’s website or liking their social media profile. Finally, the results
of our LCM provide some insights on which groups of households they informational efforts and
campaigns would be most cost-effective, since users could be segmented according to variables
available to the supplier.
We also observed that being billed collectively for hot water seems to increase misperceptions,
likely because the frequency of billing in this case is different from that of the main water bill.
Fostering individual metering might thus improve knowledge and information. In addition, an
important role should be placed on environmental concern and pro-environmental habits, which
we found linked to reduced misperceptions Although not related to the information variables,
according to our analysis, policies tackling environmental attitudes and behaviors would constitute
a relevant strategy for the effectiveness of demand-side policies. Our analysis portrays how to tackle
households in an effective manner with regards to those environmental traits.
Finally, some limitations of our analysis must be acknowledged. First, although we have tried
to control for individual psychological traits that could affect simultaneously perceptions and in-
formational choices, using the proxies available in our dataset and employing cluster-correction.
joint estimation, and LCM techniques, our analysis would benefit from a richer treatment of the
unobserved heterogeneity derived from those psychological traits in order to derive stronger causal
interpretations. Our identification strategy could also benefit from a more experimental design,
in which subjects were faced with relevant informational choices in controlled lab experiments or
by means of exploiting a randomized controlled trial or natural experiment. We encourage other
researchers to try and address this limitation in the future.
We are constrained by the availability of information stemming from the two data sources used
in our empirical exercise. Ideally, we would have liked to control for additional variables, such as
indicators of whether the bill was paid through direct billing or not. To the extent that we do
not expect any strong collinearity between such unavailable variables and those included in our
model, we are quite confident that our results are not affected by omitted variable bias. Future
studies might want to consider gathering this type of information, in order to investigate additional
relationships.
We also acknowledge that, in the case of several of our explanatory variables, we claim to derive
no conclusions about causal relationships, using them rather as control variables. This is because,
again, we are limited by the availability of data. A further difficulty is that, in the case of several
variables, we could only count on an imperfect proxy of the measure we would like to have used.
We would also have liked to have dealt for certain with the main decision maker in the household.
In this sense, our empirical exercise is affected by the fact that we ourselves have only imperfect
26
information about our subjects of study. Because of these limitations in terms of the variables
we have available and the potential for measurement error and omitted variable biases, we are
necessarily cautious about the claims we made based on our econometric analysis.
In addition, we note that misperceptions of water consumption and bill amounts are likely
affected by the share of the household budget devoted to the water. According to most recent
data, in Spain, the water accounts for a small fraction of family expenditure -around 0.6% (Su´arez-
Varela, 2020), well below the usual threshold of 3% employed to consider water poverty-. Since
these figures are similar to the ones display in most developed countries,24our analysis could be
further extended to countries with similar budget shares. However, it would be interesting to
study whether households responses to information about water pricing extend to other contexts
in which the bill represents a larger proportion of the households’ budget.
Notes
1To our knowledge, so far only Brent and Ward (2019) have explored differences between actual data and
perceptions about both water bills and consumption. However, they do not study how the level and type of
information may influence the observed differences.
2Because the literature addressing this issue in the water sector is still scarce, we discuss studies about both
water and electricity. These two sectors are linked and exhibit strong similarities. Indeed, the economic analyses of
residential water and electricity have been linked from the start (Arbu´es et al., 2003), since demand modelling and
price structures share similar features. However, the relative share of water bills on household budgets is usually
much smaller than its electricity counterpart.
3Binet et al. (2014) provide a brief discussion of analyses of the price variable to which consumers react, in both
the water and the energy sectors.
4According to INE (2019), Granada registered 223,208 inhabitants in 2018.
5The year when the survey, described below, was conducted.
6As defined by Law 40/2003 of 18 November, on Protection of Large Families.
7In a survey conducted by the water supplier in 2014, 82% of customers declared to be against receiving their
bills online (EMASAGRA, 2014).
8Unfortunately we do not have enough information to develop independent measures of the components of
perceived price. Respondents were asked simply to recall the total amount of their water bill. In theory, this
recalling exercise involves the knowledge of the tariff and the knowledge of consumption. It would have been
more interesting to isolate issues of imperfect perception due to lack of knowledge of the tariff from those due to
misperceptions of the level of consumption.
9Actual values of the bill were calculated taking into account any applicable discounts.
10The perceived value is exceeded by the actual value, yielding a negative value for the deviation measures.
11This last variable is not used, though, as an information variable but as a proxy of unobserved heterogeneity,
as we explain below.
12Note that this variable does not indicate knowledge of the price of each block and the amount of the fix
component but only a very basic awareness of the type of tariff structure.
13A positive and significant estimated of rhoij would indicate that common unobserved factors tend to increase
or decrease the errors in both equations. A negative correlation between two regression errors suggests, instead,
that omitted common factors tend to increase the error in one equation and decrease the error of the other equation
or vice versa.
14We implemented it with Stata’s (Statacorp, 2011) CMP routine (Roodman, 2011).
15Further details about this methodology can be found in Cameron and Trivedi (2005, Ch. 18.5)
16Other approaches assume the unobserved heterogeneity to follow a continuum, rather than conceiving a discrete
representation of heterogeneity leading to a finite number of latent components or classes.
27
17In principle, because of the nonlinearity of the selection equation, exclusion restrictions are technically not
essential but they are usually considered a much safer strategy than relying on the, possibly slight, nonlinearity of a
potentially misspecified functional form to identify the estimated parameters (Cameron and Trivedi, 2010, p. 558).
18Table 7 does not directly report the estimated value of ρ. Because σand ρare bounded, the CMP routine
transforms them onto an unbounded scale by using the logarithm of the σ’s and atanh(ρ), the arc-hyperbolic
tangents (inverse S-curve transforms) of the ρ’s, in order to prevent the possibility that the maximum likelihood
search process submit impossible trial values for these parameters, such as a negative value for a σ(Roodman,
2011).
19This is not surprising, since water consumption usually represents a very small proportion of total household
expenses.
20This fractional model assumes that each household has a certain probability of belonging to each class.
21Or, as in the case of most of our covariates, discrete effects of the variable changing value from 0 to 1.
22As discussed before, unfortunately, in our survey we cannot rely on specific information about individuals’
psychological traits. We were only able to proxy them to some extent by including bill not remembered as an
additional covariate and control.
23Any other quantitative estimates are available upon request.
24See, for example, Olmstead et al. (2007), which reports a budget share of 0.5%.
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A Variable descriptions
avpdcons abs: Average proportional misperception: use (absolute value)
avpdbill abs: Average proportional misperception: bill (absolute value)
billing period 1 to bil ling period 5 : Binary indicators of bimonthly billing periods
bill not descriptive : Bill is received at home but lacks sufficient detail, according to respon-
dent
bill not remembered: Bill is received at home but not remembered by respondent
clearbill: Bill is received at home and sufficiently clear to respondent
college: Either first or second household member has a postsecondary degree
consultedbill : User consulted bill while responding to the survey
dcons: Observed consumption (totalconsumption) minus the perceived (perceivedcons) con-
sumption in each of the six billing periods for which information is available for both types
of measure (cubic meters/period).
32
dbill: Observed (totalbill) minus the perceived (perceivedbill) bimonthly bill for the six billing
periods for which information is available for both types of measure (euros).
efficient apps: Household owns water-saving appliances, washer and dishwasher. The respon-
dents were asked whether they had water-efficient washer and dishwasher. Since a dishwasher
is itself a water-saving technology, we only considered the household as consistently enrolling
in environmental behaviors of the “one-shot” type – installation of water-saving technologies-
if they referred to have both water-efficient appliances.
enviro concern: user is “very concerned” about the environment
estimatesinsurvey: Number of estimates of bill and consumption provided, 0, 1, or 2
estimatedcons: Respondent provided an estimate (a perceived value) of consumption
estimatedbill Respondent provided an estimate (a perceived value) of bill
hotshared: Some of the hot water is not billed individually for each household but billed
jointly through the contributions to the “comunidad de vecinos”, akin to “condo fees”.
householdsize: Household size (number of members)
knowscampaign: User knows of water saving campaign
knowsweb: Knowledge of the water suppliers’ webpage
ownership: User owns the dwelling
page18 : Proportion of household members 18 or younger
p age65 : Proportion of household members 65 or older
pdcons: Proportional divergence, observed minus perceived consumption
pdbill: Proportional divergence, observed minus perceived water bill
pdcons abs: Proportional divergence, absolute terms, observed minus perceived consumption
pdbill abs: Proportional divergence, absolute terms, observed minus perceived water bill
satisfied with income: User claims to be satisfied with household income to cover needs
waterhabitindex : Index indicating proportion of eight water-saving behaviors practiced by
the household
B Validity of exclusion restriction.
33
OLS Consumption CMP of Consumption OLS Bill CMP of Bill
estimatedcons pdcons abs estimatedbill pdbill abs
Bill is received at home but 0.152 -0.224 0.156 0.126 -0.309∗∗ 0.150
lacks sufficient detail (0.282) (0.221) (0.270) (0.166) (0.019) (0.102)
Bill is received at home but not 0.014 -0.521∗∗∗ 0.024 -0.014 -0.975∗∗∗ 0.079
remembered by respondent (0.837) (0.000) (0.732) (0.857) (0.000) (0.334)
Billing period 1 0.039 -0.003 0.039 0.0590.020 0.058
(0.242) (0.885) (0.233) (0.060) (0.236) (0.063)
Billing period 2 0.041 0.018 0.040 -0.013 0.023 -0.015
(0.279) (0.399) (0.274) (0.643) (0.180) (0.599)
Billing period 3 0.013 0.004 0.013 -0.068∗∗ 0.026 -0.070∗∗∗
(0.683) (0.860) (0.679) (0.012) (0.119) (0.009)
Billing period 4 0.058 0.044∗∗ 0.057 -0.074∗∗ 0.036-0.077∗∗
(0.216) (0.035) (0.214) (0.014) (0.059) (0.010)
Billing period 5 0.307∗∗∗ 0.014 0.307∗∗∗ 0.357∗∗∗ -0.018 0.359∗∗∗
(0.000) (0.560) (0.000) (0.000) (0.340) (0.000)
College degree held by first or 0.044 0.2290.040 -0.002 -0.202∗∗ 0.014
second household member (0.560) (0.065) (0.583) (0.974) (0.022) (0.823)
Consulted bill while responding -0.231∗∗∗ 1.579∗∗∗ -0.255∗∗∗ 0.106 1.884∗∗∗ 0.007
to survey (0.000) (0.000) (0.000) (0.248) (0.000) (0.936)
Efficient washer and dishwasher 0.020 0.137 0.019 -0.037 -0.145 -0.023
(0.747) (0.292) (0.761) (0.601) (0.161) (0.740)
Environment is one of the 0.117 0.450∗∗∗ 0.110 -0.1450.153 -0.159
respondent’s concerns (0.181) (0.004) (0.214) (0.084) (0.134) (0.057)
Hot water partially billed -0.026 -0.010 -0.027 0.102-0.1590.115∗∗
communally (0.706) (0.930) (0.699) (0.074) (0.053) (0.044)
Household size 0.060 0.023 0.060 -0.091∗∗∗ -0.110∗∗∗ -0.081∗∗∗
(0.189) (0.693) (0.181) (0.003) (0.007) (0.009)
Knowledge of water saving 0.022 -0.063 0.023 -0.075 -0.169∗∗ -0.061
campaign (0.719) (0.565) (0.703) (0.191) (0.039) (0.291)
Knowledge of the structure of -0.074 0.531∗∗∗ -0.083 0.1080.244∗∗∗ 0.089
the tariff (0.182) (0.000) (0.138) (0.072) (0.005) (0.141)
Knowledge of the water 0.079 0.326∗∗∗ 0.074 0.052 0.348∗∗∗ 0.026
supplier’s webpage (0.255) (0.009) (0.261) (0.459) (0.001) (0.715)
Ownership of the dwelling held 0.097 0.321∗∗ 0.091 -0.151∗∗ 0.134 -0.161∗∗
by user (0.188) (0.035) (0.201) (0.044) (0.201) (0.034)
Proportion of family members 18 -0.275 -0.540 -0.267 0.278 0.147 0.262
or younger (0.266) (0.223) (0.270) (0.125) (0.610) (0.149)
Proportion of family members 65 0.122 0.236 0.118 -0.112 -0.216-0.096
or older (0.174) (0.117) (0.171) (0.173) (0.065) (0.244)
Satisfied with income -0.3110.154 -0.315-0.017 -0.325∗∗ 0.010
(0.086) (0.415) (0.078) (0.865) (0.011) (0.919)
Water-saving habits index (0-1) -0.403∗∗ 0.256 -0.408∗∗ -0.054 -0.052 -0.051
(0.037) (0.405) (0.032) (0.756) (0.828) (0.769)
Observations 895 6631 3608 6631
log-likelihood -742 -2754 -4542 -8389
χ2 251 407
p-value 0.000 0.000 0.000 0.000
p-values in parentheses
p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01
Table 11: Comprobations of validity of exclusion restriction (bill not remembered ).
34
C Further examples of quantitative effects on probability of
class membership.
Figure 3 illustrates graphically how the marginal effects of consultedbill and clearbill (averaged
through the sample households) vary depending on the values at which different binary variables
are measured, depending also on the proportion of household members under 18 (variable p age18 ).
.4 .45 .5 .55 .6
Effects on Pr(Class 1)
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1
Proportion of family members 18 or younger
knowstariff=0, knowsweb=0 knowstariff=0, knowsweb=1
knowstariff=1, knowsweb=0 knowstariff=1, knowsweb=1
Average Marginal Effects of 1.consultedbill
.52 .54 .56 .58 .6
Effects on Predicted Probability (1.C)
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1
Proportion of family members 18 or younger
ownership=0, hotshared=0 ownership=0, hotshared=1
ownership=1, hotshared=0 ownership=1, hotshared=1
Average Marginal Effects of 1.consultedbill with 95% CIs
.38.39 .4 .41.42 .43
Effects on Pr(Class 1)
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1
Proportion of family members 18 or younger
knowstariff=0, knowsweb=0 knowstariff=0, knowsweb=1
knowstariff=1, knowsweb=0 knowstariff=1, knowsweb=1
Average Marginal Effects of 1.clearbill
.4.405.41.415.42.425
Effects on Pr(Class 1)
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1
Proportion of family members 18 or younger
ownership=0, hotshared=0 ownership=0, hotshared=1
ownership=1, hotshared=0 ownership=1, hotshared=1
Average Marginal Effects of 1.clearbill
.075 .08 .085
Effects on Pr(Class 1)
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1
Proportion of family members 18 or younger
knowstariff=0, knowsweb=0 knowstariff=0, knowsweb=1
knowstariff=1, knowsweb=0 knowstariff=1, knowsweb=1
Average Marginal Effects of 1.enviro_concern
.076 .078 .08
Effects on Pr(Class 1)
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1
Proportion of family members 18 or younger
ownership=0, hotshared=0 ownership=0, hotshared=1
ownership=1, hotshared=0 ownership=1, hotshared=1
Average Marginal Effects of 1.enviro_concern
Figure 3: Average marginal (discrete) effects of consultedbill,clearbill, and enviro concern on the
probabilities of belonging to Class 1 depending on combined values of knowstariff and knowsweb
or ownership and hotshared by p age18.
Figure 4 illustrates graphically how the marginal effects of consultedbill and clearbill (averaged
through the sample households) vary depending on the values at which different binary variables
are measured, depending also on the proportion of household members over 65 (variable p age65 ).
35
.4 .45 .5 .55 .6 .65
Effects on Pr(Class 1)
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1
Proportion of family members 65 or older
knowstariff=0, knowsweb=0 knowstariff=0, knowsweb=1
knowstariff=1, knowsweb=0 knowstariff=1, knowsweb=1
Average Marginal Effects of 1.consultedbill
.52.54.56.58.6 .62
Effects on Predicted Probability (1.C)
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1
Proportion of family members 65 or older
ownership=0, hotshared=0 ownership=0, hotshared=1
ownership=1, hotshared=0 ownership=1, hotshared=1
Average Marginal Effects of 1.consultedbill with 95% CIs
.36 .38 .4 .42 .44
Effects on Pr(Class 1)
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1
Proportion of family members 65 or older
knowstariff=0, knowsweb=0 knowstariff=0, knowsweb=1
knowstariff=1, knowsweb=0 knowstariff=1, knowsweb=1
Average Marginal Effects of 1.clearbill
.38.39 .4 .41 .42
Effects on Pr(Class 1)
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1
Proportion of family members 65 or older
ownership=0, hotshared=0 ownership=0, hotshared=1
ownership=1, hotshared=0 ownership=1, hotshared=1
Average Marginal Effects of 1.clearbill
.074.076.078 .08
Effects on Pr(Class 1)
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1
Proportion of family members 65 or older
ownership=0, hotshared=0 ownership=0, hotshared=1
ownership=1, hotshared=0 ownership=1, hotshared=1
Average Marginal Effects of 1.enviro_concern
.074.076.078 .08
Effects on Pr(Class 1)
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1
Proportion of family members 65 or older
ownership=0, hotshared=0 ownership=0, hotshared=1
ownership=1, hotshared=0 ownership=1, hotshared=1
Average Marginal Effects of 1.enviro_concern
Figure 4: Average marginal (discrete) effects of consultedbill,clearbill and enviro concern on the
probabilities of belonging to Class 1 depending on combined values of knowstariff and knowsweb
or ownership and hotshared by p age65.
36
D Water bill sample
377
"""
'"
.
.
Emasagra
Granada’s Municipal Supply and
Sanitation Company
5-0 Molinos Street
18009 GRANADA
tel.902-24.22.20 - www.emasagra.es
1 OWNER - ADDRESS PROVIDED
RATE
DOMESTIC BOP 247 DE F. 29/l 2/09(WATER)
Provincial Gazette. #247 DATE 29/12/09 (Sanitation
and Wastewater treatment plant fee)
Provincial Gazette #239 DATE 16/12/09 (Garbage)
ISO
14001
CONTRACT # DATE ISSUED
51930146044 23-12-2010
INVOICE # PERIOD
10852343 2010/6
METER # DIÁMETER (mm) UNITS
021682745 20
PRIOR READING (m3) CURRENT READING (m3) USE (m3)
19-10-2010 17-12-2010
385 8
002740/02740- 927
.Granadas Municipal Supply and Sanitation Company. Tax ID# A18027722 - 58-60 Molinos Street, Granada - R.M. Granada, Volume 740, File 44, Page GR-5508, lnsc. 17'
INVOICE
Detailed WATER Invoice
Service Fee
from 0 to 16 m3
SANITATION
Fixed fee
0 to 16 m3
W. W. T. P.
From 0 to 16 m3
(•) GARBAGE COLLECTION FEE
Total Amount
Taxes NO SUJE S/ 22,12
Taxes 8,00 % S/ 14,08
Total invoice
MESSAGES
- (•) Concept attributable for accounting purposes to the council. Tax ID#
808900C
Avoid unnecessary travel by calling Customer Service: 902-
24.22.20 or by visiting www.emasagra.es.
- Your average use over this period has been
- 0,61 Eur./day, where 0,16 Euros/day corresponds to
Water.
- To receive correspondence at different address than that
shown here, call Customer Service.
Quantity
8,00
8,00
8,00
Price Amount Subtotal %VAT
6,00
0,3985 3,19 9,19 8
0,42
0,2749 2,20 2,62 8
0,2834 2,27 2,27 8
22,12 22,12 NS
1,13 1,13
STATISTICAL INFORMATION
6/09 1110 2110 3110 4110 5110 6/10
PAYMENT
The amount of this invoice will be charged shortly to your account no. in
Granada. Hidden security digits.
The payment is made by direct debit or mechanic authentication and
does not presuppose payment of prior invoices.
Figure 5: Water bill sample.
37
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