The delay in payment of residential water bill: A Duration Analysis
Approach and Application to ALGERIA
Mourad KERTOUS1, Younes BENZAIED*2 & Duc Khuong NGUYEN3
Abstract
The main purpose of this paper is to empirically investigate the reasons of delay in payment
of residential water bill in Algeria. Using a big dataset of 27363 subscribers to the water
services network and a small sample survey of 172 subscribers, we have estimated several
duration models to identify the main determinants of invoice time-to-payment. It appears that
household financial constraints, quality of offered service and nonlinear water tariff structure
have a positive impact on the delay in payment of water bill. The paper calls for a more
equitable tariff structure as well as an effort to improve the quality of offered service.
1
Laboratoire EDEHN
Université du Havre, France
Faculté des affaires internationales
25 Rue Philippe Lebon
Personnel Email : [email protected]
2
* corresponding author : University of Tunis EL Manar, Tunisia
LAREQUAD & CREM, University of Rennes 1
[email protected]
3
IPAG Business School
Introduction:
Algerian water resources are characterized by acute scarcity, quality problems, bad
distribution as well as time and space volatility. Algeria, like other similar countries in the
Middle East and North Africa, is committed to manage the sustainability of this very limited
resource to meet actual population needs, boost its fragile economy and above all preserve
this strategic resource for the next generations. Even if residential water demand is limited
when compared to irrigation demand, it must be carefully managed for at least two reasons:
First, residential water demand can only be satisfied by water of good quality (softness,
purity, etc.). Paradoxically Algeria’s freshwater is very limited and located only in some
northern regions of the country. Second, residential water needs to be regular, secure and
reliable especially during the dry season. Such constraints are difficult to satisfy in a country
where variability is a nature. So if Algeria, like other similar countries, wants to avoid, or
postpone reverting to nonconventional water (desalinization, virtual water, etc.) with
relatively higher costs, the only alternative is to rely on appropriate water demand
management. Water pricing must be seriously considered as a useful tool, along with other
non-price instruments, such as awareness, education, water conservation and participatory
management to keep the demand evolution under control. Indeed this demand is exponentially
increasing as a result of the rapid urban and economic development of an emerging country
like Algeria, where all activities require more water quantity, with acceptable quality,
available in the right time and place.
Applying the same increasing multi-step pricing scheme in the whole country, Algeria wants
to manage adequately its limited clean water resources, allow low-income households to meet
their human basic needs and incite high-income households to preserve this precious
resources by reducing their excessive water use. According to the Algerian water law of 2005,
the water pricing policy is based on the principles of financial stability, social solidarity,
encouraging water conservation and protection of the quality of water resources. However,
the national water authority in Algeria (ADE4) is facing a major problem related to the delay
of payment of water bill. Indeed, Bill payment is legally due at most 15 days after the bill
issuance and in case of late payment extra fees are incurred by subscribers. Any mistake on
invoice should be claimed within 15 days after issuance and any necessary refund would
4
Algerienne Des Eaux : the water authority in Algeria
apply to the next invoice or paid in cash. Unpaid bills are managed by the legal department
for recovery and, if unsuccessful, then water supply is stopped. In this situation, the user
supports the costs of closing and reopening the water-meter.
In addition to water scarcity and quality problems, the Algerian water authority (ADE) is
confronted to a major problem caused by long delay on bill payments that translate into
difficulties on company management and water service sustainability. Therefore, identifying
the reasons behind long bill payment delay is crucial to achieve goals of better resources
management and improvement in water supply sustainability.
Residential water demand and management has been a major issue in environmental and
resource economics as documented in recent surveys (Arbués et al. 2003; Dalhuisen et al.
2003; Whittington and Hoffman 2008). Most of this research focused on developed countries,
while very few studies focused on developing countries (see Nauges and Whittington 2010).
The main purpose of this literature is to empirically estimate the water price elasticity in order
to recommend effective public policy in favor of water demand management and control.
However, to the best of our knowledge, no paper has analyzed the late payment of water bill
and its impact on water supply sustainability. This issue is extremely important especially for
a developing country like Algeria.
In the literature, there are several studies on the Residential water demand estimation and the
WTP5. Indeed, the identification of water demand determinants and of the impact of price
changes on welfare are important for sustainable water resource management. However, the
impact of price increases may also be manifested by an extension of the payment term
invoices that can affect the proper functioning of Management Company. For example, for the
case of Ivory Coast, Diakite and Thomas (2011) estimate a water demand function to show
that an increase of the average prices (by 10 % and 20 %) gives the welfare losses of 1511 F
CFA and 3153 (ie a variation of 0,0578% to 0.12% in household average income). For the
case of France, Garcia and Reynaud (2004) simulate the impact of marginal-cost pricing
(first-best pricing) and social surplus variations in Bordeaux city. They find that moving
towards efficient prices does not result in important direct welfare effects. On average, the
impact of this policy is equal to 0.33 € per user which corresponds to less than 0.4% of the
5
In addition there are few studies about water demand in developing countries. The few studies addressing this issue are Boone
et al (2010), Madagascar; Cheesman et al (2008),Vietnam; Pattanayak et al (2006),Sri Lanka; Ahmad et al (2005), Bangladesh;
Nauges and Strand (2005), El Salvador; Persson (2002), Philippines; Asthana (1997), India; Madanat and Humplick (1993),
Pakistan; Mu (1990), Kenya; Whittington et al (1990), Haiti
initial net welfare and the yearly aggregate water consumption per user goes from 133.6 to
133.1 m3.
Other studies address the impact of restrictions on welfare. Grafton and Ward (2008) use the
consumer’s surplus approach to quantify the impact of a water restriction policy on
households' welfare in Sydney. They estimate an annual welfare loss of 235 million dollars.
For the case of the United States, Hanemann and Nauges (2005) analyze also the impact of
different water restrictions regimes on households’ behavior in Los Angeles. In summer time,
they find for voluntary programs losses between 13 $ and 106 $. For the case of Hong Kong,
Woo (1992) analyzed the water demand determinants and estimates the households' welfare
impact from reduction of the water supply hours. In three scenarios he found welfare losses of
1.18 $/hour, 2.29 $/hour and 3.77 $/hour. However, the impact of this policy on subscriber
behavior was neglected in these papers. The consequences of restrictions can occur in several
ways (for example, they can extend their payment period).
A few studies address the impact of water price increase on the water bill time-to-payment.
For the case of Manaus in Brazil, Olivier (2006) used a dichotomous variable which takes value 1
if the payment is made within 10 days and 0 otherwise. He showed that the bill payment rate
within 10 days doesn’t exceed 10 % and the price increase doesn’t have the same impact on
the different categories of subscribers. Indeed, he demonstrated that only the poorest
households consuming below the threshold of 10 m3/month experienced an increase of 31.5 %
in their water bills. For this category, he showed also that late payments have increased.
Kayaga et al (2003) analyzed the impact of these same variables on households WTP. They
demonstrated that the gender, education level, occupation, status in housing and income
positively influence households WTP for water supply. However, household size, dwelling
type and the existence of alternative water resource doesn't influence this decision
Studies aiming to analyze the factors impacting bills time-to-payment are almost nonexistent.
To address this issue, the objective of this article is to empirically investigate and identify
factors influencing time between bill issuance and subscriber payment. We referred to the
water demand literature about Willingness-To-Pay (WTP). We think that factors affecting
WTP affect time-to-payment as well. According to this literature, three groups of variables
influence households' WTP. First, socio-economic and demographic characteristics of
households which are the education level of family members, number of family members,
head of household occupation, family composition, income, expenses and the number of
assets. Second, availability of alternative water supply, the financial costs and time investment
required to collect water, the quality and reliability of water supply. Third, the household
attitude toward water management policies can also affect time-to-payment.
The paper is organized as follow. Section II explains the increasing multi-step pricing scheme
applied by water authority in Algeria and summarizes the descriptive statistics of data used in
this empirical investigation. It consists in a big database including all subscribers of Bejaia
city over 17 quarter from March 2004 until March 2008 (465 171 observations) and a second
dataset about 172 subscribers collected over a period of 45 quarters from March 1997 to
March 2008.The second dataset is completed by a socio-economic survey of the same 172
subscribers carried out in August 2008. In Section III, we analyze the time-to-payment
variable using the graphical approach offered by Kaplan-Meier survival analysis then we
refine our results with an econometric approach (Weibull model). Finally, we discuss the
empirical results to carry out policy recommendations.
II. Context and data set description
II.1. Context and water pricing system
Water resources in Algeria are characterized by an acute scarcity which will be accentuated
during the next two decades. Algeria has a semi-arid climate with alternating dry and rainy
seasons. According to the World Bank report, the Algerian available water resources
calculated to be 500 m3 per quarter per household in 2005, will fall to 350 m3 per quarter per
household in 2030.
In order to keep under control household demand for water and reduce excessive water use,
the Algerian water authority (ADE) has implemented an increasing multi-step pricing scheme
in the whole country. This nonlinear water tariff system consists in four increasing block
defined by three consumption threshold. The price of water consumption of each block is
calculated by multiplying the base price (which is also the water price of the first block) by a
factor increase. Thus, the price of the second block is the base price weighted by a factor of
3.25, the third block is weighted by a factor of 5.5 and the fourth block is weighted by a factor
of 6.5. The last block (Fourth one) is applied to industrial’s sector and tourism regardless their
quarterly consumption. Table 1 presents the composition of the water bill calculated from
ADE dataset. The per-unit water price is presented in Algerian Dinars (DA) the national
currency. Actually, an Algerian Dinars (DA) is equal 0.01 euro.
Table 1: Presentation and composition of the water bill
3
Price before 2005
(DA/m3)
4.30
Price after 2005 (DA/m )6
Block 2 ]25-55 m ]
Block 3 ]55 -82 m3]
Block 4 > 82 m3
Management fee (3 DA/ m3)
13.98
23.65
27.95
+
20.475
34.65
40.95
+
Water quality fee (4 % from total bill)
+
+
Charge of water conservation (4 %)
+
+
+ Invoice VAT
Sanitation
Fixed share (before and after 2005)
+
+
25 DA
+
+
Designation
Block 1 ]00-25 m3]
3
6.30
240 DA
II.2. Dataset description
II.2.1. Descriptive statistics of the first database (27 363 subscribers)
ADE, the national water distribution company in Algeria, has applied a four-block pricing
structure with a quarterly frequency of billing. We are the first to exploit this novel database
provided by ADE. The data describe 27363 subscribers in the Bejaia City which is located in
the north east of Algeria. The data cover a period of 17 quarters from March 2004 to March
2008.
As we propose to analyze the main determinants of invoices’ payment term, the ADE provide
a detailed individual data describing the quarterly individual water consumption of
subscribers in cubic meter, the number of days between the billing date and the date of
payment for each subscribers (bill time-to-payment), the quarterly rainfall in mm, the
quarterly invoice amount paid by each subscriber, the quarterly average and marginal prices
paid by subscriber, the total quarterly volume of water distributed by the ADE, a dummy
variable for the main three areas where subscribers are located, the kind of housing (house or
apartment), the diameters of subscribers meters, the invoicing types (on the basis of real
consumption or a flat-rate pricing), the virtual income by subscriber by period7. Table 2
presents some descriptive statistics calculated using the database that describes 27363
DA: (Algerian dinar) is the Algerian currency.
This variable is computed by adding average household income and the difference variable of Nordin (1976). This
parameter was calculated according to the method used by several authors. Miyawaki et al (2010), Mansur and
Olmstead (2007), Martinez and Nauges (2004), and of Nauges Blundell (2002) , Reitveld et al (2000) , Corral et al (
1999) and Chicoine and Ramamurthy (1986).
6
7
subscribers to the ADE network water services in the BEJAIA City during the period between
march 2004 and March 2008. The global database is composed by a 465171 observations
describing 27363 subscribers for the residential water use in the BEJAIA City.
Table 2: The main data used for the global database8
Variables (N=27363)
Mean
Std.dev
Min
Max
Invoice amount
1076.06
1277.71
240
42878.16
Quantity
33,11
29,78
0
179
Average price
62.85
86.67
10.45
1316.79
Marginal price
15.21
10.27
4,3
40,95
Rainfall
178,58
120,81
11
394
P1
5,82
0,84
4,3
6,3
P2
18,95
2,75
13,98
20,48
P3
32,06
4,66
23,65
34,65
P4
37,89
5,51
27,95
40,95
Supply
4,47
0,42
3,84
5,86
Bejaia (Medina)
0.34
0,47
0
1
Ihadedene
0,39
0,48
0
1
Quartier Seghir
0,26
0,44
0
1
Individual House
0,29
0,45
0
1
Diameter
15,22
1,04
15
20
Real consumption
0,91
0,28
0
1
Virtual income (in DA)
94488.81
146571
45543.25
682780.4
Following table 2, the data description statistics can be summarized as follow: The total
population’s average consumption is 33 m3 per quarter with a minimum of 0 m3 and a
maximum of 179 m3. The average price paid by subscribers is 62 DA/m3. The average
invoice's amount paid by subscribers is 1076 dinars per quarter. 91% of invoices have been
established on the real consumption of subscribers. 29 % of subscribers live in houses. 34 %
of subscribers live in Bejaia Medina city (neighborhood mostly built before independence).
39% of households live in Ihadedene's new district. 26 % of subscribers live in Seghir's
quarter (between the old city and the new Ihedadene's neighborhood). The majority of users
are equipped with a water meter of 15 mm. The average rainfall is 186 mm per quarter with a
minimum of 11 mm and a maximum of 394 mm.
8
For more details about the variables, see Appendix.
In table 3, we present the bill time-to-payment variable distribution expressed in number of
day. This results summarized in table 3 confirms our finding previously described about water
bills collection difficulties in Algeria.
Table 3: Distribution of bills time-to-payment, expressed in number of days
1%
5%
10 %
25 %
Bejaia City
Percentiles
3
7
9
15
50 %
27
45
115
192
481
75 %
90 %
95 %
99 %
Number of Observations
Invoices settled before the deadline
Invoices' average time-to-payment value
Average time-to-payment of all invoices until
the cut-off-date9
Std. Dev
465 171
442 715
52.90
69.76
Variance
Skewness
Kurtosis
22224.16
5,57
40.46
149.07
While payment deadline is contractually set to 15 days, the average time-to-payment is 69
days, with a median of 28 days. Only 1% of the bills are paid in less than three days, 25%
before the 15th days and 99% are paid in 481 days and more. The Skewness and Kurtosis
parameters confirm that its distribution is right skewed with a leptokurtic form. To properly
assess the shape of this variable, we generated the histogram of this distribution (figure 1) and
its Kaplan-Meier analysis (figure 2).
.02
Kaplan-Meier survival estimate
1.00
.015
0.75
Density
.01
0.50
.005
0.25
0.00
0
0
500
1000
1500
0
500
1000
1500
analysis time
Time-to-payment
Figure 1 : distribution of bill time-to-payment
9
This date corresponds to the day of collection of information.
Figure 2: Kaplan-Meier analysis of bill
Time-to-payment
II.2.2.Descriptive statistics of the survey dataset
For robustness check and to deepen the empirical analysis, we have interviewed 172
subscribers in August 2008. Indeed, this survey is very useful because it allows collecting
more detailed data about households’ socio-economic characteristics. The households level
data derived from the survey are used to provide better parameters estimation. However, the
model parameters can be under or over-estimated when socio-economic characteristics are not
included in the model to deepen the empirical analysis. The main descriptive statistics of the
survey database are summarized in table 4.
Table 4: Descriptive statistics of the sample
Variable
Quantity
Invoice amount
Price : Block 1
Price : Block 2
Price : Block 3
Price : Block 4
Average price
Marginal price
Real cons/ flat-rate pricing
school (father)
HH size
Number of girls
Number of boys
Children less than 18years
Children more than 18 years
Number of cars
House size
Number of room
Number of Kitchens
Number of Bathroom
Number of Restroom
Second home
Number of hours supply
Other resources
Water quality
Service quality
Income
Pay more
Rainfall
Mean
32.04
633.84
4.71
14.94
25.27
29.87
29.95
22.48
0.89
6.92
6.63
2.13
2.47
3.06
3.57
0.85
148.34
5.27
1.18
1.22
1.48
0.31
5.02
0.61
0.19
0.09
28667.34
0.99
156.17
Std.dev
27.90
793.61
1.17
4.73
8.01
9.46
40.30
8.43
0.31
3.49
2.29
1.50
1.51
2.05
2.17
0.85
69.84
2.45
0.50
0.65
0.70
0.46
4.00
0.48
0.39
0.29
17519.36
0.70
122.93
Min
0
26.75
2.2
2.5
4.25
5
3.82
2.2
0
1
1
0
0
0
1
0
25
1
0
0
1
0
1
0
0
0
5000
0
0
Max
157
11507.26
6.3
20.48
34.65
41.95
333.75
40.57
1
18
16
7
8
11
16
4
540
22
4
4
4
1
24
1
1
1
100000
1
429
As we see in table 4, the results of the descriptive statistics calculated using data of the
household survey can be summarized, and then we can put forward the following first order
conclusions: The sample's average consumption is 32 m3 per quarter which is inferior to the
total population average consumption (the total population is 33 m3 per quarter). However, the
sample‘s average water price is 29.95 DA per cubic meter, while the average price of the total
population is 62 DA/m3. This difference is probably due to the difference between the two
periods, the quantities consumed and the increase of the invoice's fixed charges decided by
the ADE in 2003. Indeed, before 2003, the amount of the subscription was 25 DA and since
the reform of 2003, the subscription's amount has raised to 240 DA which must increase the
total bill amount and then the average water price.
If we look to the households’ characteristics, we see that the sample’s household average size
is 6.63. However, the house average size is 148 m2, with a minimum average size of 25 and a
maximum of 540 m2. Moreover, 31 % of the surveyed people declare having a second house
and 61 % have an alternative source of water.
Concerning the water quality, the survey has shown that 19% of surveyed households are
satisfied by water quality and only 9% are satisfied by the water quality services.
Table 5: Distribution of bills based on time-to-payment expressed in number of days
Sample
75 %
90 %
Percentiles
9
15
18
Number of Observations
25
Invoices settled before the deadline
Invoices' average time to payment
35
Average time to service cut-off after invoice issuance
Std. Dev
111
467
Variance
95 %
99 %
966
2247
1%
5%
10 %
25 %
50 %
Skewness
Kurtosis
7740
7057
176.59
223.38
411.21
169099.
1
4.34
25.47
Table 5 summarizes the distribution of bills according to their time-to-payment. This analysis
shows that the survey results are quite different from those obtained from data describing the
total population of Bejaia City. In particular, the total population's time-to-payment value is
53 days while the average time-to-payment of the sample is 176 days. This difference could
be explained by the difference in the collection period for the two dataset. Indeed, the analysis
of the total population of Bejaia City is spread over 17 quarters, while the sample is observed
over 45 quarters. For the same reason we observe that the mean time-to-service cut-off are
strongly different as well with 4068 days for our survey dataset and only 1511 days for the
total population (between 31 March 2004 and 20 May 2008). Finally, the shape of the
distribution of the time-to-payment variable is leptokurtic and is spread right, as for the total
population distribution. To assess the variable distribution, we generated its histogram (figure
3) and a Kaplan-Meier survival estimate graphic (figure 4).
.008
Figure 3
1.00
Kaplan-Meier survival estimate
Figure 4
.006
0.75
Density
.004
0.50
.002
0.25
0.00
0
0
1000
2000
3000
Time-to-payment
4000
0
1000
2000
Analysis time
3000
4000
As we see in figures 3 and 4 presented above, the distribution of our duration variable doesn't
follow a normal distribution. The graphics show a high concentration of paid invoices
between 0 and 100 days, then the variable decays just after this period.
III. Empirical methodology and results
III.1. Survival analysis of invoices of the big database (27363 subscribers) : KAPLAN – MEIER
approach
To empirically analyze the bill time-to-payment determinants, the adequate approach to be
used is the Kaplan-Meier approach. The aim of this approach is to observe the shape of the
variable when segregating data according to the billing type (real consumption pricing or flat
rate pricing), the dwelling type (house or apartment), the subscriber localization (Bejaia
Medina, Ihadadene or Quartier Seghir), and the household water consumption block.
The results of this empirical analysis are presented in the next part of this paper and are
followed by the several statistical analyses to determine whether or not differences are
significant.
In figure 5 and 6, the Kaplan-Meier curve of the time-to-payment variable of the total
population of BEJAIA CITY is presented according to the billing and dwelling type
respectively. The sharp decrease which characterize these curves show that the timeframe of
bills payment is superior to the legally defined period of fifteen days. In figure 6, the data are
grouped according to the dwelling type to see if there is a difference in the bill time-topayment of household living in apartment and those living in house. The figure shows that
households living in apartment pay their water bill quickly compared to those living in a
house.
1.00
Kaplan-Meier survival estimates
1.00
Figure 6
Figure 5
0.75
0.75
0.50
0.50
0.25
0.25
0.00
0.00
0
Kaplan-Meier survival estimates
500
1000
analysis time
Real = 0
1500
0
500
1000
1500
analysis time
Flat-rate = 1
Apartment = 0
House = 1
We turn now to the total population data segregation according to the subscriber’s
localization. Data are grouped by three main areas in Bejaia City. These areas are mainly the
old city (Bejaia Medina), the Ihaddadene district and the Quartier Seghir district. From figure
7, it is clear that subscribers living in Bejaia Medina pay their bills before those living in the
other two districts. However, beyond approximately 15 days, this does not hold true anymore
and subscribers from Ihaddadene district become more reactive.
In figure 8, subscribers are grouped by consumption block. It appears that customers whose
consumption does not exceed the first block pay their bills quicker which indicate that a
relationship does exist between the marginal water price and the time-to-payment.
1.00
Kaplan-Meier survival estimates
Kaplan-Meier survival estimates
1.00
Figure 7
Figure 8
0.75
0.75
0.50
0.50
0.25
0.25
0.00
0.00
0
500
1000
0
1500
500
analysis time
BEJ = 0/IHD = 0/QSG = 1
1000
1500
analysis time
Y1 = 0/Y2 = 0/Y3 = 0/Y4 = 1
Y1 = 0/Y2 = 1/Y3 = 0/Y4 = 0
BEJ = 0/IHD = 1/QSG = 0
BEJ = 1/IHD = 0/QSG = 0
Y1 = 0/Y2 = 0/Y3 = 1/Y4 = 0
Y1 = 1/Y2 = 0/Y3 = 0/Y4 = 0
However, later on the timeline, this trend reverses and this group is less prone to paybills.
This may be related to the standard of leaving of this group of subscribers that belong to the
so called social block (first block which is composed by low income households).
Nevertheless, despite the subsidies associated with this block, many households are likely still
find difficulties to pay their bills.
III.2. Survival analysis of invoices of the small sample survey (172 Subscribers):
KAPLAN – MEIER approach
To empirically test the robustness of the big data base, regrouping the whole Bejaia City
subscribers (27363 subscribers), analysis, we conduct the same survival analysis of invoices
based on the small sample survey of 172 subscribers.
1.00
Kaplan-Meier survival estimates
1.00
Figure 10
Figure 09
0.75
0.75
0.50
0.50
0.25
0.25
0.00
0.00
0
Kaplan-Meier survival estimates
1000
2000
analysis time
Real = 0
3000
Flat-rate = 1
4000
0
1000
2000
analysis time
Sec-res = 0
3000
4000
Sec-res = 1
The Kaplan-Meier analysis for data grouped by billing type (real consumption red curve/ flatrate pricing blue curve) shows that the curve of survival probability of the subscribers billed at
flat-rate pricing decreases faster than those billed at actual consumption pricing (Figure 9).
Analysis grouped on the criteria of owning a secondary residence (red curve) or not (blue
curve) shows that customers owing a secondary residence pays their invoice more promptly
(figure 10).
Obviously, customers that can afford a second house are more likely to pay their bill on time
or faster. That is why several authors use this variable as a proxy of income for estimation of
the water demand function.
1.00
Kaplan-Meier survival estimates
1.00
Figure 12
Figure 11
0.75
0.75
0.50
0.50
0.25
0.25
0.00
0.00
0
Kaplan-Meier survival estimates
1000
2000
Analysis time
Alternative= 0
3000
Alternative = 1
4000
0
1000
2000
analysis time
Quality-W= 0
3000
4000
Quality-W = 1
Figures 11 and 12 are Kaplan-Meier curves for data grouped on the criteria of existence of
alternative source of water supply (yes red curve/no blue curve) and perceived (good red
curve and bad blue curve) quality respectively. The subscribers exclusively connected on the
public network are the quickest to pay their bills, probably fearing water supply cut-off and
penalties ensuing payment delay and service reopening. Regarding the perception of water
quality, it seems that if the subscribers are dissatisfied by the water quality, they are less liable
to pay their bills and tend to postpone their payment. Therefore, it seems that some of the
delays could be explained by subscribers’ discontentment about water quality.
Finally, quality of service and quarterly billing doesn’t have an impact on time-to-payment
probability curves. This is demonstrated by the survival analysis of figures 13 and 14.
It's clear that the distribution of our duration variable doesn't follow a normal distribution. A
glance at the graphics results shows a high concentration of paid invoices between 0 and 100
days, then the variable decays very fast after this period.
Kaplan-Meier survival estimates
1.00
1.00
Figure 13
Kaplan-Meier survival estimates
Figure 14
0.75
0.75
0.50
0.50
0.25
0.25
0.00
0.00
0
0
1000
2000
analysis time
Quality-S = 0
3000
Quality-S= 1
4000
1000
2000
analysis time
M = 0; J = 0; S = 0; D = 1
M = 0; J = 1; S = 0; D = 0
3000
4000
M = 0; J = 0; S = 1; D = 0
M = 1; J = 0; S= 0; D = 0
III.3. Econometric model, empirical estimation and results interpretations
This section is devoted to the modeling and empirical estimation of water bill time-topayment. As we have collected a novel panel data base, the first estimation is based on a panel
of 27 363 subscribers observed during a period of 17 quarters. However, for robustness
check, the second dataset obtained from a survey includes 172 subscribers observed over a
period of 45 quarters.
As discussed above, to adequately manage the demand for water, the Algerian water authority
(ADE) applied a nonlinear tarification system. This nonlinearity in water tariff structure
makes some correlations between the variables used to estimate the water bill time-topayment model. To take care for these correlations, we have specified four different models.
In the first model, we use the water average price. Then in the second model is estimated
using the marginal price. However, the consumed quantity for each household and the invoice
amount are used to specify and estimate the third and the fourth model.
As mentioned before, the “time-to-payment” variable doesn’t follow a normal distribution.
Thus traditional estimators are not appropriate in this type of distribution. This is clearly
visible at a glance on the Kaplan -Meier analysis presented in the previous sections. The
curves shape follows a Weibull distribution and this requires us to estimate a duration model.
To identify the factors affecting water bill duration, we used the basic equations of survival
analysis:
F (T )   f ( x)dx
t
0
With F(T) is the cumulative distribution function.T is the elapsed time between the billing date
and the payment date and f(x) is the probability density function indicating that the event has been
realized at the instant t).
T
S (t )  exp   h( x)dx  exp H (T )
 0

S(t) is the probability that a bill survives beyond time t10.
h(t )  F (T ) / S (T )
h(T) is the relationship between F(T) et S(T) designating the probability that the invoice at
time T experiences the result in the next time.
T
H (T )   h( x)dx
0
H(T) is a cumulative hazard function of probability that the invoice at time T experiences the
result in the next time.
Therefore, in table 6, the different specified duration models of the bill time-to-payment are
estimated using the big panel dataset (27363 subscribers over seventeen quarter). In table 7,
the duration models specified and estimated using the survey dataset (172 subscribers over 45
quarters) are presented.
The specification used to estimate the determinants of the water bill time-to-payment variable
for all subscribers of Bejaia City takes the following form were variables are described in
table 8 in the appendix:
Durationit   0  1Variableit   2 plvit   3 Supplyit   4 Diamit   5Virtuel _ incomeit 
 6 Marchit   7 juneit   8 Decemberit   9 Invoicing_ types it  10 BJAit  11IHDit  12 Houseit   it
With:
1. Variableit is the average price paid by the subscriber "i" at time "t" in Model 1;
2. Variableit is the marginal price paid by the subscriber "i" at time "t" in Model 2;
3. Variableitis the consumed quantity by the individual "i" at time "t" in Model 3;
4. Variableit is the amount of the bill paid by the subscriber "i" at time "t" in Model 4.
The specification used to estimate the determinants of the time-to-payment variable for the
sample survey dataset (172 subscribers) takes the following form:
10

S (t )   f ( x)dx  1  F (T )
T
Durationit   0  1Variableit   2 Surfaceit   3 pluvit   4 Incomeit   5 hoursit
  6 Household _ sizeit   7 Study   8 Marchit   9 juneit  10decemberit 
11Invoicing _ Typesit  12qualityit  13Sec _ resti  14other _ resit   it
Like the case of the specified duration model using dataset of all Bejaia City subscribers
(27363):
1.
2.
3.
4.
Variableit
Variableit
Variableit
Variableit
is the average price paid by the subscriber "i" at time "t" in
is the marginal price paid by the subscriber "i" at time "t" in
is the consumed quantity by the individual "i" at time "t" in
is the amount of the bill paid by the subscriber "i" at time "t" in
Model
Model
Model
Model
1;
2;
3;
4.
After the specification of econometric models, we turn now to the empirical estimation and
result interpretation to explain in depth the main factors that affect the water invoice time-topayment in Algeria. The models estimations are presented in table 6 and 7 with their standard
errors to test statistical significance.
Table 6: Weibull models Results for all subscribers ( 27363 subscriber)
Weibull
Weibull
Weibull
Variables
_t
_t
_t
Invoice amount
Quantity
0.00140***
(6.26e-05)
Marginal price
Average price
September
March
June
December
Supply
Seghir city
Bejaia city
IHD
House
Weibull
_t
3.39e-05***
(1.42e-06)
0.00231***
(0.000209)
0.000992***
(4.54e-05)
Reference
-0.0278***
(0.00557)
-0.0261***
(0.00546)
-0.0930***
(0.00609)
0.126***
(0.00648)
Reference
Reference
-0.0198***
(0.00559)
-0.0198***
(0.00547)
-0.0889***
(0.00610)
0.125***
(0.00647)
Reference
Reference
-0.0170***
(0.00558)
-0.0173***
(0.00546)
-0.0878***
(0.00610)
0.123***
(0.00646)
Reference
Reference
-0.0179***
(0.00558)
-0.0182***
(0.00546)
-0.0882***
(0.00610)
0.124***
(0.00647)
Reference
-0.339***
(0.00509)
-0.339***
(0.00533)
-0.188***
-0.350***
(0.00512)
-0.350***
(0.00534)
-0.195***
-0.357***
(0.00512)
-0.354***
(0.00534)
-0.198***
-0.356***
(0.00511)
-0.352***
(0.00533)
-0.198***
flat-rate pricing
Virtuel income
Penalty
ln_p
P
Constant
Observations
(0.00457)
-0.659***
(0.0139)
3.95e-09
(1.68e-08)
0.0114***
(9.05e-05)
-0.226***
(0.00103)
0.7978666
0.0008211
4.275***
(0.0331)
(0.00459)
-0.944***
(0.00735)
9.58e-09
(1.68e-08)
0.0115***
(9.05e-05)
-0.226***
(0.00103)
0.7975201
.0008209
4.575***
(0.0299)
(0.00458)
-0.970***
(0.00735)
1.73e-08
(1.68e-08)
0.0116***
(9.04e-05)
-0.226***
(0.00103)
0.7979107
0.0008212
4.595***
(0.0299)
464,954
464,954
464,954
Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.
(0.00458)
-0.950***
(0.00711)
9.10e-09
(1.68e-08)
0.0115***
(9.04e-05)
-0.226***
(0.00103)
0.7978487
0.000821
4.585***
(0.0299)
464,954
For robustness check and to take care for a possible correlation and endogeneity between
household consumption variables, we estimated different models. As we see from table 6, the
estimation of the four models gives relatively consistent and robust results. However, for
model choice, the value of P = 0.79 confirms the relevance of Weibull model that is used to
empirically analyze the water invoice time-to-payment in Algeria.
The average price elasticity is 0.03 (see marginal effect table in appendix 01). Indeed, a 10%
increase on water price increases the bill time-to-payment by 0.3%. Similar results are
observed for estimated models using marginal price, quantity consumed and the invoice
amount. All of these variables have a positive influence on bill time-to-payment. Therefore, a
10% increase in the marginal price leads to a 0.8% increase of the time-to-payment variable.
However, an increase of 10% of the water consumed quantity or of the total bill amount
causes respectively a 0.5% and a 0.01% increase of the time-to-payment variable. These
results confirm that the delays on bills payment are mainly due to financial difficulties. For
two users of same socio-economic characteristics (ceteris paribus), the one who pays a bill
higher on average than other would have a time-to- payment value higher of 0.3% on average.
However, the price and consumed water quantity are not the only variables explaining this
phenomenon. Rainfall has a positive effect on the time-to-payment, and it is visible through
the supply variable which has positive effect on the delay. Indeed, some supply restrictions
are imposed by the water authority (ADE) in summer. Subscribers are then obliged to stock
water to be used in case of supply restriction.
According to the seasonal dummy variables, it seems that subscribers have fewer difficulties
in paying their bills in winter than in summer. This is probably due to the seasonal effect and
climate variability in Algeria. Indeed, in summer, with average temperatures around 86 °F and
rainfall close to zero, the consumption increases and leads to an increase of the bills amount,
this leads to a longer duration.
Finally, the estimation results show that living in a house has a negative impact on time-topayment. It reduces the average time-to-payment of approximately 7 days. It is reasonable to
think that people who are able to afford a house are more susceptible to have a higher
standard of living. However, the empirical results show that subscribers living in the old city
(Bejaia Medina) and in Ihadadane area seem to pay their bills quicker than those living in the
neighborhood of low-income household as in Seghir's area. Living in these two districts
reduces the time-to-payment of apprximately 12 days on average. Finally, bills based on
actual consumption seem to be more difficult to recover than those based on a flat-rate
pricing.
The duration model estimated in table 6 draws a clear picture of the real situation of Algerian
subscribers of the public network of water services. Through a big dataset from the second
Algerian city ( The Bejaia city), the duration model shows that the structure of water tariff and
subscribers socioeconomics characteristics are the main determinants of delay in payment of
water bill by households. This results call for the implementation of more equitable nonlinear
water tariff that considers the social conditions of some subscribers.
Table 7: Weibull models Results for sample survey ( 172 subscribers)
Variables
Quantity
Weibull
_t
0.00692***
(0.000669)
Invoice amount
Weibull
_t
Weibull
_t
0.000248***
(2.50e-05)
Average price
0.00611***
(0.000575)
Marginal price
Water Quality
Penalty
Weibull
_t
0.162***
(0.0578)
0.0217***
(0.00119)
0.157***
(0.0580)
0.0215***
(0.00119)
0.259***
(0.0576)
0.0222***
(0.00119)
0.00667***
(0.000606)
0.252***
(0.0575)
0.0220***
(0.00119)
Flat-rate pricing
Study level
Household size
Size house
Second home
Number of hours
Other Resources
Income (base 1000)
Constant
Ln_P
Observations
-0.999***
(0.0637)
-0.000143
(0.00607)
0.0908***
(0.00853)
0.00188***
(0.000282)
-0.713***
(0.0428)
-0.0164***
(0.00471)
0.140***
(0.0449)
-0.00903***
(0.00115)
-0.920***
(0.0619)
-0.00117
(0.00607)
0.0961***
(0.00847)
0.00186***
(0.000282)
-0.715***
(0.0429)
-0.0161***
(0.00471)
0.132***
(0.0450)
-0.00968***
(0.00115)
-0.443***
(0.0667)
-0.000942
(0.00608)
0.123***
(0.00862)
0.00178***
(0.000284)
-0.770***
(0.0425)
-0.0162***
(0.00471)
0.115**
(0.0452)
-0.00887***
(0.00115)
-0.459***
(0.0656)
1.11e-05
(0.00609)
0.123***
(0.00861)
0.00169***
(0.000283)
-0.766***
(0.0425)
-0.0162***
(0.00471)
0.107**
(0.0452)
-0.00882***
(0.00115)
5.078***
(0.114)
-0.410***
(0.00839)
5.067***
(0.115)
-0.412***
(0.00839)
4.445***
(0.124)
-0.412***
(0.00840)
4.464***
(0.123)
-0.412***
(0.00839)
7,606
7,606
Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1
In table 7, we present the estimation results of the different duration models based on the
sample survey of 172 subscribers. The marginal effect which explain estimates parameters in
terms of elasticity are computed and presented in appendix.
The estimates parameters obtained from the sample of 172 subscribers are consistent and
confirm those of the total population. The average and marginal prices, the consumed water
quantity and the invoice amount have a positive impact on time-to-payment variable. Indeed,
a 10% increase in average price increases the time-to-payment by 4.8%. In other words, two
users having the same socio-economic characteristics, the one paying an average price 10%
higher would experience an 8 days increase in its time to payment. Empirical estimation of
the impact of the marginal price and the consumed water quantity demonstrates the same
effect. Increasing by 10 % any of these two variables would result in a 9 days increase of the
time-to-payment. A 10% increase of the house surface leads to a 1.4% increase in the time-topayment, corresponding to 2.5 days. This is probably a consequence of the volume consumed
proportionally to the house size (more bathrooms, more restrooms...).
When we look to the socioeconomics characteristics, we see that subscribers owning a second
house have a time-to-payment value reduced by 50 days compared to those owning only one.
This is in accordance with the idea that better-off are more prone to pay their bill on time as
they are not financially limited and that financial limitation is a major reason for long time-topayment. The existence of an alternative source of water supply increases the time-topaymentby 10 days. This result is surprising and goes against our expectations. Our initial
rational was that the access to an alternative source of water supply would contribute to
reduce the water quantity consumed and thereof bill amounts and the time-to-payment.More
work will be needed to clarify this contradiction but it is also possible that subscribers having
the option to use an alternative source of water supply do not feel constrained by the threat of
water supply cut-off and tend to delay their payment.
As expected, the household income has a negative impact on time-to-payment of water bill.
When income increases by 10%, time-to-payment is reduced of 7% to 7.4%, i.e. 13 days. The
daily durationof tap water availabilitynegatively affects the bill time-to-payment. This result
may be the consequence of dissatisfaction of the households about this policy, but it may also
be the result of consumption generated by the storage habits in Algeria.
If the water quality is considered good by the subscriber, these parameters increase payment
period of approximately 13 days (estimated by the invoice amount and the quantity
consumed). Household size appears, also, as a very crucial element of invoice payment. This
result is probably due to the financial difficulties of many families (over costs and over
spending). This situation increase the amount consumed and affect the households' financial
conditions. If the subscriber is penalized for failure to pay, this fee will lengthen the timepayment of the invoice. Finally, flat-rate pricing, as in the case of the total population, reduces
the invoice duration payment about 44 days (in the models estimated with average price and
marginal price). In summary, it seems that some invoices paid late are due to socio-economic
characteristics of subscribers. However, another part appears to reflect the customers’
dissatisfaction about the management quality.
Conclusion and policy recommendations:
The main originality of this paper is to conduct an original duration analysis of the water bill
time-to-payment for the Algerian case. Using a big dataset from the Algerian water authority
(ADE) describing 27363 subscribers to the water services network in Bejaia city, the results
are crucial and very important for the Algerian decision makers in the water sector.
The empirical analysis of the duration of water invoices time-to-payment reveals that the
water tariff variables partly explain the delays level recorded in the province of Bejaia.
Indeed, a 10% increase in the average price increase time resolution of 4.8 %, which
corresponds to 8 days. The same observation was also highlighted through the analysis of
models with the marginal price. A 10% increase in price would result in a marginal increase
in the duration of 9 days. However, the water tariff variables are not the only ones that explain
this phenomenon. Rainfall had a positive impact over time. This effect is probably due to the
increase in volume delivered during rainy seasons, increasing the volumes consumed and
therefore the amounts charged. This result is confirmed by the positive relationship between
the quantity supplied and the duration of payment (estimated using the total population data).
The variables related to the households living conditions (income, housing type, location of
the neighborhood, owning second house) negatively influence the duration payment. This
result brought to light a real difficulty in paying bills from one part of the population for
financial reasons.
The flat rate billing seems to negatively influence the billing period for paying invoices. This
was highlighted in all estimated models. This result is probably related to tariffs in this type of
billing, which are often less than the amounts paid in the case of a billing based on actual
consumption of subscribers. Household size also explains the saved and the interpretation is
probably related to the consumed water quantity by families, which would increase the
amount of their bill.
In conclusion, the problem of bill collection, in the case of the province of Bejaia, partly due
to socio -economic constraints, but it is also the result of local management practices that
create dissatisfaction among subscribers. This finding was confirmed by the commercial
director of the ADE. According to him, most of the delays and uncovered bills are due to
discontent subscribers regarding the service provided by the ADE (water shortages, water
quality ...). In this way, in order to find a solution to this situation, the company must make
efforts to improve the quality of offered service.
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Appendix 01: marginal effect-elasticity ( the big dataset 27363 subscribers)
d(y)/d(x)
d(y)/d(x)
d(y)/d(x)
Variables
_t
_t
_t
Invoice amount
0.0012***
(0.00005)
Consumed quantity
0.050***
(0.0022)
Marginal price
0.084***
(0.007)
Average price
March*
June*
December*
supply
Seghir city
Bejaia city*
IHD city*
House *
Flat rate pricing*
Virtuel Income
Penality
d(y)/d(x)
_t
-0.650***
(0.201)
-0.659***
(0.196)
-3.136***
(0.212)
4.505***
(0.235)
Réf
-0.616***
(0.201)
-0.628***
(0.197)
-3.123***
(0.212)
4.486***
(0.235)
Réf
-0.719***
(0.201)
-0.717***
(0.197)
-3.161***
(0.212)
4.544***
(0.236)
Réf
0.036***
(0.001)
-1.007***
(0.200)
-0.944***
(0.196)
-3.305***
(0.211)
4.603***
(0.236)
Réf
-12.336***
(0.171)
-12.395***
(0.185)
-6.919***
(0.155)
-53.147***
(0.598)
3.31e-07
(0.00000)
0.419***
(0.0033)
-12.361***
(0.172)
-12.451***
(0.185)
-6.930***
(0.155)
-54.836***
(0.628)
6.29e-07
(0.000)
0.421***
(0.0033)
-12.154***
(0.172)
-12.332***
(0.185)
-6.829***
(0.156)
-52.720***
(0.614)
3.49e-07
(0.00000)
0.418***
(0.003)
-11.783***
(0.171)
-11.945***
(0.185)
-6.614***
(0.155)
-32.079***
(0.886)
1.44e-07
(0.000)
0.416***
(0.003)
(*) dy/dx is for discrete change of dummy variable from 0 to 1
Marginal effects after streg: y = predicted median _t (predict) = 36.40
Appendix 02: marginal effect-elasticity (sample survey 172 subscribers)
Variables
Consumed quantity
Invoice amount
d(y)/d(x)
0.54***
(0.054)
Average price
d(y)/d(x)
0.019***
(0.002)
Marginal price
Water quality
Penality
Flate rate pricing
Education level
Household size
Surface
Second house
Number of hours
supply
Alternative resource
income (base 1000)
y = predicted median
_t (predict)
d(y)/d(x)
0.487***
(0.047)
d(y)/d(x)
13.50***
(5.079)
1.72***
(0.099)
-121.97***
(11.743)
-0.011
(0.480)
7.195***
(0.691)
0.148***
(0.022)
-50.75***
(2.988)
-1.298***
13.07***
(5.08)
1.70***
(0.100)
-108.45***
(10.69)
-0.09
(0.482)
7.630***
(0.689)
0.14***
(0.022)
-50.91***
(3.00)
-1.28***
22.43***
(5.43)
1.76***
(0.10)
-42.37***
(7.63)
-0.07
(0.48)
9.77***
(0.71)
0.14***
(0.022)
-54.78***
(2.99)
-1.29***
0.53***
(0.049)
0.21.77***
(5.40)
1.75***
(0.10)
-44.14***
(7.61)
0.0008
(0.485)
9.78***
(0.71)
0.13***
(0.02)
-54.48***
(2.99)
-1.29***
(0.373)
10.92***
(3.463)
-0.715***
(0.00115)
(0.37)
10.31***
(3.48)
-0.768***
(0.093)
(0.37)
9.02**
(3.51)
-0.70***
(0.09)
(0.37)
8.39**
(3.52)
-0.70***
(0.09)
79.755314
79.764487
79.375341
79.24665
(*) dy/dx is for discrete change of dummy variable from 0 to 1