This study attempts to examine the factors affecting the residential water demand level in the city of Kozani in Greece. Based on an 8-year (2005–12) detailed sample of residential water demand panel data, the values of the water price (WP) elasticity of residential demand are identified, and the influence of socio-economic and demographic factors and climate conditions on water-use levels and trends are analyzed. The system's response in terms of system input volume is examined (through the simulation model developed for the network and a pressure management (PM) application) for different scenarios of increased and decreased WP levels. Various scenarios for the real losses were examined, starting from their current level (current annual real losses), down to their economic level (economic annual real losses) after implementing PM measures. The overall objective is to determine and record the overall reaction of consumers to the changing WPs as a result of the full water cost principle implemented.

## INTRODUCTION

Within an environment of constant economic and political upheaval, one of the needs remaining intact is the uninterrupted access in adequate quantity of good quality drinking water at a socially fair price. On account of increasing urban expansion and the environmental degradation of water resources, water utilities trying to satisfy water needs have to take actions that are not only more expensive but also technically more difficult. To solve the two-dimensional problem of supplying (at least) the minimum required volume (for essential needs) of water at affordable and socially fair prices, the response of consumers to water price (WP) variations has to be defined first. These variations do not result only from the pricing policy a water utility implements, but also from external factors such as the adoption of the ‘full water cost principle’ as introduced by WFD 2000/60/EC. It may be decided to delay infrastructure expansion projects when the water-use reduction caused by increased WP levels is considered. A water utility needs to know how the consumers respond to varying WP levels in order to effectively plan its strategy toward efficient water use. Decision-makers during recent decades have been oscillating on how to manage water demand through water pricing. Economists have tried to calculate the consequences of different levels of tariffs by estimating demand functions, focusing on the calculation of price-elasticity (Arbués *et al.* 2003). The basic issues that have already been addressed are the functional form of the demand function, WP determination (Arbués *et al.* 2003; Nauges & Whittington 2010; Rinaudo *et al.* 2012; Yoo *et al.* 2014) and the effect of municipal regulations (Mansur & Olmstead 2012).

In the present study, a unique micro data set collected in Kozani city (Greece) was utilized. The sample contains 305 questionnaires related to water bills, for a period of 8-years (2005–12), collected through a respective household survey. Time unbalanced panel data exist, as residential water consumption is recorded for periods that vary across the study area. The outcome of the analysis will contribute to the evaluation of past and current policies, management practices, recommended indications for plans and programs. More specifically, after the full water costing and the implementation of the consequent full water pricing, calculation of the forecast (future) residential and total network consumption will be enabled. From a methodological point of view, this model provides alternatives to instrumental variable (IV) models for the estimation of panel data characterized by the presence of time-invariant variables and variables which vary rarely with time. A quadratic functional form with three different regression approaches, ordinary least squares (OLS), least squares dummy variables (LSDV), and IV estimators were tested, with interesting results. Price elasticity of residential water demand reflects the extent to which changes in the WP affect water consumption. It is unitless and according to theory may range from 0 (completely inelastic demand) to infinity (completely elastic demand) (Espey *et al.* 1997). The marginal price (MP) elasticity of demand is approximately −1.33, while the average price (AP) elasticity of demand is −1.59. The resulting AP elasticity of demand from the IV approach is strongly rejected for being very high, while the MP elasticity derived from the IV approach complies with the OLS approach.

An attempt is also made in Kozani's case to properly reflect the changes of the WP in relation to the system input volume (SIV). Since at the existing current annual real losses (CARL) levels the revenue water is a small part of the SIV, a pressure management (PM) virtual project (at the economic annual real losses (EARL) level) was simulated through the already developed hydraulic model of Kozani's network. The reduction of the SIV was calculated through successive changes of the WP. Various scenarios were investigated regarding the depreciation time (5, 10, 15 years), the short-run/long-run approach of the marginal cost (MC) and the variability of MC in relation to the WP change. In cases where the MC remained constant, the decreased WP led to even bigger SIV reductions (at the EARL levels). In contrast, when the MC followed the WP changes, the bigger the WP reduction was, the less was the SIV reduction that resulted (after implementing the PM project).

## A SHORT REVIEW OF WATER DEMAND ESTIMATION

### Variables

The most important issue for the choice of the price variable is whether consumers respond to change in the water's MP or AP. In the early water demand forecasting models (early 1970s), the WP variable was expressed only by the MP variable. One of the first to argue that this is incomplete was Taylor (1975). He said that the MP does not express fully the WP variable as there is an income effect when water consumption moves to another consumption block. Nordin (1976) argued that the WP variable value should be expressed as the sum of MP and the difference D, which expresses the income impact. The difference variable is equal to the difference between the current water bill and the expense in the case that the water volume of all consumption was charged at the MP. Various studies could not confirm Nordin's prediction that the coefficient of this additional variable should be equal in magnitude and opposite in sign to the income effect coefficient (Arbués *et al.* 2003). There are several reasons for that, such as the fact that usually consumers are poorly informed about the block pricing system (Nieswiadomy & Molina 1989), or that estimates are biased (Schefter & David 1985). Many studies (Billings & Agthe 1980; Griffin & Martin 1981) emphasize that the use of MPs instead of APs will result in better statistical estimates only if consumers are well informed about the pricing system.

Although a very important explanatory variable is consumer income, its estimation depends on the nature of the data available (micro or aggregate data). As Arbués *et al.* (2003) reported, the explanatory variables of the climatic effects can be introduced in various forms. Some studies used precipitation during the growing season (Foster & Beattie 1981), evapotranspiration minus rainfall (Hewitt & Hanemann 1995) and a function of temperature, number of rainy and warm days (Hoffmann *et al.* 2006), and wind and minutes of sunshine (Al-Quanibet & Johnston 1985). Billings (1987) used average monthly temperatures, summer rain, and the degrees by which mean temperature passed 58 ^{o}F. Other explanatory variables commonly used are the size of the household (Arbués *et al.* 2010), number of family members, population age (Schleich & Hillenbrand 2009), number of children etc. Household size should positively affect water use if the dependent variable is water use per household. Size, age and the owned/rented dwellings' proportions are usually used as variables too. Other housing features, such as the number of bathrooms/WCs and the stock of appliances may be relevant. Indoor usage and outdoor usage compose the residential water demand. Outdoor use mostly exhibits higher price sensitivity than the indoor one (Renwick & Green 2000).

### Data set

Aggregate data were initially used to estimate the elasticity of water demand, despite the fact that the final results concerned the ‘typical household’ water use. This took hold mainly due to lack of data. From a theoretical viewpoint, it is preferable to use microdata (Saleth & Dinar 2000). These are specific household usage data and other qualitative characteristics of their water consumption profile, and will allow an accounting for inter-household differences in price levels (Hewitt & Hanemann 1995). The studies which used microdata are relatively few because of the large volume of data required and the difficulty of determining ‘personal income’. The best option is a combination of cross-section and time series data in a panel data approach, which help in the solution of multicollinearity problems. Finally, many theoretical dynamic models (Arellano & Honoré 2001) have been proposed that combine panel data with a dynamic approach, resulting in the determination of the delay effect between change in pricing and consumer response.

### Functional form

The linear functional form, although it is often preferred because of its convenience, raises concern about the constant change in water demand at every price level. Another negative aspect of this form is that there is a price of water which will result in zero demand, which contrasts with the perception of water as an essential good. The double-log functional form is also often chosen because it provides direct estimates of price and income elasticities (Dandy *et al.* 1997) and results in a constant-elasticity demand for every price level. Another alternative could be the log–linear form. The Stone–Geary form (Gaudin *et al.* 2001; Dharmaratna & Harris 2013) leads to results where there will always be a volume of demand for water even at very high prices.

### Simultaneity

In water distribution networks which have a block rate system, a simultaneity problem for both MP and AP usually appears. So, some IV techniques, such as the two-stage least squares (2SLS) and three-stage least squares (3SLS) are needed (Ruijs *et al.* 2008). Opinions differ as there have been cases where the OLS techniques gave similar water demand elasticities as the IV techniques (Saleth & Dinar 2000), and the OLS method has been preferred for its simplicity, while in other studies (Nieswiadomy & Molina 1988) OLS results have been proved biased due to simultaneity. For simultaneity detection in WP variables a Hausman (1978) test is needed and has been addressed in three different ways by Fair (1970), McFadden *et al.* (1977) and Taylor *et al.* (1981).

## HOUSEHOLD SURVEY (CITY OF KOZANI)

Kozani is a city in the northwest part of Greece. The municipal water utility (DEYAK), which serves 50,000 people, supplied (in 2011) almost 7,000,000 m^{3} of freshwater to urban consumers (suburbs not included). The findings of a proportionate stratified random survey (Kanakoudis & Gonelas 2014a), based on the proposed formation of District Metered Areas, that took place in Kozani in 2013 are analyzed. The sample included 305 households representing 1% of Kozani's total household population. The questionnaire included 39 questions concerning household socio-economic characteristics (i.e. sex, age/occupation of head of family, fluctuation of family size, income), housing characteristics (i.e. detached house or flat, age, number of rooms, floor), water-use appliances (i.e. washing machine, dishwasher) and water-use habits (i.e. washing frequency, small-scale irrigation in private gardens). The survey referred to the 24 four-month water billing periods from 1 January 2005 until 31 December 2012. Corresponding daily weather indicators such as rainfall, temperature, wind, sunlight, cloudiness and relative humidity were taken from the Hellenic National Meteorological Service. DEYAK provided data on the structure and level of the water tariff applied, which includes seven water-use consumption blocks (0–20, 21–40, 61–80, 81–100, 101–120, 121–160, >160 m^{3}). The AP variable includes two parts, the fixed one and the one depending on the consumption level. The MP is equal to the cost of the next cubic metre in the current block of consumption.

The D variable refers to the difference between the consumer's actual water bill and the expenditures in the case that the entire consumption was charged based on the MP. The household income level was recorded as an ordered qualitative dummy variable and categorized in four groups, but was proved unreliable since the consumers' responses did not interpret the income's impact on consumption. Table 1 presents the set of available variables calculated for the 24 billing periods of the years 2005–12 for the 305 households and summary statistics for all variables. Some prices of household consumption were absent from the data recorded, so there are some gaps in the observations of price variables. In this particular sample, the average residential water consumption was 39.706 m^{3} per household per billing period, resulting in 110 L/day per capita, when the average respective value in the EU-15 countries ranges from 85 L in Lithuania to 265 L in Spain (EWA 2002). Table 2 presents the dummy variables used and the interpretation of the values which they can have.

Description of variables . | Units . | Obs . | Mean . | Min . | Max . |
---|---|---|---|---|---|

Water consumption per household per billing period | m^{3} | 6,869 | 39.706 | 1.000 | 281.000 |

AP of water including fixed charges | €/m^{3} | 6,869 | 1.267 | 0.104 | 18.578 |

MP of water | €/m^{3} | 6,869 | 1.372 | 0.747 | 18.578 |

Nordin's D | € per bill | 6,869 | 6.801 | 0.000 | 454.456 |

Cloud (average total nebulosity per billing period) | % | 7,320 | 0.494 | 0.300 | 0.670 |

Wind (average wind force per billing period) | knots | 7,320 | 2.592 | 0.527 | 5.381 |

T (average temperature per billing period) | ^{o}C | 7,320 | 13.864 | 5.527 | 24.037 |

Rain (average of the rainfall height per billing period) | mm | 7,320 | 4.987 | 2.667 | 11.058 |

RH (average relative humidity per billing period) | % | 7,320 | 64.254 | 43.416 | 76.473 |

EDU1 (primary education) – dummy variable | – | 7,320 | 0.136 | 0 | 1 |

EDU2 (secondary education) – dummy variable | – | 7,320 | 0.434 | 0 | 1 |

EDU3 (higher education) – dummy variable | – | 7,320 | 0.430 | 0 | 1 |

FAM (number of family members) | family members | 7,320 | 2.937 | 1 | 7 |

REV (household income) – dummy variable | – | 7,320 | 1.467 | 0 | 3 |

MAIS (detached house or apartment residence) – dummy variable | – | 7,320 | 0.795 | 0 | 1 |

RENT (owned or rented residence) – dummy variable | – | 7,320 | 0.838 | 0 | 1 |

FLO (floor of residence) | floor of residence | 7,320 | 1.679 | 0 | 5 |

M2 (size of residence) | m^{2} | 7,320 | 87.846 | 25.00 | 200.00 |

WC | number of baths | 7,320 | 1.192 | 1 | 3 |

AGE (age of building) – dummy variable | – | 7,320 | 1.321 | 0 | 3 |

OUT1 (water use for garden, car and sidewalk washing) – dummy variable | – | 7,320 | 0.199 | 0 | 1 |

WASHMA (frequency of washing machine use) – dummy variable | – | 7,320 | 2.536 | 1 | 5 |

Description of variables . | Units . | Obs . | Mean . | Min . | Max . |
---|---|---|---|---|---|

Water consumption per household per billing period | m^{3} | 6,869 | 39.706 | 1.000 | 281.000 |

AP of water including fixed charges | €/m^{3} | 6,869 | 1.267 | 0.104 | 18.578 |

MP of water | €/m^{3} | 6,869 | 1.372 | 0.747 | 18.578 |

Nordin's D | € per bill | 6,869 | 6.801 | 0.000 | 454.456 |

Cloud (average total nebulosity per billing period) | % | 7,320 | 0.494 | 0.300 | 0.670 |

Wind (average wind force per billing period) | knots | 7,320 | 2.592 | 0.527 | 5.381 |

T (average temperature per billing period) | ^{o}C | 7,320 | 13.864 | 5.527 | 24.037 |

Rain (average of the rainfall height per billing period) | mm | 7,320 | 4.987 | 2.667 | 11.058 |

RH (average relative humidity per billing period) | % | 7,320 | 64.254 | 43.416 | 76.473 |

EDU1 (primary education) – dummy variable | – | 7,320 | 0.136 | 0 | 1 |

EDU2 (secondary education) – dummy variable | – | 7,320 | 0.434 | 0 | 1 |

EDU3 (higher education) – dummy variable | – | 7,320 | 0.430 | 0 | 1 |

FAM (number of family members) | family members | 7,320 | 2.937 | 1 | 7 |

REV (household income) – dummy variable | – | 7,320 | 1.467 | 0 | 3 |

MAIS (detached house or apartment residence) – dummy variable | – | 7,320 | 0.795 | 0 | 1 |

RENT (owned or rented residence) – dummy variable | – | 7,320 | 0.838 | 0 | 1 |

FLO (floor of residence) | floor of residence | 7,320 | 1.679 | 0 | 5 |

M2 (size of residence) | m^{2} | 7,320 | 87.846 | 25.00 | 200.00 |

WC | number of baths | 7,320 | 1.192 | 1 | 3 |

AGE (age of building) – dummy variable | – | 7,320 | 1.321 | 0 | 3 |

OUT1 (water use for garden, car and sidewalk washing) – dummy variable | – | 7,320 | 0.199 | 0 | 1 |

WASHMA (frequency of washing machine use) – dummy variable | – | 7,320 | 2.536 | 1 | 5 |

Dummy variables . | Description of values . | ||||
---|---|---|---|---|---|

EDU1 | primary education: 1 | higher than primary education: 0 | |||

EDU2 | secondary education: 1 | other than secondary education: 0 | |||

EDU3 | tertiary education: 1 | lower than tertiary education: 0 | |||

REV (household income) | [€0–€6,000]: 0 | [€6,000–€12,000]: 1 | [€12,000–€30,000]: 2 | [€30,000–]: 3 | |

MAIS (detached house or apartment residence) | detached house: 0 | apartment residence: 1 | |||

RENT (owned or rented residence) | rented residence: 0 | owned residence: 1 | |||

AGE (age of building) | [0–10 years]: 0 | [10–25 years]: 1 | [25–40 years]: 2 | [>40 years]: 3 | |

OUT1 (water use for garden, car and sidewalk washing) | Outdoor water use only for washing verandas and watering plants in flowerpots: 0 | Additional outdoor water use for garden, car and sidewalk washing: 1 | |||

WASHMA (frequency of washing machine's use) | No use: 1 | 1–2 times per week: 2 | 3–4 times per week: 3 | More than 4 times per week: 4 | Every day: 5 |

Dummy variables . | Description of values . | ||||
---|---|---|---|---|---|

EDU1 | primary education: 1 | higher than primary education: 0 | |||

EDU2 | secondary education: 1 | other than secondary education: 0 | |||

EDU3 | tertiary education: 1 | lower than tertiary education: 0 | |||

REV (household income) | [€0–€6,000]: 0 | [€6,000–€12,000]: 1 | [€12,000–€30,000]: 2 | [€30,000–]: 3 | |

MAIS (detached house or apartment residence) | detached house: 0 | apartment residence: 1 | |||

RENT (owned or rented residence) | rented residence: 0 | owned residence: 1 | |||

AGE (age of building) | [0–10 years]: 0 | [10–25 years]: 1 | [25–40 years]: 2 | [>40 years]: 3 | |

OUT1 (water use for garden, car and sidewalk washing) | Outdoor water use only for washing verandas and watering plants in flowerpots: 0 | Additional outdoor water use for garden, car and sidewalk washing: 1 | |||

WASHMA (frequency of washing machine's use) | No use: 1 | 1–2 times per week: 2 | 3–4 times per week: 3 | More than 4 times per week: 4 | Every day: 5 |

## EMPIRICAL RESULTS

### Estimation methods

#### OLS and LSDV

*AP*and

*AP*are used instead of

_{sq}*MP, D*and

*MP*respectively in Equations (1) and (2) (Kanakoudis & Gonelas 2014b): where

_{sq}, D_{sq}*i*= 1–305 (number of household) and

*t*= 1–24 (number of billing period);

*Q*is the quantity of water volume demanded by household

_{it}*i*in billing period

*t*;

*D*denotes the difference variable measured for each household for each billing period;

_{it}*Dsq*refers to

_{it}*D*raised to the power of 2;

_{it}*MP*refers to the MP that household

_{it}*i*has to pay in billing period

*t*;

*MPsq*refers to

_{it}*MP*raised to the power of 2;

_{it}*T*is the average temperature variable in billing period

_{t}*t*;

*Rain*is the average rainfall variable in billing period

_{t}*t*;

*Wind*is the average wind variable in billing period

_{t}*t*;

*EDU2*and

_{i}*EDU3*are the dummy variables for the consumers' educational level;

_{i}*FAM*refers to the family members variable in household

_{i}*i*;

*REV*is the dummy variable that implies the income interval of household

_{i}*i*;

*MAIS*is the dummy variable for whether household

_{i}*i*is an apartment or a detached dwelling;

*RENT*is the dummy variable for whether household

_{i}*i*is owned or rented;

*FLO*is the variable that indicates the floor on which household

_{i}*i*is located;

*M2*is the variable that denotes the size of household

_{i}*i*;

*AGE*is the dummy variable that implies the age interval of household

_{i}*i*;

*OUT1*is the dummy variable for whether household

_{i}*i*consumes water in outdoor activities;

*WASHMA*is the dummy variable to express how often household

_{i}*i*uses the washing machine; is the intercept; – are the slopes (coefficients or parameter estimates) of all independent variables; is the error term; and finally

*u*is a parameter estimate of the dummy variable

_{t}*g*.

_{t}#### Instrumental variables/2 SLS

*i*, indicates the instruments for both the MP and Nordin's D variable: where

*B*is the total bill of household

_{it}*i*for billing period

*t*, while

*MP*and

_{it}*Q*have been defined above.

_{it}*B*and

*Q*and implementing an OLS regression according to Equation (4) across consumption blocks, the MP and D estimates are provided: where

*i*represents observations for each household under pricing structure

*j*, estimated

*a*represents D for consumption block

_{j}*j*and the estimated represents the MP for the ‘average’ household subject to consumption block

*j*.

*et al.*(1986), some difficulties in estimating price instruments arise from this method, and a two-stage estimation technique is considered to be a solution to the problems in the previous model. During the first phase, the formation of an instrument for

*Q*takes place from the initial residential water demand Equation (1) and then in the second phase the estimated values of

*Q*are used in (4): where

*Qe*is the estimated value from the regression of (5).

_{ij}According to Deller *et al.* (1986) the two instrumental variable approaches which should be examined are (4) and (6), which is a variation of (4).

### Results

*et al.*1997; Dalhuisen 2002). As MP elasticity ranges from −1.334 to −1.468, the water demand is proven to be price elastic. This is because the only year in which the consumption decreased (2008) was the only year when an increase in WP occurred. In the other years, the WP variations were due to deflation. AP elasticity is between the previous range only for the OLS/LSDV approach (−1.494 to −1.590) and far exceeds the IV approach. The IV approach far exceeds the values mentioned in the literature (Espey

*et al.*1997). The final expressions for the residential water demand curves are presented below. All the factors of Equation (1) were considered with their average values apart from the demands, AP, MP and D. Equation (7) is associated with AP and Equation (8) with MP:

. | OLS . | LSDV . | IV 2SLS . | . | OLS . | LSDV . | IV 2SLS . |
---|---|---|---|---|---|---|---|

lnMP | −1.550028 | −1.788599 | −1.571724 | lnAP | −1.708821 | −1.737011 | −3.343056 |

lnMPsq | −0.301894 | −0.155343 | −0.313469 | lnAPsq | 0.2036391 | 0.214560 | −1.280658 |

lnD | −0.033094 | −0.074484 | −0.037724 | ||||

lnDsq | 0.113610 | 0.125779 | 0.115239 | ||||

lnT | 0.003376 | 0.061335 | 0.003315 | lnT | 0.016983 | 0.104031 | 0.004993 |

lnRain | −0.090333 | −0.063695 | –0.091843 | lnRain | −0.134690 | −0.073035 | −0.156167 |

lnWind | −0.060425 | −0.122863 | −0.061400 | lnWind | −0.092296 | −0.177424 | −0.211932 |

EDU2 | 0.001140 | 0.004135 | EDU2 | 0.010732 | 0.010856 | ||

EDU3 | 0.001083 | 0.004860 | EDU3 | 0.016526 | 0.018500 | ||

FAM | 0.001159 | 0.000857 | FAM | 0.016743 | 0.014868 | ||

REV | 0.000208 | −0.000960 | REV | −0.008779 | −0.010199 | ||

MAIS | 0.000998 | 0.000360 | MAIS | −0.001845 | −0.001947 | ||

RENT | −0.001592 | −0.000936 | RENT | −0.007236 | −0.007612 | ||

FLO | 0.000091 | 0.000313 | FLO | 0.003123 | 0.003039 | ||

M2 | 0.000013 | 0.0000457 | M2 | 0.000677 | 0.000660 | ||

AGE | 0.003774 | 0.001877 | AGE | 0.016080 | 0.013801 | ||

OUT1 | 0.002599 | 0.001781 | OUT1 | 0.059591 | 0.058207 | ||

WASHMA | 0.001695 | 0.000782 | WASHMA | 0.017238 | 0.016777 | ||

_cons | 3.516829 | 3.324744 | 3.536038 | _cons | 3.445083 | 3.133597 | 3.592419 |

F | 12,700.53 | 25,200.62 | F | 5,312.76 | 2,649.82 | ||

Wald x^{2} | 2.30 × 10^{5} | Wald x^{2} | 13,557.59 | ||||

Rsq | 0.9764 | 0.9923 | 0.9763 | Rsq | 0.9254 | 0.9328 | 0.64 |

Root MSE | 0.06224 | 0.03571 | 0.06226 | Root MSE | 0.21881 | 0.20741 | 0.24281 |

. | OLS . | LSDV . | IV 2SLS . | . | OLS . | LSDV . | IV 2SLS . |
---|---|---|---|---|---|---|---|

lnMP | −1.550028 | −1.788599 | −1.571724 | lnAP | −1.708821 | −1.737011 | −3.343056 |

lnMPsq | −0.301894 | −0.155343 | −0.313469 | lnAPsq | 0.2036391 | 0.214560 | −1.280658 |

lnD | −0.033094 | −0.074484 | −0.037724 | ||||

lnDsq | 0.113610 | 0.125779 | 0.115239 | ||||

lnT | 0.003376 | 0.061335 | 0.003315 | lnT | 0.016983 | 0.104031 | 0.004993 |

lnRain | −0.090333 | −0.063695 | –0.091843 | lnRain | −0.134690 | −0.073035 | −0.156167 |

lnWind | −0.060425 | −0.122863 | −0.061400 | lnWind | −0.092296 | −0.177424 | −0.211932 |

EDU2 | 0.001140 | 0.004135 | EDU2 | 0.010732 | 0.010856 | ||

EDU3 | 0.001083 | 0.004860 | EDU3 | 0.016526 | 0.018500 | ||

FAM | 0.001159 | 0.000857 | FAM | 0.016743 | 0.014868 | ||

REV | 0.000208 | −0.000960 | REV | −0.008779 | −0.010199 | ||

MAIS | 0.000998 | 0.000360 | MAIS | −0.001845 | −0.001947 | ||

RENT | −0.001592 | −0.000936 | RENT | −0.007236 | −0.007612 | ||

FLO | 0.000091 | 0.000313 | FLO | 0.003123 | 0.003039 | ||

M2 | 0.000013 | 0.0000457 | M2 | 0.000677 | 0.000660 | ||

AGE | 0.003774 | 0.001877 | AGE | 0.016080 | 0.013801 | ||

OUT1 | 0.002599 | 0.001781 | OUT1 | 0.059591 | 0.058207 | ||

WASHMA | 0.001695 | 0.000782 | WASHMA | 0.017238 | 0.016777 | ||

_cons | 3.516829 | 3.324744 | 3.536038 | _cons | 3.445083 | 3.133597 | 3.592419 |

F | 12,700.53 | 25,200.62 | F | 5,312.76 | 2,649.82 | ||

Wald x^{2} | 2.30 × 10^{5} | Wald x^{2} | 13,557.59 | ||||

Rsq | 0.9764 | 0.9923 | 0.9763 | Rsq | 0.9254 | 0.9328 | 0.64 |

Root MSE | 0.06224 | 0.03571 | 0.06226 | Root MSE | 0.21881 | 0.20741 | 0.24281 |

. | OLS . | LSDV . | IV . |
---|---|---|---|

MP | −1.334 | −1.468 | −1.352 |

AP | −1.590 | −1.494 | −3.866 |

. | OLS . | LSDV . | IV . |
---|---|---|---|

MP | −1.334 | −1.468 | −1.352 |

AP | −1.590 | −1.494 | −3.866 |

## TOTAL RESPONSE OF SIV IN WP REDUCTION

Kozani's water distribution system (WDS) was modeled in the previous step and constitutes an important tool in the research work of the authors. The hydraulic model consists of 211.86 km of pipes and water mains, 1,817 nodes and three pressure zones (Figure 1). The non-revenue water (NRW) represents the volume of water that is part of the SIV, which does not generate revenues. The response of each of the three main NRW components (unbilled authorized consumption, apparent losses and real losses) to changing WP had to be investigated separately. Unbilled authorized consumption includes firefighting, irrigation of municipal gardens etc. and is independent of any WP change. Apparent losses consist of unauthorized consumption (theft or illegal use) and water meter errors. The first part reacts with the same sign in any WP change (i.e. an increase in WP leads to a theft increase), while the second is independent of any WP change. Real losses represent water volumes lost due to all types of leaks, breaks and overflows of the mains, tanks and customers' connections and service pipes, up to the point of the water meter, and are independent of any WP change. Table 5 presents the SIV, the NRW (apparent losses and real losses) and the revenue water of Kozani's WDS (Kanakoudis *et al.* 2015).

Water volumes . | m^{3}
. |
---|---|

SIV (system input volume) | 6,921,387 |

Billed metered consumption | 2,555,471 |

Unbilled authorized consumption | 138,428 |

Apparent losses | 761,353 |

Real losses | 3,466,135 |

NRW | 4,365,916 |

Water volumes . | m^{3}
. |
---|---|

SIV (system input volume) | 6,921,387 |

Billed metered consumption | 2,555,471 |

Unbilled authorized consumption | 138,428 |

Apparent losses | 761,353 |

Real losses | 3,466,135 |

NRW | 4,365,916 |

A virtual PM project (applied through the hydraulic model) was used to calculate the EARL level for different scenarios, based on calculating the net present value of the PM project cost after 5, 10 and 15 years from the installation. There were two basic versions of the MC: the short-run (SRMC) and the long-run versions (LRMC). The SRMC includes the energy cost to pump 1 m^{3} of water and the increased maintenance cost (only materials) due to the increased rate of breaks caused by the increased operating pressure. The LRMC includes (apart from the previous costs), the personnel, the insurance and the vehicle operating costs, concerning the repair and the maintenance of the distribution mains and the connection pipes due to the increased break rates. Five scenarios with increased WP and five with reduced WP were analyzed to define the variations of the SIV, both for constant MCs (Figure 2(a)) and for MCs following the MC change (Figure 2(b)).

Figure 2(a) shows that when WP changes with constant MCs, SIV reduction ranges between ±5% only for the three LRMC plans. In the SRMC plans, the SIV reduction (when the PM was applied to the EARL levels) ranges between ±20%, apart from the scenario of the 5-year SRMC plan, where the reduction reaches 25% when WP changes by 50%. Figure 2(b) shows that for all scenarios the SIV reduction varies very little (∼10% for a 50% variation of WP) but with opposite sign, apart from the scenario of the 5-year SRMC plan, where the reduction reaches 25% for a 50% in WP change, but with the same sign.

Figure 3(a) and 3(b) show the SIV reduction changes in m^{3}/year for 10-year and 15-year plans for constant and for variant MC, respectively, in relation to the WP changes. Figure 3(a) where MC remains constant, shows that the more WP decreases, the greater the reduction in SIV becomes (when PM results in equal CARL and EARL values). This is justified by the fact that less WP leads to less revenue losses due to reduction in revenue water, hence a greater reduction of SIV for the same PM cost. The opposite trend is observed in Figure 3(b) (where MC is changed in the same manner as the WP). The more WP decreases, the less the reduction in SIV after PM becomes. This is because the economic benefit from the reduction in WP (which means less revenue losses due to reduction in revenue water) does not compensate the reduction of MC which leads to less economically recoverable volume of water for the same PM cost.

## CONCLUSIONS

The paper focuses on the estimation of the factors affecting the residential water demand in the city of Kozani in Greece. The coefficients of the price variables and the climatic effects variables turned out to be statistically significant, having also the signs expected. The two specifications of water demand (as a function of AP and MP plus Nordin's D) were estimated using both OLS/LSDV and IV approaches. The AP elasticity of demand resulting from the IV approach was rejected due to its very high value, while the other AP elasticity form and MP elasticities of water demand appeared to be elastic.

The change of SIV arising from the change in WP led to equivocal results. Whenever MC remained constant, reduced WP resulted in even more reduced SIV (when the PM resulted in equal CARL and EARL values). If water utilities which are applying PM at the EARL levels (with constant MC) attempt to change WP, then there will be unexpected results. A seasonal increase in the WP to prevent expansion of the system's supplying capacity will result in reduced water volumes saved due to PM and consequently in increased SIV. This means that delay of the system's expansion (regarding networks operating with PM at the EARL levels) will be achieved with a WP reduction. The opposite and expected trend was observed whenever MC was changed in the same manner as the WP was. A higher WP reduction led to a lesser SIV reduction through PM. Increasing WP (due to increased MC) will reduce further the SIV, because it will lead to a reduction in residential consumption (due to elasticity of demand). The increased MC leads to increased EARL and a further reduction of SIV. The only scenario in which this phenomenon is not observed is when considering the 5-year plan and the SRMC. This means that reducing or increasing WP causes a change in SIV (at EARL levels) depending on the MC's volatility. So for it to be obvious what is in the utility's interest, it should be known whether the change in WP comes as a consequence of a change of MC or is independent of it.

At current WP levels, consumption is inelastic and in order to regulate residential water demand, water pricing policies may only partially meet water saving expectations. However, the NRW reduction measures will lead to SIV reduction and to a greater impact of WP change in the water balance. Full water costing and full water pricing are interrelated and should always be included as links in the same chain in any changes in utilities' pricing policies.