A note on the estimation of the residential water demand in the Midi-Pyrénées region

Transcription

1 A note on the estimation of the residential water demand in the Midi-Pyrénées region Gaston Giordana, Céline Nauges and Arnaud Reynaud May 12, 2010 PRELIMINARY VERSION DO NOTE CITE NOR QUOTE Abstract We estimate a urban water demand at the river basin level. The framework is applied to the Midi-Pyrénées region (Southwest of France) using local community data. Preliminary results suggest that the urban water demand is inelastic but not perfectly. The consumer surplus generated by water consumption at the river basin is significant. We show that public policies (restrictions of water use, changes in water price) can have a substantial impact on consumer s surplus in the Midi-Pyrénées region. Keywords : River basin, Residential water demand, Renewable resource, Scarcity. JEL s codes : Q2, Q5, L9. This work is a part of the project EAUSAGE-quant funded by the program "Eaux et Territoires" and by the research program "Pour et Sur le Développement Regional". The authors gratefully acknowledge support from the French Ministry of Environment, from the CNRS-EDD and from the Midi-Pyrénées region. We are also grateful to the Adour-Garonne Water Agency for providing some data. TSE (LERNA-INRA), University of Toulouse 1, Manufacture des Tabacs - Bât.F, 21 allée de Brienne, F Toulouse, s: ggiordana@toulouse.inra.fr, cnauges@toulouse.inra.fr, areynaud@toulouse.inra.fr. Tel: (33) Fax: (33)

2 Contents 1 Introduction 3 2 Economic Modeling 4 3 Residential water demand in the Midi-Pyrénées region Database Residential water consumption Residential water price Other determinants of residential water consumption Socio-economic variables Weather variables Water quality variables Econometric model Demand function specification Econometric methods Estimation results Estimation diagnostic Welfare analysis Theory Welfare effect of price and quality variations Compensated Variation analysis Households Welfare Costs of Quantity Restrictions Welfare Effects of Local Rivers Quality variations Conclusion 29 A Source of data 32 A.1 Water related information A.1.1 IFEN-SCEES surveys A.1.2 The Agence de l Eau Adour-Garonne withdrawal database A.1.3 Summer and rest of the year water consumption A.2 Socio-economic information A.2.1 INSEE-DGI fiscal income databases A.2.2 French census A.2.3 INSEE tourist capacity databases A.3 Climate information B Descriptive statistics for residential water determinants 33 2

3 1 Introduction A number of countries have recently moved from an historical water policy based on supply management toward more economic tools aiming at managing water demands 1. This is in line with a global trend in favor of incentive-based instruments compared to the more classical command and control approach. A necessary step for implementing incentivebased instruments is to identify water demand functions. This is the objective of this paper with a particular emphasis on the river basin as the relevant scale for implementing demand-side water policy management. The first objective of this article is to provide an assessment of the determinants of residential water consumption, with a particular focus on pricing. If there is now a consensus on the importance of efficiency criteria in water pricing determination, it is surprising to note that only a few recent studies have evaluated the pricing of water utilities. 2 The second objective is to analyze the impact of some instruments (pricing, restrictions) used by public authorities for regulating residential water users. Impacts will be addressed both in terms of direct effects on water consumption and indirect effect on welfare. It is interesting to see that, while the economics literature is quite consistent in its criticisms of water pricing by water utilities, only few studies have estimated the magnitude of the gains to be expected from moving to efficient prices. Moreover, estimates of welfare gains vary from one study to another. Swallow and Marin (1988) show that moving toward efficient prices will result in an increase of welfare within 2% of the actual surplus. Garcia and Reynaud (2004) evaluate the pricing of French water utilities. They show that moving towards efficient prices does not result in important direct welfare effects (less than 1% on average). Last, Renzetti (1992) addresses the issue of moving toward a seasonally differentiated pricing. Renzetti (1992) finds that a move to seasonally differentiated pricing raises the aggregated surplus by approximately 4%. The methodology we follow has consisted in estimating urban water demand functions at the river basin level (Midi-Pyrénées region) using local community data. Preliminary results suggest that the urban water demand is inelastic but not perfectly. The consumer surplus generated by water consumption at the river basin is significant. We show that public policies (restrictions of water use, changes in water price) can have a substantial impact on consumer s surplus in the Midi-Pyrénées region. We develop our analysis according to the following structure. In the next section, we present the model of urban water demand at the river basin level. Section 3 provides a presentation of the data used and in section 4 we provide the empirical application of this model to the French case. In this empirical section, we specify the econometric model 1 In France, each water user must paid to the Basin Agency for every cubic meter some charges aiming at indicating the social cost of water. The Basin Agency Fees include abstraction and pollution charges. Abstraction charges vary by location of user and type of resource (ground water or surface water). Pollution charges are based on pollution emitted by users. Another example of recent move toward more economicoriented tool is Brazil. Hence, following the approval of the Federal Water Law of January 1997, the Brazilian water management system has been going through a wide-ranging reform. Among the several institutional and policy innovations promoted by the law, one of the most prominent is the introduction of quality- and quantity-related water charges into the regulatory framework. 2 See (Kim 1995) and Renzetti (1999) for water pricing analysis in North America. 3

4 allowing to estimate the water demand functions. Section 5 deals with the welfare impacts of some selected water regulation policies. We finally conclude by some policy implications of our work. 2 Economic Modeling We wish to model the water demand function of the representative urban water user in municipality i. Wedenotebyy i the daily water consumption of the representative urban user in region a. The water consumption usually depends upon the water price p i.household income (denoted by I i ) is also often viewed as a potential determinant of the water consumption. 3 Last, there are several other variables related to climate or housing characteristics of the representative household that may affect its water consumption. We denote by x a the vector made of all those potential determinants (characteristics of households, income, housings, climate, etc). The water demand function of the representative urban water user in region a may be written as: y i = f(p i,i i, x i ) (1) Those types of water demand functions have been estimated since the 1950s by economists. For most studies, the primary objective was to derive a measure of the price elasticity of water demand. Numerous estimates of price elasticities for residential water demand are now available and there is a large consensus among researchers that the residential water demand is inelastic, but not perfectly. Most of the published studies report short-term price elasticities varying from -0.3 to However long-term residential water demand appears to be more price sensitive, see Nauges and Thomas (2000) among others. Identifying the urban water demand function, allows to compute the daily consumer surplus (cs i ) resulting from water consumption in municipality i. cs i = + p i f(p i,i i, x i )dp i p i f(p i,i i, x i )=g(p i,i i, x i ) (2) Naturally, the annual consumer surplus can be obtained by multiplying the daily surplus by the number of the day of the year considered. Let n i denotes the number of households located in municipality a. The urban water demand function in municipality i is given by: and the resulting regional surplus by: Y i = n i f(p i,i i, x i ) (3) CS i = n i g(p i,i i, x i ) (4) 3 In their meta-analysis, Dalhuisen et al. (2003) report that the distribution of income elasticities has a mean of 0.46 and that water demand appears to be inelastic in terms of income changes. 4

5 3 Residential water demand in the Midi-Pyrénées region In this section, we present the database and the main characteristics of residential water consumption and pricing in the Midi-Pyrénées region. 3.1 Database The database is an unbalanced panel of three periods - years 1998, 2001 and and, respectively, 232, 231 and 283 local communities in Midi-Pyrénées region. The database contains annual information about the residential water consumption of water and prices applied in each local community, as well as the socio-economic and climatic characteristics for three years. The constitution of the dataset has been made from a variety of sources: surveys from the French Environmental Institute (IFEN)for data on prices and quantities of water 4, census data from the French Statistical Institute (INSEE) for the socio-economic characteristics and a dataset from the national meteorology service is used to build the weather variables, see Appendix A. In order to assess the representativity of the sample, Table 1 depicts the number of local communities and the population sampled. The database contains 15% of the Midi-Pyrénées total population and about 6% of the local communities. The number of local communities sampled in each department varies from 4.5% to 8.8% of the total, and the share of the sampled population with respect to the total population in each department varies from to While the department of Haute-Garonne (31) is over-represented in terms of number of local communities with respect to the other departments, it is under-represented in terms of population. On the contrary, the department of Ariège is under-represented in terms of number of local communities with respect to the other departments and overrepresented in terms of population. 3.2 Residential water consumption The variable under study is the annual average domestic consumption of water per household. We have analyzed the accuracy of the data on consumed volumes for domestic use and then we have drooped some observations and corrected some others. Table 2 depicts the annual average domestic consumption per household in the Midi- Pyrenées region and in France. As can be seen the weighted average results in higher average consumption per household in both regions. Then, in small cities household water consumption is lower. As a consequence we will concentrate our analysis on the weighted average. The average consumption per household in the MP region diminishes between 1998 and 2004 but has a pick in The water use in France diminishes steadily between 1998 and 2004 hence, the pick of the MP region water consumption in 2001 does not follow the 4 Actually, the survey contains information collected by different agencies Ifen-Scees-Agences de l Eau 5

6 Table 1: Sample representativity Population Department N of Municipalities Average Median Total Sample a INSEE Sample a Sample a Sample a INSEE b Ariège (9) Shares Aveyron (12) Shares Haute-Garonne (31) Share Gers (32) Share Lot (46) Share Hautes-Pyrénées (65) Share Tarn (81) Share Tarn et Garonne (82) Share Total Share of Total Population a Data from 1999 population survey which corresponds to data for years 1998 and 2001 in the sample b Population estimation at January the first 2006 national trend and remains unexplained 5. There is also a pick in the median consumption in 2001 hence, the presence of extreme values is not a valid explanation. Looking at the percentiles of households annual consumption distribution show that there are not extreme values that may explain the shift. Rather, the communes between the 5% and the 95% percentiles have increased the annual household consumption shifting the entire distribution to the right. A possible reason to the MP region consumption pick observed in 2001 is that our sample is not balanced. This means that consumption data of some cities is not available for all the three years of the series then, the empirical distribution of water use may be shifted to the right. Table 3 exposes the annual average of water consumption per household in MP and in France for a balanced panel. This means that each commune of the sample is observed in each year. As can be seen in table 3 the consumption pick in the MP region during 2001 persists. Table 3 allows to see that, excepting year 1998, the annual households water use in the MP region is higher than the French average. Consequently, we are more akin to think that the pick in the MP region water use in 2001 is not really a pick, rather the water use 5 To our knowledge there were not any particularly events that would explain this rise in water use 6

7 Table 2: Household annual consumption Midi-Pyrenées France Year N a Consumption Weighted N a Consumption Weighted Consumption Consumption mean median mean median mean median mean median (m 3 ) (m 3 ) (m 3 ) (m 3 ) (m 3 ) (m 3 ) (m 3 ) (m 3 ) Total a Number of local communities Table 3: Household annual consumption. Balanced panel Midi-Pyrenées France Year N a Consumption Weighted N a Consumption Weighted Consumption Consumption mean median mean median mean median mean median (m 3 ) (m 3 ) (m 3 ) (m 3 ) (m 3 ) (m 3 ) (m 3 ) (m 3 ) Total a Number of local communities in 1998 seems to be too low. Moreover, this is in line with our preliminary analysis done on our sample that revealed some inconsistencies in the 1998 survey. Finally, we compare the annual water consumption per household in rural versus urban areas. As can be seen in table 4 the consumption is higher in rural communities than in urban communities 6. More precisely, in each year the average water use in urban areas is lower than in rural areas by about 21%, 22% and 41%, respectively. These differences are probably explained by the outdoor water use (gardening, swimming-pools, etc.) which is more likely in rural zones. 3.3 Residential water price Let us define the annual water bill of the representative household as: B = FC+ MP C, where C is the water use (m 3 /year/household) and FC and MP are, respectively, the fixed charge and the marginal price. While FC is independent of the volume of water (euro/year units), MP represents the price for an additional m 3 of water. The MP is composed by the 6 We continue to observe that the 1998 s consumption is too low in both categories. 7

8 Table 4: Household annual consumption in urban and rural areas (a) Rural zones (b) Urban zones Year N a Consumption Weighted N a Consumption Weighted Consumption Consumption mean median mean median mean median mean median (m 3 ) (m 3 ) (m 3 ) (m 3 ) (m 3 ) (m 3 ) (m 3 ) (m 3 ) Total cost of production plus some taxes and contributions: "resource" and "pollution" taxes collected by the regional Water Agency, participation to the FNDAE and to the waterways maintenance and other local taxes. Different kind of price structures can be defined depending on the values FC and MP 7 : 1. The two part tariff (FC,MP > 0), is composed of a fixed charge, independent of the volume of water, and a unitary price or marginal price (per m 3 ). Then, the tariff increases with the water demanded. 2. Lump-sum tariff (FC > 0,MP =0), is just composed of a fixed charge. Then, the tariff is independent of the water demanded. 3. Proportional tariff (FC =0,MP > 0), is just composed of a unitary price. Then, the tariff increases with the volume of water. The two part tariff is predominant in the sample. It is applied by 88% of the municipalities in 1998 and more than 95% in the following years. There are 10 municipalities that apply a lump-sum price and 20, only in 1998, that have implemented a proportional tariff. Given that the two-part tariff is predominant, we perform comparisons of the tariff levels on the basis of the average price (or mean bill) which is defined as B/C = FC/C+MP. We assume that C can be either the observed annual consumption per household or, alternatively, a 120m 3 annual consumption per household. In the former case, the average price, denoted AP s, indicates the bill per m 3 of water used in the year. In the later, the average price is denoted AP 120 and corresponds to the bill per m 3 for a 120m 3 /year consumption. The AP 120 allows us to compare prices per m 3 between local communities on 7 We assumed that FC and MP are fixed and independent of the volume of water 8

9 an homogeneous basis avoiding differences in the average prices dues to differences in the annual consumptions. Table 5: Water prices and price s components. Evolution between in the pooled sample. Price s components Year N AP 120 AP s MP FC euro/m 3 euro/m 3 euro/m 3 euro/year/120m 3 Not weighted averages (% variation) (% variation) (3.52) (1.07) (7.21) (2.77) (% variation) (12.62) (15.87) (21.01) (2.40) %variation (16.58) (17.11) (29.73) (0.31) Weighted averages (% variation) (% variation) (0.59) (-1.94) (5.62) (0.99) (% variation) (12.87) (15.79) (19.15) (3.79) %variation (13.53) (13.55) (25.84) (2.76) AP 120 :priceperm 3 given a consumption of 120m 3 AP s : average price, the price per consumed m 3 by a household (i.e. the mean bill) MP: marginal price, the price of an additional m 3 FC: fixed charge Table 5 exposes, for each year in the panel, the weighted and non weighted means of the average price for the observed water use (AP s ), the average price for a 120m 3 consumption (AP 120 ), and the price components (the FC and the MP). While the "Ifen-Scees-Agence de l Eau" survey is exhaustive for big municipalities, the small local communities have been sampled. Then, aiming to account for the representativeness of small local communities we have calculated the weighted means. The non weighted averages indicate that while AP 120 is 1.99 euro/m 3 in 1998, a household has payed 1.87 euro per consumed m 3 in this year (AP s ). This is due to the fixed component of the price that reduces the average price for higher consumptions. Then, households consume more than 120m 3 per year. The same ordering is observed in the following years. 9

10 Comparisons of prices between years has to be done with care. In Table 5 it can be observed that the AP 120 and the AP s has increased between 1998 and 2001, about 3.5% and 1%, respectevily and, between 1998 and 2004 about 17%. The marginal price is the price component that shows the highest raise followed by the fixed charge. The highest variations are detected between the years 2001 and The weighted average allows adjusting for the size of the city when averaging. Then, the comparison of the weighted and non weighted average indicates that small cities practices lower MP and FC resulting in lower average prices per m 3 than in large cities. Additionally, there may be differences in the water use between large and small local communities, we will analyze this in the next subsection. We note that while the non weighted averages of AP 120 and AP s show an increasing trend between 1998 and 2004, the weighted average of AP s has an unexpected bump in Neither the calculation of the non weighted means nor of the weighted ones result in prices as high as those published by the Adour-Garonne Water Agency (AEAG). The agency estimates the water service price in the Adour-Garonne watershed to 2.48 euro/m 3 in 1998, 2.62 euro/m 3 in 2001 and 2.91 euro/m 3 in Two factors explain the differences with the AEAG data. Firstly, the sample is not the same. The prices exposed in 5 correspond to a representative sample of the Midi-Pyrénées Region and not to the whole watershed. Actually, the AEAG price per m 3 of the entire water services (i.e. water distribution and wastewater collection and treatment) for the MP region in 2004 equals euro/m 3 which is close to our calculation. Secondly, the values in table 5 result from pooling all cities disregarding if the utility offers collective collection and treatment of wastewater or not. In table 3.3 are exposed the means of the average prices and price s components for those cities providing some wastewater service and for those not providing it. As expected AP 120 and AP s are higher in cities providing the collective wastewater service (Table 3.3). The non weighted means result in a AP 120 equalto2.33euro/m 3 in 1998, 2.34 euro/m 3 in 2001 and 2.64 euro/m 3 in The non weighted mean of AP 120 in 2004 is higher than the AEAG s mean. In every case, excepting the weighted average on the wastewater service subsample, AP 120 increases steadily between 1998 and The weighted and non weighted average of AP s in municipalities that provide the wastewater service increases between 1998 and 2004 but diminishes in The price s components behave similarly. The local communities that do not provide the wastewater service have all approx- 8 Data publicly available in Internet: 9 See next section for an explanation 10

11 Table 6: Water prices and price s components. Municipalities with and without wastewater collective service. Price s components Year N AP 120 AP s MP FC euro/m 3 euro/m 3 euro/m 3 euro/year/120m 3 (a) Not weighted average Municipalities without collective wastewater service Total Municipalities with collective wastewater service Total (b) Weighted average Municipalities without collective wastewater service Total Municipalities with collective wastewater service Total AP 120 :priceperm 3 given a consumption of 120m 3 AP s : average price, the price per m 3 consumed by a household MP: marginal price, the price of an additional m 3 FC: fixed charge 11

12 imately the same size as there are not significant differences between the weighted and not weighted averages. Unlikely, small cities that provide the collective wastewater service have charged lower AP 120 and AP s even if the fixed charge shows to be higher Other determinants of residential water consumption There is somehow a consensus among economist about the determinants of water demand other than water price and households income. In the following are listed and defined the other variables that have been integrated in the econometric model. The expected sign of the effect (in parenthesis) is discussed. Table B.1 depicts the descriptive statistics calculated on the pooled sample Socio-economic variables pt60ppm, proportion of the population older than 60 years old (-) 11. We expect that a higher share of elderly people decreases average water use, all other things equal, because elder persons are assumed to be less active and also because they pay more attention to the water bill so, they consume less water (CREDOC, 1997). In their study on water demand in a French region (Moselle), Nauges and Thomas (2000) found that the proportion of inhabitants older than 60 years reduces the water demanded. Similarly, the work of Nauges and Reynaud (2001) on the domestic water use in the Gironde department, found that the proportion of young people increases domestic water use. nmpermpm, mean household size (+). As the dependent variable is the annual consumption of water per household, we expect a positive effect of the household size on household water demand. Some econometric studies that analyzed the per capita demand found a negative relation between the per capita consumption and the household size (Höglund, 1999; Arbués et al., 2000). This reflects the existence of scale economies on the water demand at the household level. papparpm, proportion of apartments (-/+). We do not know which will be the impact of the proportion of apartments on water use as two opposite effects may interact. On the one hand, the proportion of apartments may have a negative effect on household water use as it reduces the potential for garden surfaces reducing the outdoor water use. On the other hand, the share of apartments may increases water use because individual metering of water consumption is not applied in every building. This can induce a higher consumption as there are not clear incentives to water conservation. However, individual metering 10 This is coherent with the smaller scale of the wastewater service. 11 The expected sign is between parenthesis. 12

13 is mandatory in new constructions since the Water Law of 1992 limiting the impact of the metering issue. pfemmepm, proportion of women (-/+); We do not have any expectation about the effect of the share of womens. codtour, touristic character of the local community (equal to 1 if the local community is "touristic" and 0 otherwise) (+); Water use per household is expected to be higher in touristic areas as the non permanent population is not taken into consideration in determining the number of household in the local community. Additionally, people in holidays are careless about water economies issues, rather they are willing to maximize their comfort during the stay. murbain, urban character of the commune (binary variable equal 1 if urban commune and 0 if rural commune) (-); As stated in table 4, water consumption per household is higher in rural zones hence, we expect a negative sign Weather variables avtempmin, annual average of the minimum temperature per day (C ), (+); avtempmax, annual average of the maximum temperature per day (C ), (+); cumrain, total annual precipitations (mm 3 /year), (-); cum_effrain, annual effective precipitations which are defined as the total annual precipitations after deduction of the evapo-transpiration index (mm 3 /year), (-); avrain, annual average of daily precipitations (mm 3 /day), (-); hotdays, number of days in the year when the temperature exceeds 25C,(+); rainydays, number of rainy days in the year, (-). All the weather variables are annual averages. The weather variables are introduced in order to measure the impact on residential water use of climatic conditions. We consider almost all the different ways in which the climatic conditions have been integrated in other econometric studies of the residential water demand (Arbués et al., 2003). While the variables that measure the amounts of precipitations capture mainly the impact of weather on the outdoor use of water like garden irrigation; the variables related to the registered temperatures additionally captures the indoor use of water (e.g. showers). Then, we expect that variables related to the temperature (avtempmin, avtempmax and hotdays) tobemore significant. 13

14 3.4.3 Water quality variables qmau, share of rivers neighboring the local community that were classified in 2001 as having bad quality water, (-); vulne, vulnerable zone to agricultural pollution of water (binary variable equal to 1 if the local community is in a vulnerable area and 0 if not), (-). These variables are aimed to capture the effect on water use of the water quality at the sources of the supplied water. The implicit assumption is that, besides any objective information about the compliance with the European quality standards of the supplied water, the household water demand is affected by the agents perception on the water quality at the source. Then, in a municipality where it is publicly known that the surrounding rivers are polluted or that an intensive agricultural activity has polluted groundwater, the agents may link it to the quality of the supplied water and reduce the quantity demanded. There are not many studies that analyses the effects of subjective perceptions of water quality on demand. In their paper, Bontemps ans Nauges (2001) analyses the impact of environmental factors on the households decision of drinking or not tap water. They used a sample of 4623 French households and found that, in an environmental quality degradation scenario, the probability of choosing bottled water increases by 0.05 up to Likewise, we expect the quality variables to affect the demand s sensitivity to price variations. Face to doubts about the quality of water, agents may diminish demand up to some minimum "tolerance consumption level". The tolerance level accounts for the water uses where the quality requirements may be somehow relaxed, like non consumptive uses (dishwash, laundry, showers, etc.) or gardening. Once the minimum tolerance level has been attained, an additional increment in water price would not result in a reduction of the quantity demanded. As can be seen in table 7, in average, about 7% of rivers are polluted in the whole region. The median share of polluted rivers is similar in rural and urban areas but, as expected due to the concentration of economic activities, the mean share is higher in urban areas than in rural ones. Likewise, the median share of polluted rivers is similar in touristic and non touristic communities but the mean value is higher in non touristic zones. The mean and median share of polluted rivers is higher in big municipalities, with more than inhabitants, than in small ones. Looking at the share of polluted rivers in each department gives us a view of the geographical distribution of the pollution problems. The median values in the departments Aveyron (12), Tarn (81) and Tarn et Garonne (82) are equal to the maximum share observed in the whole sample (see table B.1). On the opposite, the departments Gers (32) and Lot (46) have a very low proportion of polluted rivers. Finally, the remaining departments have shares of polluted rivers arround the mean and median values of the region. 14

15 Table 7: Share of polluted rivers Share of polluted rivers N mean median All sample Rural/Urban Rural Character Urban Touristic Touristic Character Non Touristic Size in < inhabitants > Ariège (9) Aveyron (12) Political Haute-Garonne (31) Division Gers (32) (Department) Lot (46) Hautes-Pyrénées (65) Tarn (81) Tarn et Garonne (82) Econometric model 4.1 Demand function specification We assume hicksian separability. Then, the representative agent maximizes a utility function with two goods: drinking water and a bundle good regrouping all the other goods. This is justified as, at least in the short term, there is no substitutes to the distributed water (excepting bottled water for small uses like drinkable water and water from individual wells in not highly urbanized areas). The separability assumption allows us to write the marshalian demand as a function of price and the household s income. Other variables that structurally determinate the amounts of consumed water are also included. An important issue is to specify a functional form that will be used for estimating the water demand function. In their meta-analysis based on 51 published articles, Dalhuisen et al. (2003) report that half of these papers have used a linear specification (lin-lin form) and that 20 articles provide estimates of price and income elasticities based on a logarithmic demand function (either semi or double logarithmic). In order to easily compare our estimates with those from the previous literature, we will consider a log-log specification. Following Equation (1), we denote by y the water consumption in cubic meters per day of the representative household in a given local community. The water demand model in log-log form can be written as follow: ln y = f(ln p, ln I,ln x β) (5) where p represents the price of water, I the representative household s income and x a 15

16 vector of exogenous variables influencing water demand (e.g., household s income, climate variables, demographic characteristics of the representative household). In Equation (5), β is a vector of parameters to be estimated. We assume a flexible form, linear log-log demand function: ln(c it )=β 0 + β 1 ln(ap it )+β 2 ln(i it )+ K β k ln(z it )+ k=3 J j=k+1 β j X it + ɛ it (6) where, subscripts i ant t represent the commune and the year respectively. Then, AP it represents the average water price per m 3 consumed (AP s,definedinsection1.3)inthe local community i and year t, I it represents the annual taxable income per household, Z it is a vector of determinants of water consumption to which the logarithmic transformation has been applied, X it is a non transformed vector of other determinants of water consumption, and ɛ it is the error term composed by a local community specific effect, u i,andan usual error e it. As it has been described before, the definition of the average price includes the volume of consumed water. This may produce a simultaneity bias that render the estimator non consistent as some independent variables can be correlated with the error term. In the next subsection we briefly describe the methods that we will implement to obtain consistent and efficient estimations. 4.2 Econometric methods Estimation of equation (6) is performed using several models based on different assumptions about the error term. Firstly, we estimate the ordinary least squares (OLS) estimator on the pooled sample which is not consistent if there exists local community specific effects correlated with some regressors. Moreover, if the individual effects are correlated with some of the independent variables, the OLS estimator is not consistent. Then, we estimate a fixed (FE) and random effects (GLS) models to test for the existence of non observable heterogeneity and, using Hausman s 1978 specification test, to test for the correlation between the individual effects and the independent variables. The random effects model is estimated using a GLS estimator and the fixed effects model using OLS on the model transformed by the within operator. The Hausman test is an exogeneity test. The GLS estimator is more efficient than the within estimator if the explanatory variables are uncorrelated with the individual error term. If some variables are correlated with the individual error term only the FE estimator is consistent. The principal drawback of the within estimator is that the coefficients of the time invariant variables are not estimated because the within transformation eliminates them. Instead we will use the instrumental variables estimator of Hausman and Taylor (1981) (HT) Amemiya and MaCurdy (1986) propose a more efficient instrumental variables estimator than HT 16

17 Table 8: Exogeneity test Test Degrees of χ 2 Statistic Prob>χ 2 Freedom Fixed Effects vs GLS Fixed Effects vs HT 4.3 Estimation results We have estimated many models in a step-wise manner. Estimation results of the preferred model are shown in Table 9. We found significant individual effects then, the OLS estimator on the pooled data is not efficient. As can be seen in table 8 we reject the null hypothesis of the Hausman s exogeneity test. This evidence for significant dependency of some of the independent variables with the individual effects hence, the GLS estimator is not consistent. Similarly, the specification test shows that the HT IV estimator results in consistent estimates of the model parameters as we can not reject the null hypothesis of coefficient equality between HT and FE. Thus, we will further analyze the estimation results of the HT model. The fourth column shows the HT estimated model. Our results indicate that water demand is inelastic, but not perfectly, and that the price elasticity depends negatively on the proportion of polluted rivers in the local community (i.e. qmau). Then, the price elasticity ranges from to , and is equal to at the mean (which is in line with price elasticity estimates in other French regions (Nauges and Reynaud, 2001; Point, 1993; Boistard, 1993)) 13. These values support our initial conjecture about the existence of a "bad quality tolerance" minimum level of consumption. A negative perception about the quality of the local communities water resources encourages households to reduce consumption up to their "tolerance level". Once the household water consumption is near to the tolerance level, the price elasticity mostly vanishes. The marginal effect of an increase in the proportion of polluted rivers, other things equals (excepting the average price and the water use), ranges from to 54.5, and but based on stronger assumptions. We will not use this IV estimator because Stata does not support unbalanced panels. 13 The values of the price elasticity that we estimated fot the MP region are also within the estimates for other European countries. Hoglünd (1997) estimated the price elasticity to using a panel from Suede. Hansen (1996) estimates the price elasticity using a sample from Copenhagen households to A recently published paper, Schleich and Hillenbrand (2009), estimate the price elasticity in Germany to around Many works have been done on Spanish data and using different techniques, resulting in price elasticity estimates that vary (for different spanish regions) from to

18 Table 9: Estimated coefficients of the residential water demand OLS FE GLS HT (1) (2) (3) (4) lave-price-moy (0.052) (0.053) (0.045) (0.05) lprix-qmau (0.583) (0.726) (0.553) (0.674) ltax-inco-hh (0.061) (0.071) (0.055) (0.062) pfemmepm (0.005) (0.006) (0.005) (0.006) pt60ppm (0.001) (0.003) (0.001) (0.001) lnmpermpm (0.132) (0.17) (0.118) (0.126) codtour (0.041) (0.062) (0.072) murbain (0.027) (0.038) (0.044) lavtempmin (0.066) (0.213) (0.093) (0.108) an (0.026) (0.018) (0.015) (0.016) qmau (0.494) (0.593) (0.698) vulne (0.024) (0.036) (0.042) propempind (0.346) (0.879) (0.45) (0.502) propempcom (0.917) (2.187) (1.181) (1.299) cons (0.582) (0.976) (0.6) (0.777) Number of observations 607 R Fischer test (p-value) Wald test χ 2 -statistic (p-value)

19 is equal to at the mean 14. Then, in municipalities that apply high prices a quality degradation of local rivers can have a positive effect on water use. While this is quite interpelling, it may reflect the fact that communes with high water prices perform expensive water treatments to make it drinkable. The elasticity of the residential water demand faced to variations of the share of polluted rivers ranges from to and it equals at the mean. Then, in average an 1% raise in the proportion of the polluted rivers surrounding a municipality reduces by 0.104% the household water use. Estimation results give further support to the conjecture about the impact on household water use of a "perception" of the quality of water sources. Actually, in local communities located in vulnerable zones to pesticides and fertilizer pollution (i.e. vulne =1), water use is reduced by 0.974% (coefficient significant at 10.5% of significance level). The unique climatic variable that has a significant effect on water consumption is the annual average of the daily minimal temperature. The temperature elasticity is equal to 0.238; a 1% increase in the annual mean daily minimum temperature increases the water use by 0.238%. In the range of what has been estimated in previous studies on other French regions, the income elasticity (variable ltax-inco-hh) equals While the touristic communes consume 0.133% more water, the urban demand is lower than the rural one by 0.133%. The proportion of women does not have a significant impact on water demand, but the increase in the proportion of elder persons increases the water consumption by 0.003%. As expected the household size increases the consumption per household; the household size elasticity (variable lnmpermpm) equals The structure of the employment in the commune affects somehow the water demand; whilst a 1% increment in the proportion of commercial employment increases water demand by 0.281%, the proportion of industrial employment has no significant effect. We have analyzed more deeply the price elasticity for different categories of local communities in the Midi-Pyrénées region. Table 10 exposes the average and quartiles of price elasticity for local communities classified as rural, urban, touristic, etc.. Thus, differences in price elasticities in each category of local community reflect different expositions to the rivers pollution (see table 7). First, let us note that there is not a significant difference in the sensitivity to price variations between rural and urban communities. As can be seen in table 10, the average price elasticity is slightly higher in urban areas than in rural ones, but the median elasticity is equal in both categories. Secondly, the household demand in touristic municipalities is a little bit more elastic than in the non touristic ones as can be noted looking at the mean and the quartiles (excepting the second one) of the price elasticity distribution. Differences in price elasticity are quite significant between big and small local communities: the mean elasticity equals in communities with less than inhabitants and just in those with more than inhabitants. Looking at the quartiles we can see that these differences persists. Finally, we analyze the price elasticity at the department level. As can be seen in table 10 the residential demand in the Lot district 15 is the most elastic of the entire 14 C C While the marginal effect is, the estimated coefficient exposed in Table 9 is 1 15 qmau qmau C We will use all through the text the word "district" as the translation from French of department. 19

20 Table 10: Price elasticity Price Elasticity N mean 1 quartile 2 quartile 3 quartile All sample Rural/Urban Rural Character Urban Touristic Touristic Character Non Touristic Size in < inhabitants > Ariège (9) Aveyron (12) Administrative Haute-Garonne (31) Division Gers (32) (District) Lot (46) Hautes-Pyrénées (65) Tarn (81) Tarn et Garonne (82) region: the mean is near the maximum of the estimated price elasticity and the first quartile equals the maximal elasticity estimated. Similarly, the Gers department has a highly elastic residential demand, relative to the other departments 16. On the opposite, the price elasticity of the residential demand in the Tarn department is the mostly null. The price elasticity is similar and constant across the local communities in the Ariège and Haute-Garonne departments. Unlikely, in the Tarn et Garonne department there is more variability in the price elasticities: while in the first quartile it equals in the last one it equals Estimation diagnostic In this subsection we evaluate the adjustment of the estimated model predictions within the sample used to perform the estimation. Additionally, we check if the idiosyncratic errors verify the normality assumption. Finally, we further analyze the individual effects. Goodness of the Fit Assessment As can be seen in Figure 1 the estimated model adjusts very well the consumption in the middle of the sample. Likewise, even if there are not many points at the extremes, the predictions remain close to the observed consumption. 16 Actually, the water demand is inelastic. 20

21 Figure 1: Predicted versus observed water consumption Residuals Analysis We evaluate if the distribution of the residuals fits, as it is assumed by the Hausman- Taylor model, the normal distribution. While this assumption is not crucial to the convergence issue of the parameters estimator it affects the validity of the significance tests based on the t-student distribution. The Shapiro-Wilk s test indicates neither the residual (ɛ it = u i +e it ) nor the usual error term component (e i t) are normally distributed. However, the graphical assessment of normality does not show huge discrepancies. Specific Effects Analysis Table 11 exposes the mean of the community specific effects by district. We can see that the averages are quite close to zero for the Tarn, Tarn et Garonne. 5 Welfare analysis 5.1 Theory The assessment of consumers welfare variations is a powerful instrument for policy analysis as it allows to rank different public policies and scenarios given their impact on the well being of the different types of consumers. The economic theory on consumer behavior proposes three alternative measures: the compensated variation (CV), the equivalent variation (EV) and the surplus variation (SV). While all three are aimed to inform about the welfare variations, they measure different things. The EV is based on the current price and 21

22 Table 11: Individual Effects by district Department N Mean Population Ariège (9) Aveyron (12) Haute-Garonne (31) Gers (32) Lot (46) Hautes-Pyrénées (65) Tarn (81) Tarn et Garonne (82) Total measures the income variation, at these prices, that would leave the consumer indifferent given the new price and its impact on the consumer s utility. Unlikely, the CV is based on the new price, and searches the income variation needed to compensate the consumer for the price variations. The residential water demand of the representative household in the local community i is defined as a function of the water price in this local community, of his income and of local characteristics. Then, on the basis of equation 6 and the estimated coefficients by the HT method we obtain (see Table 9), after averaging on time, a demand function of the form C(P i ): ˆ ln(c i ) = ˆβ 0 + ˆβ 1 ln(ap i )+ ˆβ 2 ln(īi)+ ˆβ 3 ln(ap i )qmau i + = ˆβ 0 + ln(ap i ) ˆβ 1 + ˆβ 3 qmau i + ln(īi) ˆ β 2 + Ĉ i = exp K k=4 ˆβ0 + ln(ap i ) ˆ β 1 + ˆβ 3 qmau i + ln(īi) ˆ β 2 + = e ˆ β 0 P ˆβ 1 + ˆβ 3 qmau i i Or equivalently, K k=2 Ĉ i = B i P ˆβ 1 + ˆ β 3 qmau i i Z i ˆ βk J j=k+1 K k=4 ln( Z i ) ˆ β k + K k=4 ˆβ k ln( Z i )+ J j=k+1 ln( Z i ) ˆ β k + X ˆβ j i J j=k+1 J j=k+1 X ˆβ j i ˆβ j Xi e ˆβ j Xi (7) where B i = e ( ˆβ 0 + J j=k+1 ˆβ j Xi) K k=2 Z i ˆ βk 22

23 Following Hausma (1981), we can calculate the indirect utility function and the expense function directly from the Marshal s demands if the integrability conditions are verified. As we have assumed hicksian separability and a flexible log-log specification of the water demand (see equation 6) we can easily verify the integrability conditions (IC) which resume only to one: ˆβ 1 + ˆβ 3 qmau i + C i ˆβ 2 < 0, AP i I i where ˆβ 1 + ˆβ 3 qmau i and ˆβ 2 are, respectively, the estimated price and income elasticities. This conditions is satisfied by the 607 observations in our sample (IC ranges from to ). Then, given the demand function specification 6, the CV of a price change from P 0 to P 1 is defined as: VC ( P 0,P 1,I ) = e ( P 1,u 0) e ( P 0,u 0) = e ( P 1,u 0) I (( 1 = ˆβ ) 2 1+ ˆβ 1 + ˆβ 3 qmau 1 I ˆ β 2 (P 1 x(p 1,I) P 0 x(p 0,I)) + I 1 ˆβ 2 ) 1 1 β ˆ 2 (8) I. Given the demand function of equation 7, the consumer s surplus variation of a price change from P 0 to P 1 is defined as: ΔS i = ΔS i = P 1 i P 0 i e ˆβ 0 P ˆ β 1 + ˆβ 3 qmau i i B ( i 1+ ˆβ 1 + ˆβ 3 qmau i K k=2 Z i ˆ βk J j=k+1 P 1(1+ β ˆ 1 + ˆβ 3 qmau i ) i e ˆβ j X i dp i P 0(1+ ˆ i β 1 + ˆβ 3 qmau i ) ). (9) In the next subsection we will study the welfare consequences of different scenarios on the basis of compensated variation calculations and consumer s surplus variation. 5.2 Welfare effect of price and quality variations Compensated Variation analysis In order to calculate the CV of price increments we have computed, for each municipality, the representative household water demand from equation (7), assuming two different levels of the share of polluted rivers. Firstly, we consider the share of polluted rivers observed in the sample, and secondly, we assume that no river has quality problems As if the "good ecological state" of all water resources has been reached, as stated in the European Water Directive. 23