1.  Introduction

1 This article analyzes the impact of land use on the costs of drinking water supply. Our hypothesis is that raw water quality in a catchment area varies with the land use, thus reducing or increasing the need for the treatment of drinking water and, as a result, affecting the costs of drinking water supply and water prices. The impact of land use on water quality can be considered as an externality since landowners do not bear the cost of reduced water quality if their choice of land use has a negative impact on the quality. The valuation of the externalities of land use provides important information for policy makers and regulators concerned by land use (Hascic and Wu, 2006). The objective of the present analysis is to estimate the impact of land use on the costs of drinking water supply, applying a recently proposed econometric approach (Flores-Laguna and Schnier) that makes it possible to simultaneously consider the impact of spatial factors and the choice of the organization of the water supply services (Wss).

2 Water resources, i.e., groundwater and surface water, are closely connected with the landscape and land use. In particular, non-point source pollution (Npp) of groundwater resources is often a result of a particular land use. In addition to affecting water quality, land use also affects groundwater resources through changes in recharge rates and the demand for water. Therefore, inappropriate land use, particularly poor land management, leads to chronic groundwater quality problems (Lerner and Harris, 2009). Moreover, as water drains from the land surface, it carries the residues from the land. Surface runoff, which depends on land use, is thus an important source of Npp of surface water (Tong and Chen, 2002).

3 The agricultural sector is considered to be the largest contributor to Npp through runoff and leakage of nutrients, sediment, pesticides, and other contaminants. However, land devoted to residential and development uses, such as lawns and gardens is often managed intensively, generating many pollutants. Furthermore, urban areas also have a higher percentage of impervious areas, resulting in lower percolation and higher runoff (Bhattarai et al., 2008). Compared to agricultural and urban land use, forests have an extensive root network and a considerable ability to generate porous and filtering soils. Under forest cover, nitrate levels are low (Jussy et al., 2002), and similar results can be observed for other pollutants such as pesticides.

4 The relative impacts of alternative land uses on water quality have already been studied (e.g., Hascic and Wu, 2006; Langpap et al., 2008). The objective of these studies was to analyze how water quality affects watershed ecosystem health and whether land use changes exacerbate these impacts. These authors evaluate the impacts of different land use policies on ecological quality indicators. Our study measures the effect of land uses on the cost of supplying drinking water and therefore provides a monetary assessment of land use externalities.

5 Monetary valuation of land use externalities has also been done in Abildtrup et al. (2013) who measure the value of the impact of forest land use on raw water quality on the basis of the water supply market. The basic idea is that in comparison to other land uses, the forest has a positive impact on water quality and, as a result, the costs of supplying drinking water are lower in areas with a high proportion of forest land use. When the water quality is high, fewer costs are associated with raw water treatment (e.g., purification) or with finding new sources when existing sources are contaminated. The value of land use externalities is then considered to be the water supply costs economized due to forest land use when controlling for other factors that affect the cost of water supply (e.g., water supply network characteristics). Due to ecological processes related to water flows and land uses, on the one hand, and to the technological implications of the network system of drinking water supply, on the other, spatial aspects may also have an impact on the cost of supplying water. Spatial aspects were taken into account in Abildtrup et al. (2013) by using spatially explicit data and spatial econometrics.

6 The type of management may also be an important determinant of drinking water supply costs and should therefore be included in the analysis. In France, the management regime of the Wss (direct public management vs. private delegation) has a significant impact on the price of water. However, the difference in price, which is unfavorable for delegated management, can be explained by the more difficult operating conditions, including problems related to the quantity and quality of raw water (Boyer and Garcia, 2008; Carpentier et al., 2006). This is confirmed by Fiquepron et al. (2013) who found that poorer raw water quality (in terms of pesticides) implies a higher probability of delegation of the service, and that the price of water rises with delegation. However, spatial factors and the interaction between different Wss might also influence the decision to delegate, thus affecting water supply costs. This issue was not addressed in Fiquepron et al. (2013).

7 The novelty of the present study, compared to Abildtrup et al. (2013) and Fiquepron et al. (2013), is to analyze the economic impacts of land use on the cost of drinking water supply, taking both the organizational choice of the water supply and spatial factors into account in the same model. Our price model explicitly recognizes that land uses may have an impact on drinking water prices. When estimating water prices, we consider a possible endogeneity bias related to the sample selection according to the management of the water services. We estimate an equation for the choice of management type and an equation for the price of water, accounting for the potential dependence of error terms between equations, as well as between neighboring water services. This implies the use of a sample selection model (Heckman, 1976, 1979) adapted to a spatial context, i.e., allowing for spatial lags and spatial error processes. We apply the model to analyze water prices based on data from the Vosges department, a French administrative district located in northeastern France. We apply the approach proposed by Flores-Laguna and Schnier (2012) for the estimation of sample selection models with spatial autoregressive errors. This approach has also been used by Ward et al. (2011) to estimate the impact of climate on cereal yields, taking the endogenous decision to grow cereal into account. However, these authors consider a Tobit type model, whereas we estimate a switching type model. Cho et al. (2013) also consider sample selection and spatial interaction in the analysis of the impact of tax policies on residential density. However, they apply Klier and McMillen’s (2008) linearized version of the generalized methods of moments (Gmm) estimator proposed by Pinkse and Slade (1998).

8 In the next section, we develop our model of management choice and water price, with a description of the econometric analysis in the following section. The data is then presented, followed by a discussion of the results and the conclusion.

2.  A spatial switching regression model with spatial endogenous switching

9 The municipality may manage the water service itself or entrust its management to a private operator. The choice between management regimes depends on water prices and service characteristics. This means that an endogeneity bias due to sample selection according to the type of Wss management potentially exists. Our model is thus defined as a switching regression model (Lee, 1978) based on a price function that depends on the type of management, and on a selection equation that describes the choice of management.

2.1.  Price equation

10 The pricing rule for water supply services has been shown to be different according to the management mode (Boyer and Garcia, 2008). Thus, these different pricing rules can be described by two price equations, and the management choice equation determines which of these two equations is applicable. It is assumed that the price level is explained by the service characteristics and those of the neighboring services. Obviously, if several neighboring services extract water from the same aquifer as the service in question, its price will be affected if the water resources become scarce. However, for the sake of simplicity, we do not distinguish between observed service variables and those of neighboring services in our model. Finally, we assume that the water price is affected by a stochastic disturbance (representing unobservable price shifters). This error term includes unobservable price variables of neighboring services.

11 All variables are indexed by

, which varies from 1 to , where is the number of water services directly (publicly) operated and is the number of water services under private delegation. Thus, the price equations for each management mode (`0': public management; `1': private delegation) can be written in the following general form:

12 with:

13 where

and are the regression parameters. The error terms of model and are spatially dependent on the errors of the neighboring services, where and are the spatial autocorrelation parameters and and are the spatial weights. Finally, and are with defined as:

2.2.  Choice of management regime

14 We assume that the choice of the type of management is done by comparing the expected water prices of water related to public or private management. It also depends on a predisposition of the municipality to delegate its drinking water service. The municipality will prefer private delegated management to public management for its water service if (Boyer and Garcia, 2008):

15 where

and are the expected prices of water in the case of public management and private delegation, respectively. This means that the municipality will choose private delegation if the price difference is greater than an unobserved predisposition to delegation , which can be positive or negative. It is assumed that is explained by different factors (e.g., water volume delivered, number of users, number of municipalities served by the Wss, referred to as ) that determine the price of water, as well as by variables that do not affect the price of drinking water, such as the decision of a municipality to delegate its sanitation service . This variable is used as an exclusion restriction for the identification of the sample selection model. Finally, we assume that a predisposition to delegation can be determined by unobserved variables of neighboring services. [1] The regression equation is written as follows:

16 where

is a spatial error term. The water services are spatially interdependent through their location in space, as given by the spatial weights . On the basis of Equations 6 and 7, we can write the structural equation of selection as follows:

17 Thus, if

, then the municipality chooses to delegate its water services to a private operator (). Otherwise, it chooses to directly manage its service (). A positive price differential () should in fact encourage the municipality to delegate its water service.

18 By inserting Equations 1 and 2 into Equation 8, we obtain the new management decision rule in a reduced form:

19 with:

20 where

, or . The errors are spatially autocorrelated with , the spatial autocorrelation parameter, and , the spatial weight. As a consequence, the are heteroskedastic and the probit model has to take this specificity into account for parameter estimation.

2.3.  Estimated model

21 The complete model to be estimated is composed of the selection Equation 9 and the two price Equations 1 and 2. Since water prices depend on the management decision of the municipality, estimating the price equations without accounting for this decision may cause a selection bias. In order to avoid this problem, we use the approach of Heckman (1976, 1979) extended to spatial econometric models by Flores-Laguna and Schnier (2012) to correct the potential selection bias.

22 The complete model can also be written in the following reduced form:

23 where the weights

, and are the elements of the inverse matrices , and , respectively, with the matrix of spatial weights . It is assumed that the spatial weights , and introduced in error term Equations 10, 3 and 4, respectively, are the same and take the unique notation . It is also assumed that the errors , and have a trivariate normal distribution, with mean zero and the following covariance matrix:

24 On the basis of the model composed of the selection Equation 9 and the price Equations 1 and 2, the errors

, and are i.i.d with zero mean and a covariance matrix written as follows (McMillen, 2005; Flores-Laguna and Schnier, 2012):

25 As mentioned above, the presence of spatial errors induces heteroskedasticity in the error terms in the selection equation. This is why we use the procedure of Pinkse and Slade to estimate the spatial (heteroskedastic) probit equation described below, where

are the parameters of the spatial probit model, is the index function of a probit model, and is the function of the standard normal distribution.

26 As suggested by Maddala (1983), it is possible to estimate Equations 1 and 2 simultaneously, using all observations on prices. This is highly desirable in our case since the number of observations in Regime 1 (i.e., delegated operation) is too low for a separate estimation. From the price functions conditional to each regime (see Appendix A), we pooled all observations in a single equation, so that the price model can be written once again as:

27 Assuming that

and are the same variables that determine the prices, regardless of the regime - just like and are the same spatial weights - we can then write Equation 14 as:

28 This price equation could be estimated with Kelejian and Prucha’s (1998) two-stage least squares estimator for a spatial autoregressive model with autoregressive disturbances. The method used to estimate the complete model is presented in Appendix B.

3.  Data

29 We collected a relatively complete dataset in the Vosges department, a French administrative district located in the Rhine-Meuse water basin in northeastern France. There are 283 Wss in the Vosges department that serve 515 municipalities (communes). We were forced to eliminate certain municipalities from the analysis because we did not have the price of their drinking water (56 out of the 515 municipalities). Our final sample contained 232 Wss that included the 459 remaining municipalities.

30 The price of water used in our study corresponds to the fraction of the household water bill that covers drinking water (excluding the part covering sanitation). The average price per m³ was based on a typical bill with a consumption of 120 m³ per user and per year. Taxes and fees are excluded from this price. Other data on Wss (e.g., water demand, number of users and organizational structure) are available from the Rhine-Meuse Basin Committee for the year 2008. In our sample, only 21 Wss are privately operated but they cover a large area of the department. Figures 1 and 2 represent a map of the (almost entire) Vosges department, which consists of 232 Wss. They show the spatial distribution of water prices for all Wss in the Vosges and for delegated Wss alone, respectively.

Figure 1

Water prices in the Vosges department (in / m³)

Water prices in the Vosges department (in / m³)

Figure 2

Water prices for delegated Wss (in / m³)

Water prices for delegated Wss (in / m³)

31 Land use data are obtained from the Corine Land Cover (Clc) map of 2006. The Clc map is derived from satellite images based on a scale of 1/100,000 and with a minimum mapping unit of 25 ha. The standard Clc nomenclature includes 44 land cover classes, broken down into five major types of land use. In our study, forest is represented by the three forest categories (Codes: 311, 312, and 313) and transitional woodland-shrub (code: 324). Agricultural lands correspond to all ten categories in the Clc nomenclature. Urban areas correspond to all artificial areas. Finally, the remaining areas (including grassland, swamplands, lakes and rivers) are referred to as “other land uses” and can be considered as “non-polluting uses”. The total of these different uses is equal to 100% of the total area of the Wss. Figures 3 to 6 show the proportions of the categories of land uses defined for our analysis.

Figure 3

Proportion of forest lands

Proportion of forest lands

Figure 4

Proportion of agricultural lands

Proportion of agricultural lands

Figure 5

Proportion of urban areas

Proportion of urban areas

Figure 6

Proportion of other areas

Proportion of other areas

Tableau 1

Definition of variables and descriptive statistics

Variable	Definition of variable	Mean	Std	Min	Max
Price	Drinking water price (in €/m3)	1,08	0,358	0.21	2,56
Deleg	Dummy=1 if private operation	0,09	0,29	0	1
Forest	Proportion of forest lands	0,54	0,223	0.047	1
Agri	Proportion of agricultural lands	0,15	0,153	0	0,73
Urban	Proportion of urban area	0,05	0,072	0	0,66
Other	Proportion of other areas	0,27	0,15	0	0,73
User	Number of users served by the Wss	682	1,457	14	15,871
Area	Wss area in km2	21,650	29,140	1,851	227,294
Density	Number of users per km2	34,7	54,2	1.7	467.9
Municip	Number of municipalities served by the Wss	1,87	3,269	1	30
Sanit	Dummy=1 if private operation of sanitation service	0,07	0,25	0	1

Definition of variables and descriptive statistics

Notes: Number of observations N = 232 Wss

4.  Econometric results

4.1.  Tests for spatial dependence

32 It is possible to detect spatial dependence in (linear and non linear) regressions estimated by non spatial procedures, using either the Moran

-statistic or Lagrange Multiplier (Lm) tests. Robust Lm tests (Anselin and Florax, 1995) are generally preferred because they make it possible to identify the form of spatial dependence (spatial error or spatial lag).

33 Concerning the price (linear) regression, we first computed the Moran

-statistic on the Ols residuals obtained from Equation 15. We then used robust Lm tests (for spatial error and spatial lag). These tests suggest the presence of (only) spatial autocorrelation of errors.

Tableau 2

Tests of spatial autocorrelation

	Management choice eq.
Test	Value	P-value
Moran I-statistic †	1.9430*	0.0520
Lm Lag †	0.8293	0.3624
Lm Error †	3.0530*	0.0805
	Water price eq.
	Value	P-value
Moran I-statistic	2.4317**	0.0150
Robust Lm Lag ‡	1.082	0.2980
Robust Lm Error ‡	3.2021*	0.0735

Tests of spatial autocorrelation

Notes: N = 232, N1 = 21 (delegated Wss).
***: significant at 1%; **: at 5%; *: at 10%.
† Statistic adapted to a probit specification.
‡ Robust test of Anselin and Florax (1995).

34 To test for the presence of spatial autocorrelation of errors in the selection equation (probit model), we used different statistics. First, we computed the Moran

-statistic adapted to the probit specification by Kelejian (2001). These authors used the residuals computed as . We also implemented the Lagrange Multiplier (Lm) test proposed by Pinkse (1999, 2004) who used a weighted adjustment to as a residual: . However, it is shown that the Moran -statistic of Kelejian and Prucha (2001) performs better when the explanatory variables are spatially correlated (Amaral et al., 2013). Moreover, regarding the test for the presence of a spatially lagged variable, we used the robust Lm test of Anselin and Florax (1995) using the dependent variable of the probit model and the residuals .

35 Results of spatial tests are presented in Table 2. A comparative analysis of the significance of different tests of spatial dependence shows the presence of spatial autocorrelation in error terms both in the selection (probit) equation and the price equation. Abildtrup et al. (2013) also found autocorrelation spatial errors in a similar analysis.

4.2.  Model estimation results

36 As a preliminary remark, it is important to note that the relationship between land use and water quality could be bidirectional. Land use activities have direct impacts on water resources, and it is possible to imagine that water quality also influences the sitting of land use activities in the long-term. With more detailed information on land uses (many more disaggregated land uses as well as longitudinal observations), it would probably be possible to highlight some relationships in this way. However, less than 1% of the agricultural land is irrigated in the Vosges department. Thus, we expect that the cost of water would have only a negligible impact on the profitability of agricultural land use. The impact of water cost on urban growth, and consequently urban land use, is also assumed to be negligible since the cost of water represents a relatively small share of household expenses. In Abildtrup et al. (2013) statistical test of the null hypothesis that land use was exogenous could not be rejected.

Tableau 3

Estimation results

	Type of management		Price of water
	Estimate	Std. Error	Estimate	Std. Error
Constant	-25.7052*	14.6563	-0.1164	0.5204
Sanit	4.1278***	1.2260
Density (in log)	-0.8390	0.6732	-0.0439	0.0321
User (in log)	1.3056	0.9073	0.0411***	0.0244
W X User	0.8743**	0.3798
User X φ			0.0625***	0.0077
W X Forest			-0.9327***	0.1937
W X Urban			0.9919*	0.5455
W X Other			-0.4522	0.2830
φ			0.0153	0.4299
Sae	-0.0088	0.0597	-0.0003	0.0660
Overidentifying restrictions test: χ2(3) = 0.6133 P-value = 0.8934

Estimation results

Notes: N = 232, N₁ = 21 (delegated Wss).
***: significant at 1%; **: at 5%; *: at 10%.
Sae stands for Spatial Autoregressive Error.

37 Table 3 presents estimation results of the switching regression model with endogenous switching. It is composed of the selection equation and the price equation. Since the sum of different land uses is equal to 100%, one land use must be taken as a reference (in order to avoid the dummy trap). Agricultural land use is thus taken as a reference and forest, urban and other land uses are kept as the right-hand side variables. First of all, the result of the overidentifying restriction test (resulting in a p-value of 0.8934) indicates that the conditions of moment are valid and that our Gmm estimates can be used for interpretation.

38 We first describe estimation results of the probit model (i.e., the choice between public management and delegation of Wss). It should be recalled that

for public management and when Wss is delegated to a private operator. Therefore, a positive sign for the parameter associated with a variable means that the likelihood to observe a delegated Wss is higher. For example, the parameter associated with Sanit is significantly different from zero and positive (at the 1% level) and can be interpreted as follows. The delegation of the Wss to a private operator is more likely when the operator also operates the sanitation service on behalf of the municipality. The variable Sanit is a significant determinant in the choice of management of Wss - but does not affect water prices and can be used as an exclusion restriction for identification of the sample selection model.

39 Furthermore, the estimation of a probit model allows us to identify some spatial interactions in the choice of Wss management. The coefficient associated with the number of water users in Wss is positive. This means that a greater number of water users in neighboring Wss increases the likelihood to delegate to a private operator. This result expresses the pressure on the water resource as the result of an increasing demand that indirectly (i.e., not in the Wss) and negatively affects the quality and the quantity of water available. In the case of difficult operating conditions, the municipality prefers to delegate the service. Nevertheless, we did not find significant spatial autocorrelation in the residuals.

40 The estimated price equation is presented in the two right-hand columns of Table 3. First, it appears that the price of drinking water decreases with an increase of the proportion of forest lands (relative to agricultural land use) in neighboring Wss. The associated coefficient is highly significant at the 1% level. On the other hand, urban land use has a positive impact on prices compared to agricultural land. Even if other (non-polluting) land uses have no significant effect on water prices, these results confirm that land uses are of importance for estimating water supply costs. We included both land use variables concerning only the area of the Wss and variables for the spatially lagged land use in an initial estimation. However, contrary to what was found by Abildtrup et al. (2013), only the spatially lagged land use variables were significant and, consequently, only these variables were used in the model. This shows that it is not the land uses in the area of a given Wss that are important for the supply of the ecological service of water protection, but that a larger area should be considered. Basically, this indicates that the impact of land use in the Wss areas is not constraining the Wss in providing water. This may be due to relative low costs associated with exploiting water resources in neighboring water service areas.

41 Second, a positive and significant sign on the number of users indicates that the costs increase with the number of users. This means that the marginal cost of supplying users is increasing. The coefficient on the population density is positive but not significant, i.e., population density does not have a significant impact on prices. The positive impact on prices of an increasing number of users is consistent with the results in the management equation. The decision to delegate to a private operator in the case of intense extraction of raw water is linked to the pressure on the resource and the relative difficulties of operation. Finally, we find that the interaction between the number of users and the probability of delegation is significant. This indicates that the impact of the number of users on the costs depends on the organization of the water services, and underlines the importance of considering the water service management decision when assessing the impact of land on the cost of drinking water supply. Ignoring municipalities’ self-selection of a management strategy could lead to an estimation bias. In contrast to Abildtrup et al. (2013), we do not find a significant spatial autocorrelation in the error terms. Furthermore, we believe the reason why Abildtrup et al. (2013) did find that the variables representing land use in the Wss area are significant but not in the present study (where only spatial lagged land use variables are significant) is due to the misspecification implied by ignoring the self-selection into delegation of Wss.

5.  Conclusion

42 The results of this study show that the prices of drinking water are significantly lower when the proportion of land within the forest increases. This confirms previous studies that found that forest land use compared to urban and agricultural land uses, for example, reduces the costs of drinking water supply (Langpap et al., 2008; Fiquepron et al., 2013; Abildtrup et al., 2013).

43 Previous studies have also shown that the choice of management of Wss may influence the cost of water supply. Furthermore, due to the potential interactions between Wss - competition between scarce water resources - or due to the presence of spatially correlated unobserved variables, it is relevant to consider the spatial structure of the water supply. We therefore applied a switching model with endogenous switching adapted to a spatial context. This means that the choice of management is modeled with a probit model, and allows for management-specific water price functions. The model also accounts for the potential correlation between the error term in the management choice equation and the price equation, and includes spatial factors and spatially autocorrelated errors in both equations. We found spatial interactions related to the characteristics of neighboring Wss, but no spatial autocorrelation in error terms in the management choice equation, or in prices. We specifically show that it is not the local but the forest cover instead at a larger scale that significantly reduces water supply costs. This latter result suggests that further research is still needed at the scale of water catchments, making it possible to more precisely measure the impact of land uses on water quality. Thus, targeted policies such as voluntary and incentive contracts with forest owners and farmers could be established, providing the highest possible efficiency.

44 Our results confirm that water protection service of forest have an economic value. This non-market value should be taken into account in land use regulation to ensure an efficient allocation of land uses. Furthermore, our results show that some recent policy initiatives where local water services are encouraged to negotiate contracts on land use changes with local land owners (see e.g., Abildtrup et al., 2012) may not necessary lead to social optimal regulation. We have found that land use changes in one Wss area may also benefit neighboring Wss. If the local water service manager does not take this neighbor effect into account, the protection of water resources is likely to be insufficient. Therefore, land regulation policies should consider the risk of free riding behavior if water protection initiatives are decentralized.

45 Finally, our results show that one should be careful in using marginal values to evaluate non-marginal changes in land use, because such changes may also influence the choice to delegate the water services and thereby having an indirect impact on cost of water provision.