Privately-operated Water Utilities, Municipal Price Negotiation, and Estimation of Residential Water Demand : The case of France i
Céline Nauges and Alban Thomasii E.R.N.A.-I.N.R.A., TOULOUSE
First draft March 17, 1998
Abstract
This paper addresses the issue of price negotiation between a municipality and a private water utility operator, and its implications for residential water demand estimation. Because negotiated price may depend on municipality’s specific characteristics, competing forms of price
endogeneity have to be considered when using panel data. The impact of variables such as average income, housing and system features is investigated both on municipal consumption and price. We use efficient procedures to estimate a water demand equation on a panel of French municipalities. Estimated price and income elasticities are significant and close to previous, household-level studies.
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INTRODUCTION
It is well recognized that estimating household demand for residential water is a prerequisite for any water resource policy design. In cases where water resources are scarce and conflicting uses are consequently more acute, it is important for the environmental regulator to assess properly the expected changes in water consumption, following price or quota policy schemes. Even though residential water demand may not appear the most important element in total water consumption, public opinion is becoming more concerned with possible periods of restriction in use, as well as trends of increasing water prices throughout Europe and the US.
Many empirical papers are dealing with estimation of residential water demand, most of them in the U.S. Unfortunately, empirical results on important figures such as price and income elasticities are very heterogeneous and remain often sensitive to econometric specification. Three problems are not completely resolved yet in most cases. First, accurate data on prices paid (both average and marginal) are not always available to the researcher, hence making it difficult to draw relevant inference on consumers’ behavior. Second, demand shifters such as climatic and sociodemographic variables should be included in these models. Third, when panel data are available, it is not always the case that the additional information provided by pooling cross-sections with times series is fully exploited by empirical researchers. In particular, it is important when using panel data to assess the exact nature of price endogeneity in the consumption equation. As it stands, endogeneity of water price may be caused either by instantaneous consumption entering average price, or correlation between price and unobserved heterogeneity (individual effects), or both. Incorrect model specification often leads to severe biases in demand elasticities. When average or marginal price is correlated with individual effects in panel data, it may be the case that private water utilities charge residential water prices depending on local communities’ characteristics such as average revenue, liabilities, or population density.
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Hence, a possible cause of endogeneity of price in the demand equation is that the perhead water consumption incorporates an unobservable individual effect. The latter can be considered the unpredictable part of the consumption, in the sense that it is not captured by explanatory variables introduced by the econometrician in the demand equation. If this individual effect is correlated with price for water, be it marginal price or average price, then parameter estimates are likely to be biased. The economic argument behind such a correlation is the following. When negotiation takes place between the operator and the municipality, two major variables are decided upon. First, the operator has to supply a determined level of drinkable water to consumers in the community. Second, the price charged depends not only on the system technical features, but also on expected, long-run per head water consumption. It is important to note at this point that the price for water supply and treatment is decided upon by taking into account all possible uses by the community, i.e. not only residential water use, but also industrial and municipal uses. This is because industrials and municipal authorities will also be taking advantage of the water system. When a price regime is agreed upon, yearly changes in the marginal price may occur because of technical features affecting the marginal cost of producing and delivering water to consumers from facilities. The important aspect we stress however, is that the price regime remains effective in the future. Similarly, per-head consumption moves around the expected longrun level, because of income variations, local migrations, etc. Consequently, from an empirical point of view, we may treat the unobservable component in the per-head consumption as an individual effect for the local community. Endogeneity in the price of water may therefore be present due to the possible correlation between the community-related price component, and the community-dependent per-head consumption component. The methodology of estimation proposed in the paper allows for a simple test for the existence of a negotiation-driven price regime, which depends on some unobserved component in the perhead consumption.
Another aspect of residential water demand worth investigating is the influence of metering on individual consumption. In a situation where water is charged through a fee which is
3
computed on the basis of housing and/or household characteristics alone, it is likely that an optimal use of the resource is not encouraged. On the other hand, when considering relatively more significant marginal prices for water, the fact that actual water consumption is directly charged to the individual consumer may provide the latter with enough incentives to reduce his consumption, or at least converge to an optimal regime for consumption. This consideration is of course related with moral hazard issues, in the sense that it is difficult to determine what contribution the consumer has in total consumption of the housing. Given data on individual housing density, as opposed to collective housing, it is possible to test for this metering effect.
This paper makes several contributions to the empirical literature on residential water demand. First, we discuss the issue of price negotiation between the municipality and the private operator, and its implications for residential water demand estimation. Second, we use adequate consistent and efficient estimation procedures for the case of water demand with panel data. Those instrumental-variable estimators have been but very rarely employed in the literature on water demand. The paper is organized as follows. Section II gives an overview of the literature on the estimation of residential water demand. In Section III, we present a simple and intuitive economic model of price setting and household demand for water. As this model will be estimated and tested on French data for local communities, we introduce the section by a brief description of water utilities in France. Data used, econometric methods, and estimation results are presented in Section IV. Section V concludes.
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II. OVERVIEW OF THE LITERATURE
The pioneering studies on residential water demand (Howe and Linaweaver, 1967; Gibbs, 1978; Danielson, 1979; Foster and Beattie, 1979) were mainly devoted to the US, where some regions had been affected by periods of severe drought. As a consequence, economists have been asked to look for the best way to regulate the demand side. Solutions include in particular rationing of distributed water, education programs, awareness campaigns, and multi-part pricing policies or increases in flat-rate prices. The 1980’s experienced an important increase in the number of residential water demand studies (Billings, 1982; Schefter and David, 1985; Chicoine and Ramamurthy, 1986; Nieswiadomy and Molina, 1989 among others), showing a larger interest in economic analysis and econometric methods. Researchers in the current decade (Point, 1993; Hansen, 1996; Agthe and Billings, 1996; Renwick and Archibald, 1997; Höglund, 1997) emphasize new insights such as adoption by households of low-flow equipment, welfare consequences of a price regulation and case studies of European countries.
Economists have always largely agreed on the variables to introduce in the water demand function. The consensus is that, water having no close substitute in consumption goods, the only price entering the demand function should be the price of water. However, Hansen (1996) shows that in countries like Denmark where most of the residential water is heated (70% in Copenhagen), the price of energy should also be considered. Price is not the only variable affecting water consumption. Income, size of the household, house features (age of housing, garden acreage, number of cars, domestic and sanitary appliances), weather variables may have a non negligible influence. If the choice of variables entering the water demand function has not led to much debates among authors, consensus is still difficult to obtain on multiple-block pricing. In a multiple-rate tariff framework, the consumer has to pay a fixed charge and a marginal price by cubic meter depending on his level of consumption. It leads to a non linear budget constraint and a non linear
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and a non differentiable demand function. In addition to the difficulties of deriving a demand function, researchers disagree on the proper specification of the price variable. The consumer faces few pricing blocks and consequently, few prices: the marginal price within each block and the average price defined as total water expenditure divided by total water consumption. The assumption of perfect information for the consumer advocates the introduction of the whole price system in the demand function. However, some authors are suspicious about consumers having perfect knowledge of the price system. Most models therefore either specify the average price or the marginal price corresponding to the selected block, sometimes adding, following Nordin (1975) and Taylor (1976), the « difference variable ». Specific to the multiple-part pricing, the difference variable is defined as the difference between what the consumer actually pays and what he would have been charged if all consumption units were charged at the marginal price of the last unit of consumption. This difference variable should represent the income effect embedded in the pricing schedule, an increasing tariff being seen as a tax on the first units purchased, whereas a decreasing one simulates a subsidy. The coefficient of the difference variable should then be equal in magnitude but opposite in sign to the coefficient of income. The TaylorNordin price specification has received wide acceptance despite the fact that the previous statement has been rarely verified, except in Schefter and David (1985) on simulated data.
The correct specification of consumer behavior when facing multiple-block pricing refers to Burtless and Hausman (1978) and Moffitt (1986, 1990). These authors propose a two-stage model in which the consumer first selects the block, and then maximizes his/her utility subject to a budget constraint. Hewitt and Hanemann (1995) are among the rare authors to use this kind of two-step model in water demand studies. To simplify the expression of the demand function, researchers often only consider the block where most consumers are located (a selection bias can emerge) or simply omit the choice of the block by the consumer (can lead to a simultaneity bias because the consumption depends on price but price depends also on block and so on quantity). Multiple-rate pricing consequently renders the economic analysis difficult: not taking into account the specificity of the pricing structure can generate two kinds of bias and a whole description of
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the consumer choice heavily rests on the perfect information assumption and makes the econometric treatment more difficult.
Econometric methods are often discussed in water demand studies. The question of endogeneity clearly emerges when researchers choose to introduce as a regressor the average price of water. Depending largely on total water consumption, it can produce a bias of simultaneity because total water consumption is encountered in the two sides of the equation. If the orthogonality condition between the regressors and the error terms fails, Ordinary Least Squares (OLS) technique leads to biased estimates. The endogeneity bias should then be corrected by using Instrumental Variable (IV) estimators, which, together with simultaneous equations, are being more and more commonly employed in recent water demand studies. OLS and IV procedures are inappropriate techniques when the consumer's behavior is described by a two-stage model, or in the case of panel data. The two-step representation of the consumer's choice requires Maximum Likelihood (ML) estimation procedure whether panel data should be treated with specific methods. To our knowledge, Höglund (1997) was the only one to use such techniques on panel data for Sweden.
Despite the difference among econometric methods and various kinds of available data (cross sections, time series, or both), economists generally agree that water demand, with respect to its price, is inelastic but not perfectly so. It seems also widely accepted that, in addition to price, variables such as income and size of the household have significant positive effects on water consumption. Table 1 presents a summary of the most often quoted studies, including details on data used, econometric methods, and the results in terms of price-elasticity.
Recent research on residential water demand emphasize new insights such as the possible complementarity between water and energy. Hansen (1996) shows that in Denmark, water demand is more sensitive to the price of energy than to its own price, due to the wide utilization of heated water. The study by Agthe and Billings (1996) is largely devoted to the adoption by households of new equipment such as low-flow faucets, low-flow shower-heads and drip irrigation
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for gardening. Endogenous technological change is also at the core of the Renwick and Archibald's (1997) paper. Highly desegregated data enable these authors to complete their study with some welfare analysis. In particular, they emphasize the higher sensitivity of low-income households to an increase in the price of water. Finally, numerous studies in the 1990’s were devoted to European countries, e.g. France (Point 1993), Denmark (Hansen 1996), Sweden (Höglund 1997). Despite the relative similarity of results regarding the sign and magnitude of the price-elasticity of water demand for several types of data, economic assumptions and econometric methods should ideally be conducted using repeated survey data from individual households, with appropriate econometric methods.
III. ECONOMIC CONSIDERATIONS
One of the main purposes of studying residential water demand is the estimation of the price-elasticity of demand. This requires carefully designed econometric methods in order to produce unbiased parameter estimates, hence unbiased price-elasticity estimates. When estimating residential water consumption, one should pay a particular attention to the definition of price and the way it is determined. In the case of private companies operating water utilities through a contract with the municipality, the price (marginal and average price) is commonly the result of a negotiation between the municipality and the private operator. Price is decided for the whole contracting period and will largely depend on the expected consumption regime of the municipality. The fact that the price is not solely derived from a profit maximization rule but is the outcome of a negotiation makes the analysis of the local community residential water demand more complex. A full comprehension of the determination of the water price in a municipality is a prerequisite for correctly estimating the water demand function of this local community. In what follows, we describe in more detail the French context in terms of water service and the way price for residential water is negotiated upon.
THE FRENCH W ATER MARKET
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The French 36,551 municipalities are responsible before the law for the satisfactory operation of local water services (supply, treatment and sewage). National legislation requires that adequate (both in quantity and quality) water resources be supplied to every potential user in the local community. In practice, municipalities can decide to operate water utilities by themselves (possibly in association with other local communities) through a local, public water authority. They may also prefer to delegate management of water services to a private company. In both cases, the local community may associate with others, especially when the community is small, to share a common water system or to benefit from economies of scale in operating some of the services. It must be noted that the water system (main pipelines, service connections, reservoirs, treatment facilities,...) is still publicly owned by the municipality, even if it delegates operation and possibly investment in additional facilities to the private operator. Contract-based relationships between the municipality and the private operator are the rule, and conflicts are resolved through the prevailing legal system. There are no central regulation authorities concerned with managerial and legal aspects of water supply. On the other hand, local and national environmental protection agencies may control for environmental aspects related to the service (effluent emission standards in particular). The French system is therefore different from what is found in Great Britain and in the US. In Great Britain, all water utilities are now privatelyowned since the mid-1980’s. Concentration in the water supply industry led to the creation of 10 major regional companies, that are regulated by an independent agency (OFWAT). The OFWAT designs a price-cap policy directed to all 10 private companies. In the US, about 46 percent of water utilities were public, and about 28 percent were privately owned in 1992. Private utilities are subject to public regulation, through state commissions, boards or municipal governments, whereas most public water utilities are not subject to regulation. Public regulation objectives are to adequate and safe service to customers in the local community, and to ensure that service rates are reasonable and fair, given a reasonable efficiency of the system. To do so, public regulation authorities regularly control utility rates of return and base rates (see Beecher 1997).
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In the case of France, it is well recognized that most municipalities prefer to delegate water services when they lack technical know-how and, above all, when their financial burden has become too acute. There are several reasons for this sharp increase in liabilities related to water services. First, deterioration in the quality of groundwater has led the government to impose more stringent quality standards. In order to comply with these standards on distributed water quality, municipalities may have to expand their treatment capacities, or invest in new ones. Second, the European Commission directives on water treatment and wastewater treatment plants require that the vast majority of local communities be properly equipped with such facilities before 2005. Third, the 1992 French Water Act imposes new restrictions on the management of water services by local communities, in the form of a separation in the municipality budget between water services and the other services. Consequently, since the budget for water services has to be balanced, financial transfers from general community taxes or other revenues to these services become impossible. Hence, a private operator may be preferred to a purely public management option, even if the price of water may be higher as a consequence. The two major private companies dominating the French water supply market are the « Compagnie Générale des Eaux » and « Lyonnaise des Eaux ». Table 2 presents the relative importance of private and public operators in French municipal water services in 1993.
PRICE NEGOTIATION BETWEEN MUNICIPALITY AND THE PRIVATE OPERATOR When a private company is chosen by the municipality for managing and operating the water utility, the private firm and the local community decide on the price by mutual consent. More precisely, the relationship between the municipality and the company, which has a local monopoly power is formalized by means of a contract. Considering negotiation on price for water, it is more adequate to refer to water « rate » rather than to water « price ». Indeed, the negotiation ultimately determines the whole rate structure, i.e. both the type of tariff (linear, twopart, increasing-blocks, decreasing-blocks) and the water price charged by unit consumed, for each class of users (farmers, households, industrials). The municipality and the private operator agree on three different elements: a basic tariff, a formula for annual price revision, and clauses allowing for exceptional conditions. The basic
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tariff and the formula for the price revision are determined a priori for the period of the contract. A formula for annual price revision is necessary because the private operator bears operating costs that are affected by variations in input prices and productivity earnings. Moreover, it is also true that exogenous shocks on water demand may affect operating conditions (peak periods). Consequently, the legislation has introduced the possibility of updating the contract terms when appropriate.
The negotiation between the municipality and the private operator is essentially directed on the determination of the basic tariff. The community’s water service board and the private firm have to agree on a price policy that achieves budget balancing for the private operator, while remaining consistent with the orientation of the tariff policy chosen by the municipality. The budget-balancing requirement means that the price charged to water users has to cover both operating and investment costs. Fixed costs consist basically of water system features (system size, importance of leaks among others); variable costs depend essentially on actual water consumption. The prediction of future consumption levels hence plays an essential role during the negotiation. The second element is the orientation of the local tariff policy: the water rate structure and the price charged by unit of consumption are proposed by the municipality executives in charge of water services, according to the municipality objectives.
Let us consider some examples of tariff policies for residential users iii. First, a uniform tariff aims at ensuring equal treatment to all residential users. Second, a two-part tariff (a service charge corresponding to access to water supply, plus a price per unit of water consumed) is the closest picture of the costs incurred by the water service. The service charge corresponds to fixed costs supported by the operator, while the price per unit consumed corresponds broadly to Operation and Maintenance (O&M) costs proportional to water actually supplied and consumed. This type of tariff, which reflects relatively well the expenses incurred for each customer supplied, meets the equity concern. However, in cases where the treatment and supply units reach a point of saturation, the two-part tariff fails to indicate to residential users that an increase in consumption would induce additional investment costs. Third, the proportional tariff (no service
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charge, and a constant price by unit consumed) is the simplest tariff for residential users. However, this system does not provide consumers with proper incentives. By fully reporting fixed costs on every unit of consumption charged, the proportional tariff does not accurately indicate the variation in costs induced by a variation in overall water consumption. Finally, the increasing tariff is sometimes advocated in that it better protects the water resource. It can also be recommended as a mean of redistributing incomes from consumers with a greater water consumption toward consumers with a more modest consumption.
We can easily imagine that municipality’s policy orientations are implemented according to two major steps. First, global priorities are defined in terms of broad categories of users; the municipality may for instance favor residential water consumers, promote urban development, or encourage industrial settling in the community. Second, policy objectives apply within each category of users.
ECONOMIC MODELING The determination of the basic tariff for residential users therefore reduces to a function of three variables: system features, expected water consumption, and objectives of the tariff policy. As choices made by municipalities depend on numerous factors, we consider that policy orientations are predominantly determined by some socio-demographic characteristics of the local communities. In other words, we assume that choices of the municipality and the private operator are made according to, for example, industrial activity, dominant activity (industry, farming) on the local community territory, population density, or the distribution of incomes in the municipality. Let us introduce some notation. Socio-demographic community-related characteristics are P 0 denoted Z , N are system features, C is expected future residential consumption regime. 0 0 0 P 0 Define P = P ( N , C , Z ) as the basic tariff negotiated for the residential users. P represents
the whole price structure, including marginal price(s) and possibly fixed service charges. Finally,
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let C t and Pt respectively denote the actual consumption level and the rate for water (that is actually charged in the municipality) at time t. 0 Differences between Pt and P may occur in practice during the planning period,
depending on two major categories of factors. First, from the supply side, future changes in input price levels need to be accounted for in the contract between the municipality and the private operator. A simple actualization rule is employed, letting changes in water price depend on input price indexes (labor cost, construction cost, energy,...) through a multiplicative coefficient applied to update price. Let k denote that revision (updating) coefficient. k is equal to 1 if no revision is necessary. Second, on the demand side, changes in future demand levels affect operating and maintenance costs as well, even if input price are unmodified, simply because the scale of activity is modified. Such a change in demand is reflected in the gap between actual consumption C t and 0 the expected consumption regime, C . At every period t, price has to adapt (even slightly) to the 0 change in demand around the consumption regime C , so as to equate instantaneous marginal
cost of the service with marginal price for water. Price Pt thus reads:
Pt = k.P0 (N,C 0, Z P ) + P(Ct − C 0 ) ,
(1)
where the first term is the price regime, possibly modulated by input cost changes if k is different from 1. The second expression in the right-hand side above accounts for the modification due to a 0 change in demand from the expected consumption regime. Note that since P is a price structure,
not a single price measure, it is clear that changes in Pt will affect both marginal price and possible fixed service charges.
As explained above, determinants of the municipal price policy are numerous and sometimes complex. Municipal choices may be influenced by other elements such as local lobbies or the water service existing liabilities. It is also true that these choices are likely to be related to socio-demographic variables of the municipality. Using socio-demographic, municipality-related variables to proxy determinants of the price policy is certainly a necessary simplification in the
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P absence of more accurate data. Let u denote the part of the price regime unexplained by the Z
variables, so that price charged at time t to residential users becomes
Pt = k.P0 (N,C 0, Z P ) + P(Ct − C 0 ) + u .
(2)
When negotiating on a contract for water services, both the municipality and the private operator have to make the best prediction of the consumption regime for the next years, and try to anticipate the consumption of each class of users. We focus here only on the residential users’ 0 consumption regime C , assumed to be largely determined by some of the characteristics of the
local community such as average income in the municipality, average housing size, type of C housing (individual or collective housing), average housing equipment. Let Z denote such
municipality-related characteristics, so that C = C (Z ) . 0
0
C
At each period t, actual consumption C t deviates from the expected consumption regime. These differences can be due to severe climatic conditions, a non expected variation of income or may follow from local migrations. Let X t denote these household-dependent variables, so that actual consumption at time t is
Ct = C0 (ZC ) + C(X t ,Pt ) .
(3)
As in the price equation, we have to specify an individual term α representing the consumption C regime that is not explained by variables Z .
The final model specification is:
Pt = k.P0 [ N, C0 (Z C ),Z P ] + P(Ct − C 0 ) + u (4) 0 C (5) Ct = C (Z ) + C(Xt ,Pt ) + α
C Note that the same Z variables appear at two different places in the consumption C equation above, as price depends on the expected consumption regime and therefore on the Z ’s.
Redundant variables could also be found if some of the socio-economic characteristics directly P entering the basic tariff determination are also related to the consumption regime, i.e. if the Z C and Z vectors have elements in common. This could be true of the income variable for
instance. The consumption regime is commonly affected by the level of income and average
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municipality household income could also be one of the central variable determining the tariff policy of the local community. Also, some variables omitted from the price regime equation could be as well omitted from the consumption regime equation. As a consequence, α and u would be correlated. Suppose for example that the local community has the objective of promoting industrial developments in its local area. This could have as a consequence, when negotiating the contract, a policy of cross subsidies favoring industrials and penalizing residential users, thus affecting the price regime for domestic consumers. On the other hand, the settlement of new industries could lead to a growing local population, hence to a higher, unexpected consumption regime for the local community.
To conclude this section, it is essential to keep in mind that the price (either average price or marginal price) is not exogenously given to the municipality. The local community, because of its expected-consumption regime, its specific socio-demographic characteristics and possibly pressure groups influence the price which is then charged to its consumers. An important consequence is that, when focusing on the estimation of residential water demand, some variables could simultaneously enter the price function and the consumption function. This may lead to biased estimates if such a simultaneity is not taken into account.
IV. EMPIRICAL APPLICATION
DATA DESCRIPTION We use a panel data sample of 116 local communities in eastern France, on the period 1988-1993 (T, the number of time periods is 6). These 116 municipalities are supplied by the Compagnie Générale des Eaux, a major private operator (see Section III), which provided us with annual records on aggregate residential consumption (by local community), detailed prices and various technical data on water system features. In the area considered, multiblock pricing only applies to industrials. Consequently, the price policy corresponds to a two-part tariff. For each of the 116 local communities, socio-economic information is obtained from the 1990 French census
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(INSEE 1994). Temperature and rainfall measures are collected from the local meteorological authority (Meteo-France). Summary statistics for variables are presented in Table 3.
Before estimating the residential water demand function, we test for the assumption that the price regime is influenced by the system features and the socio-economic variables. We therefore use both marginal price and average price to test for this influence. Equation (4) gives the price for a representative municipality. Estimation of this equation requires introducing the usual econometric residual. Let i denote the municipality index, t the time period index. The price equation thus becomes
Pit = k.P 0[ Ni ,C 0 (ZiC ), ZiP] + P(Cit ) +ui + uit , where u i
and u it
(6)
are the community-specific and econometric, time-varying residual
respectively. 0 The main component of the price charged at date t is the basic tariff Pi and we assume
that the component P(Cit ) is negligible in the current water price and thus can be included in the last error term uit . The form of the basic tariff function being unknown, we assume a linear form. We therefore estimate the following equation:
Pi = α 0 + α1 .Ni + α 2 .Z i + ui with Pi =
1 T
∑P ; N it
i
=
t
1 ∑N T t it
i =1, 2,..., N and Zi = (Zi , Zi ) . C
P
Pit is either marginal or average price of water in community i at time t ; N it is the vector of water system features, including both the number of service connections (CO) and the number of leaks detected (LEA). The Z i -vector includes the population density (DEN), the industrial activity rate (ACT), the proportion of private housings (HOU), the proportion of recent housings (H82), and the average household income (I).
Estimation results for the average price case are presented in Table 4. Similar results were obtained with the marginal price as the dependent variable and are not reported here. Estimated
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standard errors are computed using the White heteroskedasticity-consistent variance-covariance matrix.
It can be seen that income and the proportion of recent housings have a significant and positive effect on price charged in average on the period, in each local community. We therefore find evidence that there is a significant influence of some socio-economic characteristics of the local community on the water price charged in this community. The number of leaks detected, a variable which reflects the magnitude of maintenance and replacement costs, has also a positive effect on price. Consequently, endogeneity of both marginal and average price has to be checked carefully when estimating the residential water demand function.
ESTIMATING DEMAND : PANEL DATA ECONOMETRIC METHODS The residential water demand consumption equation to be estimated is
Cit = Xit .β + ZiC .γ +α i +ηit
(7)
where Cit represents water consumption in the local community i at time t;
X it is a vector of demand shifters including the price of water, some socio-economic and climatic variables, depending both on local community and the period;
ZC i is a vector of community-specific socio-economic variables; α i is the unexpected water consumption regime and ηit is the usual econometric residual.
As discussed in section III, the municipality-specific consumption regime is explained by C variables Z i , and deviations from this regime are determined by demand shifters X it . The α i
and ηit error terms are assumed to have both zero mean. Since both time-varying and community-specific regressors are present in the demand equation, appropriate panel data methods are required to estimate model parameters. Furthermore, the estimation method
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employed will have to be adapted to the joint presence of error components in the form of residuals and of individual (community-related) effects.
There are two possible sources of endogeneity in the equation above. First, as emphasized C in section III, Z variables could be redundant in the consumption equation, leading to an
endogeneity bias because of the correlation between some explanatory variables and the error term η it . This possible source of endogeneity has to be tested for by performing a test of exogeneity restrictions. The Hausman test uses the fact that the Least Squares estimator on a transformation of variables in Equation (7) (taking deviations from individual means, i.e. « FixedEffects » or « Within » estimation) are consistent and asymptotically efficient under the null hypothesis that explanatory variables are exogenous. It will however be inconsistent under the alternative. On the other hand, an Instrumental Variable estimator (IV) is consistent under both the null and the alternative hypothesis, but it will not be asymptotically efficient under the null. Under the null hypothesis that exogeneity restrictions are valid, the Hausman test statistic has an asymptotic chi-square distribution with degrees of freedom equal to the number of explanatory variables.
Second, endogeneity in the model may be present when the specific, community-related unexpected component of the consumption regime α i is specified as a random component, and is C
correlated with some model regressors ( Xit , Zi ). We then consider a « Random-Effects » panel data model, which requires Generalized Least Squares (GLS) estimation method. As in the first case above, the Hausman exogeneity test statistic may be computed, by comparing the GLS and the « Within » estimator. GLS estimates will be both efficient and consistent if no communityspecific characteristic has been persistently omitted or, in econometric terms, if the individualspecific effect is not correlated with explanatory variables. If this assumption fails, then the random-effects estimator will not be consistent and Within estimates have to be considered. It C remains that coefficients of the time-invariant variables Z are not identified (when deviating
the variables from their individual means, the time-invariant variables are eliminated). Hausman
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and Taylor (1981) propose a IV estimator adapted for models with both time-varying and individual-specific regressors. Let index 1 denote exogenous variables, index 2 denote endogenous explanatory variables. Regressors are decomposed into k 1 time-varying exogenous variables, k 2 time-varying endogenous variables, g1 individual-specific exogenous variables and g 2 individualspecific endogenous variables. The Hausman-Taylor (HT) estimator is based on the following matrix of instruments, written in matrix form:
A = [QX,X1, Z1C ] ,
{
where QX = Xit − Xi
} for all i and all t and the resulting HT estimator is δˆ HT = (Φ ′Ω −1/2 PA Ω− 1/2 Φ) − 1(Φ ′Ω −1/ 2PAΩ−1 / 2 C) ,
−1
with PA = A(A' A) A' and Ω ≡ E(α + η)(α +η)' .
δ$ HT is the vector of parameter estimates corresponding to initial parameters (β, γ ) , Φ is the NT × (k1 + k 2 +g 1 + g 2) -matrix of explanatory variables
( X , X ,Z 1
2
C 1
,Z 2C ) , C is water
−1/ 2 consumption (dependent variable) and PA is a projection matrix. The Ω matrix takes into
account heteroskedasticity specific to panel data models. The identification condition requires that the number of exogenous time-varying variables be greater or equal to the number of endogenous time-invariant variables.
Amemiya and MaCurdy (1986) propose a more efficient IV estimator, adding a new set of * instruments in the form of a matrix denoted X1 . This matrix is obtained by replicating each line
of the matrix X1 T times. The matrix of instruments suggested by Amemiya and MaCurdy is therefore A
AM
= [QX, X1* , Z1C ] and the identification condition in that case becomes Tk1 ≥ g 2 . The
intuition behind this estimator is that, if X1 is exogenous in the sense that we have
E(X1 itαi ) = 0 ∀i , then the individual effect α i should also be uncorrelated with X1 at every time period (i.e. before and after the current period considered).
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More recently, Breusch, Mizon and Schmidt (BMS, 1989) demonstrate that a more efficient estimator can be derived by choosing as instruments the matrix
[
A BMS = QX,(QX1 )*,(QX2 )*, BX1,Z 1C
]
{ } for all i, with the identification condition becoming Tk
where BX = Xi
1
+ (T-1) k 2 ≥ g 2 . The
argument for this estimator is stronger than for the AM estimator. BMS argue that if endogeneity is caused by a correlation between explanatory variables X 2 and the individual effect only, then the components in X 2 that vary over time but are independent from individual effects are also valid instruments.
DEMAND ESTIMATION We now estimate the residential water demand function defined in (7). The X-vector (regressors that vary over both i and t) consists of price variables (AP, MP), average taxable income (I) and the total amount of rainfall during the year and during the three summer months (TOTRAIN, RAIN). The Z-vector of time-invariant (community specific) regressors contains all other socio-economic variables. All variables are in logarithmic form. Specific panel data methods will be employed in order to answer to five main questions:
1) Do consumers respond to average price or to marginal price for water ? 2) Are marginal and average prices exogenous or endogenous variables ? 3) Are there municipality-specific effects that have been omitted in the explanatory variables ?
4) Do socio-economic and climatic conditions have significant effects on water consumption ?
5) Does individual metering matter ?
In order to determine which price variable consumers respond to (marginal, average, both or none), we estimate the water demand function including a decomposed price variable, following Opaluch (1982). The average price is decomposed into the marginal price and a second price
20
variable equivalent to the average price less the marginal price. The price decomposition is, in our case, simplified because of the linear pricing structure. We have AP= MP + (AP-MP). The model estimated is thus of the form:
C = f (MP, AP − MP, I, RAIN,Z C )
(8)
In a first step, we compute the tests described earlier to determine the appropriate estimator for model parameters. The first Hausman test checks for the exogeneity of the price variable. Within estimates are reported in Table 5. In a second step, instrumental Within estimation is performed. The instruments chosen are exogenous time-varying variables: the number of service connections (CO), the number of leaks detected (LEA), the size of the water system (NET) and the two weather variables (RAIN, TOTRAIN). The Hausman test statistic is 3.6, a value below the χ (4) critical value at the five percent level of confidence (9.49). We thus 2
conclude in favor of the exogeneity of the price variables. A second Hausman test is performed to check for the presence of individual-specific effects. GLS estimates are reported in Table 5. The Hausman test statistic is 61.9, which significantly exceeds the critical value for the χ (4) at the five percent level of significance 2
(9.49). The test « Within vs. GLS » hence rejects the null, and therefore accounts for endogeneity in the equation under scrutiny. The assertion made in the economic part is thus verified on our data: there exist persistent omitted explanatory variables in each municipality.
Results of the test call for the use of specific IV estimation procedures as proposed by Hausman and Taylor (HT), Amemiya and MaCurdy (AM) or Breusch, Mizon and Schmidt (BMS). The three estimators are computed with the associated Hausman tests, in order to check for the exogeneity assumption and the validity of the instruments chosen in each case. We assume here that X1 contains the average taxable income (I) and the two rainfall variables (RAIN and TOTRAIN) ; all three variables are initially assumed not to be correlated with the individual error term α i . X 2 contains the price variables (MP and AP-MP). Z 1 is assumed to contain all other socio-economic variables while Z 2 is assumed null. The Hausman test statistics reveal that industrial activity rate (ACT) is correlated with the individual error term. This variable is therefore
21
eliminated from the instruments and included in the Z 2 -vector. One possible explanation for the endogeneity of this variable is that the activity rate is a proxy for the municipality liabilities; these liabilities are not available to us and are likely to be correlated with α i . After eliminating the activity rate from the matrix of instruments, all three Hausman tests confirm the correctness of our choices. We only report in Table 5 the BMS estimates, as they are the most efficient, and yield estimates that are numerically close to HT and AM estimates.
We now consider the tests proposed by Opaluch (1982). The parameter associated to marginal price, β1 , is -0.072 whereas the coefficient of the second price variable, β 2 is equal to -0.216 (see Table 5). Both are significantly different from zero. The test statistic associated with the equality restriction for these parameters is
[( β
2
− β1 ).(var(β2 − β 1))−1 / 2 ] , which is normally
distributed under the null. The test statistic is equal to 4.15, which exceeds the critical value of 1.96 at the 5% level of significance. Therefore, neither the marginal price model nor the average price specification can be rejected. This result can be explained by the fact that the correlation between the marginal and the average price is close to one. This significant correlation is linked to the overwhelming part of marginal price in the average price. If we decompose the average price as the sum of the marginal price and the ratio [fixed charges over total quantity consumed], it appears that the former is largely superior to the latter.
Therefore, we consider a second specification for the residential demand equation, in which the only price variable is average price. Moreover, household water expenditures in France represent on average 1.5 to 2 percent of households net income, and few consumers know the marginal price of water whereas most of them remember their last water utility bill. The average price model is of the form
C = f (AP, I, RAIN, Z C )
(9)
Estimation results for this model are presented in Table 6. The five Hausman tests lead to the same conclusions as for Equation (8) that is, exogeneity of the explanatory variables and
22
among them the average price of water, and the presence of local community-specific effects. Exogeneity of average water price could appear surprising at first, but if we recall the result above concerning the high degree of correlation between marginal and average prices, the explanation is clear. The component of average price depending on total water consumption is negligible in regard to the marginal price.
Let us comment on the results concerning the other explanatory variables. We will consider parameters estimated by the BMS procedure, as this method allows for identification of all parameters and is the most efficient IV estimator. The parameter associated with average price is significantly different from zero. Consumers would respond to changes in the average price of water by lowering consumption by about 22% of the relative change in the average price. The price-elasticity of -0.22 is close to the value estimated by Point (1993) on France (-0.17). Average taxable income has a statistically significant positive effect on the consumption of water (around 0.1). It is important to note that the local communities in which the proportion of recent housings (built after 1982) is large use relatively less water, all other things equal. The explanation can be the lower age of existence of the system pipes, hence reducing the probability of leaks. The results also emphasize that local communities in which more housings are equipped with a bath tub consume much more water than communities where housings are more largely equipped solely with a shower or a washbasin. Hence, inside consumption seems to dominate in the total amount of water consumed. In other words, the share of water intended to sprinkling is small in this region of France. This fact can be related to the non-significant rainfall variable. An interesting result concerns water meters. Living in an individual housing has a statistical significant negative effect (-0.44) on water consumption. The presence of individual water metering has therefore a non negligible influence. To this respect, many public and private operators in France have considered a generalization of water metering systems in the near future, to provide consumers with incentives for adequate day-to-day management of their water use. OLS estimations are also performed on Equations (8) and (9). OLS coefficients are rather similar to the ones estimated by specific panel data methods. The reason is that, explanatory variables being exogenous, no bias of simultaneity occurs.
23
V. C ONCLUSION
Many empirical papers dealing with the estimation of residential water demand largely document the endogeneity issue of average price in the demand equation. When using aggregate data on a panel of municipalities, it is important to determine precisely the source of price endogeneity, which may be due to local community effects. The way price is negotiated between the municipality and the private operator is an important determinant of water consumption trends, and it often depends on expected consumption regime at the local community level for the planning period. Consequently, socio-demographic variables appear both as water demand shifters and as determinants of the municipal price regime. In the case of France, many water utilities are privately operated, though publicly owned. In that case, water price is negotiated between the local community and a private operator for a given planning period. Local community-dependent variables such as average income and average housing characteristics are determinant in the setting of price rates and contract terms.
This paper proposes a model of water price determination in the case of a private company operating a municipal water utility. We highlight in particular the importance of expected consumption per head within the municipality in the price policy adopted. The model is estimated using a panel sample of French municipalities. Estimation results indicate that households respond to both average and marginal prices, with a significant but low price elasticity of -0.22 in the case of average price. A significant income effect is also found, with an income elasticity estimated at 0.1. Furthermore, residential water consumption is significantly lower when individual housing with meter recording is dominant. This result advocates for the development of water metering in collective housings. As far as policy implications for regulating the demand side are concerned, it is not immediate that a price policy would induce a substantial reduction in residential consumption. Indeed, residential demand appears poorly sensitive to price variations. Hence, non-price policies such as
24
low-flow equipment promotion, awareness campaigns and education programs should also be considered. Short-run determinants of residential water consumption are now well established and should be completed by long-run considerations. In particular, household equipment in durable, water-consuming goods could be targeted by policy makers. Subsidy programs for low-flow facilities and new technology adoption may prove useful to complement price policies in periods of severe water shortages.
25
REFERENCES
AGTHE, D.E., and R.B. B ILLINGS [1996], « Water-Price Effect on Residential and Apartment Low-Flow Fixtures », Journal of Water Resources Planning and Management, 20-23. AMEMIYA, T. and T.E. MA CURDY [1986], « Instrumental-Variable Estimation of an ErrorComponents Model », Econometrica, 54(4), 869-880. AHN , S.C. and P. SCHMIDT [1995], « Efficient Estimation of Models for Dynamic Panel Data », Journal of Econometrics, 68, 5-27. AHN , S.C. and P. SCHMIDT [1997], « Efficient Estimation of Dynamic Panel Data Models: Alternative Assumptions and Simplified Estimation », Journal of Econometrics, 76, 309-321. ANDERSON , T.W. and C. HSIAO [1981], « Estimation of Dynamic Models with Error Components », Journal of the American Statistical Association, 76, 598-606. ARELLANO , M. and S. B OND [1991], « Tests of Specification for Panel Data: Monte Carlo Evidence and Application to Employment Equations », Review of Economic Studies, 58, 277297. BALESTRA, P. and M. N ERLOVE [1966], « Pooling Cross Section and Time Series Data in the Estimation of a Dynamic Model: The Demand for Natural Gas », Econometrica, 34, 585-612. BEECHER, J.A. [1997], « Water Utility Privatization and Regulation : Lessons from the Global Experiment », Water International, 22, 54-63. BILLINGS, R.B. [1982], « Specification of Block Rate Price Variables in Demand Models », Land Economics, 58(3), 386-394. BREUSCH, T.S., MIZON , G.E. and P. SCHMIDT [1989], « Efficient Estimation Using Panel Data », Econometrica, 57(3), 695-700. BURTLESS , G. and J.A. HAUSMAN [1978], « The Effect of Taxation on Labor Supply: Evaluating the Gary Negative Income Tax Experiment », Journal of Political Economy, 86(6), 1103-1130.
26
CHICOINE, D.L., DELLER S.C. and G. RAMAMURTHY [1986], « Water Demand Estimation Under Block Rate Pricing: A Simultaneous Equation Approach », Water Resources Research, 22(6), 859863. CHICOINE, D.L. and G. R AMAMURTHY [1986], « Evidence on the Specification of Price in the Study of Domestic Water Demand », Land Economics, 62(1), 26-32. CREPON , B., K RAMARZ F. and A. TROGNON [1993], « Parameter of Interest, Nuisance Parameter and Orthogonality Conditions: An Application to Autoregressive Error Component Models », mimeo, INSEE. DANIELSON , L.E. [1979], « An Analysis of Residential Demand For Water Using Micro TimeSeries Data », Water Resources Research, 15(4), 763-767. DELLER , S.C., C HICOINE, D.L. and G. RAMAMURTHY [1986], « Instrumental Variables Approach to Rural Water Service Demand », Southern Economic Journal, 53(2), 333-346. FOSTER , H.S., Jr. and B.R. BEATTIE [1979], « Urban Residential Demand for Water in the United States », Land Economics, 55(1), 43-58. GUELLEC , A. [1995], « Le prix de l’eau », Assemblée Nationale, Paris. GIBBS, K. [1978], « Price Variable in Residential Water Demand Models », Water Resources Research, 14(1), 15-18. HANSEN , L.G. [1996], « Water and Energy Price Impacts on Residential Water Demand in Copenhagen », Land Economics, 72(1), 66-79. HAUSMAN , J.A. and W.E. T AYLOR [1981], « Panel Data and Unobservable Individual Effects », Econometrica, 49(6), 1377-1398. HÖGLUND , L. [1997], « Estimation of Household Demand for Water in Sweden and its Implications for a Potential Tax on Water Use », mimeo, University of Göteborg. HEWITT, J.A. and W.M. HANEMANN [1995], « A Discrete/Continuous Choice Approach to Residential Water Demand under Block Rate Pricing », Land Economics, 71(2), 173-192. HOWE , C.W. and F.P. LINAWEAVER [1967], « The Impact of Price on Residential Water Demand and Its Relation to System Design and Price Structure », Water Resources Research, 3(1), 13-32. I NSEE [1994], Recensement Général de la Population, Paris.
27
MOFFITT, R. [1986], « The Econometrics of Piecewise-Linear Budget Constraints », Journal of Business and Economic Statistics, 4(3), 317-328. MOFFITT, R. [1990], « The Econometrics of Kinked Budget Constraints », Journal of Economic Perspectives, 4(2), 119-139. NIESWIADOMY, M.L. and D.J. MOLINA [1989], « Comparing Residential Water Demand Estimates under Decreasing and Increasing Block Rates Using Household Data », Land Economics, 65(3), 281-289. NORDIN, J.A. [1976], « A Proposed Modification of Taylor’s Demand Analysis: Comment », The Bell Journal of Economics, 7, 719-21. OPALUCH , J.J. [1982], « Urban Residential Demand for Water in the United States: Further Discussion », Land Economics, 58(2), 225-227. P HILLIPS , C.F. [1993], The regulation of public utilities, Public Utilities Report, Inc., Arlington, Virginia. P OINT , P. [1993], « Partage de la ressource en eau et demande d’alimentation en eau potable », Revue économique, 4, 849-862. RENWICK , M. and S. A RCHIBALD [1997], « Demand Side Management Policies for Residential Water Use: Who Bears the Conservation Burden », mimeo, University of Minnesota. SCHEFTER , J.E. and E.L. DAVID [1985], « Estimating Residential Water Demand under Multi-Part Tariffs Using Aggregate Data », Land Economics, 61(3), 272-280. T AYLOR , L.D. [1975], « The Demand for Electricity: A Survey », The Bell Journal of Economics, 6, 74-110.
28
Table 1. Summary of some studies in residential water demand Authors
Data*
Study area
Econometric method
Price-Elasticity value
Howe-Linaweaver (1967)
CS
USA
OLS
-0.23
Gibbs (1978)
CS
Miami, Florida (USA)
OLS
-0.51
Foster-Beattie (1979)
CS
USA
OLS
-0.52
Billings (1982)
TS
Tucson, Arizona (USA)
IV
-0.70
Schefter-David (1985)
CS
Wisconsin (USA)
OLS
-0.12
Chicoine et al. (1986)
CS
Illinois (USA)
Simultaneous equations
-0.71
Chicoine-Ramamurthy (1986)
CS-TS
Illinois (USA)
OLS
-0.48
Nieswiadomy-Molina (1989)
CS-TS
Denton, Texas (USA)
IV, 2SLS
-0.86 1 to -0.36 2
Point (1993)
CS
Gironde (France)
OLS
-0.17
Hansen (1996)
TS
Copenhagen (Denmark)
OLS
-0.10
Santa-Barbara, California (USA) Sweden
2SLS
-0.33
Panel data techniques
-0.20
Renwick-Archibald (1997) CS-TS Höglund (1997)
CS-TS
*: CS for Cross Section, TS for Time Series 1: consumers are facing increasing block rates 2: consumers are facing decreasing block rates
Table 2. Local water services in France
public operators
private operators
Water supply
Wastewater treatment
15% of the population
55% of the population
900 local communities
2650 local communities
85% of the population
45% of the population
3500 local communities
1750 local communities
Source: Guellec (1995).
Table 3. Descriptive statistics for variables in the sample
Variable
Y AP MP DEN AGE60 HH ACT HOU BATH CAR H49 H82 I RAIN TOTRAIN CO LEA NET with
Type
CS-TS CS-TS CS-TS CS CS CS CS CS CS CS CS CS CS-TS CS-TS CS-TS CS-TS CS-TS CS-TS
Mean Standard Minimum Maximum Deviatio n 152.68 40.43 8.95 3.37 8.00 3.32 265.87 490.65 18.51 5.53 42.96 8.55 90.64 4.14 75.11 17.03 82.94 10.92 81.31 7.13 38.87 20.24 13.21 7.45 106 797.44 16 325.22 183.97 46.68 774.21 112.41 5 106.00 5 515.00 273.00 285.00 197.00 184.00
76.00 334.00 3.34 20.66 3.09 19.48 8.69 3 818.33 6.60 48.57 25.45 66.67 76.38 100.00 10.10 100.00 26.67 96.22 62.16 96.21 2.32 88.46 1.00 39.31 63007.00 180 533.00 108.00 299.70 474.10 1 087.50 78.00 15 907.00 2.00 908.00 2.00 511.00
Y, average annual consumption of residential water (cubic meter/subscriber) ; AP, average price of residential water defined as total bill divided by total consumption (FF/cubic meter) ; MP, marginal price of water defined as the price of the last unit of consumption (FF/cubic meter) ; DEN, population density (number of inhabitants/square kilometer) ; AGE60, proportion of inhabitants aged more than sixty in the whole population of the community ; HH, proportion of households composed of one or two members ; ACT, industrial activity rate ; HOU, proportion of private housings in the population of the community homes ; BATH, proportion of homes equipped with a bath ; CAR, proportion of homes of which the occupant owns one or more car ; H49, proportion of housings built before 1949 in the total population of housings (including occasional housings, second homes, and vacant housings); H82, proportion of housings built after 1982 in the total population of housings (including occasional housings, second homes, and vacant housings); I, average taxable income (FF/taxable household) ; RAIN, total amount of rainfall measured in June, July and August ; TOTRAIN, total amount of rainfall measured in year t ; CO, number of service connections; LEA, number of leaks detected ; NET, size of the water system (kilometers of mainlines).
Table 4: Estimation of the price equation parameters
Variable Estimated Coefficient
t statistic
constant
-7.19 (**)
-2.836
DEN
0.04
1.465
ACT
-0.01
-0.216
HOU
0.03
1.084
H82
0.06 (**)
2.486
I
0.73 (**)
3.401
LEA
0.17 (*)
1.757
CO
-0.07
-0.658
Notes : (*) and (**) indicate a parameter significant at the 5% and 1% level respectively. Number of observations : 116. R2 : 0.244.
TABLE 5. MODEL WITH DECOMPOSED PRICE VARIABLE Test
Degrees of freedom
Test statistic
P-value
4 4 2 4 4
3.550 61.879 3.964 5.129 2.552
0.470 1.2e-012 0.138 0.274 0.635
OLS -4.883(**) (-4.666)
Within ...
GLS -0.481 (-1.465)
BMS -0.458 (-1.394)
MP
-0.158(**) (-7.653)
-0.019 (-0.818)
-0.086(**) (-4.838)
-0.072(**) (-3.550)
AP-MP
-0.172(**) (-12.067)
-0.265(**) (-11.350)
-0.210(**) (-13.082)
-0.216(**) (-10.796)
0.472(**) (8.803)
0.024 (0.574)
0.123(**) (3.333)
0.109(**) (2.885)
RAIN
0.024 (0.892)
-0.007 (-0.755)
-0.010 (-1.038)
-0.008 (-0.907)
DEN
-0.000 (-0.892)
...
-2.4e-005 (-0.148)
-1.6e-005 (-0.099)
-0.102(*) (-2.388)
...
-0.169(*) (-2.543)
-0.171(**) (-2.577)
0.043 (0.686)
...
0.160 (1.660)
0.164 (1.696)
0.833(**) (3.787)
...
1.039(**) (2.999)
1.051(**) (3.031)
-0.239(**) (-8.105)
...
-0.207(**) (-4.504)
-0.203(**) (-4.364)
BATH
0.099 (1.492)
...
0.072 (0.697)
0.060 (0.585)
CAR
0.394(*) (2.571)
...
0.464(*) (1.928)
0.462 (1.916)
H49
0.060(**) (4.115)
...
0.057(**) (2.596)
0.058(**) (2.614)
H82
-0.170(**) (-11.220)
...
-0.176(**) (-7.468)
-0.178(**) (-7.459)
Within / Within+instruments Within / GLS Within / HT HT / AM AM / BMS constant
I
AGE60 HH ACT HOUSE
t statistics are in parentheses ; significance at the 5% and 1% level denoted by (*) and (**) respectively ; ... : not identifiable.
TABLE 6. AVERAGE PRICE MODEL Test
Degrees of Test statistic freedom
Within / Within+instruments Within / GLS Within / HT HT / AM AM / BMS
P-value
3
2.219
0.528
3 1 4 4
17.497 1.302 2.544 2.971
5.6e-4 0.254 0.637 0.563
OLS -5.786(**) (-5.119)
Within ...
GLS -0.487 (-1.357)
BMS -2.740(**) (-3.216)
-0.244(**) (-10.007)
-0.205(**) (-9.858)
-0.217(**) (-11.143)
-0.215(**) (-10.605)
0.491(**) (8.438)
0.061 (1.344)
0.106(*) (2.489)
0.092(*) (2.104)
RAIN
0.010 (0.355)
-0.017 (-1.675)
-0.017 (-1.688)
-0.017 (-1.688)
DEN
-0.000 (-0.812)
...
-3.7e-005 (-0.149)
-2.2e-005 (-0.086)
AGE60
-0.065 (-1.412)
...
-0.135 (-1.323)
-0.222(*) (-2.089)
0.005 (0.078)
...
0.133 (0.897)
0.063 (0.421)
ACT
0.835(**) (3.498)
...
1.047(*) (1.961)
6.219(**) (3.357)
HOU
-0.310(**) (-10.011)
...
-0.302(**) (-4.334)
-0.436(**) (-5.223)
BATH
0.180(*) (2.535)
...
0.209 (1.331)
0.589(**) (2.886)
CAR
0.568(**) (3.435)
...
0.705 (1.908)
-1.233 (-1.622)
H49
0.088(**) (5.600)
...
0.086(*) (2.567)
0.036 (0.953)
H82
-0.126(**) (-7.960)
...
-0.117(**) (-3.297)
-0.119(**) (-3.349)
constant AP I
HH
t statistics are in parentheses ; significance at the 5% and 1% level denoted by * and (**) respectively ; ... : not identifiable.
i
To be presented at the EAERE annual meeting in Venice, June 1998. Part of this paper was
written while the second author was visiting University of Wisconsin-Madison. We thank O. Alexandre (Cemagref Strasbourg), M. Muller (CGE Région Est) for the data used in the paper, R. Boumahdi and M. Moreaux for helpful comments. All remaining errors are ours.
ii
E.R.N.A.-I.N.R.A., Université des Sciences Sociales de Toulouse, 21 Allée de Brienne, 31000
Toulouse, France. Email:
[email protected],
[email protected]
iii
The 1992 Water Act also prohibits a lump sum fee to be charged to residential consumers.
