The Effects of Source Water Quality on Drinking Water Treatment Costs: A Review and Synthesis of Empirical Literature

Abstract

Watershed protection, and associated in situ water quality improvements, has received considerable attention as a means for mitigating health risks and avoiding expenditures at drinking water treatment plants (DWTPs). This study reviews the literature linking source water quality to DWTP expenditures. For each study, we report information on the modeling approach, data structure, definition of treatment costs and water quality, and statistical methods. We then extract elasticities indicating the percentage change in drinking water treatment costs resulting from a 1% change in water quality. Forty-six elasticities are obtained for various water quality parameters, such as turbidity, total organic carbon (TOC), nitrogen, sediment loading, and phosphorus loading. An additional 29 elasticities are obtained for land use classification (e.g., forest, agricultural, urban), which often proxy source water quality. Findings indicate relatively large ranges in the estimated elasticities of most parameters and land use classifications. However, average elasticities are smaller and ranges typically narrower for studies that incorporated control variables consistent with economic theory in their models. We discuss the implications of these findings for a DWTP’s incentive to engage in source water protection and highlight gaps in the literature.

1. Introduction

Drinking water treatment plant (DWTP) design and operation is based on, among other considerations, the physical, chemical, and microbiological characteristics of its source water. Within design limits, DWTPs respond to water quality declines by altering treatment processes (e.g., retention time, chemical dosing, etc.) to meet potable water standards and performance objectives. Dramatic declines in water quality, due to severe algal blooms or the presence of cyanobacteria, may occasionally result in temporary plant shutdowns and drinking water advisories (Henry 2013, Kansas Department of Health and Environment 2011, Snider 2014). When water pollution regularly exceeds design thresholds, DWTPs may purchase new capital assets or develop alternate source water resources (Hanson et al. 2016, Jones et al. 2007), which, in turn, can lead to higher water rates for consumers. The effect of reduced source water quality is thus a potential decrease in consumer welfare and, notwithstanding temporary shutdowns, an unequivocal increase in treatment costs. Estimates of these welfare effects have been included in US Environmental Protection Agency (EPA) assessments of surface water quality regulations (Griffiths et al. 2012).

Source water protection (SWP), defined broadly as actions that safeguard source water conditions from adverse impacts prior to intake, has received growing attention as part of a multi-barrier approach to mitigating water-related health risks and avoiding treatment costs. For instance, the 1996 amendments to the US EPA’s Safe Drinking Water Act authorized funding for SWP programs and required states to perform assessments of source waters to determine their susceptibility to contamination (Tiemann 2014). Recent additions to California’s Water Code establish source watersheds as part of a DWTP’s infrastructure; financing for repair to source watersheds is also made available (California Water Code §108.5 2016). Moreover, recent literature indicates that dozens of municipalities are engaged in SWP activities (sometimes referred to as water funds or natural infrastructure), such as land acquisition and management, compensation to landowners for adopting best management practices, and public education campaigns (Abell et al. 2017, Bennett et al. 2014, Carpe Diem West 2011, Dudley and Stolton 2003, Gartner et al. 2013, Herbert 2007). These practices have, in some instances, been linked to reductions in key water quality impairments, including turbidity, pesticides and nutrients, with the latter subsequently linked to lower algae concentrations and a lower probability of algal and cyanobacteria bloom events. Boston has a well-known SWP program. Since the 1980s, the city has undertaken extensive watershed management efforts, at a cost of $135 million for land acquisition alone, to avoid the cost of constructing and operating a filtration plant (Alcott et al. 2013). As a result, the city has maintained a waiver from filtration under the US EPA’s Surface Water Treatment Rule. Other high-profile examples of municipalities engaged in SWP include New York, Denver, Salt Lake City, San Antonio, Santa Fe, and Seattle (Bennett et al. 2014, Carpe Diem West 2011). Outside the US, SWP has been adopted by cities as diverse as Munich, Stockholm, Sydney, Tegucigalpa, Tokyo, and Victoria (Capital Regional District 2017, Dudley and Stolton 2003).

The notion that SWP is more cost effective than traditional treatment processes is common—but evidence from high-quality benefit-cost analyses (BCAs) is limited (Gartner et al. 2013, Herbert 2007). The validity of any such analyses partially rests on having an accurate understanding of linkages between ecosystems, hydrologic systems, and DWTPs. This review, motivated to better understand these linkages and to facilitate BCAs, consolidates available evidence from studies that use cost functions, or related approaches, to quantify the relationship between measures of water quality and treatment cost. From these studies, we extract elasticities that indicate how costs respond to marginal changes in water quality. Average elasticities are then calculated for key water quality measures. We discuss the implications of this review for SWP decisions and highlight notable gaps in the literature.

2. Theoretical Framework

Production theory provides an overarching framework for the avoided treatment cost literature (Varian 1992). Most studies we looked at, regardless of data structure or statistical methods, relate source water quality to treatment costs using either a cost function or price function approach. Some studies use alternate approaches that rely, sometimes implicitly, on the underlying cost minimization assumption inherent in these functions. We address these approaches later. Here we develop cost and price function models for a DWTP using non-purchased source water.

Cost functions define the minimum cost needed to produce a predetermined output. They are well-suited for modeling DWTP behavior, which is usually constrained by some form of revenue control (i.e., caps on revenue, service charges, or rates-of-return) and a requirement to meet customer demand for set water rates (Estache and Rossi 2002, Renzetti and Dupont 2009). Cost functions are classified as either short- or long-run. In the short-run, capital inputs are assumed fixed and a DWTP minimizes costs by optimally choosing quantities of the variable inputs. In the long-run, capital is also variable, as new treatment facilities can be constructed or source waters tapped, and optimization occurs in the choice of all inputs. Formally, short- and long-run cost functions for a single-output DWTP are

$$c_{\mathit{\text{sr}}}=f(y,P_X,K,Q)$$

$$c_{\mathit{\text{lr}}}=f(y,P_X,P_K,Q),$$

where c_sr represents short-run total costs, c_lr long-run total costs, y the volume of potable water, P_X a vector of variable input prices, P_K a vector of capital input prices, K a vector of quasi-fixed capital inputs, and Q a vector of source water characteristics. For concreteness, Q can be viewed as a set of physical, chemical, and microbiological water quality measures. Since these parameters affect a DWTP’s choice of treatment technology, capital stock in the short-run function can itself be considered a function of Q (i.e., modeled as K(Q)). Statistical estimation of the cost function requires a specified functional form (e.g., linear, Cobb-Douglas, and trans-log).

The price function is a related modeling approach. It is based, as before, on cost minimization, but also hinges on the assumption that water rates are set equal to a DWTP’s long-run average costs (Abildtrup et al. 2013). This latter condition is applicable to DWTPs—typically publicly managed systems—that operate under a balanced budget constraint. The price function for such a DWTP is

$$r=f(y,P_X,P_K,Q),$$

where r is the water rate and the remaining elements are defined as before.¹ Similar to the cost function, statistical estimation requires a specified functional form.

3. Literature Search and Selection Criteria

We conducted a thorough search for studies linking treatment costs and source water quality, which considered peer-reviewed and gray literature from multiple disciplines, including economics, environmental science, and civil engineering. Three ex ante defined criteria were used to identify studies relevant for this review. Specifically, a study needed to

• establish an original, quantitative functional relationship between costs and source water quality or select proxies for water quality;

• use historic cost information obtained from community water systems (CWSs); and

• clearly describe data sources, methodological procedures, and results.²

The criteria are deliberately imprecise in several respects to accommodate the broad spectrum of source water issues facing treatment facilities, and to allow for differences in research aims and data availability. Studies meeting our criteria make use of various physical, chemical, and microbiological water quality parameters. These parameters represent different spatial scales (e.g., source water body, source watershed, etc.) and methods of measurement. Similarly, studies make use of diverse cost measures that vary with respect to expenditure types, timeframes, and units of measurement.

Included in the review are studies that proxy water quality with land use classifications. Broad causal relationships between land use and surface water quality are well established; they indicate that forestland, relative to agriculture and urban land, is associated with lower concentrations of non-point source pollutants (e.g., suspended sediment, nutrients) and more desirable microbiological communities (Baker 2003, Dudley and Stolton 2003). Forestland is also associated with better groundwater quality (Lerner and Harris 2009), which is vulnerable to both point and nonpoint source pollution. Depending on geological and hydrological characteristics of the aquifer, it can take years, decades, or centuries, for surface water to infiltrate to the aquifer wherein it becomes a component of a DWTP’s source water (Lerner and Harris 2009). We consider, but ultimately exclude, studies that employ precipitation and streamflow as proxy measures for water quality. While precipitation often leads to deteriorated water quality via increased runoff, its effects can be ambiguous, being dependent on the importance of the runoff relative to a dilution effect that reduces contaminant concentrations (Holmes 1988, Vincent et al. 2016). Moreover, both precipitation and streamflow measures confound issues of water availability and water quality, which are known to have distinct effects on treatment costs (Heberling et al. 2015, Renzetti 2001).

We require that studies use historic cost information from CWSs. Studies employing predicted cost data, pilot programs, or non-community systems are consequently excluded from the review. Predicted costs are expenditures estimated for a certain type of treatment technology, or set of technologies, using engineering or statistical relationships developed elsewhere. These costs, while suitable to many applications, introduce measurement error that can bias estimated relationships if they are correlated with model covariates such as output volume or source water quality. This error can be substantial, with predictions differing from actual costs by +50 to −30% (McGivney and Kawamura 2008). Even when tailored to a specific DWTP, predicted and actual costs will differ since the former are based on historical averages that ignore site-specific differences in some plant design features, operational practices, input prices, and customer characteristics.

Finally, we exclude from the review several studies that are missing vital pieces of information, or are reproduced elsewhere, but that otherwise meet the selection criteria. Most of these studies are not centrally concerned with avoided treatment costs. A complete list of studies not meeting our selection criteria, and a rationale for their exclusion, is available upon request.

4. The Avoided Treatment Cost Literature

An initial literature search identified several hundred potentially relevant manuscripts, from which 24 met the aforementioned criteria. Despite similar frameworks, these studies exhibit considerable heterogeneity due to differences in motivation, data availability, and modeling approaches. Characteristics of the studies are reported in Table A; they pertain, unless otherwise noted, to the preferred specification of the model relating costs to source water quality. Where there is ambiguity about a characteristic, we report the most likely information based on available evidence and note the uncertainty. An augmented version of Table A containing additional information and a database of elasticities that can be sorted or filtered are available in Appendix B - Supplementary Material.

4.1. Geography and Motivating Factors

A majority of the 24 selected studies are based in the US (n = 15), with the remainder conducted in Canada, France, India, Japan, Malaysia, and Spain. In the US, roughly 47% (n = 7) use subnational samples (i.e., they evaluate data for a single DWTP or region). The US studies are concentrated in the Midwest (Forster et al. 1987, Forster and Murray 2007, Heberling et al. 2015), but also include Oregon (Moore and McCarl 1987), Texas (Dearmont et al. 1998), Oklahoma (Oklahoma Water Resources Board 2011), and the Great Lakes Region (Murray 2001). By comparison, 66% of non-US studies use subnational samples. All national level analyses pertain to high-income countries where there is access to DWTP-related databases maintained by government agencies or professional associations.

The selected studies cite a diverse set of objectives and underlying motivations. Nonpoint source pollution from agricultural runoff (e.g., sediment, nutrients, pesticides) is the key concern for many US studies (n = 8), as well as for France-based Abildtrup et al. (2013) and Fiquepron et al. (2013). For these analyses, avoided treatment costs represent a lower-bound estimate of externalities imposed by upstream agriculture. Another more geographically disperse set of studies (n = 7) are principally concerned with how forest landscapes, and associated disturbances (e.g., logging, wildfire), affect source water quality within associated watersheds. In a recent example, Vincent et al. (2016) find a negative correlation between forestland (relative to non-forestland) and short-run treatment cost at Malaysian DWTPs. The correlation is significantly larger for virgin forestland than logged forestland. These analyses, in contrast to those motivated by nonpoint source pollution, view avoided treatment costs to be a lower-bound estimate of ecosystem services benefits provided by forest resources. The remaining studies cite other motivations, including evaluating water quality standards, omitted variable bias in cost efficiency estimates, welfare implications of source water quality changes, and endogeneity between technology choice and ecosystem service values. Avoided treatment costs are a secondary concern for these analyses.

4.2. Data Structure

The specifics of any analysis are largely dictated by the structure and content of available data. Many studies rely on cross-sectional survey data (n = 13) that may not be designed to assess avoided treatment costs. Four studies use data obtained from American Water Works Association member surveys (Holmes 1988, Mosheim 2006, Mosheim and Ribaudo 2017, Piper 2003). These surveys are primarily intended to provide CWS managers with organizational and operational information about other treatment systems. They are not based on a random sampling framework.

Selected studies also make use of panel (n = 6) and time-series (n = 5) data. While these data may be obtained via surveys, they are more likely to entail direct communication with water providers and more targeted information gathering. An advantage of these data structures is the potential to control for unobserved characteristics (e.g., treatment processes, population traits, input price variation) that when omitted from cross-sectional analyses may bias estimated model coefficients. In practice, however, less than half of the studies using panel or time-series data employ estimation techniques that capitalize on this benefit.

Datasets vary considerably in their number of observations. Among cross-sectional analyses, observations range from fewer than 50 (Ernst et al. 2004, Freeman et al. 2008, Mosheim and Ribaudo 2017, Oklahoma Water Resources Board 2011, Renzetti 2001, Warziniack et al. 2017) to nearly 1000 (Price et al. 2017). The smallest panel datasets contain 5 years of annual observations for fewer than 15 DWTPs (Forster and Murray 2007, Murray 2001). In contrast, the largest dataset, exploited by Vincent et al. (2016), contains 15 years of monthly observation for 41 DWTPs. Time-series datasets used by Moore and McCarl (1987), Honey-Rosés et al. (2014), and Heberling et al. (2015) have 247, 963, and 1826 daily observations, respectively. Singh and Mishra (2014) use 144 monthly observations.

Studies can be further classified by their unit of analysis. Most are conducted at the DWTP level (n = 14), and therefore relate expenditures incurred at a treatment facility to measures of that facility’s influent water quality. A second group of studies are conducted at the CWS level (n = 8), which often operate multiple DWTPs that draw from source waters with different water quality characteristics. Similarly, Fiquepron et al. (2013) and McDonald and Shemie (2014) use units based on geopolitical boundaries that also contain multiple DWTPs and source waters. Cost data in these studies typically reflect expenditures for all DWTPs within the unit of analysis, while covariates, including source water quality measures, are usually defined as the weighted average across the DWTPs. Most studies evaluate DWTPs that rely on surface water inputs (n = 18), while the remaining studies evaluate both surface water and groundwater facilities. There are no studies that pertain exclusively to groundwater DWTPs. Since surface water systems are on average larger than groundwater systems, the datasets used by selected studies consist of relatively large DWTPs (US EPA 2009b). In the US, where most facilities are small groundwater systems, the average CWS produces 3700 m³/day of potable water.³ By comparison, average production in the US based studies ranges from 3530 to 183,700 m³/day. Across all studies, the DWTPs evaluated by Abildtrup et al. (2013) and Fiquepron et al. (2013) have the smallest production. In Abildtrup et al. (2013) production ranges from 4 to 7640 m³/day, with an average of 290 m³/day. The DWTPs evaluated by Horn (2011) and Warziniack et al. (2017) exhibit the largest range in production; both studies include facilities producing ≤600 m³/day and ≥1,000,000 m³/day.

4.3. Cost, Water Quality, and Control Variables

There are several differences between the cost, water quality, and control variables used in the selected studies. These differences should be considered when comparing results across studies as they will affect estimated relationships between costs and water quality measures irrespective of differences in study sites.

Cost variables are expressed in a variety of different currencies, time periods, and production quantities. For this review, however, the principle difference pertains to the scope of expenditures encompassed by the variable. In their most restricted form, costs are limited to expenditures related to a single type of input. Dearmont et al. (1998), Forster and Murray (2007), and Warziniack et al. (2017) exemplify this approach; they establish a function relationship between expenditures on treatment chemicals and changes in source water quality. Many studies (n = 8) use a broader definition of costs that includes expenditures for multiple inputs into the treatment process (e.g., labor, chemicals, electricity). These costs, henceforth referred to as O&M costs, are themselves heterogeneous, with some studies also including expenditures related to facility maintenance, source water acquisition, and treated water distribution. In their broadest form, costs include expenditures on all variable and capital inputs. Horn (2011), Ernst et al. (2004), and Renzetti (2001) define costs in this manner, where capital expenditures are based on dedicated construction costs, depreciation, and debt payments. Studies utilizing a price function approach (Abildtrup et al. 2013, Fiquepron et al. 2013, Piper 2003) fall into this category since water rates are assumed to reflect long-run average costs.

Water quality measures can be classified as either water parameters, watershed loading, or land use characteristics. Water parameters describe the physical, chemical, and microbiological traits of source water, and are usually presented in terms of pollutant concentrations. Selected studies employ a variety of parameters, namely: temperature, pH, conductivity, turbidity, total organic carbon (TOC), nitrogen, and calcium carbonate.⁴ Turbidity is the most common parameter (n = 12); it is near universally monitored by DWTPs and used by operators to optimize treatment processes, assess performance, and monitor compliance (Crittenden et al. 2012, Pizzi 2005). Abdul-Rahim and Mohd-Shahwahid (2011) and Dearmont et al. (1998) emphasize the combined effects of particulate matter and acidity/alkalinity on chemical dosage decisions by evaluating the multiplicative interaction of turbidity and pH. A related approach, employed by Freeman et al. (2008) and Renzetti (2001), is to construct a water quality index (WQI) that incorporates multiple water quality parameters. The former index is composed of TOC, turbidity, and alkalinity, and the latter composed of fecal coliform, lead, aluminum, benzene, polychlorinated biphenyl, and trichlorobenzene. In a few studies, rather than source water quality, water quality parameters represent the difference between source water and treatment water quality (Abdul-Rahim and Mohd-Shahwahid 2011, Dearmont et al. 1998, Forster et al. 1987, Horn 2011, Mosheim 2006, Mosheim and Ribaudo 2017, Piper 2003). This specification, while likely a more accurate representation of the data generating process, is difficult to implement given that raw and treated water quality data are rarely available in the same database.

In contrast to parameters, watershed loading measures describe the quantity of sediment, nutrients, or pesticides entering surface water due to runoff. We identify these variables with the qualifier load (e.g., sediment load, pesticide load). Load measures, broadly speaking, are defined in terms of mass per unit time, and are thus equivalent to the product of a pollutant’s concentration and a volumetric flow rate. Fiquepron et al. (2013) include a measure of the proportion of source waters that are in guideline noncompliance, which we also categorize as a loading measure because it concerns contamination at the watershed scale. Finally, land use characteristics describe the proportion of land within an area (e.g., watershed, service area, geopolitical boundary) with a certain land cover or land use designation. The most common categories are forestland, agriculture, and urban—where watersheds with a greater proportion of forestland, or smaller proportions of agriculture and urban land, are expected to have better water quality and lower treatment costs. Classifications such as grassland, rangeland, and barren land are also occasionally employed (Fiquepron et al. 2013, Warziniack et al. 2017). Forster and Murray (2007) and Murray (2001) disaggregate agricultural land by their predominant tillage practices: conventional tillage with ≤15% crop residue, conventional tillage with 15–30% crop residue, ridge and mulch tillage, and untilled land. Similarly, Fiquepron et al. (2013) disaggregate agricultural land into low-intensity cereal crop production and higher-intensity vine cultivation, market gardening, and arboriculture. Vincent et al. (2016) decompose forestland by logging practices in their analysis of Malaysian DWTPs.

Control variables (i.e., covariates other than water quality measures) are included in cost and price functions to control for factors that may bias parameters of interest. Economic theory offers some insight in this regard (see Section 2), but fails to provide guidance for a considerable number of possible variables. Moreover, there are circumstances, particularly with panel and time-series analyses, where it would be inappropriate to include variables suggested by theory. Thus, whether a set of control variables captures the key confounding factors depends on the particulars of the data and the modeling procedure. Many studies incorporate control variables, exceptions being Ernst et al. (2004), Freeman et al. (2008), Honey-Rosés et al. (2014), McDonald and Shemie (2014), and Oklahoma Water Resources Board (2011). The most common control variable, consistent with economic theory, is the volume of treated water (i.e., production output). Several studies also explicitly control for some combination of labor, chemical, and energy prices (Holmes 1988, Horn 2011, Mosheim 2006, Mosheim and Ribaudo 2017, Price et al. 2017, Renzetti 2001).⁵ This price data may be obtained directly from water providers, or are extracted from census data, regional price schedules, and supplier price lists. For short-run cost functions, fixed capital stock, when included, is modeled as treatment capacity (Price et al. 2017) or as the ratio of operating profit and the opportunity cost of capital (Mosheim 2006, Mosheim and Ribaudo 2017). For long-run functions, capital prices are defined as the ratio of capital costs to fixed tangible assists (Horn 2011) or the average interest rate on debt (Renzetti 2001). Additional control variables pertain to weather conditions, source water type (e.g., surface water, groundwater), systems characteristics (e.g., treatment processes, network density, management regime), and service population characteristics (e.g., population density, residential deliveries, non-residential deliveries). The latter category is relevant when the dependent variable includes distribution costs and it is necessary to control for factors affecting delivery.

4.4. Modeling Approach and Estimation

Most studies, as previously noted, can be classified as using a cost (n = 19) or price (n = 3) function approach. An alternative method, employed by Moore and McCarl (1987) and Honey-Rosés et al. (2014), is to model factor inputs (e.g., alum usage, energy usage), which are then multiplied ex post by input prices to determine cost. Within each of these functional approaches there exist a number of possible model specifications and estimators. Several studies employ univariate models (n = 17), whereby a single equation, or multiple independent equations, relate treatment costs to water quality measures.⁶ Remaining studies develop multivariate models that relate costs to water quality measures using a system of equations. For example, treatment costs may be modeled as a function of turbidity (i.e., a cost function) and turbidity modeled as a function of land use characteristics (i.e., a turbidity model). Once model parameters are estimated, the recursive relationship between the two equations can be exploited to estimate the effect of changes in land use on treatment costs. The advantage of this approach is that the cost function contains only those predictors that directly affect the DWTP operations, while still allowing auxiliary land use, or watershed loading measures, to affect costs indirectly. Such models are used with regards to pesticide exceedance (Fiquepron et al. 2013), phosphorus load (Heberling et al. 2015), sediment load (Holmes 1988), and land use classifications (Forster and Murray 2007, Murray 2001, Singh and Mishra 2014, Warziniack et al. 2017). A smaller set of studies use multivariate models to other ends. Piper (2003) jointly estimates a price function and a water demand function to evaluate how changes in source water quality affect consumer welfare. Both Mosheim (2006) and Renzetti (2001) jointly estimate a cost function and input share equations using seemingly unrelated regression (SUR).

For statistical estimation of a model, it is necessary to specify a functional form. It is possible, although not always practiced, to test multiple specifications to determine the form that best represents the data generating process. We classify studies based on the specified relationship between cost and water quality measures. The log-linear specification is used the most frequently because of its ability to capture nonlinearity and ease of interpretation (n = 14), followed by linear, polynomial, trans-log, and semi-log specifications. The trans-log specification, used only by Mosheim (2006) and Renzetti (2001), is highly flexible; it allows for nonlinearities and complex interactions among covariates.

OLS is the most frequently used estimator among selected studies (n = 11). For many datasets, however, the underlying assumptions of OLS are violated and alternate estimators are more appropriate. Dearmont et al. (1998) and Moore and McCarl (1987) use estimators to address biased variances, and subsequent issues with inference, associated with heteroskedasticity and autocorrelation. Similarly, Abildtrup et al. (2013) and Fiquepron et al. (2013) address endogeneity, as well as heteroskedasticity, concerns in their respective price functions using a three-stage estimator based on instrumental variable and generalized methods of moments. The former study also employs a spatial autocorrelation (SAC) framework, where treatment costs are a function of forestland within a CWS’s neighboring service areas, in addition to the immediate area, via a spatial-lag component. Heberling et al. (2015) consider O&M costs using an error correction model (ECM). The model, evaluated with a maximum likelihood estimator (MLE), finds that changes in water quality have both short-term and long-term effects on treatment costs.⁷ The MLE is also used by Horn (2011), Mosheim and Ribaudo (2017), and Price et al. (2017) to estimate stochastic cost frontier (SCF) models, which relax the cost minimization assumption by allowing for cost inefficiencies in the production process. Horn (2011) finds that inclusion of source water quality in the cost function significantly affects efficiency estimates for Japanese water providers. Price et al. (2017) find no evidence of this effect for Canadian DWTPs. Vincent et al. (2016) uses panel fixed-effects estimator to account for unobserved heterogeneity between DWTPs. Finally, Piper (2003) employs three stage least squares (3SLS), and Mosheim (2006) and Renzetti (2001) iterative least square (ILS), to jointly estimate their respective systems of equations.

5. Water Quality Elasticities of Cost

From each selected study, we extract water-quality elasticities of cost, which are defined as the percentage change in costs resulting from a 1% change in source water quality. The principal advantage of elasticities is that they are unit-less, and thus allow for the comparison of results across studies using diverse data structures, variable definitions, and statistical methodologies.⁸ The elasticities employed here are more precisely defined as point elasticities evaluated at a study’s average DWTP. The basic formula is η = (∂c/∂q)(q̄/c̄) where c is the cost measure, q is the source water quality measure, and an overbar denotes the variable mean. Specific formulae depend on several factors, including the specified functional relationship (e.g., linear, log-linear, polynomial, etc.), presence of temporal or spatial lags, whether water quality measures reflect source water conditions or the difference between source and treated water, and whether water quality affects costs directly or indirectly via a linking equation in a multivariate analysis. We make the required calculation for each water quality measure, summing, differencing, and multiplying coefficients as appropriate. Whenever possible we also calculate an elasticity’s standard error. These calculations are made using the restrictive assumption of independence between coefficients, which, while clearly erroneous in many cases, is necessary given that covariance matrixes are rarely reported.⁹ Descriptions of the calculations used for each study are available in Appendix B.

Elasticities, and corresponding standard errors, from US and non-US studies are presented in Tables 1a and 1b, respectively. We test for statistical significance of the elasticities at p-value < 0.1 using one- and two-tailed t-test. One-tailed tests are applied to water quality parameters, watershed loading variables, and forestland, since the direction of their effect on treatment costs is unambiguous. Two-tailed tests are applied to other land use classifications. Turbidity elasticities are statistically significant in nearly all instances, ranging from an unexpected −0.11 (Murray 2001) to 0.30 (Forster and Murray 2007). The latter estimate suggests that a 1% decrease in turbidity leads to a 0.3% reduction in chemical treatment costs at sample averages. In the Heberling et al. (2015) ECM, a 1% decrease in turbidity has an immediate effect of 0.02%, and a long-term effect of 0.11% on O&M costs. Price et al. (2017) find a similar elasticity of 0.10 on O&M costs, but in a reparameterization of their main model also find that DWTPs using conventional, direct or in-line filtration, and membrane technologies are roughly twice as responsive to changes in turbidity as those using only disinfection technologies. However, these differences are statistically insignificant. Moore and McCarl (1987) relate turbidity to two different cost measures: 1) alum expenditures and 2) alum and lime expenditures. Similarly, Singh and Mishra (2014) relate turbidity to 1) chemical expenditures and 2) O&M expenditures. In both studies, turbidity elasticities are slightly, albeit insignificantly, smaller under the broader definition of costs. Sediment load elasticities, which like turbidity reflect responses to changes in particulate matter, are also significant in all instances, ranging from 0.05 (Holmes 1988) to 0.41 (Forster et al. 1987).

Table 1.

a: Elasticities from U.S. Studies
Reference	Water Quality Measure	Elasticity	Reference	Water Quality Measure	Elasticity
Dearmont et al. (1998)	Turbidity	0.27 (0.12)*	McDonald and Shemie (2014)	Sediment load	0.26
	pH	0.27 (0.12)*		Phosphorus load	0.19
Ernst et al. (2004)	L: Non-forest	Ref	Moore and McCarl (1987)	Turbidity (alum)	0.22 (0.02)*
				Temperature (alum)	−0.39 (0.12)*
	L: Forest	−0.83		Turbidity (alum & lime)	0.21
Forster et al. (1987)	Turbidity	0.12 (0.04)*	Mosheim (2006)	Turbidity	0.09 (0.03)*
	Sediment load	0.41 (0.02)*
			Mosheim and Ribaudo (2017)	Nitrogen	0.06 (0.02)*
	Turbidity	0.30 (0.08)*		Turbidity	−0.11 (0.12)
	Pesticide load	0.27 (0.20)*
	L: Ridge/mulch tilled†	Ref		Pesticide load	−0.43 (0.37)
Forster and Murray (2007)	L: Tilled w/ <15% residual†	0.40 (0.24)*		L: Ridge/mulch tilled†	Ref
	L: Tilled w/ 15–30% residual†	0.03 (0.03)	Murray (2001)	L: Tilled w/ <15% residual†	0.10 (0.13)
	L: Untilled†	0.02 (0.10)		L: Tilled w/ 15–30% residual†	0.11 (0.13)
	L: Non-agriculture†	0.60 (0.28)*		L: Untilled†	−0.04 (0.12)
				L: Non-agriculture†	0.12 (0.15)
	TOC	0.77 (0.23)*	Oklahoma Water Resources Board (2011)	TOC	0.55
	WQI	−0.53 (0.23)*
Freeman et al. (2008)‡	L: Forest	−0.38 (0.23)*
	L: Urban	0.22 (0.10)*	Piper (2003)	Calcium carbonate§	0.003 (0.001)*
	L: Non-forest vegetation	−0.15 (0.07)*
	Turbidity (short term)	0.02 (0.01)*		Turbidity	0.19 (0.11)*
	pH (short term)	−0.04 (0.06)
	TOC (short term)	−0.04 (0.03)		TOC	0.46 (0.19)*
Heberling et al. (2015)	Turbidity (long term)	0.11 (0.04)*		L: Non-forest/non-urban†	Ref
	pH (long term)	−0.01 (0.06)	Warziniack et al. (2017)	L: Forest (via turbidity)†	−0.32 (0.22)*
	TOC (long term)	0.10 (0.29)		L: Urban (via turbidity)†	0.08 (0.08)
	Phosphorus load (long term)†	0.02 (0.01)*		L: Forest (via TOC)†	−0.06 (0.07)
				L: Urban (via TOC)†	0.34 (0.56)
Holmes (1988)	Turbidity	0.07 (0.02)*
	Sediment load†	0.05 (0.02)*

b: Elasticities from Non-U.S. Studies
Reference	Water Quality Measure	Elasticity	Reference	Water Quality Measure	Elasticity
Abdul-Rahim and Mohd-Shahwahid (2011)	Turbidity	0.07 (0.03)*	Horn (2011)	TOC	0.06 (0.02)*
	pH	0.07 (0.03)*
	L: Agriculture	Ref		Turbidity	0.10 (0.02)*
	L: Forest (service area)	−0.48 (0.15)*		Turbidity (conventional)	0.12 (0.03)*
	L: Urban (service area)	0.004 (0.03)		Turbidity (filtration)	0.13 (0.05)*
Abildtrup et al. (2013)	L: Other (service area)	−0.21 (0.08)*	Price et al. (2017)	Turbidity (disinfection)	0.06 (0.04)*
	L: Forest (entire region)	−0.77 (0.26)*		Turbidity (membrane)	0.14 (0.07)*
	L: Urban (entire region)	0.38 (0.22)*		Turbidity (other)	0.08 (0.07)
	L: Other (entire region)	−0.49 (0.36)		Turbidity (untreated)	0.06 (0.08)
			Renzetti (2001)	WQI	0.80 (0.22)*
	Nitrate	0.05 (0.01)*
	Pesticide exceedance†	0.02 (0.01)*
Fiquepron et al. (2013)	L: Urban/agriculture	Ref		Turbidity (chemical)	0.20 (0.08)*
	L: Forest	−0.07 (0.03)*		Turbidity (O&M)	0.19 (0.07)*
	L: Grassland	0.02 (0.02)	Singh and Mishra (2014)	L: Non-forest†	Ref
	L: VIARMA	0.02 (0.01)		L: Forest (chemical)†	−1.71 (0.87)*
				L: Forest (O&M)†	−1.58 (0.80)*
				L: Non-forest	Ref
Honey-Rosés et al. (2014)	Conductivity	0.86	Vincent et al. (2016)	L: Virgin forest	−0.47 (0.19)*
				L: Logged forest	−0.32 (0.14)*

Notes. Water Quality Measure: L=land use variable; O&M=operation and maintenance; TOC=total organic carbon; VIARMA=vine cultivation, arboriculture, and market gardening; WQI=water quality index. Elasticity: Ref=reference land use category

^*Statistically significant at p<0.1. One-tailed test used for water quality parameters, watershed loading variables, and forestland. Two-tailed tests used for all non-forestland classifications.

^†Elasticity estimated via a multiple-equation recursive relationship.

^‡Study estimates multiple single-predictor regression models; thus, reference land use is all classifications other than the one included in the model.

^§Variable is defined as the difference between source and treated water quality. Reported elasticity does not adjust for treated water quality and underestimates the effect of source water quality changes on treatment costs.

The TOC elasticities obtained from Freeman et al. (2008), Horn (2011), and Warziniack et al. (2017) are statistically significant, although they range widely from 0.06 to 0.77. In contrast, Heberling et al. (2015) find no significant short- or long-term relationship between TOC and O&M costs. Four elasticities relate to nutrient levels (i.e., nitrogen, nitrate, and phosphorus load), which have been linked to higher algae concentrations, and, when inadequately treated, adverse health outcomes. These elasticities, with the exception of McDonald and Shemie (2014), are statistically significant and fall within the relatively narrow range of 0.02 and 0.06. McDonald and Shemie (2014) find a considerably larger elasticity of 0.19, but insufficient information is provided to test for its significance. Vastly different elasticities, −0.43 and 0.26, are obtained from Forster and Murray (2007) and Murray (2001) for pesticide load. Fiquepron et al. (2013) find an elasticity of 0.02 for pesticide exceedance, indicating that a 1% increase in incidence of pesticide non-compliance is associated with a 0.02% increase in long-run average costs. Finally, Piper (2003) finds an elasticity of 0.003 for calcium carbonate and Honey-Rosés et al. (2014), the only study to evaluate desalinization, find an elasticity of 0.86 for conductivity.

Land use elasticities must be interpreted relative to a reference category, denoted by Ref in Tables 1a and 1b. Estimated forest elasticities are universally negative, implying that forestland leads to improved source water quality relative to all other land use classifications. Ernst et al. (2004) model the relationship between treatment costs and forestland using non-forestland as the reference category. They find a forest elasticity of −0.83. This indicates that a 1% increase in forestland within a source watershed—corresponding to an equivalent decrease in non-forestland—will, on average, reduce costs by 0.83%. Freeman et al. (2008), Singh and Mishra (2014), and Vincent et al. (2016) also use non-forestland as a reference category. Singh and Mishra (2014) find considerably larger elasticities, in absolute terms, than those found elsewhere, with a 1% increase in forestland leading to a 1.71% reduction in chemical expenditures and a 1.51% reduction in O&M expenditures. Vincent et al. (2016) distinguish between virgin and logged forestland, finding that a 1% increase in virgin forest reduces O&M costs by 0.47% while an increase in logged forest reduces costs by 0.32%. Results from the Abildtrup et al. (2013) SAC model, where agriculture land serves as the reference category, indicate a forest elasticity of −0.48 for land use changes in the immediate service area and −0.77 when changes in neighboring service areas are incorporated. Lastly, Fiquepron et al. (2013) find a forest elasticity of −0.07 using low-intensity agriculture and urban land as the reference category.

Results for other land use classifications are more ambiguous. Estimated elasticities for urban land are mostly positive, being statistically significant relative to non-urban land in Freeman et al. (2008) and agriculture land in Abildtrup et al. (2013) when changes in neighboring service areas are incorporated. In Warziniack et al. (2017), where land use affects chemical costs indirectly as predictors of turbidity and TOC, the elasticity for urban land is significant with regards to turbidity but insignificant for TOC. Forster and Murray (2007) decompose agricultural land in Ohio watersheds by tillage practices, finding that traditionally tilled land, as well as non-agriculture land, has a positive and significant elasticity relative to conservation tillage. However, a similar analysis of tillage practices in the Great Lakes Region does not support these findings (Murray 2001). Elasticities for other land use classifications (i.e., grassland, rangeland, vine cultivation) are largely insignificant.

We summarize the findings presented in Table 1 by calculating mean elasticities for water quality measures most pertinent to SWP. All elasticities are weighted equally and assumed independent for these calculation, and no attempt is made to group elasticities by DWTP characteristics, modeling approach, or scope of the cost measure. We limit each calculation (i.e., the mean elasticity for each water quality measure) to a single elasticity per study to prevent values from being dominated by analyses with multiple elasticities for the same water quality measure.¹⁰ Three sets of mean elasticities are presented in Table 2. Since these elasticities are calculated from a small, sometimes highly variable, set of observations, values are unlikely representative of all DWTPs. The first set (column 4) is calculated using all relevant elasticities from the selected studies, including those without standard errors. The second set (column 6) is calculated using all relevant elasticities with standard errors, thus allowing standard errors to be calculated for the mean elasticity estimates. Results from this set show a mean turbidity elasticity, based on 12 observations, of 0.14 (CI: 0.10, 0.18).¹¹ This estimate varies little between US and non-US studies, and has a relatively small standard error compared to other water quality parameters. The mean nitrogen/nitrate elasticity, based on 2 observations, is 0.06 (CI: 0.04, 0.08), and, as with turbidity, varies little between US and non-US studies. In contrast, the mean TOC elasticity is eight times larger among US studies than non-US studies. The mean sediment load, phosphorus load, and pesticide load elasticities, which are based exclusively on US studies, are 0.23 (CI: 0.21, 0.25), 0.02 (CI: 0.00, 0.04), and −0.08 (CI: −0.49, 0.33), respectively. The negative value for pesticide load counters expectations but is insignificant.

Table 2.

Average Elasticities for Select Water Quality Measures

Water Quality Measure	Classification	All elasticities		Elasticities w/ SE		Elasticities w/ SE from studies using key controls
		Number of Estimates	Mean	Number of Estimates	Mean (SE)	Number of Estimates	Mean (SE)
	US	9	0.14	9	0.14 (0.03)*	4	0.12 (0.01)*
Turbidity	Non-US	3	0.12	3	0.12 (0.03)*	1	0.10 (0.02)*
	Total	12	0.14	12	0.14 (0.02)*	5	0.12 (0.01)*
	US	4	0.47	3	0.44 (0.14)*	1	0.10 (0.29)
TOC	Non-US	1	0.06	1	0.06 (0.02)*	1	0.06 (0.02)*
	Total	5	0.39	4	0.35 (0.10)*	2	0.08 (0.29)
	US	1	0.06	1	0.06 (0.02)*	1	0.06 (0.02)*
Nitrogen/Nitrate	Non-US	1	0.05	1	0.05 (0.01)*	0
	Total	2	0.06	2	0.06 (0.01)*	1	0.06 (0.02)*
	US	3	0.24	2	0.23 (0.01)*	1	0.05 (0.02)*
Sediment load	Non-US	0		0		0
	Total	3	0.24	2	0.23 (0.01)*	1	0.05 (0.02)*
	US	2	0.10	1	0.02 (0.01)*	1	0.02 (0.01)*
Phosphorus load	Non-US	0		0		0
	Total	2	0.10	1	0.02 (0.01)*	1	0.02 (0.01)*
	US	2	−0.08	2	−0.08 (0.21)	0
Pesticide load	Non-US	0		0		0
	Total	2	−0.08	2	−0.08 (0.21)	0
	US	3	−0.51	2	−0.35 (0.16)*	0
Forest (non-forest)	Non-US	2	−0.98	2	−0.98 (0.41)*	1	−0.39 (0.12)*
	Total	5	−0.70	4	−0.67 (0.22)*	1	−0.39 (0.12)*
Forest (non-forest, agriculture, urban)	US	3	−0.51	2	−0.35 (0.16)*	0
	Non-US	4	−0.70	4	−0.70 (0.21)*	2	−0.58 (0.10)*
	Total	7	−0.62	6	−0.58 (0.15)*	2	−0.58 (0.10)*

Statistically significance for one-tailed test: * p<0.1

Note. Reference land use categories are reported in parentheses following the category of interest. Standard errors are reported in parentheses following average elasticities. Mean elasticities are calculated from a small, sometime highly variable, set of observations; thus, caution should be taken when applying these values to other contexts.

Mean land use elasticities must be interpreted relative to the reference category indicated in parentheses. First, we estimate, based on 5 observations, a mean forest elasticity of −0.67 (CI: −1.10, −0.24) for studies using non-forestland as the reference. This elasticity is slightly smaller among US than non-US studies. Next, we estimate a mean forest elasticity for studies using any combination of non-forestland, agriculture land, or urban land as the reference. The resulting forest elasticity of −0.58 (CI: −0.87, −0.29) is smaller than the previous estimate but remains statistically significant.

The third set of mean elasticities (column 8) is calculated using only studies that mitigate potential omitted variable bias by 1) incorporating control variables consistent with economic theory in their models, or 2) using a panel fixed-effects estimator when panel data is employed. The identification of these studies is necessarily subjective as some control variables, namely input prices, can be implicitly controlled for when there is little variation in these variables across observations (i.e., observations are spatially or temporally concentrated), or through spatial, temporal, or panel fixed effects. We therefore elect to exclude studies that clearly do not account for key confounding factors. Mean elasticities for these studies are generally smaller, and in some instances also have narrower confidence intervals, than previous estimates. The most notable differences are for TOC and sediment load, which now have elasticities of 0.08 (CI: −0.49, 0.65) and 0.05 (CI: 0.01, 0.09), respectively — the former being highly insignificant. The mean turbidity elasticity is slightly smaller at 0.12 (CI: 0.10, 0.14), while the nitrogen/nitrate elasticity, now based on a single observation, is 0.06 (CI: 0.02, 0.10). The forest elasticity for studies using non-forestland as the references category, also based on a single observation, is −0.39 (CI: −0.63, −0.15). There is little change in the forest elasticity from studies using any combination of non-forestland, agriculture land, or urban land as the reference.

6. Discussion and Conclusion

Water-related ecosystem services are regularly subject to pressure from anthropogenic activities and changing climate conditions. SWP has emerged as a framework for protecting these services; it is widely viewed as an essential and cost-effective component of a multi-barrier approach to providing safe drinking water (Ernst et al. 2004, Gartner et al. 2014, McDonald and Shemie 2014). Indeed, several regulatory agencies have adopted regulations or guidelines concerning the protection of source watersheds, including in the US EPA’s Safe Drinking Water Act. Numerous municipalities are engaged in SWP activities for the expressed purpose of reducing O&M expenditures and averting, or at least delaying, the purchase of costly capital assets at DWTPs (Bennett et al. 2014, Carpe Diem West 2011, Dudley and Stolton 2003, Herbert 2007). For many municipalities, however, SWP policy decisions are made without adequate quantitative information about the impact land management practices have on source water conditions, or the subsequent link between source water conditions and treatment costs (Dudley and Stolton 2003, Gartner et al. 2013, Ryan 2000). An improved understanding of these relationships is therefore essential to striking the best possible balance between protecting in situ water quality and purifying water via engineered treatment processes, and for improving the design of SWP programs.

We review the literature establishing a functional relationship between treatment costs and source water quality, and, from select studies, extract elasticities reflecting the responsiveness of DWTP expenditures to changes in water quality. Overall, results suggest that marginal changes in water quality measures lead to statistically significant but modest gains in avoided treatment costs. Estimated turbidity elasticities are the most robust; they are markedly consistent given the diversity of data and analytical methods utilized. Elasticities are more varied for other water quality measures, including TOC, phosphorus load, sediment load, and forestland—the latter variation possibly due to heterogeneity in forest types (e.g., temperate, tropical), topography, and management regimes. We also calculate mean elasticities for select water quality measures. These estimates, reported in Table 2, provide a useful summary of existing evidence but should be regarded cautiously given the small number of available observations.

To provide some context to the estimated elasticities, we calculate avoided treatment costs for representative DWTPs from Abildtrup et al. (2013), Forster and Murray (2007), Mosheim (2006), Price et al. (2017), Vincent et al. (2016), and Warziniack et al. (2017). For these DWTPs, the estimated benefit from a 1% reduction in source water turbidity ranges from $121 to $13,060 (2015 USD) annually. The corresponding benefit from a 1% increase in forestland in the source watershed ranges between $201 and $63,293 annually. Whether these benefits justify the cost of SWP activities is highly contextual, depending on site-specific ecologic, hydrologic, and DWTP characteristics. However, some broad insight can be gleaned with regard to forestland impacts on representative DWTPs from Abildtrup et al. (2013), Forster and Murray (2007), Vincent et al. (2016), and Warziniack et al. (2017). In these studies, a 1% increase in forestland corresponds to the conversion of between 955 and 22,680 hectares in the average watershed or service area. Costs of forestland conversion and protection vary widely but are usually at least several hundred dollars per hectare (McDonald and Shemie 2014), implying that SWP costs greatly exceed benefits for these representative DWTPs. Generally speaking, Heberling et al. (2015) and Vincent et al. (2016) reach similar conclusions in their respective analyses. Pyke et al. (2002) find that costs typically exceed benefits for SWP programs using riparian buffers to mitigate agricultural runoff, but that benefits exceed costs for programs using conservation tillage practices. McDonald and Shemie (2014) conclude that SWP is a cost-effective option for 28% of major world cities. Their analysis identifies the least cost approach to SWP using a mix of spatially targeted interventions (e.g., reforestation, riparian restoration, payment to landowner for adopting best management practices), but also relies on a relatively large water quality elasticity of 0.5 to determine benefits. Regardless, evidence suggests that SWP will not be cost effective in most situations where estimated benefits are limited to avoided water treatment expenditures. Accounting for additional treatment costs (e.g., reservoir dredging and sludge disposal), health impacts, reduced risk of contamination, secondary beneficiaries (e.g., recreationists and homeowners), and potential income streams from managed lands (e.g., logging) may yield different results. In addition, Adhikari et al. (2016) find evidence of household willingness-to-pay for restoration of a source watershed located far from the municipality it supplies. This suggests households may value SWP beyond the benefits from avoided treatments costs and independent of improved recreational experiences, reduced wildfire risk to homes, or aesthetics.

Findings from this review expose several key knowledge gaps. Foremost among these gaps is the relationship between source water quality and long-run treatment costs. The choice of technology at a DWTP is partially determined by source water conditions. McDonald et al. (2016) offer evidence to this effect, finding a negative relationship between source water quality and the probability of using more advanced treatment technologies. Further evidence is found in the numerous accounts of DWTPs augmenting their water treatment infrastructure in response to worsening water conditions. For example, Dunlap et al. (2015) report that Waco, Texas spent $65 million to construct a dissolved air flotation plant in order to mitigate taste and odor problems resulting from frequent algal bloom events. Similarly, Des Moines, Iowa built a nitrate removal facility to address periodic spikes in source water nitrate; and Wichita, Kansas and Celina, Ohio addressed algae-related concerns with the addition of preozonation and granular activated carbon processes to their treatment systems, respectively (Davenport and Drake 2011, Jones et al. 2007, Oneby and Bollyky 2006). What is unknown, however, is the extent that source water quality, or uncertainty about future water quality, affects long-run costs after controlling for confounding factors such as the price of capital inputs. While some of these issues are evaluated in Horn (2011), Renzetti (2001), Abildtrup et al. (2013), Fiquepron et al. (2013), and Piper (2003), no definite conclusions can be made regarding the effects of water quality on long-run costs relative to short-run costs. In addition, reservoir dredging, sludge disposal, and in situ treatment (e.g., algaecide) are periodic but costly activities that have been ignored in cost function analyses (Babatunde and Zhao 2007, Buckley et al. 2014). As with capital expenditures, exclusion of these expenditures leads to an underestimation of the effect of source water quality on treatment related costs.

Another knowledge gap concerns the dearth of studies evaluating most water quality measures. Apart from turbidity, where the effect on variable treatment costs appears reasonably well understood, there is an insufficient elasticity of cost estimates from studies that control for confounding factors. Additional research is needed on widespread water quality issues, including TOC, nitrogen and nitrate, phosphorus, algae, and harmful algal and cyanobacteria blooms. Given the heterogeneity of source water conditions, some DWTPs will be affected by less common chemical and biological contaminants (e.g., sodium, perchlorate, trace metals). Evaluation of these parameters is warranted when their effect on treatment costs can be distinguished from that of other water quality measures and when SWP activities can be used to reduce contamination.

Continued research on land use is also needed, particularly with regards to differentiating the effects of various agricultural, forestland, and storm water management practices. For example, similar to Vincent et al. (2016), there is potential to evaluate the relative effects of low-, medium-, and high-intensity forest management approaches on treatment costs. While equilibrium relationships are of primary interest, research on the dynamics between changes in these management practices and treatment costs would also prove beneficial. Related knowledge gaps concern nonlinearities in water quality measures and interactive effects of multiple water quality measures. Results from studies using trans-log and third-order polynomial specifications indicate the presence of complex nonlinearities between treatment costs and water quality measures not captured in most studies. Likewise, results from studies using interaction terms between water quality measures (e.g., Abdul-Rahim and Mohd-Shahwahid 2011, Dearmont et al. 1998) or WQIs (e.g., Freeman et al. 2008, Renzetti 2001) suggest there are interactive effects not captured by most studies. Further exploration of these issues would aid BCAs that involve non-marginal changes in source water quality or changes in multiple quality measures.

Water quality elasticities of costs may vary across output levels, treatment technologies, source water types, seasons, and geographic regions. Of selected studies, only Mosheim (2006), Mosheim and Ribaudo (2017), and Price et al. (2017) investigate this type of heterogeneity. A particularly notable gap in the literature concerns small-scale groundwater systems, which comprise the vast majority of treatment systems but have not been evaluated separate from surface water systems.

A final knowledge gap concerns the presence of thresholds in water treatment processes. Cost function analyses usually assume smooth functional relationships between costs and source water quality measures. But these relationships often contain discontinuities related to predefined thresholds in the treatment processes. Beyond a defined threshold, for example, reduced source water quality can trigger utilization of chemical additives (Heberling et al. 2015, Sohn et al. 2008), inactive capital (Honey-Rosés et al. 2013, Jones et al. 2007), and alternate source waters (Towler et al. 2010). In the long-run, as discussed above, it can also trigger the construction of new capital resources. Incorporating thresholds into cost function analyses will be complicated since relevant threshold values will differ by location and are often known only to plant operators; nonetheless, it may ultimately prove a better representation of treatment technology in many situations.

Filling these knowledge gaps will require a multi-pronged approach. Some issues are better suited to cross-sectional or panel data that exhibit considerable variation in treatment technologies, source water, and service population characteristics. Other issues will be better assessed with detailed time-series analysis that can account for certain context-specific aspects of water treatment, such as atypical water quality measures and threshold effects. Likewise, some approaches will be better suited to decision making at national or regional levels and others to a DWTP level. As additional studies become available, meta-regression may help to address some knowledge gaps.

The main obstacle to conducting any analysis is data availability. There exist only a few datasets containing the information required to quantify links between treatment costs and water quality—and many are small non-random samples. Engineering equations offer an alternate approach to assessing these links, but no study to our knowledge has compared behavioral and engineering cost models to determine the validity of this approach. Thus, there is need for both the targeted collection of new data and for the comparison of behavioral and engineering cost models. Doing so will be vital to continued research on avoided treatment costs and benefits of SWP activities.

Appendix A

Table A.

Characteristics of Selected Studies (Abbreviations Defined in Table Notes)

Reference	Data Characteristics	Data Structure	Analysis Approach	Dependent Variable	Water Quality Measure	Control Variables
	Country Source type Output (Y) in 1000 m3/day	Unit of obs. Data type # obs.*	Model type Estimator Specification
Abdul-Rahim and Mohd-Shahwahid (2011)	Malaysia SW	DWTP PNL n=144 (i=6, t=24)	Cost function Panel est.† Log-linear	Chemical costs (MYR/m3/day): Average daily chemical costs per m3 of output over two-week period.†	Turbidity‡ × pH	Treated water Rainy season (d) FE-DWTP
Abildtrup et al. (2013)	France SW & GW Av: 0.29 Mn: 0.004 Mx: 7.64	CWS† CRS n=232	Price function SAC, IV-GMM Linear	Consumer price (EUR/m3): Average price (publicly managed systems) or marginal price (privately managed systems) per m3 of residential-use water. Average price is based on consumption of 120 m3/year. Taxes, abstraction fees, and pollution fees are excluded.	Land use (%): Forest Agriculture (ref) Urban Other	Treated water Population Population density # municipalities # intakes Private system (d)
Dearmont et al. (1998)	USA SW Av: 27.67 Mn: 1.08 Mx: 109.76	DWTP PNL n=540 (i=12, t=45)	Cost function CHTA Polynomial	Chemical costs (USD/100 MGL/mth): Chemical cost per 100 million gallons of output per month.	Turbidity‡ × pH Chemical contam. (d)	Treated water Precipitation
Ernst et al. (2004)	USA SW	DWTP CRS n=27	Cost function OLS Polynomial	Total costs (USD/MGL/yr): O&M and amortized capital costs per MGL of output per year.	Land use (%): Forest Non-forest (ref)
Fiquepron et al. (2013)	France SW & GW Av: 0.16 Mn: 0.03 Mx: 0.63	Department CRS n=93	Price function IV-GMM Linear	Consumer price (EUR/m3): Average price per m3 of residential-use water based on consumption of 120 m3/year. Aggregation to the department level is based on survey weights from a stratified sampling procedure.	Nitrate Pesticide exceedance Land use (%): Forest Grassland VIARMA Urban/agriculture (ref)	GW/total intake (%) Population density Private/total systems (%)
Forster et al. (1987)	USA SW Av: 3.53 Mn: 1.04 Mx: 23.34	DWTP PNL n=257 (i=12, t=25)	Cost function OLS Log-linear	Chemical costs (USD/day): Average daily chemical costs over month period.	Turbidity‡ Sediment load	Treated water Retention time
Forster and Murray (2007)	USA SW Av: 12.71 Mn: 0.23 Mx: 53.40	DWTP PNL n=55 (i=11, t=5)	Cost function OLS Log-linear	Chemical costs (USD/MGL/yr): Chemical costs per MGL output per year.	Turbidity Pesticide load Land use (%): Tilled w/ <15% residual Tilled w/ 15–30% residual Ridge/mulch tilled (ref) Untilled Non-agriculture	Treated water
Freeman et al. (2008)	USA SW Mn: >3.79 Mx: <378.54	DWTP CRS n=40	Cost function OLS Semi-log	Chemical costs (USD/MGL/yr): Chemical costs per MGL output per year.	TOC WQI Land use (%): Forest Urban Non-forest vegetation	Year (d)
Heberling et al. (2015)	USA SW Av: 18.74 Mn: 2.01 Mx: 38.31	DWTP TMS n=1826	Cost function ECM, MLE Log-linear	O&M costs (USD/1000 GL/day): Chemical, pumping, and GAC costs per 1000 GL of output per day.	Turbidity pH TOC Phosphorus load Temperature >23°C (d)	Lagged costs Treated water Process shutdown (d) Pool elevation Years (d) Spring & summer (d) Actual TOC measure (d)
Holmes (1988)	USA SW Av: 163.43	CWS CRS n=132	Cost function OLS Log-linear	O&M costs (1000 USD/yr): Chemical, labor, energy, water acquisition, and distribution costs per year.	Turbidity Sediment load	Treated water Price of labor Price of electricity
Honey-Rosés et al. (2014)	Spain SW Av: 82.19	DWTP TMS n=247	Energy use func. OLS Linear	Energy usage (kWh/m3/interval): Amount of energy used per m3 of output per daily/sub-daily interval.	Conductivity
Horn (2011)	Japan SW† Av: 38.47 Mn: 0.58 Mx: 1109.48	CWS† CRS n=392	Cost function SCF, MLE Log-linear	Total costs (Million JPY/yr): Source water intake, purification, distribution, dedicated construction, operation, depreciation, and inventory shrinkage costs per year.	TOC‡	Treated water Price of labor Price of capital
McDonald and Shemie (2014)	USA SW	Municipality CRS n≈100	Cost function OLS Linear	O&M costs (Million USD/yr): O&M costs per year.	Sediment load Phosphorus load
Moore and McCarl (1987)	USA SW	DWTP TMS n=963	Chemical use func. COAC Eq1: Log-linear Eq2: Linear	Chemical usage (lbs/day): Amount of alum (Eq1) and lime (Eq2) used per day.	Turbidity (Eq1) Temperature (Eq1) pH (Eq2)	Treated water (Eq1) Alum (Eq2)
Mosheim (2006)	USA§ SW & GW Av: 131.93	CWS CRS n=184	Cost function SUR, NL-ILS Translog	O&M costs per year (USD/yr): Chemical, labor, and energy costs per year.	Turbidity‡	Treated water Price of labor Price of electricity Price of chemicals Capital stock Combined W&WW (d) Source is SW (d) Source is GW (d) Population>100,000 (d) Network density Res./total deliveries (%)
Mosheim and Ribaudo (2017)	USA§ SW & GW Av: 146.81	CWS CRS n=48	Cost function SCF, MLE Log-linear	O&M costs per year (USD/yr): Chemical, labor, and energy costs per year.	Nitrogen‡	Treated water Price of labor Price of electricity Price of chemicals Capital stock Agriculture/total N (%)
Murray (2001)¶	USA SW Av: 58.32 Mn: 2.15 Mx: 181.51	DWTP PNL n=65 (i=13, t=5)	Cost function OLS Log-linear	Chemical costs (USD/MGL/yr): Chemical costs per MGL of output per year.	Turbidity Pesticide load Land use (%): Tilled w/ <15% residual Tilled w/ 15–30% residual Ridge/mulch tilled (ref) Untilled Non-agriculture	Treated water
Oklahoma Water Resources Board (2011)	USA SW	DWTP TMS n=12	Cost function OLS† Linear	Chemical cost (USD/MGL/mth): Monthly average of chemical costs per MGL of output across eight-year period.	TOC
Piper (2003)	USA§ SW & GW	CWS CRS n=309	Price function 3SLS Log-linear	Consumer price (USD/GL): Average price per GL of residential-use water.	Calcium carbonate‡	Treated water GW/total intake (%) Source is GW (d) Population density Debt/assets Regions (d)
Price et al. (2017)	Canada SW & GW Av: 12.88	DWTP CRS n=994	Cost function SCF, MLE Log-linear	O&M costs (1000 CAD/yr): Chemical, labor, and energy costs for source water acquisition and treatment per year.	Turbidity	Treated water Price of labor Price of electricity Price of chemicals Capacity Conventional treat. (d) Filtration treat. (d) Disinfection treat. (d) Membrane treat. (d) Other treat. (d) Source is SW (d)
Renzetti (2001)	Canada SW	CWS† CRS n=40	Cost function SUR, ILS Translog	Total cost (CAD/yr): Labor, energy, and capital costs per year.	WQI	Treated water Price of labor Price of electricity Price of capital Water availability Var. of water availability Source is lake (d)
Singh and Mishra (2014)	India SW Av: 1310.00†	DWTP TMS n=144	Cost function OLS† Eq1: Log-linear Eq2: Log-linear	Chemical/O&M costs (INR/ML/mth): Chemical costs per ML of output per month (Eq1). Chemical, energy, repair, maintenance, establishment, and transport costs per ML of output per month (Eq2).	Turbidity Land use (%): Forest Non-forest (ref)	Lagged costs Treated water
Vincent et al. (2016)	Malaysia SW Av: 12.61 Mn: 0.06 Mx: 147.70	DWTP PNL n=3894 (i=41, t=168)	Cost function Panel FE Log-linear	O&M costs (MYR/mth): Chemical, labor, energy, and maintenance cost per month.	Land use (%): Virgin forest Logged forest Non-forest (ref)	Treated water DWTP upgrade (d) Precipitation Years (d) Months (d) FE-DWTP
Warziniack et al. (2017)	USA SW Av: 183.70 Mn: 0.20 Mx: 4163.90	DWTP CRS n=37	Cost function OLS Log-linear	Chemical costs (USD/MGL/yr): Chemical costs per MGL of output per year.	Turbidity TOC Land use (%): Forest Urban Non-forest/non-urban (ref)	Treated water Conventional treat. (d) Filtration treat. (d) Disinfection treat. (d) Advanced treat. (d)

Notes. Data characteristics GW=groundwater; SW=surface water. Data structure DWTP=drinking water treatment plant; CWS=community water system; CRS=cross-sectional data; PNL=panel data; TMS=time series data. Analysis approach COAC=Cochrane-Orcutt autocorrelation; CHTA=cross-sectional heteroskedastic and time wise autocorrelation; ECM=error correction model; FE=fixed effects; IV-GMM=instrumental variable generalized methods of moments; ILS=iterative least squares; MLE=maximum likelihood estimator; NL-ILS=nonlinear iterative least squares; OLS=ordinary least squares; SUR=seemingly unrelated regression; SAC=spatial autocorrelation; SCF=stochastic cost frontier; 3SLS=three stage least squares. Dependent variable CAD=Canada dollar; EUR=euro; GL=gallons; GAC=granular activated carbon; INR=India rupee; JPY=Japan yen; O&M=operation and maintenance; MYR=Malaysia ringgit; MGL=million gallons; ML=million liters; USD=USA dollar. Water Quality Measure TOC=total organic carbon; VIARMA=vine cultivation, arboriculture, and market gardening; WQI=water quality index. The term load is used to identify water quality measures that pertain to the amount of material entering surface water due to runoff. Reference land use categories, dummy variables, percentage/proportion variables are denoted by (ref), (d), and (%), respectively.

^*Total number of observations are denoted by n. For panel data, n is decomposed into the number of panel observations i and time observations t.

^†Information based on available evidence but uncertainty exists regarding the unit of analysis, estimator, or definition of the dependent variable. Additional information is available in Appendix B.

^‡Variable is defined as the difference between source water and treated water quality.

^§Study uses data from the 1996 American Water Works Association member survey.

^¶Entry pertains to the Great Lakes Basin analysis; characteristics of the Maumee River Basin analysis are reported in Forster and Murray (2007).