A panel study of water recirculation in manufacturing plants

Abstract

Manufacturing plants routinely recirculate water to meet their process and cooling needs. This ability and willingness to recirculate water distinguishes manufacturing plants from most households and agricultural producers. The motivation for this research is to investigate the factors influencing manufacturing plants’ water recirculation decisions. The paper analyses a unique, balanced panel dataset of 2725 manufacturing plants that responded to the 1986, 1991 and 1996 Industrial Water Use Surveys. Investigation of the raw data shows that manufacturing plants routinely start and stop recirculation activities. Building on previous analysis based on only the 1996 dataset, a statistical model is developed to explain observed variations in the volume of water recirculated and water recirculation intensity (recirculation relative to intake) across the three time periods. Specifically, this paper applies a Heckman two-stage estimation procedure that jointly considers two facets of firms’ recirculation behaviour: first, the discrete decision of whether to recirculate and, second, the decision of how much to recirculate. Potential endogeneity of internal input costs is addressed through instrumental variables. Explanatory variables include the scale of operations, water-use costs and dummy variables that account for plants’ location and technology. Results indicate that water use costs, the scale of operations and the need to treat water prior to its use are important determinants of water recirculation decisions. This paper concludes by considering the policy implications of the empirical findings.

Les usines de fabrication font circuler l’eau de façon routinière pour assurer leurs besoins de procédure et de refroidissement. Cette volonté et habileté pour faire circuler l’eau dans les usines de fabrication les distinguent de la plupart des producteurs résidentielles et agricoles. La motivation pour cette recherche est de faire une enquête pour déterminer les facteurs qui influencent les décisions de circulation dans ces usines. Nous basons notre analyse sur un ensemble de données d’un panneau équilibré composant de 2 725 usines de fabrication qui ont répondu aux sondages d’utilisation industrielle de l’eau des années 1986, 1991, et 1996. L’investigation initiale des données brutes démontre que les usines de fabrication, sur routine, débutent et arrêtent leurs activités de circulation. En ajoutant à notre analyse précédente, basée uniquement sur l’ensemble de données de 1996, notre modèle statistique cherche à expliquer les variations visibles dans le volume d’eau qui ce fait circuler, ainsi que l’intensité de l’eau circuler (recirculation relative à l’absorption) à travers les trois périodes de temps mentionnées. Plus spécifiquement, nous employons le processus à deux niveaux d’estimation « Heckman » qui considère de rejoindre deux facettes du comportement de recirculation des usines. La première facette est la décision discrète de soit circuler l’eau ou non, et la deuxième est la décision de déterminer combien d’en faire circuler. L’endogénéité potentielle des coûts soumis à l’interne est adressé à travers des variables instrumentales. Les variables explicatives incluent la gamme des opérations, les coûts de l’utilisation de l’eau et des variables muettes qui prennent en considération les locations et technologies des diverses usines. Les résultats indiquent que les coûts de l’utilisation de l’eau, la gamme des opérations et le besoin de traiter l’eau avant son utilisation sont des déterminants importants dans les décisions de faire circuler l’eau. Le journal termine en considérant les implications politiques des résultats empiriques.

Introduction

Manufacturing plants routinely recirculate water to meet their process and cooling needs. This ability and willingness to recirculate water distinguishes manufacturing plants from most households and agricultural producers. The volume of recirculation carried out in the manufacturing sector can be quite significant. For example, an increase in the volume of recirculated water of 1% by manufacturing firms in Canada would release enough water to supply the inhabitants and businesses of a city of 500,000 people.

A key focus of recirculation research is to determine the factors that influence a plant’s decision-making regarding water recirculation. The motivation behind the analysis in this paper is two-fold. The first motivation is that the factors influencing firms’ water recirculation decisions have received relatively little empirical analysis to date. Understanding these factors may be important in designing water management schemes as well as in predicting future water demands.

The second motivation arises from the observation that environmental regulations in many countries may encourage socially inefficient decision-making regarding all facets of industrial water use, including recirculation. This may be because the prices for industrial intake water and water discharges are not required to reflect their social opportunity cost (Organisation for Economic Co-operation and Development [OECD] 2003). In Canada, for example, the absence or very low level of fees for direct water withdrawals, and the under-pricing of publicly supplied water, have promoted excessive water use and discouraged conservation (Renzetti 2007). It is important to understand the factors influencing industrial water use – including internal recirculation – before assessing the potential efficacy of alternative policy instruments for promoting efficient water use.

The purpose of this paper is to analyze the factors that influence a plant’s decision-making regarding water recirculation. The paper uses a balanced panel dataset created by combining cross-sectional surveys that track plant-level water use activities in 1986, 1991 and 1996. This longitudinal approach is new to the literature as all previous studies have only utilized cross-sectional data. The advantage of a longitudinal approach is that it can provide some insight into the effects of factors that do not vary over time (e.g. plant location) and those that do (e.g. the cost of recirculation).

Literature survey

There are two streams in the literature that consider the economic dimensions of industrial water use, including water recirculation. The first considers aggregate water use patterns. For instance, Bruneau and Renzetti (2010) show that aggregate industrial water intake in Canada fell by 17% between 1981 and 1996. This was despite the fact that real industrial output rose by 29% over the same period. At the same time, however, industrial water recirculation fell by 25%, an even greater decrease than that of intake water. Thus, one implication of these observations is that the amount of water consumed by industrial activities (i.e. the difference between intake and discharge) rose by 21%. This suggests that policies that encourage more water recirculation may have unexpected consequences in terms of increased water consumption.

The second stream of the literature employs econometric models to examine firms’ decisions regarding water and other inputs. Early efforts are surveyed by Renzetti (2002). The most recent efforts to estimate industrial water demands while accounting for water recirculation are Dupont and Renzetti (2001), Chao-Hsien et al. (2006), Féres (2007) and Bruneau et al. (2010).

Dupont and Renzetti (2001) estimate a cost function for the aggregate Canadian manufacturing sector that includes water intake and recirculation as variable inputs. The authors found that the own-price elasticity of water recirculation is –0.66. As well, the relationship between water intake and recirculation is stronger when water intake is process-related rather than related to cooling and steam production.

Chao-Hsien et al. (2006) model water demands in the Taiwanese integrated circuit industry using a combined engineering process-econometric model. The authors assume firms calculate the optimal water recirculation rate as a function of internal water costs and external water prices. Once internal water costs are estimated from a cross-sectional sample of 25 firms, a negative relationship between optimal water intake and external water prices is derived.

Féres (2007) uses a cross-sectional survey of approximately 500 manufacturing firms in the state of São Paulo, Brazil, to estimate an endogenous switching regression model of manufacturing water intake demands. The model estimates two water intake demand equations: one for those firms that choose to recirculate water and one for those that choose not to recirculate. The estimated model indicates that the discrete decision whether to recirculate water is positively related to the price of intake water but negatively influenced by the cost of capital.

Bruneau et al. (2010) employ observations from the 1996 cross-sectional Canadian Industrial Water Use Survey (IWUS) in order to estimate a Heckman two-stage model of recirculation water demand. In the first stage, long-run factors such as relative water scarcity and production technologies are found to influence the decision whether to recirculate water. In the second stage, the imputed prices of intake water and water recirculation, as well as the scale of operations, are found to influence the choice of the optimal quantity of water to recirculate. Increases in intake prices and the scale of operations lead to increased water recirculation, with increases in the imputed price of recirculation having the opposite effect.

Analysis of the Industrial Water Use Survey responses

The data used in this study come from the Industrial Water Use Survey (IWUS) provided by Statistics Canada (Tate and Scharf 1983; Tate and Scharf 1989; Tate and Scharf 1995; Scharf et al. 2002). The survey reports establishment-level data covering water-related activities within manufacturing plants across Canada. Data include water uses, quantity and sources of intake water and discharge, treatment activities for both intake and discharge, operating and maintenance expenditures on each category of water use, and the type, quantity and purpose of water recirculation and recirculating activities. The survey also includes information about the location of the plant, the size of its labour force and the primary manufacturing activity of the plant.

Water that is recirculated or reused is defined as “water which is discharged from the plant or from a particular process within the plant, and which is subsequently recirculated into the same process or into a different process within the plant” (Scharf et al. 2002, 10). Recirculating activities are recorded depending on the purpose of recirculation. Plants can recirculate water for process purposes only, for cooling and steam production recirculation only or for both purposes. Process water includes all water that comes into direct contact with products and/or materials. It can be consumed in milling and special processes or included in the final output. Cooling and steam production water, on the other hand, does not come into direct contact with products, materials or byproducts of the processing operation. It includes bypass water used for cooling, and water used for the production of steam for either process operations or electric power. A third category, other recirculation, accounts for sanitary services.

If plants report recirculation, they report how much and for what purpose. One issue that arises in reviewing the IWUS data is whether reported volumes of zero water recirculation really are zero or are, in fact, a reporting error. This paper takes the approach that a reported zero volume of recirculation can be treated as such. First, plants have no incentive to misrepresent recirculation as there are no external fees applied and no regulations penalizing recirculation. Second, recirculation requires physical structure such as pumps and pipes. Plant managers who respond to the survey will know whether they have the capacity to recirculate or not and, if they have the capacity, whether it was used. They may not know how much water was recirculated but they would know if none was recirculated.

There are three ways to characterize water recirculation activities at the plant level. The first is recirculation volume. This is the amount of recirculation (in cubic metres) that a plant engages in within a year. All of the econometric studies to date (including Bruneau et al. 2010) seek to explain observed variations in recirculation volumes. Alternately, one can look at the recirculation rate. This is the ratio of recirculated water to total intake volume, and it measures the intensity of recirculation activities. Using the recirculation rate allows one to assess whether recirculation volumes and intake volumes respond one to one with changes in scale or water costs. If they do, then recirculation intensity may reflect technological constraints where both intake and recirculation are in a fixed ratio. The third way to characterize recirculation-related activities is the recirculation frequency. This is the proportion of plants within a given sub-sector or geographic area that report some recirculation activities in a particular period.

The IWUS was conducted in 1976, 1981, 1986, 1991 and 1996, with subsequent surveys covering 2005 and 2007 (but with different sampling methodologies). This paper uses the 1986, 1991 and 1996 surveys to construct the database, because the surveys carried out in 1976 and 1981 did not include questions related to expenditures. Specifically, the database has a balanced panel of 2725 manufacturing plants that provided responses to the 1986, 1991 and 1996 surveys. Thus, the paper restricts attention to those manufacturing plants that were in operation and responded to the survey in each of those three time periods.

Bruneau and Renzetti (2010) report on an analysis of plants’ intake and recirculation volumes as well as their recirculation rates over the 1986–1996 period. The analysis in this paper focuses on plants’ water recirculation frequencies. Table 1 summarizes recirculation frequencies for those plants in the IWUS which have been surveyed in all three time periods. If a plant recirculated some amount of water in a period it is denoted Y for yes, and N for no if it did not. The table separates recirculation into process, cooling and total recirculating. The first rows show the total number of plants that report some recirculation in each of the survey years. As shown, recirculating frequency changes over time and across activities. Recirculation frequency is higher for cooling than for process recirculating. Recirculation frequency was highest in 1986 among the plants in the sample, falling in 1991, and then rebounding somewhat in 1996.

Table 1. Number of plants that recirculate: 1986, 1991, 1996. Y = Yes, N = No.

Recirculation activity		Total		Process*		Cooling
Total plants/year	2725	# that recirculate	Share of plants	# that recirculate	Share of plants	# that recirculate	Share of plants
1986 survey		1957	0.72	1356	0.50	1811	0.66
1991 survey		1413	0.52	820	0.30	1262	0.46
1996 survey		1638	0.60	1062	0.39	1464	0.54
No change in status		1126	0.413	1039	0.381	1025	0.376
Recirculated in all three periods	Y Y Y	857	0.314	310	0.114	660	0.242
Did not recirculate in any period	N N N	269	0.099	729	0.268	365	0.134
Began recirculating		397	0.146	503	0.185	436	0.160
Recirculated in 1991 and 1996 but not in 1986	N Y Y	188	0.069	175	0.064	197	0.072
Recirculated in 1996 only	N N Y	209	0.077	328	0.120	239	0.088
Stopped recirculating		716	0.263	797	0.292	783	0.287
Recirculated in 1986 only	Y N N	450	0.165	599	0.220	491	0.180
Recirculated in 1986 and 1991 but not in 1996	Y Y N	266	0.098	198	0.073	292	0.107
Changed status		486	0.178	386	0.142	481	0.177
Recirculated in 1986 and 1996 but not in 1991	Y N Y	384	0.141	249	0.091	368	0.135
Recirculated in 1991 only	N Y N	102	0.037	137	0.050	113	0.041

^* Process recirculating includes “other recirculating”.

The first observation is that 544 plants of the 2725 plants in the sample that had recirculated water in 1986 reported no recirculation in 1991. The actual number of plants that reported no recirculation is actually higher than 834 since some plants began reporting positive recirculation in 1991 (see below). For processing purposes, at least 536 plants that had recirculated in 1986 reported no recirculation, while for cooling purposes at least 549 plants reported no recirculation. In each category, at least 20% of plants that recirculated water in 1986 did not report any recirculation in 1991.

Since recirculating frequencies rebounded in 1996, some of these plants may have restarted their recirculation activities. This can be checked by tracking the sequence of recirculation choices. The three time periods provide eight possible permutations of Y or N. These are separated into four broad categories. Data are reported in Table 1.

The first category shows the fraction of plants that either recirculated water or reported no recirculation at all in each of the three periods. This category constituted 41% of the plants, with only 10% of plants failing to recirculate any water at any time. Twenty-seven percent (27%) of plants have never recirculated water for process purposes, while only 13% of plants did not recirculate water for cooling purposes.

The second category shows the fraction of plants that began reporting recirculation within the sample periods (NYY and NNY). About 15% of plants that did not recirculate in 1986 began recirculating some water by 1996. About 19% of plants began process recirculating, with two thirds of these beginning in 1996.

The third category shows those plants that stopped recirculating by 1996, but which had recirculated some water in 1986 (YNN and YYN). This constitutes about one quarter of all plants, with slightly higher rates for processing and cooling purposes separately. In each category, the number of plants that ceased recirculation was highest in 1991. Note that even though the total number of plants that recirculated in 1996 was higher than in 1991, there was still a large fraction of plants that had stopped. Aggregate data simply obscures this experience of individual plants.

The fourth category shows that 18% of plants switched recirculation efforts over the three periods (YNY and NYN). About 14% of plants stopped in 1991 and then restarted recirculation efforts in 1996. About 4% started in 1991 and then stopped in 1996.

Similar patterns to those outlined above can be found in geographically disaggregated data (not reported here). Though provinces do differ, with some having a greater fraction of plants that recirculate, the breakdown into the eight combinations of Y and N is remarkably consistent across the country. It does not appear to be the case that plants in different provinces are more likely to stop, start or switch any more than in other regions of Canada.

However, the pattern for two-digit industry does differ. For instance, in the wood industries, 27% never changed, 7% started recirculating, 46% stopped and 20% switched. But in chemical and chemical products industries, 51% did not change, 13% started, 20% stopped and 16% switched. So the technologies used in those industries apparently do matter. The potential roles of plant location and technological differences are examined in the econometric model below.

Another way to look at this phenomenon is to consider conditional probabilities. The data identify the probability that a plant recycles in period t + 1 given its behaviour in period t. Results are presented in Table 2. First, there were 1957 plants that recycled in 1986, but only 1123 of these that continued in 1991 (calculated from plants with YYY, YYN, YNN and YNY status). Hence, only 57% of plants that recycled in 1986 continued into 1991. Using 1991 as the base year, the data show that 74% of plants that recycled in 1991 continued into 1996 (calculated from plants with YYY, YYN, NYY and NYN status). Pooling these results together shows that 64% of plants continued recycling into the subsequent period. Considering only those plants that recirculated water in 1986 and 1991 (calculated from plants with YYY and YYN status), 76% continued to recirculate water in 1996.

Table 2. Conditional probabilities of recirculating.

	1986 base year	1991 base year	Combined	1986 + 1991 base year
Total recirculation
Condition probability of recirculated in period t + 1 given plant did in period t	0.57	0.74	0.64	0.76
Condition probability of recirculating in period t + 1 if plant did not in period t	0.38	0.45	0.42	0.44
Ratio of probabilities	1.52	1.64	1.52	1.72
Process recycling
Condition probability of recirculating in period t + 1 given plant did in period t	0.37	0.59	0.46	0.61
Condition probability of recirculating in period t + 1 if plant did not in period t	0.23	0.30	0.27	0.31
Ratio of probabilities	1.64	1.95	1.68	1.96
Cooling recycling
Condition probability of recirculating in period t + 1 given plant did in period t	0.53	0.68	0.59	0.69
Condition probability of recirculating in period t +1 if plant did not in period t	0.34	0.41	0.39	0.40

Table 2 also shows the fraction of plants that did not recycle in the base year but began to recycle in the next period. Not surprisingly, the conditional probability is lower at around 42%. Note that those plants that did not recirculate water in 1986 or 1991 still had a 44% probability of recirculating in 1996.

Together, the conditional probability of recycling is about 1.5 times higher if the plant had recycled in the previous period than if it had not. Nonetheless, a past history of failing to recirculate water does not preclude a plant from starting in any period.

This discussion of the responses to the IWUS provides some insights into manufacturing plants’ recycling behaviour over time. Perhaps the most surprising set of results, given the likely capital-intensive nature of the decision to recirculate water internally, is the frequency with which plants move in and out of the state of being a recycler. However, these data do not explain why plants are changing their recirculation behaviour. The plants may change recirculation decisions because they change size, face higher water costs or face new water regulations. The statistical analysis reported in the next section examines these hypotheses.

Econometric model

This paper seeks to explain the observed behaviour of Canadian manufacturing plants regarding the decision to recirculate water. This section draws on the model description in Bruneau et al. (2010). A formal statement of the estimation model is available there. There are several features of the data that inform the estimation of the relationship between the observed volume of recirculated water and the factors that explain those volumes.

The first feature was discussed in the preceding section. Some plants never recirculate, some always recirculate and others switch between states. The predominance of observations with no recirculation implies that applying ordinary least squares (OLS) as the estimation method is likely to lead to biased coefficient results (Baltagi 2008). A more general estimation procedure is more appropriate in this case. In this more general model, firms are assumed to self-select in the sense that they choose whether to develop the capacity to recirculate and, conditioned on their decision to undertake internal water recirculation, they choose how much water to recirculate. However, an examination of the distribution of the non-zero observations of the recirculation variable indicates it is non-normal. This suggests that the estimation procedure may lead to inconsistent estimation results. A non-parametric approach to estimating the selection model may address this issue, but is beyond the scope of this paper (Honoré 1992).

The second feature is that the costs for water-related expenditures may be jointly determined with the volumes of water used. If the water-related marginal costs were to be used as variables explaining the observed volumes of water used, this could lead to a simultaneity bias in the estimated coefficients. In this case, it is necessary to instrument the water-related marginal costs in order to avoid this endogeneity bias.

The third feature of the data is that plants differ in their location (and, as a result, in the water regulations under which they operate) and in the technologies that they employ in their production processes. These differences should be accounted for when seeking to explain differences in observed recirculating behaviour.

The final feature of the data is that they are a balanced panel of 2725 plant-level observations over three time periods (1986, 1991 and 1996).

When taken together, these features lead us to employ an Instrumental Variables Heckman two-stage estimation model (Heckman 1979). The Heckman two-stage selection model contains two equations: the decision equation in which the discrete choice of whether to recirculate is modeled, and the recirculation equation in which the continuous choice of the volume of water to recirculate is modeled. The decision equation is estimated using a Probit model where the dependent variable is a dummy taking the value of 1 if the plant is observed to recirculate a positive volume of water in 1986 (that is, it has the capacity to recirculate in 1986 and subsequent time periods). An important feature of the model is that it permits two separate reasons for observing no recirculation in a given time period: first, the plant may never recirculate and, second, the firm may have the capacity to recirculate but finds it optimal to not recirculate in a given time period.

Regressors reflect the assumption that the decision to recirculate will be influenced by factors such as a plant’s scale and production technology as well as local water supply conditions. Thus, the explanatory variables include the scale of the plant (represented by the number of workers employed at the plant), and dummy variables that characterize the plant’s province and its two-digit industrial classification. An additional dummy variable is set equal to 1 if the plant treats its raw water intake prior to use.

The second equation is estimated using two-stage least squares (2SLS), and the sample is restricted to those plants reporting positive recirculation volumes. Right-hand side variables are those which economic theory predicts will influence the marginal decision of how much water to recirculate: the instrumented marginal costs and the scale of operations. A time trend is added to account for changes in the plant’s technology. The decision and recirculation equations are estimated as a simultaneously determined system in order to test for correlation across the two features of the plant’s water use. As discussed in Bruneau et al. (2010), if the equations’ errors are correlated but the equations are estimated separately, this may lead to biased coefficient estimates.

With respect to input costs, the IWUS does not report the costs of non-water inputs but does provide information regarding the costs of water use. Specifically, the IWUS provides observations on plants’ operating and maintenance expenditures for each of water intake, water recirculation and water treatment prior to discharge. In making decisions regarding these activities, manufacturing plants do incur costs associated with pumping, treating and storing intake water, but usually face no external prices, with the exception of publicly supplied plants which face an external price for intake water. An additional feature of these water-related costs is that they are likely to be partially co-determined with the quantity of water used.

Thus, the procedure uses a two-step process to construct the marginal costs of water intake, recirculation and discharge. First, the total cost of water is regressed against its quantity, and quantity squared for intake, recirculation and discharge. The estimated coefficients from these equations are used to calculate the predicted marginal cost of each of the three forms of water use. In the second stage, instruments are created by regressing the estimated marginal costs against a set of variables thought to be correlated with them but exogenous to the firm. As Table 3 sets out, the explanatory variables chosen are the following: a dummy for the region of the country (either Ontario and the West or Quebec and the Maritimes), a time trend, a dummy for whether the plant is part of a “heavy” water using industry (Standard Industrial Classification [SIC] codes 10, 25, 36 and 37), and the level of in-plant capital expenditures related to the water system.

Table 3. Instrumental variable estimates of marginal costs where the dependent variable is the estimated marginal cost derived from the regression equation TC = a₀ + a₁Q + a₂Q². TC (total cost) measures the total reported annual expenditure, and Q (quantity) is the total reported annual volume of water.

	Marginal cost of intake		Marginal cost of recirculation		Marginal cost of discharge
	Estimate	Standard error	Estimate	Standard error	Estimate	Standard error
Constant	–0.0232794	(0.0014794)	0.0120988	(0.0000421)	0.1825571	(0.0009584)
TREATdum	0.0007064	(0.0011985)	–0.0000252	(0.0000341)	–0.0004222	(0.0007764)
Region	0.0004683	(0.0002767)	–6.01e-06	(7.88e-06)	–0.0002884	(0.0001793)
dum86	0.0034971	(0.0009264)	–0.000108	(0.0000264)	–0.0022664	(0.0006002)
dum91	0.0019034	(0.000846)	–0.0000723	(0.0000241)	–0.0011929	(0.000548)
SIC10	–0.0013141	(0.0007315)	0.0000713	(0.0000208)	0.0008085	(0.00047390
SIC16	–0.0012382	(0.0017731)	0.0000516	(0.0000505)	0.0007386	(0.0011487)
SIC18	0.0000221	(0.0019763)	0.0000538	(0.0000563)	–0.0000875	(0.0012803)
SIC27	0.0131126	(0.0012859)	–0.0001371	(0.0000337)	–0.0049533	(0.0007665)
SIC29	0.0131126	(0.0012859)	–0.0002736	(0.0000366)	–0.0082857	(0.000833)
SIC30	–0.0013086	(0.0013186)	0.000066	(0.0000375)	0.0007961	(0.0008543)
SIC32	–0.0010044	(0.0012287)	0.0000617	(0.000035)	0.0006161	(0.000796)
SIC35	–0.00082	(0.0010644)	0.00005	(0.0000303)	0.0004842	(0.0006895)
R2	0.1267		0.0831		0.0792
F	19.31		13.98		17.92

SIC: Standard Industrial Classification code.

In addition to input costs, it may be expected that the level of output could influence the desired volume of water to recirculate. The scale of production at each plant is represented by the reported number of workers. The IWUS did request the dollar value of production, but the response rate on this question was very low (less than 20%) and so it was not used. Several sets of binary variables are also used as explanatory variables. One binary variable indicates whether plants treat their intake water prior to using it. Additional sets of binary variables identify the province in which the plant is located (with Newfoundland and Labrador being the omitted province), the industrial sector of the plant (with food products being the omitted sector) and the time period of the observation (with 1986 being the omitted observation). The regressions are unable to include dummies for both 1991 and 1996 as the 1991 dummy is perfectly correlated with the dummy variable identifying recirculation capacity.

Finally, the two-stage model is estimated using two different dependent variables in the recirculation equation. In the first case, the annual volume of water recirculated in the plant is the dependent variable. In the second case, the dependent variable is a measure of recirculation rate, or intensity, defined as the annual volume of water recirculated divided by the annual volume of intake water. Table 4 provides descriptive statistics for all of the variables used in the estimation model.

Table 4. Descriptive statistics of variables in estimation model.

Variable	Units	Mean	St. dev.^1	Min^2	Max
Scale of production	#workers	198.34	459.94	13	1500
MC^3-intake	$/m^3	0.0384	0.0211	0.002	0.062
MC-recirculation	$/m^3	0.1274	0.0198	0.006	0.217
MC-discharge	$/m^3	0.2396	0.2411	0.0159	0.358
Treatment prior to use		0.6423	0.4790	0	1
Nova Scotia		0.0341	0.1815	0	1
New Brunswick		0.0385	0.1924	0	1
Quebec		0.2384	0.4261	0	1
Ontario		0.4135	0.4925	0	1
Manitoba		0.0380	0.1913	0	1
Saskatchewan		0.0239	0.1529	0	1
Alberta		0.0729	0.2599	0	1
British Columbia		0.1140	0.3178	0	1
Beverage		0.0055	0.0739	0	1
Rubber		0.0285	0.1664	0	1
Plastics		0.0211	0.1439	0	1
Textiles		0.0051	0.0714	0	1
Wood		0.0781	0.2684	0	1
Paper		0.0440	0.2051	0	1
Primary metals		0.0524	0.2230	0	1
Fabricated metals		0.0834	0.2765	0	1
Transportation		0.0790	0.2697	0	1
Minerals		0.1022	0.3030	0	1
Petroleum		0.0080	0.0894	0	1
Chemicals		0.0916	0.2885	0	1
Volume of water recirculated	m^3	2,223,852	1.89e+07	0	4402000
Recirculation rate		3.6954	47.725	0	7.8176

¹ St. dev.: standard deviation.

² The minimum and maximum values for the following variables are reported at the 5% and 95% percentiles in order to preserve confidential of responses: scale of production, volume of water recirculated, and recirculation rate.

³ MC: marginal cost.

Estimation results

Table 5 reports estimated coefficients and standard errors for each of the decision and recirculation equations using the annual volume of water recirculated as the dependent variable in the recirculation equation. Table 6 reports the estimated coefficients for the same model but using the recirculation intensity as the dependent variable.

Table 5. Two-stage coefficient estimates for recirculation volume. The dependent variable in the decision equation is a binary variable with a value of 1 if the plant recirculates water and 0 otherwise in 1986.

Variable	Decision equation	Standard error	Recirculation volume equation	Standard error
Constant	–2.55e+09	2.32e+09	–0.2893028*	0.1089496
MC-intake	2.94e+11**	1.62e+11
MC-recirculation	–3.43e+11*	1.46e+11
MC-discharge	–1.82e+10**	1.02e+10
Number of workers	13090*	545	0.0001256*	0.0000565
Treatment dummy			1.475931*	0.0349829
1996 dummy	27295	819894	–0.4888256*	0.0344649
SIC10 (food)			–0.167787*	0.0494193
SIC15 (rubber)			0.0890838	0.2575433
SIC16 (plastic)			0.16573	0.1149624
SIC18 (primary textile)			–0.2622304*	0.1164642
SIC19 (textile products)			0.005741	0.2451123
SIC25 (wood)			–0.3530821*	0.071002
SIC27 (paper)			–0.0921502	0.0980839
SIC29 (primary metal)			0.0143288	0.0814031
SIC30 (fab. metal)			–0.2189309*	0.0663837
SIC32 (trans. equip.)			–0.1337754**	0.0695691
SIC35 (minerals)			–0.1144455**	0.0615119
SIC36 (petroleum)			–0.2034461	0.2017814
Nova Scotia			0.3459141*	0.1348769
New Brunswick			0.0432986	0.1272549
Quebec			0.3555532*	0.105737
Ontario			0.2821644*	0.103216
Manitoba			0.3017064*	0.1294429
Saskatchewan			–0.1012715	0.1434234
Alberta			0.5345518*	0.1201144
British Columbia			0.1830715	0.1116779
Mills λ			1807906*	1161100
Wald χ^2(31)	801.87
Probability > χ^2	0.00
Number of observations	8175		5776

MC: marginal cost. SIC: Standard Industrial Classification code.

^* 5% level of significance using robust standard errors.

^** 10% level of significance using robust standard errors.

Table 6. Two-stage coefficient estimates for recirculation intensity. The dependent variable in the decision equation is a binary variable with a value of 1 if the plant recirculates water and 0 otherwise in 1986.

Variable	Decision equation	Standard error	Recirculation equation	Standard error
Constant	–5092478	7963703	–0.2893028*	0.1089496
MC-intake	4.94e+08	5.55e+08
MC-recirculation	–5.16e+08	5.03e+08
MC-discharge	–3.06e+07	3.50e+07
Number of workers	1.978102	1.873804	0.0001256*	0.0000565
Treatment dummy			1.475931*	0.0349829
SIC11 (bev.)			–0.4888256*	0.0344649
SIC15 (rubber)			–0.167787*	0.0494193
SIC16 (plastic)			0.0890838	0.2575433
SIC18 (primary textile)			0.16573	0.1149624
SIC19 (textile products)			–0.2622304*	0.1164642
SIC25 (wood)			0.005741	0.2451123
SIC27 (paper)			–0.3530821*	0.071002
SIC29 (primary metal)			–0.0921502	0.0980839
SIC30 (fab. metal)			0.0143288	0.0814031
SIC32 (trans. equip.)			–0.2189309*	0.0663837
SIC35 (minerals)			–0.1337754**	0.0695691
SIC36 (petroleum)			–0.1144455**	0.0615119
SIC37 (chemicals)			–0.2034461	0.2017814
Nova Scotia			0.3459141*	0.1348769
New Brunswick			0.0432986	0.1272549
Quebec			0.3555532*	0.105737
Ontario			0.2821644*	0.103216
Manitoba			0.3017064*	0.1294429
Saskatchewan			–0.1012715	0.1434234
Alberta			0.5345518*	0.1201144
British Columbia			0.1830715	0.1116779
Mills λ			5863.187	3987.99
Wald χ^2(31)	13.95
Probability > χ^2	0.0159
Number of observations	8175		5776

^* 5% level of significance using robust standard errors.

^** 10% level of significance using robust standard errors.

With respect to the role of the variables representing the marginal costs of water use on the observed volumes of water recirculated, Table 5 shows that the marginal cost of water recirculation has a negative and significant impact on the volume of water recirculated. The other marginal costs are statistically significant at the 10% level. Increases in the cost of intake are correlated with increases in the volume of water recirculated – suggesting that intake and recirculation are substitutes. Conversely, increases in the cost of treatment prior to discharge lower recirculation volume – perhaps by depressing water use generally. The scale of plant operations (as represented by the number of workers) positively influences water recirculation volumes.

Table 5, column 2 shows the results for the recirculation equation which identifies plants having the capacity to recirculate as its dependent variable. Both the scale of plant operations and the need to pretreat water prior to use make it more likely that a plant will have the capacity to recirculate. The role of the pretreatment dummy variable is particularly important as it indicates that a potential motivation for investing in the capacity to recirculate is to avoid the costs of pretreating additional intake water. Several of the provincial dummy variables exhibit positive and significant coefficients (recall the omitted province is Newfoundland and Labrador). These may reflect province-specific regulations or other policies that promote developing the capacity to recirculate water. The provincial dummies may also be capturing regional climate-related differences that have an influence on water scarcity in some regions. A number of the industry-subsector dummy variables are significant (the omitted industry being SIC37), indicating that there are some important technology-related features across manufacturing subsectors that explain observed differences in recirculating behaviour. Finally, the time period dummy exhibits a negative and significant coefficient. This indicates that, all others things being equal, the likelihood of plants having the capacity to recirculate water in 1996 was lower than in 1986. The last thing to see from Table 5 is the estimate of the Mills variable (λ). The estimated coefficient on the selectivity variable is positive and significantly different from zero, and this indicates the presence of self-selection bias. Thus, if the self-selecting behaviour of firms had not been accounted for, the estimated coefficients in the recirculation equation would have been biased.

An examination of the estimated coefficients reported in Table 6 demonstrates that there are interesting differences between the estimated coefficients just discussed and those for the model that uses the water recirculation intensity as the dependent variable. First, none of the marginal cost variables display statistically significant coefficients. Indeed, none of the explanatory variables in the recirculation equation exhibit significant coefficients. Thus, when the coefficients of the marginal costs of water use are compared across Tables 5 and 6, it appears that plants are optimizing with respect to the volume of recirculation water (conditioned on their choosing to have the capacity to recirculate) but may not with respect to the intensity of that recirculation effort. It seems to be the case that the volume of water intake and the volume of water recirculated change proportionately within each plant. The results suggest that plant recirculation intensity may be tied to water-use technologies and, as a result, are not sensitive to marginal changes in water-related costs. That is, plants that have the capacity to recirculate may be tied to a particular recirculation technology that cannot be altered in the short run to reflect changes in water-related marginal costs.

Turning to the coefficients of the decision equation in Table 6, they are the same as those in Table 5. The key difference is that, in contrast to Table 5, the lambda (λ) coefficient is not statistically significant.

The estimation models appear to perform better using the volume of recirculation water as the dependent variable in the recirculation equation. These coefficients are explored further. Table 7 reports the elasticities for selected variables using the estimated coefficients from Table 5. While the STATA (StataCorp LP 2014) routine used to estimate the model does not provide standard estimates for the calculated elasticities, their pattern of statistical significance follows that for the estimated coefficients upon which they are based. Table 7 shows that all of explanatory variables display inelastic relationships with the volume of recirculation water or the decision to have the capacity to recirculate water. Thus, the plants’ operating environment – as reflected by the water-related marginal costs they face, the scale of their operations and the need to pretreat intake water – plays an important role in decisions related to water recirculation.

Table 7. Elasticity estimates (using coefficients from Table 5).

Variable	Recirculation decision	Recirculation volume
MC-intake	NA	0.08
MC-recirculation	NA	–0.24
MC-discharge	NA	–0.31
Number of workers	0.05	1.04
Intake treatment	0.64	NA

NA: not available. MC: marginal cost.

Conclusions

Industrial water use is an important part of most developed economies’ total water use, and one that is differentiated from other sectors’ water use by the prevalence of recirculating. This feature means that encouraging greater industrial water recirculation is a potentially important form of water conservation that could provide water for other sectors. The analysis of several years of observations from Canada’s Industrial Water Survey data shows that there are remarkably complex patterns of behaviour that can be observed over time (Tate and Scharf 1983; Tate and Scharf 1989; Tate and Scharf 1995; Scharf et al. 2002). Some plants either never or always recirculate water, while a sizeable number of plants are observed to recirculate in some time periods and not recirculate in others.

The statistical analysis provides insight into the factors influencing the observed recirculating behaviour. The marginal costs of water use influence the volume of water recirculation (although not the intensity of recirculation) largely as economic theory would predict. Increases in the scale of production lead to more water recirculation and raise the likelihood of a plant having the capacity to recirculate. This last observation is tempered by the recognition that using the number of production workers as a proxy for the level of output may be introducing a degree of endogeneity bias into the model.

Location and technology effects play a significant role in explaining the likelihood of a plant having the capacity to recirculate. The possibility that the provincial dummies are reflecting differences in regulations merits further investigation. Furthermore, the need to pretreat water strongly increases the likelihood of a plant having the capacity to recirculate water. Finally, judging by the estimated coefficients on the time period dummy variables, the time period under observation is characterized by a declining likelihood of plants having the capacity to recirculate, although those plants that retain that capacity do not exhibit a declining trend in recirculation volumes.

The estimation model was general enough to examine the decision to possess the capacity to recirculate as well as the related decision regarding the volume of water to recirculate. The estimated Mills ratio coefficient clearly shows that these decisions are linked. At the same time, they are influenced by different factors. The discrete decision whether to have the capacity to recirculate appears most directly influenced by “long-run” factors such as the technology used in the production process, the location of the plant and the need to pre-treat intake water. Conversely, decisions regarding the volume of water to recirculate are influenced by the marginal costs of water-related activities as well as the scale of operations.

While being conscious of the limitations of the empirical model (in particular, the lack of input prices for energy and capital as explanatory variables for plant’s recirculation levels), there is some policy relevance of the findings. First, recirculation volumes are somewhat sensitive to prices and, as a result, may be influenced by regulatory pricing strategies. For instance, subsidies for recirculation could be effective, as would be increasing intake costs (through municipal water prices or fees for self-supplied permits to take water). That water intake prices are generally too low suggests that a more rational water pricing strategy would have a secondary benefit of increasing recirculation volumes at the same time.

Second, to the extent that recirculation frequencies differ across provinces, this suggests that plants’ willingness to invest in recirculation capacity could be policy responsive. However, the model does not identify what the specific provincial drivers (e.g. fiscal policies related to investments, environmental policies related to water discharges or land use policies relating to plant location) are and, as a result, we are constrained in making pronouncements regarding the reasons for the findings regarding the provincial dummy variables. This appears to be a potentially valuable avenue for future research.

Acknowledgements

This paper was supported in part by Environment Canada under research contract K1531-06-1002, and by the Canadian Water Network. We are grateful to two anonymous reviewers, Michel Villeneuve, and Diane Dupont, for their comments, and Siobhan Costelloe for translating the abstract. This paper reflects the opinions of the authors, and all errors and omissions are our own.