WATER RESOURCES RESEARCH, VOL. 40, W01401, doi:10.1029/2003WR002192, 2004
A panel data analysis of commercial customers’ water price responsiveness under block rates Klaus Moeltner Department of Resource Economics, University of Nevada, Reno, Nevada, USA
Shawn Stoddard Truckee Meadows Water Authority, Reno, Nevada, USA Received 23 March 2003; accepted 24 November 2003; published 24 January 2004.
[1] The existing literature on nonresidential water demand has primarily employed cross-
sectional models based on time-aggregated data. In this study, we analyze panel data models of commercial water demand that build on monthly observations of water use and marginal prices for individual customers. This allows for a closer investigation of the temporal aspects of commercial water demand. We show that commercial water demand can exhibit strong seasonal patterns. These temporal consumption patterns aggravate simultaneity problems associated with block pricing if they are not explicitly accounted INDEX TERMS: 6314 Policy Sciences: Demand estimation; 9805 for in demand specifications. General or Miscellaneous: Instruments useful in three or more fields; 9820 General or Miscellaneous: Techniques applicable in three or more fields; KEYWORDS: commercial water demand, block-rate pricing, random effects, temporal effects, simultaneity bias, instrumental variables Citation: Moeltner, K., and S. Stoddard (2004), A panel data analysis of commercial customers’ water price responsiveness under block rates, Water Resour. Res., 40, W01401, doi:10.1029/2003WR002192.
1. Introduction [2] Past investigations of urban water demand have primarily focused on residential customers. In contrast, water demand by commercial, industrial, and institutional (c/i/i) establishments has received little attention in the academic and professional literature. As does research on residential demand, the few existing c/i/i studies focus primarily on the estimation of price elasticities and on demand forecasts. They are essentially cross-sectional in nature, investigating variability in water use across firms and production steps rather than over time. With few exceptions, the implicit time horizon for these analyses is usually a calendar year. Considering that most U.S. utilities bill c/i/i customers on a monthly basis, and that an establishment’s monthly consumption is likely to vary throughout a given year, this requires use of a dependent variable that is aggregated in some form. [3] For example, studies based on firm-level data use consumption figures that are aggregated over time, such as daily or monthly averages [Lynne et al., 1978; Ziegler and Bell, 1984], or annual totals [Renzetti, 1988, 1992; DeRooy, 1974]. Other analyses combine temporal with cross-sectional aggregation. Examples are those by Babin et al. [1982], who aggregate water demand over all firms within a given twodigit SIC category and State for a given year, and Williams and Suh [1986], whose dependent variable is the annual water demand for all commercial establishments within a given municipality. [4] This use of an aggregated consumption measure also calls for an aggregation of the measurement for monthly Copyright 2004 by the American Geophysical Union. 0043-1397/04/2003WR002192
marginal price. Babin et al. [1982], for example, use average water prices for a given state, while Williams and Suh [1986] derive their price variables from typical monthly water bills for a given municipality. In studies utilizing firm-level data, water price has been computed as annual average per 1000 gallons [Renzetti, 1988, 1992], estimated through auxiliary regressions of total cost on functions of water consumption [Ziegler and Bell, 1984], or directly expressed as a function of total water cost and the cost of other production inputs [DeRooy, 1974]. Of the studies cited above, only Lynne et al. [1978] employ firmspecific marginal prices, corresponding to an establishment’s average monthly consumption during the time period of interest. [5] The advantage of such aggregate models is that they are generally less sensitive to outliers and measurement errors compared to specifications based on observations corresponding to individual firms and billing periods. On the other hand, estimated parameters and price elasticities from such models will generally not reflect behavior at the firm level, as discussed by Stoker [1984, 1993]. Therefore, if the consistent estimation of water price responsiveness at the firm level is the primary focus of a demand analysis, a panel data set of monthly consumption for a variety of establishments and sufficiently long time horizon is needed. This is especially important in cases where utilities, in addition to implementing periodic across-theboard rate changes, employ block schedules based on monthly water use. This creates an environment where monthly marginal prices may change frequently for a given customer. This, in turn, could aggravate aggregation bias in a model using averages or totals over time or cross-sectional units for consumption and explanatory variables [Stoker, 1984].
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[6] To avoid such aggregation problems, we propose in this study a panel data model of commercial water demand that builds on monthly observations of water use and marginal prices for individual customers and several calendar years. We estimate this model for a variety of Standard Industrial Classification (SIC) categories. As we will show, commercial water demand can exhibit strong seasonal variability. These temporal consumption patterns can aggravate simultaneity problems associated with block pricing if they are not explicitly accounted for in demand specifications. [7] The remainder of this text is structured as follows: In the next section we develop the econometric model for this analysis. The empirical part of this study then discusses data and estimation results. Concluding remarks and a summary of key findings are given in section 5.
2. Model Formulation [8] While c/i/i units utilize water in a variety of ways [e.g., Dziegielewski et al., 2000], water can essentially be considered an input into an establishment’s production process. Ideally, like any factor demand model, a model of water demand ought to be derived from an economic optimization process [Hanemann, 1998]. Since output is subject to choice for most c/i/i customers, the appropriate economic framework would be profit maximization. However, this requires knowledge of prices of all other factor inputs and all outputs. Given the multitude of production inputs and end products associated with even a single firm, this requirement far exceeds the scope of data sets traditionally available to public water utilities, such as the one underlying this study. Thus we abstract from any production-theoretic modeling and aim instead for econometric consistency in this application. [9] The estimation of water demand of heterogeneous firms over time under tiered price schedules poses several econometric challenges. First, since water usage is presumably linked to some unobserved, time invariant firm characteristics, regression errors can be expected to be correlated within a given unit for the entire time period under consideration. Ignoring this correlation will result in biased standard errors and unreliable t-values for estimated coefficients [e.g., Baltagi, 1995]. Second, unobservable components driving consumption may exhibit time trends and seasonal patterns commensurate to market activities, regional economic conditions, and the timing of exogenous price changes. If included regressors are correlated with such time effects, parameter estimates will be plagued by omitted variable bias. Third, the block rate nature of the billing schedule introduces a simultaneity problem into the model due to the reciprocal causality flow between quantity and price. Failing to address the simultaneity problem can severely bias estimation results [e.g., Deller et al., 1986; Renzetti, 1988, 1992; Hewitt and Hanemann, 1995]. In addition, water demand for our sample will also depend on the price of sewer services, as these charges are directly pegged to monthly water consumption. Fortunately, sewer charges are not tiered by consumption in this application, which preempts the need to address schedule-related simultaneity problems for this price component as well. Since marginal sewer charges are invariant over consumption, they can be simply added to applicable marginal water prices.
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[10] We start our model development with a standard random effects specification [e.g., Baltagi, 1995]. For a given establishment i, water demand in month t can be expressed as yit ¼ x0i bx þ ct bc þ pit bp þ eit
ð1Þ
where eit ¼ mi þ eit ;
xi is a k by 1 vector of firm attributes, ct is a climate indicator for period t, pit is the observed marginal price for combined water and sewage services associated with firm i and month t, bx is a k by 1 set of parameters corresponding to the elements in xi, the remaining b-terms are scalars corresponding to their associated regressors, and eit is an error term. As indicated in equation (1), this error is decomposed into a firm-specific constant mi (invariant over time) and an idiosyncratic normally distributed error eit with mean zero and common variance se2. Following standard procedure, we further stipulate the distribution of mi as multivariate normal with h i E½mi ¼ 0; E mi m0j ¼ s2m ITi
i¼j
h i E ½mi ¼ 0; E mi m0j ¼ 0
i 6¼ j
ð2Þ
where E denotes the expectation operator, ITi is an Ti Ti identity matrix, and symbol Ti denotes the total number of time periods included in the sample for firm i. Thus each establishment ‘‘draws’’ a firm-specific constant term from a normal distribution with mean zero and variance sm2. As indicated in equation (2), these random effects are uncorrelated across customers. In addition, we assume that mi, ei and all regressors are uncorrelated within and across c/i/i units. [11] The firm-specific error term mi introduces the stipulated correlation across observations for a given establishment. As indicated above, correlation patterns over time may also exist. One could incorporate such effects through a two-way error component model using fixed or random effects for time periods in addition to the error decomposition described in equation (2) [e.g., Baltagi, 1995]. We propose instead to capture time effects explicitly by including indicator variables for calendar months in our final model specification. This better utilizes information contained in our data and allows for more flexibility in generating demand forecasts. As we will demonstrate, the incorporation of time effects corrects omitted variable problems associated with model (1). The expanded model with time indicators is thus yit ¼ x0i bx þ ct bc þ pit bp þ m0t bm þ eit ;
ð3Þ
where mt denotes a vector of month indicators corresponding to time period t, bm is the associated coefficient vector, and the error structure is as in equation (1). [12] The remaining specification issue to be addressed in both models is the endogeneity of pit resulting from the tiered water price schedule. Following existing studies [e.g., Deller et al., 1986; Renzetti, 1988, 1992], we apply an
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instrumental variable procedure to purge our marginal price variable of simultaneity problems. This technique is based on two-stage least squares (2SLS) estimation. In the first stage, observed per-unit charge for combined water and sewer services in a given month is regressed on all exogenous variables included in the model plus some additional explanatory components. In our application, these identifiers are the listed per-unit charges for first and second tier consumption from the water utility’s billing schedule, the applicable tier threshold corresponding to a given customer and month, and marginal sewer price. Predictions for marginal price from this first-step specification are then used to replace the original price variable. In order to preserve intrafirm correlation as specified in equations (1) and (3) for both regression steps, we use a generalized 2SLS estimator adapted to panel data models. This specification was first suggested by Balestra and Varadharajan-Krishnakumar [1987]. A description of the model is also given by Baltagi [1995, chap. 7]. [13] In order to show the impact of capturing time effects we estimate both models given by equations (1) and (3). Also, for illustrative purposes, we follow Lynne et al. [1978] and estimate an aggregate panel data model that employs average monthly consumption for a given firm and year, as well as marginal prices corresponding to these aggregate consumption figures. As we will show, only the specification with monthly consumption, simultaneity-corrected price terms, and seasonal effects generates plausible price coefficients and elasticities for our sample of firms.
3. Data [14] Our data set comprises information on monthly water consumption of nonresidential customers of a western U.S. water utility for the time period January 1993 to December 2000. In a first selection process, establishments were chosen from the entire population of c/i/i accounts for the utility’s General Metered Water Services according to the following criteria: (1) uninterrupted consumption history for at least four consecutive years (2) availability of basic building characteristics from assessor files, and (3) ability to clearly match an establishment with a two-digit SIC category. The second step of data preparation entailed the final selection of two-digit SIC groups suitable for an analysis of price responsiveness. The criteria for this selection were at least 100 firm-years included in a given group, and a reasonable degree of homogeneity with respect to water use. The latter criterion was implemented to avoid an excessive dominance of cross-sectional variability in water use and pricing structure over temporal consumption patterns. This consideration is driven by the fact that only some very basic observed firm characteristics are available for this analysis (see below). This may lead to omitted variable problems related to unobserved firm characteristics for SIC groups with high diversity in water needs and usage patterns. [15] The resulting SIC categories are listed in Table 1. Table 1 depicts the two-digit SIC code and definition, the main underlying firm types, observation counts for firms, firm-years, and firm-months, and basic statistics on annual water consumption. The first category, Wholesale TradeDurable Goods (referred to as ‘‘Wholesale’’ in the remainder of this text) covers a wide variety of manufactured
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products. The unifying element for this category is the extensive usage of warehouses and storage facilities and associated cooling needs. Eating and Drinking places (‘‘Eat and Drink’’) are presumably similar in their needs for drinking water, cooling, cleaning and sanitation. Depository institutions (‘‘Banks’’) represent a classic office environment with water needs for cooling and sanitation. In addition, many of these establishments have some form of landscaping with associated irrigation needs. The category labeled Auto Repair, Services, and Parking (‘‘Automotive’’) includes carwashes as a unique customer type with regard to water usage. Generally, this category was incorporated as an example of an SIC group that exhibits limited seasonal variation in water usage. Amusement and Recreation Services, in turn, comprise many service facilities with high indoor and outdoor water needs for pools, showers, and sports fields. It should be noted, however, that the public golf courses included in this group draw irrigation water mainly from private sources, which are supplemented by limited amounts of public water during the summer months. The final category listed in Table 1, Educational Services (‘‘Schools’’) comprises both private commercial establishments (vocational schools, career development centers, etc.) and public facilities (elementary and secondary schools, Community Colleges, etc.). While water needs are presumably similar for most establishments (sanitation, cooling, some outdoor irrigation), economic incentives to respond to price changes are probably less pronounced for the public segment of these institutions given their public service nature. [16] As shown in Table 1, annual water consumption varies widely across firms, even within a given SIC group. Such pronounced variability in annual water needs is expected at this rather general level of aggregation. We presume that this scale effect is reasonably well explained by the firm characteristics captured in our models (see below). [17] As depicted in Figures 1 –6, all included SIC groups exhibit distinct and similar seasonal consumption patterns with highest monthly averages during summer and lows during winter. This reflects primarily the increased need for water-based cooling and irrigation during the warmer months of the year [e.g., Dziegielewski et al., 2000]. As expected, seasonal effects are subtler for the Automotive category, probably due to relative stable customer demand throughout the year and reduced cooling and irrigation needs during summer. [18] Water and sewer fees for our data are given in Table 2. Water charges consist of fixed monthly service fees and marginal charges per 1000 gallons of water. Marginal prices follow an increasing block rate with two blocks for all firms. As indicated in Table 2, rate thresholds depend on the diameter of service pipes and thus vary over establishments. In addition, the utility implemented three across-the board increases in marginal prices for both tiers during the research period, and a minor tier change for the three larges diameters in 1993. A 3.5% service tax is levied on the total monthly bill and applies to all customers. [19] Sewer fees are shown in the second half of Table 2. They comprise a monthly fixed charge and a constant marginal rate per 1000 gallons of water used in a given month. As shown in Table 2 these fees are identical for most
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Table 1. Firm Counts and Water Consumption by SIC Codesa Two-Digit SIC Code 50
58 60
75
79
82
Two-Digit SIC Definition
Number of Firms
Number of Firm-Years
Number of Firm-Months
Minimum
Mean
Maximum
53
386
4490
10
390
4501
112 39
785 262
9214 3033
28 11
768 402
4818 3360
80
556
6467
11
344
3704
17
123
1438
122
1639
13872
47
360
4207
42
2587
30538
wholesale trade-durable goods motor vehicles, parts, and supplies furniture and homefurnishing lumber and construction materials professional and commercical equipment computers and software medical and hospital equipment electrical goods plumbing and heating eqiupment farm and industrial machinery sporting and recreational goods eating and drinking places depository institutions commercial banks savings institutions credit unions auto repair, services, and parking car rentals automotive parking automotive repair shops carwashes amusement and recreation services dance studios and schools theatrical producers and services bowling centers commercial sports health clubs public golf courses misc. amusement and recreation services educational services elementary and secondary schools colleges and universities libraries vocational schools
Annual Water Consumption
a
Consumption figures are in 1000 gallons (1 gallon = 3.785 L).
customers, although selected segments of establishments, roughly corresponding to two-digit SIC codes, are charged at different rates. Of the SIC groups considered in this study, only Automotive Repair, Services, and Parking (SIC 75) is associated with a SIC-specific sewer schedule. All other firms face the marginal rates given in the last row of Table 2.
Marginal sewer charges were adjusted three times during the research period. It should be noted that these changes were implemented at points in time different from those associated with changes in water rates. Overall, the data exhibit substantial variability in both marginal prices of water and sewer services across firms and over time. All
Figure 1. Monthly water use for Wholesale.
Figure 2. Monthly water use for Eat and Drink. 4 of 9
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Figure 5. Monthly water use for Amusement and Recreation.
Figure 3. Monthly water use for Banks. prices are translated into 2000 figures using appropriate CPI converters. [20] In summary, the list of explanatory variables considered in this analysis comprises firm attributes, which are square footage (‘‘squ_feet’’), number of floors (‘‘stories’’), age of building (‘‘age’’), and age squared (‘‘age_squ’’), time variables labeled mo_2 (=February), mo_3 (=March), etc, with January as baseline month, and price information, including instrumented price (‘‘price’’), marginal water rates, tier thresholds, and sewer fees. To capture weather effects on consumption, we also include cooling degree days (‘‘cldg’’), measured in increments of 10, in all estimated models. The dependent variable in all specifications is the log of monthly water consumption in 1000 gallons.
[21] Table 3 captures estimation result for three different model specifications for each SIC category. Model 1 is the most extensive specification. It includes all regressors, and is estimated through the generalized 2SLS procedure sug-
gested by Balestra and Varadharajan-Krishnakumar [1987]. Specifically, the price variable in model 1 incorporates the fitted values from a first stage random effects regression of combined water and sewer price, with water price measured based on observed monthly consumption, against marginal water rates for each tier, tier threshold, sewer rate, firm attributes, cooling degree days, and month indicators. The value of the standard deviation for the firmspecific error component is denoted as and given beneath model 1 results for each SIC group. [22] Model 2 employs the same instrumentation process for price as model 1, but omits the month indicators. Model 3, in turn, is a random effects specification based on average monthly consumption per firm-year. This variable, in log form, is regressed against firm characteristics, cooling degree days, and price, where the water component of price is the marginal rate that corresponds to the average monthly consumption for a given firm-year. These aggregate terms for price and quantity are similar to those employed by Lynne et al. [1978]. Model 3 is included in
Figure 4. Monthly water use for Auto Repair and Services.
Figure 6. Monthly water use for Schools.
4. Estimation Results
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Table 2. Water and Sewer Pricesa Water Charges, Nominal $ Pipe Diameter 00
3/4 100 1 1/200 200 400 600 800 3/400 100 1 1/200 200 400 600 800 All All Tax on total charge
Charges service charge service charge service charge service charge service charge service charge service charge tier threshold tier threshold tier threshold tier threshold tier threshold tier threshold tier threshold per 1000 gal, 1st tier per 1000 gal, 2nd tier
1/93 to 5/93
6/93 to 9/94
10/94 to 4/98
5/98 to 12/00
6.80 6.90 7.40 8.10 11.50 11.90 13.90 10000 25000 45000 85000 900000 950000 950000 1.32 1.57 3.50%
8.60 9.10 10.50 12.30 19.30 19.90 21.80 10000 25000 40000 80000 890000 910000 910000 1.59 1.81 3.50%
10.02 10.61 12.24 14.34 22.50 23.20 25.41 10000 25000 40000 80000 890000 910000 910000 1.85 2.11 3.50%
10.02 10.61 12.24 14.34 22.50 23.20 25.41 10000 25000 40000 80000 890000 910000 910000 1.76 2.43 3.50%
Sewer Charges, Nominal $ SIC Category All 20 54 58 70 72 75 80 82 Other
Charges Service Service Service Service Service Service Service Service Service Service
charge charge charge charge charge charge charge charge charge charge
per per per per per per per per per per
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000
gal gal gal gal gal gal gal gal gal gal
1/93 to 3/94
4/94 to 3/95
4/95 to 10/95
10/95 to 12/00
3.00 1.46 1.25 1.44 1.34 1.51 1.24 1.20 1.18 1.26
3.00 2.28 1.95 2.25 2.09 2.36 1.94 1.87 1.84 1.97
3.00 2.39 2.05 2.36 2.19 2.48 2.03 1.96 1.93 2.07
4.12 2.94 2.16 2.84 2.43 3.24 2.14 2.03 1.98 2.19
a
Read 1/93 to 5/93 as January 1993 to May 1993.
Table 3 to illustrate the effect on estimated coefficients of converting monthly observations into annual aggregates. [23] To guard against the detrimental effects of gross outliers and data points with excessively high leverage on coefficient estimates, preliminary results generated by model 1 were subjected to a thorough outlier analysis for each SIC category. This procedure included a visual screening for problematic data points using residuals-versus-fitted plots and leverage-versus-residual-squared (L-R) plots [e.g., Hamilton, 1992], and an analytical test based on Belsley et al.’s [1980] DFBETA statistic with focus on the price coefficient. While the graphical methods help identify data points with extreme values for residuals (equal to fitted values minus observed sample values for log-consumption) and leverage (equal to the relative impact of the explanatory variable vector associated with a given observation on model results), DFBETA measures the standardized change in a specific regression coefficient when an observation is excluded from the sample. These inspections led to the elimination of months with zero consumption (less than 1% of observations for each SIC group), and observations with DFBETA values in the 1st and 99th percentile. These corrections provided for stabilized model results for all subsamples. [24] As shown in Table 3, model 1 generates negative and significant parameter estimates for ‘‘price’’ for almost all SIC groups. The only exception is SIC 82, Educational Services, for which the price coefficient is negative, but not significantly different from zero. This may be a manifesta-
tion of the hypothesized reduced ability of public institutions to react to price changes. Differences in results over SIC groups are more pronounced with respect to firm attributes. For example, the coefficient for square footage is only significant for Wholesale, Banks, and Schools. In contrast, the coefficient for ‘‘stories’’ emerges significant only for the Banks category. To some extent, the lack of significance for these basic building indicators may reflect a lack in variability of these attributes within a given firm group. This is somewhat less of a problem for ‘‘age’’, which is estimated to have a positive and significant effect on consumption for four of the six subsamples (Wholesale, Eat and Drink, Automotive, and Schools). Much of this effect is probably attributable to the increased occurrence of leaks and the reduced usage of water-conserving technology for cooling facilities in older structures. The coefficient for ‘‘age squared’’ is arbitrarily close to zero for all groups, indicating that the overall age effect is approximately linear in fractional terms given the log specification of the dependent variable. A similar result holds for cooling degree days. Presumably, the effect of this weather indicator is largely absorbed by the month dummies in this model specification. Perhaps the most striking result flowing from model 1 are the high levels of significance for most month indicators and subsamples. In addition, the magnitude of coefficient estimates for these terms closely mirror the seasonal patterns shown in Figures 1 – 6. For example, consumption peaks during summer are especially pronounced for Banks and Schools, followed by Amusement and Recreation and
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Table 3. Estimation Results Wholesale TradeDurable (SIC 50)
Eating and Drinking (SIC 58) SE
Auto Repair and Services (SIC 75)
Banks (SIC 60) Coefficient
SE
Coefficient
SE
Amusement and Recreation (SIC 79)
Educational Services (SIC 82)
Coefficient
SE
Coefficient
SE
Variable
Coefficient
SE
Coefficient
Price sq_feet Stories Age age_sq cldg mo_2 mo_3 mo_4 mo_5 mo_6 mo_7 mo_8 mo_9 mo_10 mo_11 mo_12 Constant su
0.061 0.007 0.581 0.014 0.000 0.000 0.091 0.126 0.151 0.391 0.551 0.774 0.829 0.803 0.651 0.505 0.225 2.541 1.42
(0.031)a (0.002)b (1.028) (0.006)b (0.000)b (0.000) (0.050)c (0.050)a (0.050)b (0.050)b (0.057)b (0.090)b (0.079)b (0.053)b (0.050)b (0.050)b (0.050)b (1.126)a
0.045 0.007 0.425 0.006 0.000 0.000 0.034 0.016 0.034 0.180 0.280 0.347 0.416 0.429 0.344 0.229 0.055 3.434 0.834
Model 1 IV-Random Effects, (0.011)b 0.093 (0.046)a (0.004) 0.030 (0.007)b (0.426) 0.893 (0.297)b (0.003)a 0.005 (0.008) (0.000)b 0.000 (0.000) (0.000) 0.001 (0.000) (0.021) 0.015 (0.073) (0.021) 0.033 (0.073) (0.021) 0.486 (0.073)b (0.021)b 1.270 (0.075)b (0.024)b 1.550 (0.083)b (0.038)b 1.793 (0.130)b (0.033)b 1.925 (0.113)b (0.022)b 1.870 (0.077)b (0.021)b 1.737 (0.075)b (0.021)b 1.271 (0.075)b (0.021)b 0.163 (0.074)a (0.447)b 0.660 (0.409) 0.741
With Months 0.063 (0.023)b 0.006 (0.011) 0.286 (0.362) 0.029 (0.004)b 0.001 (0.000)b 0.001 (0.000)b 0.011 (0.036) 0.065 (0.036)c 0.003 (0.036) 0.071 (0.036)a 0.229 (0.041)b 0.440 (0.064)b 0.484 (0.056)b 0.426 (0.038)b 0.220 (0.036)b 0.081 (0.036)a 0.020 (0.036) 2.057 (0.391)b 1.254
0.141 0.013 0.624 0.012 0.000 0.000 0.091 0.196 0.248 0.561 0.823 0.919 0.917 0.867 0.747 0.633 0.186 3.716 0.992
(0.054)b (0.024) (0.734) (0.010) (0.000)c (0.001) (0.089) (0.090)a (0.091)b (0.091)b (0.102)b (0.158)b (0.139)b (0.095)b (0.092)b (0.092)b (0.090)b (0.937)b
0.023 0.001 0.324 0.028 0.001 0.000 0.191 0.291 0.586 1.259 1.529 1.573 1.708 1.765 1.646 1.075 0.301 2.960 0.679
(0.031) (0.001)a (0.275) (0.005)b (0.000)b (0.000) (0.045)b (0.045)b (0.046)b (0.047)b (0.053)b (0.082)b (0.071)b (0.049)b (0.048)b (0.048)b (0.046)b (0.353)b
Price sq_feet Stories Age age_sq cldg Constant
0.054 0.007 0.594 0.000 0.000 0.001 2.543
(0.030)a (0.002)b (0.859) (0.006) (0.000)c (0.000)b (0.943)b
0.014 0.007 0.419 0.006 0.000 0.001 3.445
Model 2 IV-Random Effects, No Months (0.011) 0.240 (0.052)b 0.032 (0.022) (0.004) 0.031 (0.007)b 0.006 (0.010) 0.291 (0.345) (0.430) 0.919 (0.311)b a b 0.033 (0.009) 0.024 (0.004)b (0.003) b c (0.000) 0.000 (0.000) 0.000 (0.000)b b b (0.000) 0.004 (0.000) 0.001 (0.000)b (0.452)b 0.332 (0.436) 2.070 (0.374)b
0.013 0.010 0.606 0.005 0.000 0.002 3.819
(0.053) (0.027) (0.806) (0.010) (0.000) (0.000)b (1.026)b
0.294 0.001 0.345 0.010 0.000 0.004 2.747
(0.036)b (0.001) (0.440) (0.006) (0.000) (0.000)b (0.556)b
Price sq_feet Stories age age_sq cldg Constant
0.180 0.007 0.606 0.006 0.000 0.003 2.107
(0.064)b (0.002)b (0.670) (0.010) (0.000)a (0.001)c (0.777)b
0.064 0.007 0.434 0.011 0.000 0.001 3.290
(0.024)b (0.004)c (0.412) (0.006)c (0.000) (0.001)a (0.441)b
Model 3 Aggregate Random Effects 0.095 (0.077) 0.293 (0.055)b 0.029 (0.007)b 0.007 (0.008) 0.330 (0.258) 0.695 (0.304)a c 0.021 (0.012) 0.009 (0.009) 0.000 (0.000) 0.000 (0.000) 0.004 (0.002)a 0.001 (0.001) b 1.614 (0.493) 1.298 (0.356)b
0.055 0.012 0.377 0.005 0.000 0.000 4.079
(0.082) (0.025) (0.745) (0.015) (0.000) (0.002) (0.974)b
0.131 0.001 0.423 0.019 0.001 0.000 3.657
(0.045)b (0.001) (0.429) (0.007)b (0.000)b (0.001) (0.550)b
a
Significant at 5%. Significant at 1%. c Significant at 10%. b
Wholesale. This corresponds well to the consumption patterns depicted in Figures 1 – 6. [25] The values for the standard deviation of the firmspecific error term appear of reasonable magnitude. Generally, this component accounts for 60 – 80% of overall variability in the error term for each subsample. A Lagrange Multiplier (LM) test clearly rejects the null hypothesis of sm = 0, i.e., the absence of firm-specific effects. This supports our assumption of intrafirm correlation. [26] The omission of month indicators in model 2 has a clear impact on all model coefficients associated with regressors that exhibit temporal variability. Most notably, price coefficients for Eat and Drink, Automotive, and Amusement and Recreation are now insignificant, while the price coefficients for the remaining SIC groups emerge as positive and significant. These biased results are largely attributable to two underlying effects. First, as shown in Table 2, four of the six across-the-board increases in marginal prices for water and sewer services occurred during the months of April through June, which also mark the beginning of the water-intensive summer period. This introduces a
positive correlation between price and consumption. In absence of explicit time indicators, a relatively larger share of this correlation is borne by the price term. Second and most importantly, monthly consumption for any firm is more likely to exceed tier thresholds during the cooling and irrigation-intensive summer season. Therefore the instrumented price from the first stage regression is not simply a function of firm-specific tiers and marginal charges, but also of temporal variability in water needs. If time indicators are omitted in the second regression stage, simultaneity problems between water charges and water use are re-introduced into the model, and price coefficients are biased upward. [27] It should be noted that the cooling degree day variable in model 2 is positive and significant for all SIC groups. In the absence of month indicators, ‘‘cldg’’ is the only term capable of capturing seasonality effects in consumption. Clearly, though, this weather indicator is not an adequate substitute for month indicators with respect to the elimination of simultaneity problems between price and consumption for the subsamples of firms and the research period considered in this analysis.
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Table 4. Estimated Price Elasticities C.I. (95%) Sample Point Mean 25th percentile 50th percentile 75th percentile
Price, $/1000 gal
Point Elasticity
Lower
Upper
Wholsesale Durable Goods (SIC 50) 4.414 0.269 0.537 4.174 0.255 0.508 4.502 0.275 0.548 4.812 0.294 0.586
0.001 0.001 0.001 0.001
Mean 25th percentile 50th percentile 75th percentile
Eat and Drink (SIC 58) 5.016 0.226 4.808 0.216 5.133 0.231 5.522 0.249
0.334 0.320 0.342 0.368
0.118 0.113 0.120 0.129
Mean 25th percentile 50th percentile 75th percentile
4.492 4.349 4.677 4.813
Banks (SIC 60) 0.418 0.404 0.435 0.448
0.823 0.796 0.857 0.882
0.013 0.012 0.013 0.014
Mean 25th percentile 50th percentile 75th percentile
Automotive Repair and Services (SIC 75) 4.414 0.278 0.477 4.114 0.259 0.445 4.455 0.281 0.482 4.752 0.299 0.514
0.079 0.074 0.080 0.085
Mean 25th percentile 50th percentile 75th percentile
Amusement and Recreation (SIC 79) 4.431 0.625 1.094 5.431 0.766 1.341 6.431 0.907 1.588 7.431 1.048 1.834
0.156 0.191 0.226 0.261
[28] Model 3, our aggregate random effects specification is plagued by similar problems. Price coefficients are positive and significant for four of the six subsamples, and insignificant for the remaining two. In this model, average monthly consumption for a given year is likely higher for years with pronounced summer peaks, for any firm. The price variable in this specification is defined as the marginal price level that would apply if this aggregate quantity were actually observed in a given month. Accordingly, this price term is more likely to correspond to the second tier charge for any firm in years with relatively high water needs. In consequence, the bias-inducing simultaneity between consumption and marginal price persists even in this aggregate specification. It should be noted that Lynne et al. [1978] do not encounter this problem in their analysis of commercial water responsiveness. In their study consumption is aggregated over all months of the applicable research period. This eliminates all temporal variability in consumption for a given firm and, by design, any positive correlation between water use and price levels induced by tiered rate schedules. [29] Given the semilog form of the estimated demand equation, price elasticities change with price levels. Table 4 displays combined price levels at several sample points and associated elasticity estimates derived from model 1 for the five SIC groups with significant price coefficients. The last two columns of Table 4 show the upper and lower bounds of a 95% confidence interval for each estimated elasticity. Elasticity estimates at price means range from 0.23 to 0.63 in absolute value over subsamples. They are of comparable magnitude for Wholesale, Eat and Drink, and Automotive (0.23 to 0.28), somewhat higher for Banks (0.42), and highest for Amusement and Recreation (0.63). Overall,
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these estimates are comparable in magnitude to those derived by Lynne et al. [1978] and Williams and Suh [1986] for the commercial sector. However, this cross-study comparison of estimated elasticities must be undertaken with caution, as each of these studies focuses on different subcategories of c/i/i establishments.
5. Conclusion [30] This study shows that additional insight into commercial customers’ water demand can be gained by adding a temporal dimension to a data set of cross-sectional observations. We find that monthly water demand for our six samples of two-digit SIC groups is characterized by a distinct seasonal pattern. This pattern is similar to the distribution of monthly consumption observed for residential customers with clear summer peaks and winter lows [e.g., Miaou, 1990; Lyman, 1992]. [31] In the presence of tiered pricing schedules for water, this seasonality effect in conjunction with periodic acrossthe-board price changes introduces a positive, temporal correlation between monthly consumption and marginal water prices for any given firm. We show that conventional two-step models designed to control for simultaneity between price and consumption related to cross-sectional differences in price schedules will still be flawed by price endogeneity if these seasonal consumption effects are not explicitly controlled for in the second estimation step. As illustrated by the Automotive subsample, this temporal simultaneity can affect price coefficients even if seasonal consumption patterns are not very pronounced. Furthermore, we show that schedule-related price-endogeneity can persist even in an aggregate specification based on year-averaged consumption if the sample data exhibit sufficient annual variability in seasonal water needs. [32] Naturally, a considerable component of such temporal consumption effects could be captured through a richer set of firm-specific attributes than those available for this analysis. However, we find that in absence of detailed information on individual establishments, time proxies such as month indicators perform well in modeling seasonal consumption patterns and in purging model specifications based on monthly consumption from endogeneity problems related to block rate schedules. [33] Acknowledgments. We thank Kimberly Rollins and J. Scott Shonkwiler for helpful suggestions and comments. This research was supported in part by the Nevada Agricultural Experiment Station, publication 51031428.
References Babin, F. G., C. E. Willis, and P. G. Allen (1982), Estimation of substitution possibilities between water and other production inputs, Am. J. Agric. Econ., 64(1), 148 – 151. Balestra, P., and J. Varadharajan-Krishnakumar (1987), Full information estimations of a system of simultaneous equations with error component structure, Econ. Theory, 3, 223 – 246. Baltagi, B. H. (1995), Econometric Analysis of Panel Data, John Wiley, Hoboken, N. J. Belsley, D. A., E. Kuh, and R. E. Welsch (1980), Regression Diagnostics, John Wiley, Hoboken, N. J. Deller, S. C., D. L. Chicoine, and G. Ramamurthy (1986), Instrumental variables approach to rural water service demand, South. Econ. J., 53(2), 333 – 346. DeRooy, J. (1974), Price responsiveness of the industrial demand for water, Water Resour. Res., 10(3), 403 – 406.
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Dziegielewski, B., J. C. Kiefer, E. M. Opitz, G. A. Porter, G. L. Lantz, W. B. DeOreo, P. W. Mayer, and J. O. Nelson (2000), Commercial and Institutional End Uses of Water, Am. Water Works Assoc., Denver, Colo. Hamilton, L. C. (1992), Regression With Graphics, Brooks/Cole, Pacific Grove, Calif. Hanemann, W. M. (1998), Determinants of urban water use, in Urban Water Management and Planning, pp. 31 – 75, McGraw-Hill, New York. Hewitt, J. A., and W. M. Hanemann (1995), A discrete/continuous choice approach to residential water demand under block rate pricing, Land Econ., 71(2), 173 – 192. Lyman, R. A. (1992), Peak and off-peak residential water demand, Water Resour. Res., 28(9), 2159 – 2167. Lynne, G. D., W. G. Luppold, and C. Kiker (1978), Water price responsiveness of commercial establishments, Water Resour. Bull., 14(3), 719 – 729. Miaou, S.-P. (1990), A class of time series urban water demand models with nonlinear climatic effects, Water Resour. Res., 26(2), 169 – 178. Renzetti, S. (1988), An econometric study of industrial water demands in British Columbia, Canada, Water Resour. Res., 24(10), 1569 – 1573.
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Renzetti, S. (1992), Estimating the structure of industrial water demands: The case of Canadian manufacturing, Land Econ., 68(4), 396 – 404. Stoker, T. M. (1984), Completeness, distribution restrictions, and the form of aggregate functions, Econometrica, 52(4), 887 – 908. Stoker, T. M. (1993), Empirical approaches to the problem of aggregation over individuals, J. Econ. Lit., 31(4), 1827 – 1874. Williams, M., and B. Suh (1986), The demand for urban water by customer class, Appl. Econ., 18, 1275 – 1289. Ziegler, J. A., and S. E. Bell (1984), Estimating demand for intake water by self-supplied firms, Water Resour. Res., 20(1), 4 – 8.
K. Moeltner, Department of Resource Economics, University of Nevada, Reno, NV 89557-0105, USA. (
[email protected]) S. Stoddard, Truckee Meadows Water Authority, 1155 Corporate Boulevard, P.O. Box 30013, Reno, NV 89520-3013, USA.
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