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Jan./Feb. 2014, Vol. 27, Issue 1

Are Residential Customers Price-Responsive to an Inclining Block Rate? Evidence from British Columbia Are residential customers price-responsive to an inclining block rate? Using BC Hydro’s bimonthly billing data, the authors document statistically significant price elasticity estimates to provide BC Hydro with the support for using a residential inclining block rate (RIB) as a tool for energy conservation. Michael Li, Ren Orans, Jenya Kahn-Lang and C.K. Woo

I. Introduction With a winter peak demand of 10,319 MW in 2012,1 BC Hydro is an integrated utility owned by the Canadian province of British Columbia (B.C.) that serves 94 percent of end users in the province.2 While 90 percent of its generation is from low-cost hydroelectric resources,3 BC Hydro will have to meet incremental demand with more-expensive resources given the increasingly more-expensive

energy sources and its aging infrastructure, built over two decades ago. Additionally, B.C. has established a goal of self-sufficiency by 2016, mandating BC Hydro to meet its growing demand through domestic power sources.4 According to BC Hydro’s 2013 Integrated Resource Plan, electricity demand in B.C. is expected to grow 40 percent in the next two decades, and 66 percent of the expected demand increase by 2020 must be met through

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Table 1: Estimates from Residential Demand Studies of Jurisdictions Similar to B.C. Study

Data Sample

Short-run [6_TD$IF]Elasticity

Jurisdiction

Long-run Elasticity

Bernstein and Griffin (2005)

Annual consumption by state for 1977–2004

Washington

0.079

0.161

Herriges and King (1994)

Monthly billing data for a rate experiment for 1500 customers

Wisconsin

0.02 (Summer) 0.04 (Winter)

Not available

in 1984–85 Hsiao and Mountain (1994)

Monthly sales by municipal utility in 1989

Ontario

0.0 to 0.07

Not available

Henson (1984)

Monthly data for 1077 households observed during 1977–78

Bonneville Power Administration

0.11 to 0.28

Not Available

demand-side-management (DSM).5 The 2010 provincial Clean Energy Act stipulates that electricity pricing is one of the permissible DSM tools to achieve the conservation goal.6 eplacing a residential flat rate with an inclining block rate can reduce the residential class’ consumption because of the price-induced conservation behavior of households.7 In 2008, BC Hydro filed a residential inclining block (RIB) rate application,8 which was approved by the British Columbia Utilities Commission (BCUC).9 In Mar. 2011, the BCUC directed BC Hydro ‘‘to provide a full analysis of elasticity at different levels of consumption’’10 (emphasis added). In Nov. 2013, BC Hydro filed its analysis as Appendix C of its RIB Rate Re-pricing Application.11 Based on BC Hydro’s filed analysis, this article answers the timely and relevant question: are residential customers in B.C. priceresponsive to a RIB rate? Using the bimonthly billing data for Apr. 2004 to Mar. 2012, the article

R

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documents statistically significant (p-value < 0.01) price elasticity estimates between 0.08 and 0.13 for the relatively large customers, thus supporting BC Hydro’s use of a RIB rate to achieve the province’s twin goals of energy conservation and selfsufficiency.

specifications (e.g. linear versus log-linear, static versus dynamic). o benchmark our estimates reported below, Table 1 presents the estimates from residential demand studies of jurisdictions similar to B.C.14 These estimates corroborate those used by Avista15 and Pacific Corp16 in the Pacific Northwest in their integrated resource plans.

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II. Extant Estimates The residential demand literature is large, reporting a wide range of elasticity estimates.12 A case in point are the residential estimates reported in a 2004 meta-analysis, summarizing (a) 123 short-run estimates that range from 0.004 to 2.01, with an average of 0.35; and (b) 125 long-run estimates that range from 0.04 to 2.25, with an average of 0.85.13 The variance in these estimates is due to differences in data samples (e.g. time series versus crosssectional data, regional versus customer level), estimation methods (e.g. simple versus complicated), as well as model

III. Data BC Hydro’s RIB rate has a twostep rate structure, where a residential customer pays a lower per-unit rate for electricity consumption below a 1,350 kWh bimonthly threshold, and a higher per-unit rate for electricity consumption above the 1,350 kWh threshold. Figure 1 portrays the CPI-adjusted real electricity rates by fiscal year (April–March) for the eight-year sample period of Apr. 2004–Mar. 2012. It shows that small customers with bimonthly consumption below the 1,350 kWh threshold saw only a

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[(Figure_1)TD$IG]

Figure 1: Real Electricity Prices by Fiscal Year (April–March) for the Period of Apr. 2004–Mar. 2012

small, temporary real rate decrease after the RIB rate took effect in fiscal year 2009 (F2009). The lack of step-1 rate variation presages the challenge of precise estimation of the price elasticity of small customers. Figure 1 also shows large step-2 rate increases faced by large customers with bimonthly consumption above the 1,350 kWh threshold. Thus, there is sufficient price variation to [(Figure_2)TD$IG] precisely estimate the large

customers’ price elasticity, as confirmed by our regression results reported below. Figure 2 shows little year-toyear consumption change for the small customers in the sample period; and our regression analysis cannot detect statistically significant (p-value 0.01) elasticity estimates for these customers.17 Hence, the remainder of this article will not discuss the small customers’ price responsiveness.

Figure 3 shows the large customers’ average bimonthly consumption by fiscal year. It suggests consumption reduction in response to the RIB implementation and the ensuing step-2 rate increases. The consumption reduction, however, could be an artifact of non-price factors, such as the economic slowdown in the post-RIB years. Hence, we use a regression analysis to delineate the factors contributing to the consumption changes shown in this figure.

IV. Elasticity Estimates Based on the double-log demand model detailed in Appendix, our regression analysis uses the entire billing data file of BC Hydro’s 1.6 million residential customers, so as to preempt possible criticisms of small sample bias and noncompliance with the BCUC’s March 2011 directive of a comprehensive elasticity analysis. Our eight-year sample period is chosen to capture four pre-RIB years. It does not include earlier years due to the lack of DSM spending data. he dependent variable is the natural log of per account consumption differentiated by bimonthly billing cycle (April– May, . . ., February–March), region (Lower Mainland, North, Southern Interior, and Vancouver Island), dwelling type (singlefamily detached house, row/ townhouse, apartment, mobile home, and other), and space

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Figure 2: Bimonthly Average Consumption of Small Customers by Fiscal Year (April–March) for the Period of Apr. 2004–Mar. 2012

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[(Figure_3)TD$IG]

V. Detailed Estimates To comply with the BCUC’s March 2011 directive, this section details price elasticity estimates differentiated by region, dwelling type, space heating, and consumption size. A. Region-specific estimates

Figure 3: Bimonthly Average Consumption of Large Customers by Fiscal Year (April– March) for the Period of Apr. 2004–Mar. 2012

heating (electric versus nonelectric). Our eight-year sample has 1,920 observations (=8 years * 6 billing periods per year * 4 regions * 5 dwelling types * 2 space heating fuels). Table 2 summarizes our elasticity estimates based on the double-log model and its two variants. It shows statistically significant (p-value < 0.01) price elasticity estimates between 0.08 and 0.13, in line with those in Table 1. he elasticity estimates come from the regression results in Table 3. The adjusted

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R2 values of around 0.9 indicate that the estimated regressions fit the data well. All coefficient estimates have the expected signs and are statistically significant (p-value < 0.01), except for (a) heating degree days in Model 2, which suggests that cold weather only significantly impacts consumption of customers with electric heating; and (b) electric space heating indicator and the correction term in Model 3. Thus, they support the empirical validity of the elasticity estimates in Table 2.

Region-specific estimates are found by estimating four region-specific versions of Models 1–3. For clarity, we label the region-specific Model 1 as Model 1A, Model 2 as Model 2A, and Model 3 as Model 3A. Each version corresponds to a region’s data for the customers living in that region; hence, it does not have the regional dummies as the right-hand-side (RHS) variables. The sample size for each version is 480 (=1,920 4) observations. Table 4 reports similar elasticity estimates for the Lower Mainland, North, and Vancouver Island regions. The estimates for the Southern Interior region, however, are relatively smaller in magnitude. Thus, some regional variance exists in residential price responsiveness in B.C.

Table 2: Statistically Significant (p-Value < 0.01) Price Elasticity Estimates for large Customers; Sample Period = Apr. 2004–Mar. 2012. Model

Estimate Standard Error

1. Equation (1) in Appendix 2. Model 1 plus an interaction term of heating degree

0.10 0.13

0.0218 0.0195

days (HDD) times an electric space heating indicator 3. Model 2 sans the bimonthly billing cycle indicators

Remarks Basic specification The additional regressor captures the HDD-dependent effect of electric space heating

0.08

0.0223

The deletion of billing cycle indicators removes the effect of residual seasonality beyond ambient temperature

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Table 3: Regression Results for Models 1–3 in Table 2; Sample Period = Apr. 2004–Mar. 2012; p-Values in Parentheses. Variable

Model 1

Model 2

Model 3

Dependent mean

7.951

7.951

7.951

Adjusted R2 Root mean squared error

0.897 0.122

0.918 0.109

0.890 0.126

ln Pt = natural-log of the real marginal price ln Yt = natural-log of the real per capita income

0.1012 (<0.0001) 0.3391 (<0.0001)

0.1269 (<0.0001) 0.3680 (<0.0001)

0.0844 (<0.0001) 0.2235 (<0.0001)

Hjkt = 1 if electric space heating, 0 otherwise

0.2438 (<0.0001)

0.1827 (<0.0001)

0.0065 (0.6521)

W1kt = cooling degree days W2kt = heating degree days

0.00061 (<0.0001) 0.00012 (<0.0001)

0.00077 (<0.0001) 0.00001 (0.7917)

0.00044 (<0.0001) 0.00034 (<0.0001)

Hjkt * W2kt lnSkt = natural-log of BC Hydro’s real DSM spending

0.0277 (<0.0001)

0.00027 (<0.0001) 0.0192 (<0.0001)

0.00020 (<0.0001) 0.0277 (<0.0001)

Cjkt = correction term

0.2089 (<0.0001)

0.3591 (<0.0001)

0.0081 (0.6226)

Note: Appendix fully describes each variable’s construction. It also explains the statistical role of the correction term in the last row of this table. For brevity, this table does not report the statistically significant (p-value < 0.01) coefficient estimates for the intercept, binary indicators for region and billing period.

Table 4: Region-Specific Price Elasticity Estimates; Sample Period = Apr. 2004–Mar. 2012; Statistically Significant Estimates (p-Value < 0.01) in Bold. Model 1A: Model 1 without

Model 2A: Model 1A plus the HDD-dependent

Model 3A: Model 2A sans the

the region indicators

effect of electric space heating

effect of residual seasonality

Lower Mainland

0.1105

0.1297

0.1074

North Vancouver Island

0.1172 0.1457

0.1473 0.1494

0.1236 0.1489

Southern Interior

0.0771

0.1166

0.0306

Region

B. Dwelling-specific estimates Dwelling-specific estimates are found by estimating five dwelling-specific versions of Models 1–3. For clarity, we label the dwelling-specific Model 1 as Model 1B, Model 2 as

Model 2B, and Model 3 as Model 3B. Each version corresponds to a dwelling type’s data for the customers living in that dwelling type; and hence, it does not have the dwelling-type dummies as the RHS variables. The sample size

for each version is 384 (=1,920 5) observations. Table 5 shows that customers living in single-family detached houses are more price-responsive than those in the remaining four dwelling types. This is expected because single-family customers

Table 5: Dwelling-Specific Price Elasticity Estimates for Models 1–3 in Table 2; Sample Period = Apr. 2004–Mar. 2012; Statistically Significant Estimates (p-Value < 0.01) in Bold. Dwelling type

Model 1B: Model 1 without the

Model 2B: Model 1B plus the HDD-dependent

Model 3B: Model 2B sans the

dwelling type indicators

effect of electric space heating

effect of residual seasonality

0.0807

0.1389

0.0358

Row/townhouse Apartment

0.0336 0.0328

0.0716 0.0406

0.0632 0.0409

Mobile home Other

0.0302 0.0935

0.1041 0.0071

0.0287 0.0527

Single-family detached house

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Table 6: Space-Heating-Specific Price Elasticity Estimates; Sample Period = Apr. 2004–Mar. 2012; Statistically Significant Estimates (p-Value < 0.01) in Bold.

Space heating

Model 1 sans the space heating

Model 1 sans the space heating

indicator and its related

indicator, the HDD interaction term,

HDD interaction term

and the billing cycle indicators

Electric

0.1360

0.1042

Non-electric

0.0894

0.0351

tend to have higher consumption and, therefore, more kWh priced at the step-2 rate and more room for conservation. There are anomalous estimates that are positive for row/ townhouse and other dwelling types, but these estimates are mostly statistically insignificant (pvalue > 0.01). Thus, the estimates in Table 5 reflect large variance in residential price responsiveness by dwelling type. C. Space-heating-specific estimates Space-heating-specific estimates are found by estimating two versions of equation (1): one with billing cycle dummies and one without. Each version corresponds to the data for the customers with a particular space heating: electric versus nonelectric; and hence, it does not have the space heating indicator and its related HDD interaction term as RHS variables. The sample size for each version is 960 (=1,920 2) observations.

Table 6 reports that customers with electric space heating are more price-responsive than those with non-electric space heating. This is expected because customers with electric space heating tend to have relatively higher consumption and, therefore, more conservation potential. D. Size-specific estimates Size-specific estimates are found by estimating two versions of Models 1 to 3. Each version corresponds to the data for the customers belonging to a particular consumption size: 1,350–2,400 kWh versus Over 2,400 kWh. The average peraccount consumption for a given kWh size is constructed using the bimonthly consumption data for customers of that kWh size. Hence, each version is estimated using a sample of 1,920 observations. Table 7 reports that customers with consumption of over 2,400 kWh are more price-responsive

Table 7: Size-Specific Price Elasticity Estimates for Models 1–3 in Table 2; Sample Period = Apr. 2004–Mar. 2012; Statistically Significant Estimates (p-Value < 0.01) in Bold.

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Consumption Size

Model 1

Model 2

Model 3

1,350–2,400 kWh

0.1286

0.1287

0.0714

Over 2,400 kWh

0.1792

0.1810

0.1627

than those with consumption of 1,350–2,400 kWh. This confirms that customers with higher consumption are more priceresponsive that those with lower consumption.

VI. Conclusion The results in Table 2 are BC Hydro’s large residential customers’ elasticity estimates based on the billing data of BC Hydro’s entire residential class. They provide a basis for estimating the price impact on energy consumption of BC Hydro’s large customers, who are generally more price-responsive than smaller customers. The statistically significant price elasticity estimates of 0.08 to 0.13 are in line with those found for other winter-peaking jurisdictions with relatively low rates. he estimates in Table 2 represent average priceresponsiveness of large customers because their detailed elasticity estimates are found to vary by region, dwelling type, space heating type, and consumption size, as shown in Tables 4–7. Low price responsiveness is typically observed for customers with relatively low consumption (e.g. apartment residents with nonelectric space heating). High responsiveness is found for customers with relatively high consumption (e.g. those living in single-family detached houses with electric space heating). Recognizing the differentials in customer price responsiveness, BC

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Hydro’s two-step RIB rate fulfills the provincial mandate of achieving energy conservation and self-sufficiency, while equitably allocating the increasing supply costs among its residential customers without adverse bill impacts on small customers.

Appendix: Double-Log Demand Model

contains binary indicators to capture the systematic variations in consumption that are unrelated to such metric variables as price, income and weather. These indicators are: Dj = binary dwelling type indicator = 1 if the customers used to compute ln Qjkth reside in dwelling type j for j = single-family detached house, row/townhouse,

Our double-log demand model is: lnQ jkht ¼ a þ S j g j D j þ Sk lk Rk þ hHh þ Sm ’m Bm þ blnPt

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þ clnYt þ v1 W 1kt þ v2 W 2kt þ dlnS jkht þ uC jkht þ e jkht

(1)

In Equation (1), the dependent variable is ln Qjkht = natural-log of the per-account bimonthly consumption of large customers residing in dwelling-type j (e.g. single-family detached house) in BC Hydro’s service region k (e.g. Lower Mainland) with space heating fuel type h (electric versus non-electric) in period t (e.g. April–May 2004). The construction of ln Qjkht implies a sample size of 1,920 observations (=8 years * 6 billing periods per year * 4 regions * 5 dwelling types * 2 space heating fuels), sufficiently large to precisely detect and quantify residential price elasticity estimates. n addition to the intercept a, the first set of right-hand-side (RHS) variables in Equation (1)

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customers with electric space heating; 0 otherwise. With coefficient h > 0, this variable aims to capture the effect of electric space heating on consumption. Bm = binary billing cycle indicators; Bmt = 1 if lnQjkht corresponds to bill cycle m for m = April–May, . . ., December– January; 0, otherwise. When Bmt = 0 for all m, the billing cycle is February–March. With coefficient wm, this variable aims to capture the residual seasonality of consumption not captured by the weather variables listed below. he second set of RHS variables has the following metric variables: ln Pt = natural-log of the real marginal price faced by the large customers, whose coefficient b < 0 measures the price elasticity. When b is around 0.1, it is similar to the estimates reported in Table 1. ln Yt = natural-log of the real per capita income reported by BC Stats, whose coefficient c > 0 is the income elasticity. Since electricity is essential to everyday living, consumption is expected to be income-inelastic, implying c < 1. W1kt = cooling degree days in region k and period t, whose coefficient v1 > 0 measures the marginal effect of hot weather on consumption. W2kt = heating degree days in region k and period t, whose coefficient v2 > 0 measures the marginal effect of cold weather on consumption.

apartment, and mobile home; 0, otherwise. When Dj = 0 for all j, the dwelling type is ‘‘other.’’ With coefficient gj, this variable aims to capture the systematic variations of consumption among dwelling types. Rk = binary region indicator = 1 if the customers used to compute ln Qjkht reside in region k for k = Lower Mainland, North and Southern Interior; 0, otherwise. When Rk = 0 for all k, the region is Vancouver Island. With coefficient lk, this variable aims to capture the systematic variations of consumption among regions. Hh = binary space heating indicator = 1 if the per account consumption corresponds to

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lnSjkht = natural-log of BC Hydro’s real DSM spending for dwelling type j, region k, heating type h, and period t, whose coefficient d < 0 measures its marginal effect on consumption. Cjkht = correction term to control for the estimation bias caused by the endogenous step-2 price in the regression.18 ejkht = random error with zero mean and finite variance. It captures the variation in lnQjkht not explained by the postulated regression line. We use ordinary least squares (OLS) to consistently estimate the coefficients in Equation (1). These OLS estimates are unbiased, even though the error term may be serially correlated and may not have a constant variance.19& Endnotes: 1. See http://www.bchydro.com/ content/dam/BCHydro/customerportal/documents/corporate/ regulatory-planning-documents/ integrated-resource-plans/currentplan/2012-electric-load-forecastreport.pdf, Table 4.2. 2. See http://www.bchydro.com/ energy-in-bc/our_system.html 3. See http://www.bchydro.com/ energy-in-bc/our_system/generation. html 4. See http://www.bchydro.com/ content/dam/BCHydro/customerportal/documents/corporate/ regulatory-planning-documents/ integrated-resource-plans/currentplan/0000-nov-2013-irp-summary.pdf 5. See http://www.bchydro.com/ content/dam/BCHydro/customerportal/documents/corporate/ regulatory-planning-documents/ integrated-resource-plans/currentplan/0000-nov-2013-irp-summary.pdf 6. See http://www.leg.bc.ca/39th2nd/ 1st_read/gov17-1.htm#section1 92

7. Ren Orans, Michael King, Chi Keung Woo and William Morrow, Inclining for the Climate: GHG Reduction via Residential Electricity Ratemaking, 147(5) PUBLICUTILITIES FORTNIGHTLY 40–45 (2009). 8. See http://www.bcuc.com/ ApplicationView.aspx?ApplicationId= 187 9. http://www.bcuc.com/ Documents/Proceedings/2008/ DOC_19585_G-124-08_BCH_RIB.pdf 10. See http://www.bcuc.com/ Documents/Proceedings/2011/ DOC_27176_G-45-11_BCH-RIB-RePricing-Reasons.pdf 11. See http://www.bchydro.com/ content/dam/BCHydro/customerportal/documents/corporate/ regulatory-planning-documents/ revenue-requirements/2013-rib-raterepricing-application.pdf 12. See http://www.bchydro.com/ content/dam/hydro/medialib/ internet/documents/info/pdf/ 2008_ltap_appendix_e.pdf 13. James A. Espey and Molly Espey, Turning on the Lights: A Meta-Analysis of Residential Electricity Demand Elasticities, 36 JOURNAL OF AGRICULTURAL AND APPLIED ECONOMICS 65–81 (2004).

stating, ‘‘We estimate customer class price elasticity in our computation of electricity and natural gas demand. Residential customer price elasticity is estimated at negative 0.15. Commercial customer price elasticity estimated at negative 0.10.’’ (pp. 2–7); at http://www.avistautilities.com/ inside/resources/irp/electric/Pages/ IRParchive.aspx 16. PacifiCorp 2007 Integrated Resource Plan, Appendices (p. 12, p. 22), at http://www.pacificorp.com/ es/irp.html. The residential elasticity estimates are found by estimating an econometric equation that explains per-customer usage during 1982–2005 using real electricity price, real natural gas price, real household income, weather, and lagged usage. The 0.1 non-residential elasticity is based on the Department of Energy’s 2006 Demand Response Report to the Congress. 17. This does not mean small customers are price-insensitive. All it means is that the limited data variations do not allow our precise detection of these customers’ price responsiveness.

14. Mark Bernstein and James Griffin, Regional Differences in the PriceElasticity of Demand for Energy, 2005; at http://RAND.org/pubs/technical_ reports/2005/RAND_TR292.pdf, pp. 82–84; Joseph Herriges and Katherine King, Residential Demand for Electricity Under Block Rate Structures: Evidence from a Controlled Experiment, 12(4) JOURNAL OF BUSINESS AND ECONOMIC STATISTICS 419– 430 (1994), Table 4; Cheng Hsiao and Dean C. Mountain, A Framework for Regional Modeling and Impact Analysis: An Analysis for the Demand for Electricity by Large Municipalities in Ontario, Canada, 34(3) JOURNAL OF REGIONALSCIENCE 361–385 (1994), Table 3; Steven E. Henson, Electricity Demand Estimates under Increasing-Block Rates, 51(1) SOUTHERN ECONOMIC JOURNAL 147–156 (1984), Table 11.

18. Suppressing the subscripts for notational simplicity, this term is computed as C = (1 Z)ln(1 Z)/ Z + ln(Z), where Z = estimated share of the residential customers with the Step-2 marginal price based on a logistic regression model of the actual share of Step-2 customers. Its coefficient estimate u captures the coefficient of correlation between an unobserved factor causing a customer’s consumption going beyond the 1,350 kWh threshold and the unobserved factor affecting the size of that customer’s consumption. Its sign is opposite to that of the correlation coefficient. We expect its coefficient u < 0, implying that, if an unobserved factor causes a customer to consume beyond the 1,350 kWh threshold, it also magnifies the customer’s consumption, see KENNETH TRAIN, QUALITATIVE CHOICE ANALYSIS (Cambridge, MA: MIT Press 1986) at 94.

15. Avista Utilities 2007 Electric Integrated Resource Plan, filed with the Idaho Public Utilities Commission,

19. JAN KMENTA, ELEMENTS OF ECONOMETRICS (New York: Macmillan 1986) at 269.

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