A NON-TECHNICAL ANALYSIS OUTLINING THE MAJOR DIFFERENCES BETWEEN THE BRATTLE AND PEG APPROACHES TO X FACTOR MEASUREMENT

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1 Page 1 of 22 A NON-TECHNICAL ANALYSIS OUTLINING THE MAJOR DIFFERENCES BETWEEN THE BRATTLE AND PEG APPROACHES TO X FACTOR MEASUREMENT By Dr. Jeffrey I. Bernstein and Dr. Paul R. Carpenter December 4, 2007

2 Page 2 of 22 I. INTRODUCTION This report, in a non-technical manner, addresses the major differences between the Brattle and PEG approaches to the determination of the X factor pertaining to the forthcoming incentive regulation (IR) plan. In order to discuss these issues, we analyze the differences according to each of the X factor components. In this way, it is possible to discern the extent of the contrasting approaches both conceptually and in terms of the X factor calculation. Thus, the report is organized as follows: Section 2 discusses the productivity differential (PD) of the X factor; Section 3 focuses on the input price differential (IPD) component; Section 4 discusses the average use (AU) term; Section 5 proceeds to outline the components required to augment the X factor from a price cap to a revenue-per-customer cap. That is, output quantity growth, and customer growth respectively. 1 Apart from the X factor components, Section 6 pertains to an analysis of PEG s service-specific X factors. Lastly, Section 7 concludes. II. THE PD COMPONENT OF THE X FACTOR The PD term in the X factor is the difference between the total factor productivity (TFP) growth rates of the gas distribution industry and the economy. A positive (respectively negative) PD term means that the industry s TFP growth rate is greater (respectively less) than the economy rate. Both Brattle and PEG employ a PD component, and in addition, use the same measure of economy-wide TFP growth, namely the private business sector s 1 PEG has also arbitrarily proposed a stretch factor. In addition, in Dr. Bernstein s evidence of August 1, 2007 entitled, Incentive Regulation, And X Factor Analysis: Implications For Ontario s Gas Utilities, and in responses to interrogatories Board Staff IR# 21 and 30, he has explained that since the OEB s regulatory framework involves price rebasing at the end of the forthcoming incentive regulation period, it would be redundant to include a positive stretch factor. Price rebasing adjusts prices so as to include productivity improvements attained by the regulated firm. Therefore rebasing ensures that consumers benefit from the firm s productivity gains, and thus a stretch factor would be tantamount to double counting these gains in the X factor. 2

3 productivity growth rate calculated by Statistics Canada. 2 Page 3 of 22 However, Brattle and PEG s industry productivity trends are computed by distinctly different approaches. PEG s approach depends on the following elements. 1. The basis for PEG s industry TFP measure is its frequently revised econometric cost model. This model uses a sample of 36 U.S. local distribution companies (LDCs) for the years In a series of reports Drs. Carpenter and Bernstein have shown that PEG s econometric results suffer from statistical maladies, lead to economically unreasonable results, are unstable and are based on tenuous assumptions. 4 We will not repeat these extensive criticisms, but suffice it to say, these extensive deficiencies persist in PEG s latest attempt. 5 For example, the PEG model still generates results which indicate inordinately small output effects on cost. In addition, a consequence of minor modifications dramatically alters the peer group selection for Enbridge and Union. PEG s results appear to rest on a razor s edge. In a word, the econometric results are unreliable. It is not the case as Dr. Lowry has stated (Technical Conference Transcript, November 27, 2007, page 36 lines 13 and 14) of the perfect being the enemy of the good, but rather the unreliable obfuscating the sensible. 2 Statistics Canada Table , Productivity Measures and Related Variables - National (Annual) provided by PEG in response to EGD IR#30 as Attachment A (also in response to EGD IR# 2, workpaper 2.6, T14). 3 Price Cap Index Design for Ontario s Gas Utilities March 15, March 30, 2007; Rate Adjustment Indexes for Ontario s Natural Gas Utilities, June 8, 2007, June 20, 2007, November 6, 2007, November 20, Incentive Regulation And X Factor Analysis: Inplications For Ontario s Gas Utilities by Jeffrey I. Bernstein, August 1, 2007, Report of Paul R. Carpenter, PhD, For Enbridge Gas Distribution Inc, by Paul R. Carpenter, August 2, 2007, Further Report On PEG Econometric Cost Model Of Dr. Paul R. Carpenter And Dr. Jeffrey I. Bernstein For Enbridge Gas Distribution Inc. and X Factor Guideline And Measurement For Ontario s Natural Gas Distribution Industry by Jeffrey I. Bernstein and Paul R. Carpenter on November 6, Price Cap Index Design for Ontario s Gas Utilities March 15, 2007; Rate Adjustment Indexes for Ontario s Natural Gas Utilities November 20,

4 Page 4 of From its econometric model, PEG selects a peer group or subset of the 36 U.S. LDCs that is applicable to Enbridge, and a peer group applicable to Union. These peer groups are, as a matter of fact, U.S. LDCs. The basis for any peer group selection is only as reliable as the econometric model itself. Indeed with every revision of its model, PEG has altered its peer group selection for both Enbridge and Union. In addition, peer group variability occurs in PEG s analysis as a result of alternative methods to calculate capital service prices. The so-called GD and COS approaches used to measure capital service prices result in alternative U.S. peer groups for both Enbridge and Union. PEG has even disavowed its peer group analysis in some revisions of its econometric analysis. 6 PEG relies once again on a new set of U.S. peers. In its latest report 3. PEG uses the results from its (36 U.S. LDC-based) econometric model and data from its selected U.S. peers to calculate the peer group-specific TFP indices. The trend of these indices forms industry TFP growth for Enbridge or Union, depending on the relevant peer group. To wit the resulting industry TFP growth rates used in PEG s PD component actually pertain to the U.S. firms. 7 PEG s industry growth rates are often referred to in this proceeding as elasticity-based TFP growth rates, signifying their econometric origin. Since the peer group plays a prominent role in PEG s latest attempt, we shall discuss its peer group selection criteria. First, from its econometric model, PEG estimates the degree of returns to scale for all 36 U.S. LDCs. Second, although Enbridge and Union 6 On page 46 of the June 20 report PEG states, In comparing the suitability of these methods, we find that the econometric approach is less sensitive to the random variations in the TFP trends of the comparatively small peer groups. A suitable peer group for Enbridge is, in any event, unavailable. We therefore recommend the use of the econometric projections to establish the TFP growth of both companies.. But on pages vii and viii of their November 6, 2007 report PEG says, We recommend that the TFP targets for Enbridge and Union be set at their peer group trends because they are easier to understand and the selection of peer groups is straightforward with the new econometric model. 4

5 Page 5 of 22 are not part of the sample of firms used in the econometric model, PEG uses the model results and data for both firms to estimate returns to scale for Enbridge and Union (see tables 8a, 8b, 9a, 9b on pages of PEG s November 20 report). 8 Third, the peer group is defined as those U.S. LDCs having similar degrees of returns to scale as either Enbridge or Union. There are three major problems with this approach to peer group selection. 1. The validity of the peer group selection rises and falls with the adequacy or inadequacy of the econometric cost model. An unreliable model de facto indicates an unreliable peer group. There are no other analyses used to determine peer group selection. 2. The criterion relies on the assumption that the econometric estimates characterizing the 36 LDCs cost of providing services also pertains to Enbridge and Union. This is an assumption invoked by PEG. There are no statistical tests conducted to test this assumption. PEG uses its econometric cost model to estimate the degree of returns to scale for each of the 36 LDCs that form its sample of firms. Next with these same results, it estimates scale for Enbridge and Union and then determines the peer group to be those firms with similar scale economies. In a sense the entire exercise assumes at the outset what it is designed to conclude. 3. The criteria is based on a single dimension; the degree of returns to scale. No other variables are used by PEG to select the set of peers. Yet the choice of any set of peers is in fact multidimensional, not unidimensional as PEG assumes. For example, the pace of technological change and the extent of scope economies in 7 PEG discusses a second approach to the measurement of industry TFP growth, but with this revision opts for the method discussed in the text (see pages 43-51of PEG s latest report). 5

6 Page 6 of 22 the production of alternative services are relevant to a peer group selection. Also, the characteristics and number of a firm s services would be germane. In particular, do the firms supply only gas distribution services, or do they also provide storage and transportation services? The characteristics and utilized proportions of the inputs used by the LDCs are also pertinent to the selection of peers. Specifically, do firms use cast iron mains and in what proportions to other factors of production? Do the firms contract-out for particular input requirements or do they use in-house skills and equipment? Lastly, there are criteria for peer selection that are not dependent on firm performance or decisions. For example, do firms predominately operate in urban or rural areas, do firms operate in similar climates, do firms operate in similar terrain and do firms operate under similar regulatory regimes? All of these considerations are absent from PEG s single dimension framework for peer group selection. The Brattle approach differs from PEG in a number of respects. 1. Brattle s measure of industry TFP growth does not rely on any econometric model. Industry TFP is computed using index number procedures and relies directly and solely on actual data pertaining to prices and quantities of outputs produced and inputs used by LDCs. This approach is consistent with Statistics Canada s measurement of economy-wide TFP, as the agency employs an index number methodology. The benefits of directly using actual data to calculate industry TFP growth are undeniable. The approach is more transparent and simpler as there is no black box econometric cost model. The results are readily auditable by all parties using standard spreadsheet programs and there is no requirement to utilize complex statistical software. Lastly, it is significantly easier to update the X factor for future IR plans. 8 Notice the estimated parameters resulting from the econometric model are based on all 36 U.S. LDCs, 6

7 Page 7 of Brattle calculates industry TFP growth employing data from the same 36 U.S. LDCs that form PEG s sample in its econometric model. In fact, the reason Brattle used this sample of firms is to avoid questions regarding such differences. The difficulties of peer group selection and PEG s vacillation on this topic have already been discussed. As a consequence, Brattle has not formally adopted a peer group for Enbridge or Union. However, in response to Undertaking JTF 21 Brattle has calculated X factors for two subsets of the 36 LDCs; the gas-only group, and the north-east group. In both cases the X factors are less than those calculated for all 36 firms. 3. Brattle s calculation is based on a revenue-weighted TFP index. TFP growth rates that are used in the calculation of IR plans typically employ revenue weights and not PEG-type elasticity weights. In fact, Statistics Canada calculates TFP growth for the overall economy and various sub-sectors and industries using revenue weights. Thus Brattle s approach is consistent with the Statistics Canada measure of economy-wide TFP growth used in the PD component of the X factor. Brattle s revenue-weighted TFP index is the correct approach to the measurement of industry TFP. 1. Under an IR plan, industry TFP growth rates should capture the historic trend in service usage and the associated revenues from these services; in this case LDC services. Failure to do so could result in either unwarranted financial reward or excessive financial penalty. However, PEG s elasticity-based industry TFP growth rates do not capture service usage. Because of this deficiency, PEG is required to introduce an average use (AU) term into its X factor. This AU term attempts to introduce service usage, but as will be discussed in Section 4 below, it and these parameters are the same for all of the firms. 7

8 Page 8 of 22 fails. Brattle s calculation of industry TFP growth, by virtue of its methodology, incorporates directly the historic trend in services usage. 2. Brattle s revenue weighted industry TFP growth rates captures the major sources of demand associated with LDC services; the numbers of customers and the volumes of throughput. 9 The reason is that Brattle obtains revenues according to customer class such that for each customer class there are data on the number of customers and volumes. 10 Hence the revenues for any particular customer class consist of all sources of revenues relevant to that customer class. For example, for one customer class, suppose there are 5 customers, each customer pays an access or demand charge of $2.00, and a unit volume charge of $0.50. In addition, total volume for this customer class is assumed to be 1000 units. Now revenue for this customer class is $510 [= (5 x $2.00) + (1000 x $0.50)]. 11 Thus the revenue figure includes both the number of customers and the volumes of throughput. 3. The IR plan considered by the OEB involves a single price cap or a single revenue-per-customer cap. Both of these plans do not distinguish between access and usage charges and sources of demand. There is no price cap associated with customer access charges and no price cap associated with throughput volume charges. There is a single price cap for all services which averages across the number of customers and the volumes of throughput. Similarly there is a single revenue-per-customer cap. Brattle s revenue weights used in its calculation of the industry TFP growth rate are consistent with these price cap and revenue-percustomer cap plans. The weights incorporate all sources of revenue, but revenues 9 As noted, PEG does not use revenue weights in its PD component, but does so in it AU term. We shall discuss differences in Brattle and PEG revenue weights in Section 4 pertaining to the AU term. 10 See the discussion on pages in Dr. Jeffrey I. Bernstein and Dr. Paul R. Carpenter, X Factor Guideline and Measurement for Ontario s Natural Gas Distribution Industry, November 6, We abstract from the cost of gas, which is irrelevant to this discussion. 8

9 PD Component (GD) 12 Industry TFP Growth - Economy TFP Growth = Page 9 of 22 are not distinguished according to access and usage charges. There is no requirement to do so according to the plans considered by the OEB. To summarize, both Brattle and PEG use the same measure of economy-wide TFP growth from Statistics Canada. In addition, the data providing the basis for both Brattle and PEG s industry TFP growth calculations emanate from the same 36 U.S. LDCs. In this way, both Brattle and PEG compare Canadian economy-wide TFP to U.S. industry productivity growth in their respective PD components. Differences between Brattle and PEG with respect to industry TFP growth rates are the following: PEG s is econometrically-based, Brattle is index number-based, PEG uses a U.S. peer group arising from its econometric model, Brattle does not rely on any one peer group, but computes industry TFP growth rates from data on all 36 LDCs, as well as for the gas-only and north-east sub-groups of the 36 firms, PEG uses elasticity weights from its econometric model while Brattle uses revenue weights based directly on actual data. Brattle = PEG = PEG s figures throughout this report refer to those applicable to Enbridge. 9

10 Page 10 of 22 PD Component (COS) Industry TFP Growth - Economy TFP Growth = Brattle = PEG = 1.48 III. THE IPD COMPONENT OF THE X FACTOR The IPD term measures the difference between the input price growth rates of the economy and the industry. Thus a positive (respectively negative) IPD term means that the economy s input price growth rate is greater (respectively less) than the industry rate. Both Brattle and PEG have an IPD term in their respective X factor calculation. With respect to the economy-wide input price growth rate, both Brattle and PEG calculate the same rate and in the same manner. It is equal to the sum of the economywide rate of inflation and the economy-wide TFP growth. For example, if inflation is 2% and TFP growth is 0.5% then input price growth is 2.5% [= 2% + 0.5%]. 13 This example indicates that there is a link or interrelationship between productivity and input price growth rates. Accordingly, therefore there must also be a link between the PD and IPD components of the X factor. TFP and input price growth rates must be defined in a consistent fashion. In particular the input prices used in the calculation of industry TFP growth must be the same input prices used to construct industry input price growth. Failure to do so introduces arbitrary and inconsistent components into the X factor calculation. 13 The rationale for this discussion is discussed on page 18 in Dr. Bernstein, Incentive Regulation, and X Factor Analysis: Implications for Ontario s Gas Utilities, August 1,

11 Page 11 of 22 Brattle is careful to use the same input prices for both its industry TFP and input price growth rates. 1. Although PEG calculated economy-wide input price growth in a manner consistent with economy-wide TFP growth, it neglected to measure in a consistent fashion industry TFP and input price trends. This inconsistency is critical because input prices play an important role in the measurement of industry TFP growth. Specifically, since TFP growth is the difference in output and input growth, input prices are used to construct input growth rates. 2. The following steps describe the computation of input growth in a relatively simple context. a) Suppose there are three inputs; labor, capital, and materials and services (M&S)) each with its own growth rate. In order to combine these growth rates into a single rate requires the construction of a weighted average of individual input growth rates. b) To construct the weights requires both the price per unit and the quantity for each input. Next, the cost of labor input is its price times the quantity of labor used. In the same manner as for labor, calculate the capital input cost and the cost of M&S inputs. Accordingly, total cost is the sum of the three input costs and each input cost share equals the ratio of input cost to total cost. These input cost shares define the weights. c) Multiply each cost share by the corresponding growth rate for each input and add these weighted growth rates to form the input quantity growth. 11

12 Page 12 of The objective of the preceding example was to demonstrate that input prices enter the calculation of industry TFP growth through the weights used to measure industry input quantity growth. This means that consistency among the PD and IPD components of the X factor requires the same input prices to be used in the calculation of industry TFP and input price growth rates. Therefore, Brattle employs the input prices associated with the 36 U.S. LDCs to form its input price growth rate and these same prices are used in its industry rate of TFP growth. 4. PEG does not employ any such consistency in its use of input prices across its PD and IPD components. PEG uses different industry input prices in its IPD term from the industry input prices in its PD component. This results in inconsistent and arbitrary selection of input price growth rates. In fact the inconsistency problem is quite significant in PEG s case because PEG uses input prices in a more extensive manner than does Brattle. PEG uses the input prices of the 36 LDCs to measure cost which is the dependent variable (or variable to be explained) in its econometric cost model. Further, these input prices are themselves utilized as drivers to explain cost. Hence the pervasive use of the 36 LDC input prices to forge industry TFP in PEG s case exacerbates the PD and IPD inconsistency problem. Indeed, at the very least given PEG s method of estimating industry TFP growth from its peer groups, consistency requires that PEG use the input prices associated with each of its peer groups. A peer group is a peer group, if used for productivity it must also be used for input prices, since, as previously explained, these prices also enter into the calculation of productivity growth. 5. Lastly, PEG erroneously believes it should measure the input prices faced by Enbridge and Union. Not only is this inconsistent with its industry TFP approach, but violates a fundamental principle of setting the X factor. The X factor should 12

13 Page 13 of 22 not be dependent on the performance of the regulated firms under consideration. The following example illustrates this standard of immutability. Suppose that a regulated industry experiences a trend toward higher input prices, but the regulated firm in question has signed long-term contracts related to hiring and purchasing certain factors of production, so that it is unaffected by the upward trend in input prices. The immutability of the X factor serves to reward the firm for its foresight in signing long-term contracts. However, suppose that the regulated industry experiences a trend toward lower input prices. In this case the immutability of the X factor serves appropriately to penalize the firm because of its detrimental long-term contracts. This is precisely how competitive markets operate. They reward and penalize individual firms for their superior or inferior performance relative to their rivals rather than to itself. PEG s approach to input price measurement would confiscate the regulated firm s reward for superior performance or inappropriately reward the firm for inferior performance by passing through the actual prices faced by the regulated firm in conducting their operations. To summarize, both Brattle and PEG use the same method and measure of economy-wide input price growth rate in their respective IPD terms. Differences between Brattle and PEG arise with respect to industry input price growth rates and are the following: Brattle employs the same input prices for the 36 U.S. LDCs in its calculation of industry TFP and input price growth rates. This consistency is not satisfied by PEG, who utilizes input prices unrelated to either the 36 LDCs, or its peer groups. PEG s industry input price growth rate is inconsistent with its industry TFP growth calculation. It is important to recognize that just as the PD component compared U.S. industry TFP growth to Canadian economy-wide TFP growth (for both the Brattle and PEG approaches), consistent use of the appropriate input 13

14 Page 14 of 22 prices results in Brattle comparing U.S. industry input price growth to Canadian economy-wide input price growth. PEG computes input price growth based on prices assumed to be faced by Enbridge and Union, and thereby PEG violates the immutability standard in setting the X factor. Brattle does not violate this standard. IPD Component (GD) Economy Input Price Growth - Industry Input Price Growth = Brattle = 0.41 PEG = 0.25 IPD Component (COS) Economy Input Price Growth - Industry Input Price Growth = Brattle = 0.20 PEG = IV. THE AU COMPONENT OF THE X FACTOR Since PEG inappropriately uses elasticity-weighted industry TFP growth rates, it introduces what it refers to as an AU component to reflect trends in service usage. As explained in Section 2, Brattle does not require such a term since from the outset it correctly calculates industry TFP growth based on revenue weights. These weights accurately and directly reflect the trend in service usage. If computed correctly, the end result of including PEG s AU term converts the elasticityweighted industry TFP growth into a revenue-weighted measure. Thus the combination 14

15 Page 15 of 22 of the PD and AU terms would be just a circuitous way of adjusting industry TFP growth so that it becomes correctly based on revenue weights. In this regard, this also means that there would not be any requirement for PEG s econometric cost model. In other words, excluding the AU term and calculating industry TFP growth using revenue weights leads to identical X factors as including the AU term and calculating industry TFP using elasticity weights. The problem is that PEG does not correctly measure its required AU term. 1. PEG does not base its AU term on its peer group of firms that comprise its elasticity-weighted industry TFP growth. Rather it measures the AU terms for Enbridge and Union. Thus its AU term is inconsistent with its PD component, and by employing Enbridge and Union specific information it violates as well the immutability standard in setting the X factor. 2. Since PEG s AU term is inconsistent with its PD component, the latter is still erroneously based on elasticity-weights and therefore does not reflect the historical trend in service usage. 3. PEG s AU term equals the difference between revenue-weighted and elasticityweighted output growth rates. Thus these two growth rates are required to measure PEG s AU component. Although it is incorrect to use Enbridge and Union growth rates, PEG s actual calculation of these growth rates is also problematic. PEG s elasticity-weighted output growth is derived by using the results from its econometric model. Besides the many problems and deficiencies of this model, recall the model uses the sample of all 36 U.S. LDCs. Enbridge and Union are not part of the sample. Thus PEG relies on the untested assumption that the econometric estimates characterizing the 36 LDCs cost of providing services also pertains to Enbridge and Union. Moreover, since all 36 firms are used in the estimation, PEG s Enbridge and Union-specific peer groups 15

16 Page 16 of 22 are not any more relevant to the AU calculation as are any of the remaining 36 LDCs. 4. PEG s revenue-weighted output growth is the other expression in its AU term. PEG calculates Enbridge and Union specific revenue-weighted output growth rates. But PEG assumes that these weights are fixed and thereby do not change over time. Not only is this incorrect since revenue shares do vary over time, but it is inconsistent with its elasticity-weighted measure. In this latter case the elasticities vary over time. Therefore Enbridge s revenue and elasticity-weighted output growth rates are mutually inconsistent and the same conclusion applies to Union s growth rates. AU Component (GD) Brattle Not Applicable PEG AU Component (COS) Brattle Not Applicable PEG V. OUTPUT GROWTH AND CUSTOMER GROWTH COMPONENTS OF THE X FACTOR When revenue rather than prices are capped, the X factor consists of an additional term that reflects the growth in output quantities. The reason for this additional component is 16

17 Page 17 of 22 due to the fact that revenue growth must equal the sum of the growth rates in output prices and output quantities. For example, suppose a firm supplies a single type of service at price $2 per unit and sells 1000 units. Thus by definition of revenue, the firm s revenue equals $2000 [= $2 x 1000]. Now if the firm s price is growing by 3% per year and units sold are growing by 2% per year then revenue must grow by 5% [= 3% + 2%]. This means that a revenue cap is the sum or combination of a cap on prices and a cap on output quantity. The preceding discussion reveals that if industry output growth is zero then revenue and price growth rates are equal. This implies that the X factor for a revenue cap regime must equal the X factor for a price cap plan. However, if output growth is positive then revenue growth exceeds price growth and so the X factor for a revenue cap plan must be less than the X factor under a price cap environment. For example, if the X factor for price caps is 0% and industry output growth is 0.5%, then the X factor for a price cap regime is -0.5% [= 0% - 0.5%]. The converse is true when output growth is negative. Consequently, revenue growth falls short of price growth and so the X factor for a revenue cap plan must be greater than the X factor applicable to price caps. Therefore the X factor for a revenue cap plan equals the X factor applicable to a price cap plan net of the regulated industry s output quantity growth rate. Both Brattle and PEG employ an output growth term in its revenue cap X factor. 14 However, Brattle s and PEG s calculation of industry output growth rates differ. Brattle uses the industry growth rate developed for its price cap X factor. The reason is that the output growth rate in the two regimes must be equal, otherwise the IR plan adopted by the Board would reveal a significant inconsistency. The plan would breach the basic definition that revenue growth must equal the sum of price growth and output growth. This outcome is erroneous. 17

18 Page 18 of 22 Once again, PEG is inconsistent in its treatment among the X factor components. PEG s industry output growth rate is incorrect for three reasons: 1. It is not based on revenue weights but rather uses cost weights, and so there is no guarantee that revenue growth equals the sum of price and quantity growth. 2. It is not based on its peer group of firms and is thereby inconsistent with PEG s treatment of industry TFP growth within the PD component. 3. It is based on Enbridge and Union data and therefore violates the immutability standard. Turning to a cap on revenue-per-customer growth, by the definition of revenue-percustomer, its growth rate must equal the difference between revenue growth and the growth in customers. An increase in revenue increases revenue per-customer, and so revenue-per-customer rises, while an increase in customers decreases revenue-percustomer and so revenue-per-customer falls. This means that when customer growth is zero then revenue and revenue-per-customer growth rate are equal. In this case the X factor for a revenue-per-customer regime equals the X factor for a revenue cap plan. However, if customer growth is positive then revenue-per-customer growth falls short of the growth in revenue and as a consequence the X factor for a revenue-per-customer plan is greater than the X factor for a revenue cap regime. The converse is true for a negative growth rate in customer growth. Therefore the X factor for a revenue-per-customer plan equals the X factor applicable to a revenue cap plan plus the regulated industry s customer growth rate. Furthermore, following from the discussion between revenue and price cap X factors, the X factor for a revenue-per-customer cap equals the X factor for a price cap minus industry output growth and plus industry customer growth. 14 Unlike Brattle, PEG does not show the transition from price caps to revenue caps. But in its June report PEG discusses the components of a revenue cap plan. 18

19 Page 19 of 22 Both Brattle and PEG employ a customer growth term in its revenue-per-customer cap X factor. However, Brattle s and PEG s calculation of industry customer growth rates differ. Once again, PEG is inconsistent in its treatment among the X factor components. PEG s industry customer growth rate is incorrect for three reasons: 1. It is not based on revenue weights, but rather just simply adds up the number of customers. PEG treats large customers the same as small customers, residential customers the same as commercial and industrial customers. To see that this is incorrect suppose that a firm has two customers. Customer 1 contributes 75% of revenue and customer 2 contributes 25% of revenue. Now suppose the firm loses customer 1. This represents a decrease in 50% in the number of customers [= 100% (1-2)/2], while a decrease in 75% of revenue [= 100% ( )/1.00]. The latter calculation is more accurate when considering revenue-per-customer growth where customers contribute differentially to revenue growth. 2. It is not based on the customers for PEG s peer group of firms and is thereby inconsistent with PEG s treatment of industry TFP growth within the PD component. 3. It is based on Enbridge and Union data and therefore violates the immutability standard. Customer and Output Components (GD) Industry Customer Growth Industry Output Growth = Brattle = 0.53 PEG = 0.44 Customer and Output Components (COS) Industry Customer Growth Industry Output Growth = Brattle =

20 Page 20 of 22 PEG = 0.32 VI. SERVICE CLASS-SPECIFIC X FACTORS The next issue concerns PEG s analysis of differentiating X factors by service classes. PEG commits two fundamental errors. The first error is that PEG mistakenly assumes that it is possible to identify service-specific productivity growth rates and by implication, PEG incorrectly assumes that it can identify the total cost for a specific service. However, since LDCs supply multiple services with joint and common costs then it is impossible to measure service-specific total cost and productivity growth rates. As Bernstein-Sappington (Journal of Regulatory Economics 1999) recognize: Furthermore, joint products and common factors of production preclude the measurement of product-specific productivity and input price growth rates. (Pages 6 and 7) If it were possible to measure the rate of growth of input prices and total factor productivity growth specifically for products that are subject to price cap regulation, then the distinction between regulated services and other services would pose no conceptual difficulties. However, such measurement is generally not possible because of joint products and common factors of production. (Pages 12 and 13) PEG commits its second error when it attempts to measure its service specific X factors. Since data cannot be constructed for service specific TFP growth rates and service specific total cost, PEG arbitrarily assumes that the non-measurable ratio of service specific total cost to total cost for the regulated firm equals the measurable ratio of service specific revenue to total revenue. Because of the existence of joint and common costs this assumption cannot be true and is not verifiable in any event. Therefore PEG s analysis and calculation of its service specific X factors must be rejected on the basis of its arbitrary assumptions and flawed analytical development. 20

21 Page 21 of 22 VII. CONCLUSION This report concludes that there are serious deficiencies with PEG s X factor recommendation: 1. It is based on a deficient econometric model. 2. It uses elasticity weights rather than revenue weights to calculate industry TFP growth rates. 3. It inappropriately utilizes Enbridge and Union specific data, while ignoring the same data from its own peer groups. 4. It calculates the components of its X factor in an inconsistent manner. X Factors (GD) (average annual percent) Brattle PEG Productivity Differential (A) -0.93% 1.35% Input Price Differential (B) 0.41% 0.25% Not Average Use (C) Applicable -1.16% Stretch Factor (D) 0.00% 0.50% X Factor Price Cap (E=A+B+C+D) -0.52% 0.94% Customer Growth - Output Quantity Growth (F) 0.53% 0.44% X Factor Revenue-Per-Customer Cap (G=E+F) 0.01% 2.54%* 21

22 Page 22 of 22 * PEG excludes the Average Use (AU) factor (C) from its X-Factor Revenue-per-customer cap. X Factors (COS) (average annual percent) Brattle PEG Productivity Differential (A) -0.87% 1.48% Input Price Differential (B) 0.20% -0.22% Not Average Use (C) Applicable -1.28% Stretch Factor (D) 0.00% 0.50% X Factor Price Cap (E=A+B+C+D) -0.67% 0.48% Customer Growth - Output Quantity Growth (F) 0.53% 0.32% X Factor Revenue-Per-Customer Cap (G=E+F) -0.14% 2.08%* * PEG excludes the Average Use (AU) factor (C) from its X-Factor Revenue-per-customer cap. 22