STOCHASTIC FRONTIER ESTIMATION FOR GAS TRANSMISSION PIPELINES

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1 A C I L A L L E N C O N S U L T I N G REPORT TO DAMPIER TO BUNBURY PIPELINE 19 SEPTEMBER 2013 STOCHASTIC FRONTIER ESTIMATION FOR GAS TRANSMISSION PIPELINES AUSTRALIA AND U.S. DATA,

2 ACIL ALLEN CONSULTING PTY LTD ABN LEVEL FIFTEEN 127 CREEK STREET BRISBANE QLD 4000 AUSTRALIA T F LEVEL TWO 33 AINSLIE PLACE CANBERRA ACT 2600 AUSTRALIA T F LEVEL NINE 60 COLLINS STREET MELBOURNE VIC 3000 AUSTRALIA T F FOR INFORMATION ON THIS REPORT PLEASE CONTACT: DR. LEO YANES, PRINCIPAL, ACIL ALLEN CONSULTING L.YANES@ACILALLEN.COM.AU MOB: (+61) TEL: (+61) CONTRIBUTORS: JOEL ETCHELLS, CONSULTANT, ACIL ALLEN CONSULTING DR. RICHARD LENTON, PRINCIPAL, ACIL ALLEN CONSULTING PROF. CHRIS O DONNELL, SCHOOL OF ECONOMICS, UNIVERSITY OF QUEENSLAND LEVEL ONE 50 PITT STREET SYDNEY NSW 2000 AUSTRALIA T F SUITE C2 CENTA BUILDING 118 RAILWAY STREET WEST PERTH WA 6005 AUSTRALIA T F ACILALLEN.COM.AU RELIANCE AND DISCLAIMER SUGGESTED CITATION FOR THIS REPORT ACIL ALLEN (2013). STOCHASTIC FRONTIER ESTIMATIO FOR GAS TRANSMISSION PIPELINES: AUSTRALIA AND U.S. DATA, REPORT FOR DAMPIER TO BUNBURY PIPELINE THE PROFESSIONAL ANALYSIS AND ADVICE IN THIS REPORT HAS BEEN PREPARED BY ACIL ALLEN CONSULTING FOR THE EXCLUSIVE USE OF THE PARTY OR PARTIES TO WHOM IT IS ADDRESSED (THE ADDRESSEE) AND FOR THE PURPOSES SPECIFIED IN IT. THIS REPORT IS SUPPLIED IN GOOD FAITH AND REFLECTS THE KNOWLEDGE, EXPERTISE AND EXPERIENCE OF THE CONSULTANTS INVOLVED. THE REPORT MUST NOT BE PUBLISHED, QUOTED OR DISSEMINATED TO ANY OTHER PARTY WITHOUT ACIL ALLEN CONSULTING S PRIOR WRITTEN CONSENT. ACIL ALLEN CONSULTING ACCEPTS NO RESPONSIBILITY WHATSOEVER FOR ANY LOSS OCCASIONED BY ANY PERSON ACTING OR REFRAINING FROM ACTION AS A RESULT OF RELIANCE ON THE REPORT, OTHER THAN THE ADDRESSEE. IN CONDUCTING THE ANALYSIS IN THIS REPORT ACIL ALLEN CONSULTING HAS ENDEAVOURED TO USE WHAT IT CONSIDERS IS THE BEST INFORMATION AVAILABLE AT THE DATE OF PUBLICATION, INCLUDING INFORMATION SUPPLIED BY THE ADDRESSEE. UNLESS STATED OTHERWISE, ACIL ALLEN CONSULTING DOES NOT WARRANT THE ACCURACY OF ANY FORECAST OR PROJECTION IN THE REPORT. ALTHOUGH ACIL ALLEN CONSULTING EXERCISES REASONABLE CARE WHEN MAKING FORECASTS OR PROJECTIONS, FACTORS IN THE PROCESS, SUCH AS FUTURE MARKET BEHAVIOUR, ARE INHERENTLY UNCERTAIN AND CANNOT BE FORECAST OR PROJECTED RELIABLY. ACIL ALLEN CONSULTING SHALL NOT BE LIABLE IN RESPECT OF ANY CLAIM ARISING OUT OF THE FAILURE OF A CLIENT INVESTMENT TO PERFORM TO THE ADVANTAGE OF THE CLIENT OR TO THE ADVANTAGE OF THE CLIENT TO THE DEGREE SUGGESTED OR ASSUMED IN ANY ADVICE OR FORECAST GIVEN BY ACIL ALLEN CONSULTING.

3 Roma to Brisbane DBP Efficiency Score Transcontinental Gas Pipeline Co-12 Questar Overthrust Pipeline Co-12 Midcontinent Express Pipeline -12 VIC Transm Sys Tennessee Gas Pipeline Co-12 ANR Pipeline Co-12 Wyoming Interstate Co-12 White River Hub-12 AC I L AL L E N C O N S U L T I N G Executive summary The Dampier to Bunbury Pipeline (DBP) has commissioned ACIL Allen Consulting (ACIL Allen) to conduct a Stochastic Frontier Analysis (SFA) to benchmark Australian gas transmission pipelines internationally, to inform its submission to the Economic Regulation Authority (ERA) on rate of return guidelines and in particular, comparison against a benchmark efficient entity. SFA provides an estimate of the production possibility frontier. This estimate can be used to calculate individual firm technical efficiency. A firm s given input use is used to calculate the theoretical maximum output, which is benchmarked against the actual output of the firm. In conducting the estimation, ACIL Allen has used a dataset comprising of U.S. data for the year 2012 from the Federal Energy Regulatory Commission (FERC) for 63 transmission pipeline companies and Australian data for the years 2011 to 2013 for the DBP, Victoria Transmission System and the Roma to Brisbane Pipeline. Inclusion of the US firms in the dataset for benchmarking the Australian firms allows for more powerful benchmarking techniques (such as SFA), leading to more rigorous decision making in the regulatory process. The efficiency scores for each firm in the dataset when applying SFA are presented in Figure ES1. An efficiency score of 1 can be interpreted as a perfectly efficient firm. The graph shows that the efficiency scores of Australian firms are comparable to the typical efficiency score of the firms in the data set. In consequence, analysis incorporating U.S. data provides useful information in understanding the benchmark efficient entity in Australia. Figure ES 1 Efficiency Scores per firm 1.00 US Australia Mean Efficiency = Firm ID Source: ACIL Allen calculations. ii

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5 Executive summary ii 1 Introduction Background Terms of Reference 2 2 Stochastic Frontier Estimation 3 3 Estimation Data Estimation results Efficiency Scores Econometric testing Stochastic frontier maximum likelihood vs. ordinary least squares ( =0) Inclusion of a time trend Inclusion of efficiency time effects Cobb-Douglas vs. translog specification Other diagnostic tests and sensitivities 13 4 Conclusions 14 Appendix A Dataset used in the base case A-1 List of figures Figure ES 1 Efficiency Scores per firm ii Figure 1 Capital in use and gas throughput: Full dataset view 7 Figure 2 Operations expenses and gas throughput: Full dataset view 7 Figure 3 Capital in use and gas throughput: Observations up to 500PJ/Yr 8 Figure 4 Operations expenses and gas throughput: Observations up to 500PJ/Yr 8 Figure 5 Efficiency Scores per Firm 11 Figure 6 Histogram of efficiency scores 12 List of tables Table 1 Maximum likelihood estimation: Cobb-Douglas, panel data 9

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7 1 Introduction Regulation covering Australian gas pipelines (the National Gas Rules, NGR) sets a requirement for comparison against a benchmark efficient entity. The Dampier to Bunbury Pipeline (DBP) has commissioned ACIL Allen Consulting (ACIL Allen) to conduct a Stochastic Frontier Analysis (SFA) to compare the production efficiency of Australian gas transmission pipelines internationally. 1.1 Background The NGR requires the regulators of gas pipelines to establish rate of return guidelines. The procedure to be followed by the regulators in making and publishing the guidelines are outlined in the NGR. The first step involves the publication by each regulator of draft proposed guidelines. The Economic Regulation Authority of Western Australia (ERA) has recently released its Draft Rate of Return Guidelines 1 and opened the process for public submissions. This report has been commissioned by DBP to inform its submission to the ERA. The guidelines are required to set out: the methodologies that the regulator proposes to use in estimating the allowed rate of return, including how those methodologies are proposed to result in the determination of a return on equity and a return on debt in a way that is consistent with the allowed rate of return objective the estimation methods, financial models, market data and other evidence the regulator proposes to take into account in estimating the return on equity and return on debt. The important aspect of these requirements is the definition of the allowed rate of return objective, which is defined in Rules 87(3) and (4) to be: commensurate with the efficient financing costs of a benchmark efficient entity with a similar degree of risk as that which applies to the service provider in the provision of reference services a weighted average of the return on equity for the access arrangement period in which that regulatory year occurs and the return on debt for that regulatory year. In consequence, the establishment of the benchmark efficient entity is of fundamental importance to the regulatory process and its outcomes. Benchmark Efficient Entity The ERA s Draft Guidelines define the benchmark efficient entity as: 2 A pure-play regulated gas network business operating within Australia without parental ownership, with a similar degree of risk as that which applies to the service provider in respect of the provision of reference services. 1 Available at accessed 7 September ERA (2013). Draft Rate of Return Guidelines, page11, paragraph 53. 1

8 The treatment of the benchmark efficient entity in the ERA s Draft Rate of Return Guidelines presents two issues. First, the ERA s Draft Guidelines do not provide guidance on the methodology and evidence to be used in supporting the choice of a proposed firm (the benchmark efficient entity) as the relevant efficient benchmark. Second, the methodologies and parameter values proposed by the ERA for calculating the rate of return rely on a relatively small sample of firms. A small dataset poses problems for the reliability of statistical estimation. Given that Australia has a small number of gas transmission pipelines, it makes sense to expand the sample population by including overseas firms. Aside from providing a better picture of industry operations, the inclusion of overseas firms allows the use of better techniques for efficiency analysis, such as SFA. 1.2 Terms of Reference DBP has commissioned ACIL Allen to conduct international benchmarking of Australian gas transmission pipelines. Consideration of overseas data provides access to broader evidence and thereby enables more rigorous decision making in the regulatory context, particularly in regard to the understanding of the benchmark efficient entity in Australia. More specifically, accessing a larger dataset enables the use of powerful statistical benchmarking techniques, such as the estimation of a production frontier. This in turn permits a more rigorous approach to benchmarking Australian firms. If only Australian data is considered, it is unlikely that sufficiently many observations will be available to conduct robust statistical analysis. This study will inform DBP s submission to the ERA, as part of the consultation process relating to the Guidelines for the Rate of Return for Gas Transmission and Distribution Networks. Whilst this study focusses on gas transmission pipelines, essentially the same approach could be used for gas distribution networks. There are two key methodologies available to conduct the benchmarking of Australian gas transmission pipelines: Data Envelopment Analysis (DEA) and Stochastic Frontier Analysis (SFA). SFA is recognised as the most powerful technique, and DBP has agreed to this approach. SFA is a statistical technique, while DEA is deterministic. DEA uses linear programming to envelope the cloud of data points and effectively assumes that the most productive firm lies on the production frontier. On the other hand, SFA recognises that there may be sources of deviations from the frontier other than technical efficiency, for example, measurement errors in the data. By implementing a stochastic framework, SFA allows for statistical testing and provides a rigorous approach to efficiency benchmarking. More specifically, the SFA method accounts for statistical noise and measurement error within a selected sample and it can be used to conduct a range hypothesis tests regarding the most appropriate functional form of a theoretical production frontier as well as the selection of inputs for analysis. As a technique that relies on stochastic methods, a sufficient number of observations are needed. As with any econometric analysis there is more than one way to specify the model design and therefore ACIL Allen has included diagnostic testing including model specification and robustness checks. 2

9 2 Stochastic Frontier Estimation This section provides a brief theoretical background for SFA and explains how the estimation was conducted. As outlined in Coelli et al (2005) 3, the economic performance across firms can be measured using estimates of efficiency. In particular, this report attempts to measure technical efficiency, which reflects a firm s ability to obtain the maximum quantity of output from a given set of inputs. A firm s efficiency is a relative measurement. Consequently, the challenge associated with analysing efficiency is to estimate a production possibility frontier (PPF) or theoretical maximum production against which an individual firm s performance can be benchmarked. The technological possibilities of a firm can be summarised using a production function: where is output (more generally, a vector of outputs), and ) is an nx1 vector of inputs. Often, production functions will be non-linear, which poses problems for conducting linear regression analysis. In some instances, the production function can take a functional form which can be linearised by taking logarithms. To estimate the stochastic PPF, this study uses a model specification which will allow such a transformation: a twofactor Cobb-Douglas functional form. The stochastic functional form is as follows: (1) where is gas throughput of firm, measured in PetaJoules (PJs) per annum is a constant, often associated with the environment the firms operate in, such as the national institutional framework or the technological level of the industry is capital used by firm i, per annum. In this study, capital is measured by depreciation divided by the price of capital, namely, the 10 year interest rate on treasury bonds measures firm s annual operations expense quantity index, including labour, materials and maintenance. Operations expenses are converted to a quantity index through division by the Producer Price Index (PPI), base 2012=1 is the elasticity of output with respect to capital is the elasticity of output with respect to the operations expenses quantity index is a standard statistical noise component, assumed to follow a Normal distribution and to be independently, identically distributed (iid). is an error term accounting for firm inefficiency. It is assumed to follow an asymmetric distribution, most often half-normal, truncated Normal or exponential. This study will use the half-normal distribution assumption is the exponential function. (2) 3 Coelli, T; Prasada Rao, D.S.; O'Donnell, C.J. and Battese, G.E. (2005). An Introduction to Efficiency and Productivity Analysis. 2 nd ed., Springer. 3

10 Taking natural logarithms in equation (2), the (stochastic) Cobb-Douglas function is linear in its logarithmic form: Equation (3) is the central equation in this study. It is a typical regression equation, except for the fact that is contains two error terms:, which is statistical noise, and which measures firm inefficiency. For ease of notation, lowercase variables denote logarithms, so equation (3) is rewritten as: with,, and. In conducting the estimation, other model specifications were considered. A commonly used alternative is the translog function (refer to chapter 8 of Coelli et al, 2005). The two-factor (stochastic) translog function is given by: (3) (4) (5) In choosing between Cobb-Douglas and translog specifications, it is important to consider the following points. First, comparison of equations (4) and (5) shows that the Cobb-Douglas functional form is more parsimonious than the translog form. For more than two factors, the translog contains a large number of cross-interaction terms. 4 Second, the translog is a more flexible functional form, and on this basis, it could be expected to fit the data better. However, this study conducts econometric specification testing to ascertain whether the improvement in fitting the data by using a translog function is significant, relative to the Cobb-Douglas specification. Section 3.4 finds that the translog does not significantly improve fit relative to the Cobb-Douglas. Third, the marginal products of production inputs (capital, operations, materials, maintenance, etc.) are more readily interpretable in the Cobb-Douglas form. In particular, the marginal product of capital in the Cobb-Douglas is given by and for the quantity index of operations expenses, it is given by. In the translog form, the marginal products are more complex and depend on cross-interaction terms. Fourth, the translog functional form can be interpreted as a second order Taylor expansion of a production function. As with all Taylor expansions, the functional form will then be applicable only in the neighbourhood of the Taylor expansion. On the other hand, the Cobb- Douglas is a global specification. 4 The translog generalises to n-factors as follows:, where. The number of regression coefficients will grow rapidly with the number of production factors, and this will reduce degrees of freedom, as well as imply marginal products which are more complex and harder to interpret. 4

11 Fifth, following from the fourth point, if a production function exists, it could take a Cobb- Douglas form. However, strictly speaking, a production function could not take a translog form. After giving due consideration to the above points, the study opts for the more parsimonious Cobb-Douglas functional form. In order to move to a statistical estimation framework, stochastic production frontiers account for statistical noise arising from the omission of variables on the right-hand side of equation (1) or measurement or approximation errors associated with the choice of functional form for by including error terms in the equation: where: is the logarithm of gas throughput of a selected firm (measured PJs). the input vector and materials consists of the logarithm of input quantities, such as capital, labour is a vector of unknown parameters, to be estimated and are the error terms defined above. The asymmetry of the distribution for arises because output values are bounded from above by the stochastic variable exp, where exp() is the exponential function and the inefficiency errors ( ) can only take non-negative values. Further details on the distributions of the two error terms are contained in chapter 9 of Coelli et al (2005). Using the estimated production frontier, a measure of technical efficiency taking a value on the (0,1) interval, is obtained by taking the ratio of the observed output to the corresponding stochastic frontier output: (6) (7) Thus, the efficiency score measures the output of an individual firm relative to the output that could be produced by a fully efficient firm using the same input vector. Equation (6) is the regression to be estimated. The estimation can be conducted by a variety of methods, including Corrected Ordinary Least Squares (COLS), Generalized Method of Moments (GMM), Bayesian approaches and Maximum Likelihood. Of the available methods, Maximum Likelihood is the most common approach, and is the method selected for this study. The next section presents the details of the estimation, starting with a description of the data, estimation results and diagnostic statistical testing of the regression results. 5

12 3 Estimation 3.1 Data The dataset ACIL Allen has gathered for this study consists of 68 observations arranged in a panel (longitudinal data) of 66 firms, providing sufficiently many degrees of freedom to conduct robust statistical analysis. To obtain this many observations, ACIL Allen used data from the U.S. Federal Energy Regulatory Commission (FERC), and more specifically, Form 2 data for Data on Australian gas transmission pipelines covering the period was compiled from publicly available sources such as the Australian Energy Regulator (AER), the ERA and company financial reports. Over this period data was available for three regulated firms: DBP, the Victoria Transmission System and the Roma to Brisbane Pipeline. U.S. dollar (USD) values have been converted to Australian dollars (AUD) using a Purchasing Power Parity exchange rate of 0.7 AUD:USD. 5 Section conducts sensitivity analysis allowing an alternative exchange rate at parity (AUD:USD = 1). The data consists of: Output: Measured by annual pipeline throughput (PJ/Yr) Quantity indices of factors of production: capital in use, calculated as depreciation plus amortization, divided by the price of capital. The price of capital is measured by the interest rate of 10 year treasury bonds (U.S. and Australian treasuries) operations expenses, including labour, materials and maintenance, divided by the Producer Price Index (base 2012=1) The following scatter diagrams present a visualisation of the data, along with a basic trend. 5 Sourced from OECD, accessed 6 September

13 Gas Throughput (PJ/Yr) Gas Throughput (PJ/Yr) AC I L AL L E N C O N S U L T I N G Figure 1 Capital in use and gas throughput: Full dataset view 3,500 3,000 2,500 2,000 y = x R² = ,500 1, U.S. Australia 0 2,000 4,000 6,000 8,000 10,000 12,000 14,000 16,000 18,000 Capital (Real 2012 A$ Million) Source: ACIL Allen calculations, U.S.: FERC form 2, Australia: AER, ERA and company financial reports. Figure 2 Operations expenses and gas throughput: Full dataset view 3,500 3,000 2,500 2,000 y = x R² = ,500 1, U.S. Australia Operations: Labour, Materials & Maintenance (Real 2012 A$ Million) Source: ACIL Allen calculations, U.S.: FERC form 2, Australia: AER, ERA and company financial reports. The above figures show the entire dataset. To better highlight how Australian firms compare against U.S. firms, the next two figures show a more detailed picture by focussing on the dataset only up to 500PJ/Yr of throughput. 7

14 Gas Throughput (PJ/Yr) Roma to Brisbane-2011 Vic Trans Sys-2011 DBP-2011 DBP-2013 DBP-2012 Roma to Brisbane-2011 Gas Throughput (PJ/Yr) Vic Transm Sys-2011 DBP-2011 DBP-2012 DBP-2013 AC I L AL L E N C O N S U L T I N G Figure 3 Capital in use and gas throughput: Observations up to 500PJ/Yr y = x R² = ,000 1,500 2,000 2,500 3,000 U.S. Australia Capital (Real 2012 A$ Million) Source: ACIL Allen calculations, U.S.: FERC form 2, Australia: AER, ERA and company financial reports. Figure 4 Operations expenses and gas throughput: Observations up to 500PJ/Yr y = x R² = Operations: Labour, Materials & Maintenance (Real 2012 A$ Million) U.S. Australia Source: ACIL Allen calculations, U.S.: FERC form 2, Australia: AER, ERA and company financial reports. From Figures 1-4, it can be seen that there is significant correlation between throughput and the calculated quantity indices for capital and operations expenses. In terms of capital, the 8

15 graphs show the Australian firms sit above and below the simple line of best fit which in simple terms suggest the Australian firms are no more or no less efficient than the typical firm in the dataset. In terms of operations, the Australian firms tend to sit on or below the line of best fit suggesting in simple terms that the Australian firms are less efficient than the typical firm in the dataset. Section 3.2 proceeds to use the above data to estimate the stochastic production frontier. 3.2 Estimation results The statistical estimation was conducted and independently replicated and corroborated using a variety of statistical software, including STATA and R. This process ensured that results were independently replicable and avoids the potential for human or computational error. Estimation was conducted on the Cobb-Douglas regression form (based on equations (4) and (6)in section 2): The regression analysis was conducted using maximum likelihood estimation provided by the Frontier 4.1 package 6. The estimation exploits the panel structure of the dataset. Estimation results are shown in Table 1. (8) Table 1 Maximum likelihood estimation: Cobb-Douglas, panel data Coefficient Estimate Standard Error z Value Pr(> z ) Intercept: b *** ln( Capital): b ** ln(operations Expenses): b s *** Significance codes: 0 *** ** 0.01 * Log Likelihood value: Unbalanced Panel Data Number of cross-sections: 66 Number of time periods: 3 Number of observations: 68 Source: ACIL Allen calculations. These results show that all coefficients are statistically significantly different from zero. The marginal products of quantity indices of capital ( ) and operations expenses ( ) are positive. is the estimated sum of the variance of the error terms, and :. is the share of the variance accounted for by the inefficiency term:. In this case, over 90.7 per cent of the variance is explained by the inefficiency term,. Notice that since is constrained to lie in the (0,1) interval, standard significance testing is not appropriate. To ascertain the significance of, a log-likelihood ratio test is 6 The Frontier package is available for use with R ( and also in a standalone version ( 9

16 required. This is the first test reported in Section 3.4, which shows that significantly different from zero. is statistically 3.3 Efficiency Scores Efficiency scores for each firm are calculated using the estimated coefficients and production factor or input values. Equation (7) shows how this calculation is carried out and Figure 5 shows the efficiency scores for each of the firms in the dataset. The horizontal axis in Figure 5 shows the observation number (firm identifier), while the vertical axis shows the efficiency score for firm i:, measured relative to a hypothetical firm which would operate with 100 per cent efficiency. In other words, the hypothetical benchmark is a firm which, using the same inputs as the observed firm, would transform those same inputs into the greatest possible output, using the technological frontier estimate presented in Table 1. The data labels keep track of the firm identifier and the year corresponding to the observation. For observations of particular interest, the firm identifier has been replaced with the firm s name. This has been done for all of the Australian firms and those U.S. firms which are closest to the production frontier. Inspection of Figure 5 shows that the efficiency scores of Australian firms are comparable to the typical efficiency score of the firms in the data set. In consequence, analysis incorporating U.S. data provides useful information in understanding the benchmark efficient entity in Australia. In order to determine the optimal parameters for the benchmark efficient entity, a more thorough study is warranted, which would preferably include data on firms from other countries. 7 7 The current analysis is limited to the inclusion of US firms due to time constraints. 10

17 Roma to Brisbane DBP Transcontinental Gas Pipeline Co Questar Overthrust Pipeline Co Efficiency Score Midcontinent Express Pipeline -12 VIC Transm Sys Tennessee Gas Pipeline Co-12 ANR Pipeline Co Wyoming Interstate Co-12 White River Hub-12 AC I L AL L E N C O N S U L T I N G Figure 5 Efficiency Scores per Firm 1.00 US Australia Mean Efficiency = Firm ID Source: ACIL Allen calculations. The efficiency scores can also be plotted in a histogram, which provides useful information in relation to their distribution. This is shown in Figure 6, from which it is apparent that the distribution of efficiencies is centred around the middle of the range, with a mean efficiency score of

18 Frequency AC I L AL L E N C O N S U L T I N G Figure 6 Histogram of efficiency scores Mean Efficiency = Efficiency scores Source: ACIL Allen calculations. The next section provides a variety of statistical tests which were applied to the estimation results presented in Table Econometric testing In the context of SFA estimation via maximum likelihood, the main diagnostic testing is conducted through likelihood ratio tests, which enable comparisons of nested models Stochastic frontier maximum likelihood vs. ordinary least squares ( =0) A likelihood ratio test ascertains whether the stochastic frontier maximum likelihood approach offers a statistically superior fit to ordinary least squares (OLS). The SFA approach assumes that the inefficiency terms ( ) are distributed asymmetrically, whereas OLS assumes symmetrically distributed errors. The likelihood ratio test results return a 2 - statistic value of 11.8 (1 degree of freedom), which implies that the null hypothesis of =0 is rejected with a significance of , that is, the probability that >0 is higher than Inclusion of a time trend The inclusion of a time trend in the Cobb-Douglas estimating equation would imply the following estimating equation. The Cobb-Douglas model is nested within the above model by setting. This hypothesis is tested with a likelihood ratio test. The likelihood ratio test results return a 2 - statistic value of 0.01 (1 degree of freedom), which implies that the null hypothesis of cannot be rejected with a significance of 0.91, that is, the probability that is Hence the inclusion of a time trend is unwarranted and this is not surprising given the use of data over a short time horizon. 12

19 3.4.3 Inclusion of efficiency time effects AC I L AL L E N C O N S U L T I N G The SFA specification allows for efficiency scores to vary over time according to the Battese and Coelli (1992) 8 specification. The null hypothesis is that This hypothesis can be tested by a likelihood ratio test that compares the Cobb-Douglas preferred model vs. the same model estimated using Frontier 4.1 s option to allow variation over time of the efficiency scores. The likelihood ratio test results return a 2 -statistic value of 0.26 (1 degree of freedom), which implies that the above specification is inappropriate Cobb-Douglas vs. translog specification The base case Cobb-Douglas estimating equation is given by A translog specification is given by., The Cobb-Douglas model is nested within the translog model by setting. This hypothesis is readily tested with a likelihood ratio test. The likelihood ratio test results return a 2 -statistic value of The 5 per cent critical value for a 2 distribution with 4 degrees of freedom is 9.488, which implies that the null hypothesis of is not rejected and the Cobb-Douglas functional form is appropriate. In fitting the translog function, efficiency scores were calculated and the chart equivalent to Figure 5 shows similar results to the Cobb-Douglas. Based on these results, the study team believes that the additional complexity that the translog form implies is unwarranted, particularly given the good fit attained by the Cobb- Douglas model Other diagnostic tests and sensitivities The asymmetric nature of the errors highlighted in section 2 (particularly ) means that most standard diagnostic tests cannot be applied to SFA estimation by maximum likelihood, which drops the assumption of symmetrically distributed errors. Diagnostic testing would require significant theoretical modification of the test statistics, which lies outside the scope of this study. A sensitivity of central interest is the foreign exchange assumption used for conversion of U.S. dollar denominated variable to Australian dollars. The base case uses a value of 0.7 AUD:USD. A sensitivity assuming parity (1 AUD:USD) was run and the only noteworthy change was an increase in the intercept from to Efficiencies dropped slightly, with U.S. firms efficiency scores falling by an average of and Australian firms efficiency scores falling by an average of Battese, G.E., and T.J. Coelli (1992), "Frontier Production Functions, Technical Efficiency and Panel Data: With Application to Paddy Farmers in India", Journal of Productivity Analysis, 3,

20 4 Conclusions This study has used transmission pipeline throughput, capital and operations expenses data sourced from the U.S. FERC and Australian firms covering the period. The dataset contains 68 observations arranged in an unbalanced panel structure. The key findings of this study are summarised as follows: First, Australian gas transmission pipelines within the dataset are not amongst the most efficient entities. In consequence, there is a case for international benchmarking of the industry when establishing the benchmark efficient entity. Second, the inclusion of overseas data in the benchmarking analysis provides a greater number of observations, and thereby allows the use of powerful techniques, such as SFA, bringing greater rigour to regulatory decision making. Third, average efficiency scores in the gas transmission pipeline industry are relatively low when compared to other industries. Typical efficiency scores in other industries are around the 90 per cent range. The mean efficiency for this dataset is 47 per cent. While the drivers of pipeline efficiency are yet to be determined, a hypothesis to explain this result could be that transmission pipelines are a very capital intensive industry, with limited ability to affect throughput, other than track demand and supply conditions in the gas market that a particular pipeline services. Hence, if a transmission pipeline is operating with excess capacity, there are limited strategies it can implement to reduce its use of inputs. Capital is sunk, and hence depreciation is fixed to a large degree. Operations expenses are, to some extent, fixed: Maintenance is likely governed by a set schedule, labour use is likely already at a minimum as well as a small component of costs. Materials are also likely to be a small component of costs. Hence, when facing excess capacity, the responses available to pipeline management appear to be limited and as a consequence, it is possible that the industry may operate with excess inputs, leading to low efficiency scores. This study has not considered certain aspects specific to each pipeline, such as the type of terrain, climate, population metrics, market characteristics, etc. In addition, pipelines are long term investments with economic lives of over 25 years, and a longer time perspective would allow a richer picture of how firm efficiency is changing over time. The above discussion highlights the importance of further investigation into the drivers of pipeline efficiency. Fourth, recent studies 9 on the railway industry focus on the impact of different types of regulatory regimes on the efficiency of the regulated firms. A similar approach could be implemented to study the drivers of gas pipelines, with the type of regulation being one of the candidate drivers to explain efficiency patterns. Fifth, whilst this study has found some reasonably strong statistical relationships, it is far from being definitive. This study has accessed a limited dataset and a more comprehensive dataset would be desirable in order to conduct further rounds of estimation. This further study could then inform the parameterisation of the benchmark efficient entity and the resulting choice of dataset for more robust decision making in the regulatory context. The team views the study as an exploratory investigation into the efficiency benchmarking of Australian gas transmission pipelines. A similar approach could also be applied to the benchmarking of gas distribution networks. 9 Friebel, G.; Ivaldi, M. and Vibes, C. (2010). Railway (De)Regulation: A European Efficiency Comparison", Economica, vol. 77, n. 305, p

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22 Appendix A Dataset used in the base case Name ID Year Capital Opex PJ East Tennessee Natural Gas, LLC Midwestern Gas Transmission Company Southern Natural Gas Company, L.L.C Tennessee Gas Pipeline Company, L.L.C National Fuel Gas Supply Corporation Texas Eastern Transmission, LP Texas Gas Transmission, LLC Algonquin Gas Transmission, LLC Equitrans, L.P CenterPoint Energy - Mississippi River Transmission, LLC Natural Gas Pipeline Company of America LLC Panhandle Eastern Pipe Line Company, LP Transcontinental Gas Pipe Line Company, LLC Trunkline Gas Company, LLC CenterPoint Energy Gas Transmission Company, LLC Colorado Interstate Gas Company, L.L.C El Paso Natural Gas Company, L.L.C Florida Gas Transmission Company, LLC Northwest Pipeline GP Transwestern Pipeline Company, LLC Southern Star Central Gas Pipeline, Inc MIGC, LLc ANR Pipeline Company WBI Energy Transmission, Inc Great Lakes Gas Transmission Limited Ptrshp Tallgrass Interstate Gas Transmission LLC Questar Pipeline Company Northern Natural Gas Company Trailblazer Pipeline Company LLC Wyoming Interstate Company, L.L.C Questar Overthrust Pipeline Company Sabine Pipe Line LLC Viking Gas Transmission Company Gas Transmission Northwest LLC Northern Border Pipeline Company Mojave Pipeline Company, L.L.C Chandeleur Pipe Line Company Kern River Gas Transmission Company IPOC as Agent/Iroquois Gas Trans. Sys. L.P Dominion Cove Point LNG, LP TransColorado Gas Transmission Company LLC Dauphin Island Gathering Partners Ozark Gas Transmission, L.L.C Maritimes & Northeast Pipeline, L.L.C Vector Pipeline L.P Alliance Pipeline L.P Gulfstream Natural Gas System, L.L.C Guardian Pipeline, L.L.C North Baja Pipeline, LLC MarkWest New Mexico L.L.C Cheyenne Plains Gas Pipeline Company, LLC Carolina Gas Transmission Corporation Golden Pass Pipeline LLC MarkWest Pioneer, LLC ETC Tiger Pipeline, LLC Bison Pipeline LLC Rockies Express Pipeline LLC Southeast Supply Header, LLC Cimarron River Pipeline, LLC White River Hub LLC Empire Pipeline, Inc Midcontinent Express Pipeline LLC Kinder Morgan Louisiana Pipeline LLC Roma to Brisbane Pipeline - QLD Dampier to Bunbury WA Dampier to Bunbury WA Dampier to Bunbury WA Victorian Transmission System A-1