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Article Excerpt
Local distribution companies (LDCs) play the role of purchasing and delivering natural gas to their consumers, and state regulators oversee the pricing of natural gas to consumers. The common method of regulation, based on the cost of service, provides arguably little incentive for the LDC to optimally manage their procurement activities. In the light of recent deregulation and other changes, benchmarking-based regulatory schemes are being increasingly perceived as the right direction to pursue. Various states are experimenting with simple benchmark mechanisms that have inherent deficiencies and are often criticized. In this paper, we propose and characterize a new kind of benchmark that we call a policy benchmark as a mechanism for regulation. Using variance as the measure of risk, we formulate the regulator's and the LDC's problems as multiple-objective optimizations. We provide rigorous characterizations of the dominance frontiers for a two-stage model. We also provide multistage formulations that take into account various natural gas market microstructures. We compute solutions under estimated from relevant real-world data and illustrate that the structures of the dominance frontiers remain unaltered from the characterizations provided by a stylized two-stage modal.
Subject classifications: natural gas; regulation; benchmarks; linear incentive contracts; policy benchmarks.
Area of review: Policy Modeling and Public Sector OR.
History: Received January 2007; revisions received June 2007, August 2007, September 2007; accepted September 2007.
Published online in Articles in Advance July 16,2008.
1. Introduction
Local distribution companies (LDCs) purchase natural gas from wellheads and deliver it to consumers. The distribution of natural gas is a natural monopoly, and hence consumers usually (1) do not have a choice in picking their LDC. State regulators therefore oversee the pricing of natural gas to their consumers. With the deregulation of various stages of the natural gas market, procurement costs for LDCs have become, relatively, very volatile. Financial contracts that help quantify and transfer risk are now increasingly available and have become a necessary part of procurement strategies to ensure stable and low prices to consumers.
The most common method that been adopted by state regulators to oversee pricing is cost of service regulation (Laffont and Tirole 1993). In this arrangement, the regulator carries the burden of inspecting all purchasing and risk-management activities of the LDC. After a hearing, which is a part of the inspection process, the regulator approves or disapproves various procurement costs. The regulator also fixes a "return on investment" on the investments made by the LDC. The total fee to consumers is then the sum of the approved procurement costs and allocation toward meeting the return on investment (see Avery et al. 1992 for a detailed formulation of the LDC's optimization problem).
Under cost of service regulation, LDCs have arguably little incentive to optimally manage their procurement activities (Shleifer 1985). Formal models that out this lack of incentive can be found in Baron and Bondt (1981) and Isaac (1982). Moreover, the deregulation of parts of the natural gas markets (at the wellheads and the interstate pipelines) and the recent fundamental shift (Yu and Yu 2004) in natural gas supply/demand balance gas caused prices of gas at wellheads to become very volatile. Consequently, the fee to consumers has become sensitive to the LDC's risk-management strategy. Finally, with the increasing availability of various heading contracts are now facing a tremendous increase in resource requirements for the inspection and hearing process and van still rarely infer with confidence whether the LDC's procurement is being well managed. As with other states, this problem is a real consideration for the Indiana Utility Regulatory Commission (IURC), with which we are involved as arms length technical advisors through our affiliation with Purdue's State Utility Forecasting Group. The recent volatilities in about the need for better mechanisms on which to base regulatory evaluations of LDC performance.
Shleifer (1985,p.391) suggests that: "what the regulator needs is some relatively simple benchmark, other than the e firm's present or past performance, against which to evaluate the firm's present or past performance, against which to evaluate the firm's potential. With such a benchmark, he can decide what the firm's costs ought to be, and set the price accordingly." In a benchmark-based regulation scheme, the regulator initially chooses and announces a benchmark along with the structure of a "bonus" mechanism (bonus function) At the end of the period under consideration, LDC procurement costs for the period are compared to the benchmark and the bonus is calculated. Finally, the regulator allows the LDC to pass the sum of the procurement cost and bonus as the fee to consumers. It should be noted that usually the bonus can be either positive, depending on the LDC's performance relative to the benchmark. The benchmark, together with the bonus function, forms the benchmark contract--that is, the benchmark-based regulation scheme.
In this paper, we propose and characterize a new kind of benchmark, which we call a policy benchmark, as a mechanism for benchmark in this case is simply the choice of a procurement policy. The value of the benchmark is then equal to the cost procurement that would have been realized if the benchmark policy was used. Policy choices are restricted to policy that depend only on publicly available data/information and contracts. LDCs usually have access to more information and more exotic contracts that would enable them to beat policy benchmarks. Still, policy benchmarks incorporate natural gas price dynamics and can also take into account various LDC-specific constraints such as location and storage capacity. We restrict our attention to bonus functions that are linear functions of the difference between the benchmark and the LDC's procurement cost.
The regulator whishes to choose a policy benchmark and a bonus function to minimize the fee to consumers (in terms of both the mean and variance). Once the benchmark and the bonus functions are chosen and announced by the regulator . the LDC's objective is to choose a procurement strategy that maximizes their bonus (again in terms of both mean and variance). Hence, the cost to consumers depends on the benchmark, the bonus function, and the procurement strategy adopted by the LDC in nontrivial ways. Once has to keep in mind that the regulator can potentially pick different policy benchmarks for different LDCs that come under its regulatory oversight. This would allow the regulator to account for the different in physical characteristics that exist amongst various LDCs and affect the performance that should be expected. Such characteristics include locational price distributions, storage costs, and demand patterns.
The problem of finding the best benchmark policy is illdefined when the regulator does not have precise knowledge of the LDC's policy space. One possibility is to possible benchmark. However, the result is dependent on the approximation used, and the approximation is difficult because of the great range of options and exotic contracts to which LDCs have access. Hence, we will simply assume that the LDC's policy space is unknown t the regulator and larger than the policy space to which the regulator has access Under such generality, we seek to find we set of benchmark polices form which the regulator should choose.
WE begin with a review of the relevant literature. Then, in [section]2, using variance as our measure of risk, we formulate the regulator's problem and the LDC's problem as two-stage multiple-objective optimizations. After a brief introduction to mean-variance theory, we define various dominance frontiers that describe preference relations for both the LDC and the regulator. In [section]3, our goal is to characterize the set of benchmark policies that the regulator should choose from [gamma]. We also characterize other related dominance frontiers and provide qualitative insights that would serve as guidelines for regulators. In [section]4, we provide multistage formulations of the regulator's and LDC's problems. By using a specific numerical example, further insights and discussions of rewards/fees and their dependence on benchmark choices as well as solutions to the multistage problems under relevant parameters are explored in ][section]5. We conclude in [section]6. Proofs of all lemmas and theorems are in the online appendix that can be found at http://or.journal.informs.org/.
1.1. Prior Benchmarks and Related Literature
The choice of the benchmark as well as the bonus function are difficult decisions that regulator needs to make Two choices for benchmarks are common in the literature and have been used experimentally by various state regulators (Laffont and Tirole 1993, Shleifer 1985). One uses historical prices and the other is based on averaging either spot prices or other LDC procurement costs. Given the frequent changes that the natural gas market has been subjected to in the recent past, historical price-based benchmarks are often criticized as being an unreliable measure. The average (or more generally the weighted average) of spot prices is a very volatile benchmark and is incapable of incentivising an efficient balance between mean and risk of associated costs, and hence is not of LDC procurement costs has been criticized because LDCs differ in size, geographical location, pipeline connectivity, demand distribution, and various other factors that make them non-comparable to each other. The bonus functions that have been considered in the literature and have been used in practice have almost always been either linear or piecewise-linear functions of the difference between the procurement cost and benchmark (Laffont and Tirole 1993, Predergast 1999, Holmstrom and Milgrom 1987, Grinbatt and Titman 1989).
Amongst the of benchmark that use historical prices, linear incentive contracts have been well studied in the literature. These contracts use a benchmark based on historical data, along with an affine bonus function (Laffont and Tirole 1993). Amongst the benchmarks that use average spot prices, yardstick regulation has been the most explored. Yardstick regulation uses the average of wellhead spot prices with a linear or piecewise-linear bonus function (Shleifer 1985). For more details on the specific mechanisms adopted (or experimented with) by various state regulators and their effectiveness, refer to Yu and Yu (2004). Another approach to regulation is lagged price adjustment, which is proposed in Baumol (1968) and Bailey (1974). This approach allows the LDC to reap the benefits of reducing procurement costs for some time until the price is brought down. However, as is argued in Shleifer (1985), this approach is not sufficient and can easily be bettered by yardstick regulation.
The problem of motivating one party to act on behalf of another is known as the principal-agent problem. Hence, the problem we consider can be thought of as a principal-agent problem, with the regulator being the principal and the LDC being the agent. Several papers have analyzed the principal-agent problem using generalized models (Laffont and Martimort 2002). The classical principal-agent model uses two scalar parameters, both unobservable to the principal, to model the characteristics and activities of the agent. They are the efficiency parameter [beta] and the effort variable e. The...
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