The role of model specification in finding the influence of ownership and regulatory regime on utility cost: the case of Swedish electricity distribution.I. INTRODUCTIONThe restructuring restructuring  The transformation from one representation form to another at the same relative abstraction level, while preserving the subject system's external behaviour (functionality and semantics). of network industries during the last two decades has typically involved privatization privatization: see nationalization. privatization Transfer of government services or assets to the private sector. Stateowned assets may be sold to private owners, or statutory restrictions on competition between privately and publicly owned of state and municipally owned utilities and a change in regulatory regime from costofservice, or rateofreturn, regulation to incentivebased regulation. These reregulatory initiatives have been encouraged by economic theories that predict that private suppliers and competition increase cost efficiency. (1) Such outcomes have in fact been observed in electricity and water distribution (Kumbhakar and Hjalmarsson 1998; Saal and Parker 2000). (2) Nevertheless, the restructuring seen in different countries varies from complete privatization of multiple utility services and a heavy reliance on cost incentives, in for example England and Wales England and Wales are both constituent countries of the United Kingdom, that together share a single legal system: English law. Legislatively, England and Wales are treated as a single unit (see State (law)) for the conflict of laws. , to no or only marginal adjustments, exemplified by the water, wastewater, and district heating District heating (less commonly called teleheating) is a system for distributing heat generated in a centralized location for residential and commercial heating requirements. sectors in Sweden. (3) The wide variety of adopted policies can be attributed to the empirical difficulty of establishing a unified view of how utility performance is affected by different ownership and regulatory arrangements. The mainstream predictions are questioned by, for example, Kwoka (2005a, 2005b) and Bhattacharyya et al. (1995), who suggest that publicly owned Publicly owned can refer to:
A tentative explanation to why conclusions vary is the specific conditions that prevail in each country and industry; however, the studies referred to above also suggest that ownership and regulation might not affect performance by themselves but rather through combinations with other factors. In addition, behavioral assumptions and model specifications vary, which can potentially inflate inflate  deflate differences in empirical outcomes. Bhattacharyya et al. (1995), Berg, Lin, and Tsaplin (2005), Hattori, Jamasb, and Pollitt (2005), Aubert and Reynaud (2005), Pombo and Taborda (2006), and Goto and Tsutsui (2008) all use stochastic By guesswork; by chance; using or containing random values. stochastic  probabilistic frontier (i.e., dual disturbance) specifications, whereas Kwoka (2005a, 2005b) and Saal and Parker (2000) use single disturbance specifications. The choice between dual and single disturbance specifications is related to the assumption of utility objective, because a frontier specification rests on an assumption of costminimization while a function through the average of the data assumes that utilities follow any arbitrary objective. If it can be assumed that utilities minimize costs, then frontier methods have superior economic properties because the presence of a frontier is consistent with the behavior of economic optimization optimization Field of applied mathematics whose principles and methods are used to solve quantitative problems in disciplines including physics, biology, engineering, and economics. with a departure from the frontier interpreted as a lack of ability and/or luck. However, the choice of utility objective is not straightforward and although a majority of the studies surveyed above apply frontier specifications, it has been claimed that a costminimizing assumption could be overly restrictive (Kwoka 2005a). It can nevertheless be argued that most incentivebased approaches encourage costminimization and they typically compose a double incentive structure to separately reward frontier reductions and penalize pe·nal·ize tr.v. pe·nal·ized, pe·nal·iz·ing, pe·nal·iz·es 1. To subject to a penalty, especially for infringement of a law or official regulation. See Synonyms at punish. 2. inefficiency. A dual disturbance specification is more appropriate in that case. The potential influence from a costofservice regulation is more likely to influence the general cost level, which suggests that a single disturbance specification is preferred. It should be noted that the net cost effect is arbitrary if incentives are only created for either frontier shifts or inefficiency reductions. A further specification consideration is the choice between fixed and random coefficients. The generalized gen·er·al·ized adj. 1. Involving an entire organ, as when an epileptic seizure involves all parts of the brain. 2. Not specifically adapted to a particular environment or function; not specialized. 3. random coefficient coefficient /co·ef·fi·cient/ (ko?ahfish´int) 1. an expression of the change or effect produced by variation in certain factors, or of the ratio between two different quantities. 2. specification has become popular in the domain of choice experiments because of its ability to reduce the negative consequences of finite sample sizes, uncertainty about functional form and poor data quality (Allenby et al. 2005; Train 2003). The timevariant inefficiency specification is a special case of this model, which has been advocated for frontier models (Alvarez, Arias, and Greene 2004). (5) Models that permit inefficiency to be timevariant have been applied in electricity distribution by Farsi, Filippini, and Greene (2006) and although their interest was primarily the measurement of utilitylevel inefficiency, they also illustrate that the coefficient values are sensitive to this specification. In the case of estimating utility cost functions, the researcher must be aware that individual utilities operate under different environmental and network characteristics and that this heterogeneity het·er·o·ge·ne·i·ty n. The quality or state of being heterogeneous. heterogeneity the state of being heterogeneous. is partly unknown and partly unobserved. For panel data and regular fixed coefficient models, one can thus expect unaccounted for An inclusive term (not a casualty status) applicable to personnel whose person or remains are not recovered or otherwise accounted for following hostile action. Commonly used when referring to personnel who are killed in action and whose bodies are not recovered. variation over both utilities and time, which suggest that the random coefficient model is more appropriate. A fixed coefficient specification might therefore offer an additional explanation to the inability of establishing a robust influence from independent variables. All studies surveyed above use fixed coefficients and include ownership and/or regulation either as a dummy Sham; makebelieve; pretended; imitation. Person who serves in place of another, or who serves until the proper person is named or available to take his place (e.g., dummy corporate directors; dummy owners of real estate). effect only (Aubert and Reynaud 2005; Berg, Lin, and Tsaplin 2005; Hattori, Jamasb, and Pollitt 2005; Kwoka 2005b; Pombo and Taborda 2006) or as a combination of a dummy only and a dummy interacting effect (Bhattacharyya et al. 1995; Goto and Tsutsui 2008; Kwoka 2005a). There have so far been few applications of random slope coefficient models, especially in combination with stochastic frontier models (see Christopoulos, Lolos, and Tsionas 2002; Greene 2004; Wang 2002 for early applications), and to the best knowledge of the author, none has yet been applied in electricity distribution. The random coefficient specifications should therefore be particularly relevant to contrast against the traditional fixed coefficient specifications. Following the above, the purpose of this paper is to investigate the effects from different econometric e·con·o·met·rics n. (used with a sing. verb) Application of mathematical and statistical techniques to economics in the study of problems, the analysis of data, and the development and testing of theories and models. specifications related to utility objective/the design of regulatory regime and influences from unknown/uncertain heterogeneous factors. Identification is possible by using the same dataset and by including the same variables for each of these assumptions. The Swedish electricity distribution sector provides a suitable framework in this respect because publicly (6) and privately owned utilities have existed in parallel for almost a century and a revised regulatory regime was implemented in 2003 with stronger incentives for reduced cost inefficiencies. The prereform regime restricted utilities to increase prices at a faster rate than input prices and separate benchmarks were used to reduce inefficiency. The new regulatory model intends to reduce the regulator's information disadvantage by comparing utilities' revenue to the cost of a fictitiously fic·ti·tious adj. 1. Of, relating to, or characterized by fiction; imaginary. 2. a. Accepted or assumed for the sake of convention: a fictitious belief. b. designed, average performing utility. (7) This translates into a preference for inefficiency reductions over frontier shifts both for the pre and postregime and the outcome from a single disturbance model is therefore unpredictable by construction. The remainder of this paper is structured as follows. Section II provides a theoretical review of the link between ownership, regulation, and cost efficiency and also syntheses the introductory and theoretical sections into three specific hypotheses. Section III outlines the methodology used while Section IV describes the model specifications and data characteristics. The paper ends with estimation outputs and conclusions in Sections V and VI, respectively. II. THEORY AND HYPOTHESES Private enterprises arc generally regarded as a superior alternative to publicly owned organizations because profitmaximizing firms have stronger incentives to minimize costs. In addition, publicly owned organizations are believed to suffer from broad and illdefined objectives, no bankruptcy constraint Constraint A restriction on the natural degrees of freedom of a system. If n and m are the numbers of the natural and actual degrees of freedom, the difference n  m is the number of constraints. and an absence of a residual claimant CLAIMANT. In the courts of admiralty, when the suit is in rem, the cause is entitled in the Dame of the libellant against the thing libelled, as A B v. Ten cases of calico and it preserves that title through the whole progress of the suit. (BlomHansen 2003: Savas 1987). In addition, Niskanen's (1971) idea of public bureaucrats' budget maximizing behavior diverts these organizations even further from minimum production cost. Under the assumption that regulators can effectively prevent excessive pricing, private ownership should hence be a promizing alternative to public ownership. However, because of asymmetric information Asymmetric Information Information available to some people but not others. Notes: In other words, the asymmetric information is held by only one side, meaning someone is keeping a secret. , conflicting interests and costly regulation, there has been an increased realization that regulations, like markets, are subject to failures (e.g., James 2000). As a response, network regulators have increasingly relied on incentive models as a way to increase managerial effort and in turn, to reduce costs. The incentives are typically created by benchmarking utilities against comparable units. (8) The theoretical synthesis is therefore that private owners and (stronger) financial incentives will reduce costs. These effects are only reliably evaluated under appropriate model specifications, that is under a dual disturbance structure when separate incentives are applied for frontier and/or inefficiency reductions and when unobserved/unknown heterogeneity is accounted for. Alternative specifications can be expected to generate arbitrary outcomes in terms of coefficient signs and significance levels. This allows the formulation of the following hypotheses for the Swedish electricity distribution sector: H1: Privately owned utilities are more cost efficient than publicly owned utilities. H2: Cost inefficiency will be lower after the introduction of the revised incentivebased regulation in 2003. H3: The frontier shift will be arbitrary after the introduction of the revised incentivebased regulation in 2003. III. METHODOLOGY The single disturbance function for panel data can be specified as: [y.sub.it] = [[beta].sub.0] + [[beta].sub.0i] + [beta][X.sub.it] + [gamma][Z.sub.it] + [[epsilon].sub.it] (1) where [y.sub.it] is a cost measure for firm i at time t, [[beta].sub.0] is the intercept, [[beta].sub.0i] is a firmspecific random effect with 0 mean and [[sigma].sub.[beta]0.sup.2] variance, [X.sub.it], is a vector of inputs and outputs, and [Z.sub.it] represents firmspecific exogenous Exogenous Describes facts outside the control of the firm. Converse of endogenous. factors (i.e., factors outside the control of the utilities, such as ownership and regulatory characteristics), [[beta].sub.0i] is further assumed to be uncorrelated with [X.sub.it], [Z.sub.it], and [[epsilon].sub.it]. This model is denoted the random effects model In statistics, a random effect(s) model, also called a variance components model is a kind of hierarchical linear model. It assumes that the data describe a hierarchy of different populations whose differences are constrained by the hierarchy. and is estimated using maximum likelihood. A random coefficient version of the random effects model can be specified as: [y.sub.it] = [[beta].sub.i][X.sub.it] + [[gamma].sub.i][Z.sub.it] + [[epsilon].sub.it](2) with [[beta].sub.i] = [beta] + [[theta Theta A measure of the rate of decline in the value of an option due to the passage of time. Theta can also be referred to as the time decay on the value of an option. If everything is held constant, then the option will lose value as time moves closer to the maturity of the option. ].sub.i], E[[[theta].sub.i]  [X.sub.it]] = 0 and E[[[theta].sub.i] [[theta]'.sub.i][X.sub.it]] = [SIGMA] (and similarly for [[gamma].sub.i]) as proposed by Swamy (1970). Empirical implementations of the random coefficient model require an estimator of [SIGMA] and the early applications relied on the empirical variance of n least square estimates. More recent applications use simulated maximum likelihood (McFadden and Train 2000), which is also the estimation technique applied here. Analogously a·nal·o·gous adj. 1. Similar or alike in such a way as to permit the drawing of an analogy. 2. Biology Similar in function but not in structure and evolutionary origin. with Equation (1), Pitt and Lee (1981) suggest that the specification of a dual disturbance panel data function can be formulated as: [y.sub.it] = [[beta].sub.0] + [beta][X.sub.it] + [gamma][Z.sub.it] + [[upsilon up·si·lon or yp·si·lon n. Symbol The 20th letter of the Greek alphabet. ].sub.it] + [u.sub.i] (3) with notations as in Equation (1) and under the assumptions that [[upsilon].sub.it] and [u.sub.i] are uncorrelated and that [[upsilon].sub.it] is also uncorrected with all regressors. [[upsilon].sub.it] represents a normally distributed random error term with mean 0 and variance [[sigma].sub.[upsilon].sup.2], and [u.sub.i] is a halfnormally distributed, timeinvariant inefficiency term with mean 0 and variance [[sigma].sub.u.sup.2] This model is commonly referred to as the stochastic frontier model and is estimated by maximum likelihood. A relevant question at this stage is how observed heterogeneity [Z.sub.it] influences cost as there are at least three alternatives: (1) in the main cost function as displayed in Equation (3); (2) as explanation to a truncated mean A truncated mean or trimmed mean is a statistical measure of central tendency, much like the mean and median. It involves the calculation of the mean after discarding given parts of a probability distribution or sample at the high and low end, and typically discarding an of inefficiency, that is [u.sub.i]~truncated truncated adjective Shortened N([[mu].sub.i], [[sigma].sub.u.sup.2]) with [[mu].sub.i] = [eta][Z.sub.it] as suggested by Stevenson (1980) and later extended to panel data by Battese and Coelli (1995) and Greene (2007); and (3) as heteroskedasticity of inefficiency, that is [[sigma].sub.ui.sup.2] = exp exp abbr. 1. exponent 2. exponential ([lambda][Z.sub.i]) as suggested by Greene (2007). In addition, combinations of these specifications, using whole or parts of [Z.sub.it], could be employed, which introduces a potentially large number of ways in which observed heterogeneity influences cost. The choice of where and how [Z.sub.it] is specified is ultimately an empirical question that will be further dealt with in the subsequent section on model and data properties. Because the assumption that [[sigma].sub.ui.sup.2] is time invariant (programming) invariant  A rule, such as the ordering of an ordered list or heap, that applies throughout the life of a data structure or procedure. Each change to the data structure must maintain the correctness of the invariant. has been found to be a significant restriction, Greene (2005) proposes to add an additional firmspecific random term, which changes Equation (3) to: [y.sub.it] = [[beta].sub.0] + [[beta].sub.0i] + [beta][X.sub.it] + [gamma][Z.sub.it] + [[upsilon].sub.it] + [u.sub.it] (4) with [[beta].sub.0i] being normally distributed with mean 0 and variance [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII ASCII or American Standard Code for Information Interchange, a set of codes used to represent letters, numbers, a few symbols, and control characters. Originally designed for teletype operations, it has found wide application in computers. ]. In a further extension, Greene (2005) also suggests that [beta], [gamma], [eta], and [lambda] can vary over firms with the restriction that they follow a prespecified distribution. Such a random coefficient stochastic frontier model can be written as: [y.sub.it] = [[beta].sub.i][X.sub.it] + [[gamma].sub.i][Z.sub.it] + [[upsilon].sub.it] + [u.sub.it] (5) with [[upsilon].sub.it] ~ N(0, [[sigma].sub.[upsilon].sup.2],) and [u.sub.it] ~truncated N([[mu].sub.it], [[sigma].sub.uit.sup.2]) where [[mu].sub.it] = [[eta].sub.i], [Z.sub.it] and [[sigma].sub.uit.sup.2] = [[sigma].sub.u.sup.2] exp([[lambda].sub.i][Z.sub.it]). Both Equations (4) and (5) are estimated using simulated maximum likelihood. IV. MODEL AND DATA Similar to recent studies, a twooutput system consisting of kWh delivered and number of customers served is adopted (Cronin and Motluk 2007; Goto and Tsutsui 2008). Garcia and Thomas (2001) claim that amount of physical output and number of customers are a superior representation of output characteristics for utilities compared to any single output measure. The input factors consist of price of capital, labor, and electricity purchased, which also concur CONCUR  ["CONCUR, A Language for Continuous Concurrent Processes", R.M. Salter et al, Comp Langs 5(3):163189 (1981)]. with contemporary procedure (e.g., Farsi, Filippini, and Greene 2006; Kwoka 2005a, 2005b). Price of capital is defined as the sum of depreciation and interest divided by total operational assets. Operational assets are used as a proxy for the stock of capital because inventory data are not available and, as pointed out by Aubert and Reynaud (2005), any capacity measure would not reflect the total capacity or depreciation of capital. (9) Although similar definitions have been used previously for electricity distribution (e.g., Nemoto and Goto 2006), one can note that equity expenses are not included because they are not reported by utilities. This could distort the cost measure if owners' rate of return is timevariant and/or if networks are subject to expansion or termination. However, it has been concluded by the Swedish regulator regulator, n the mechanical part of a gas delivery system that controls gas pressure that allows a manageable flow of drug vapor to escape. regulator see reducing valve. that the variation in Weighted Average Cost of Capital (WACC WACC See: Weighted average cost of capital ) is primarily because of interest variation which is included in this measure. Price of labor is average monthly salaries, net taxes, on a county level as reported by Statistics Sweden Statistics Sweden, or Statistiska centralbyrån (SCB), is the government agency responsible for producing official statistics on Sweden. National statistics in Sweden date back to 1686 when the parishes of the Church of Sweden were ordered to start keeping records on the . Average population labor statistics are regarded as superior to those reported by utilities because the utilities' statistics tend to have unreasonably high variability and a large proportion of missing values In statistics, missing values are a common occurrence. Several statistical methods have been developed to deal with this problem. Missing values mean that no data value is stored for the variable in the current observation. . (10) The price of electricity is included because utilities need to purchase electricity to cover network losses and pay for transit on the high voltage The term high voltage characterizes electrical circuits, in which the voltage used is the cause of particular safety concerns and insulation requirements. High voltage is used in electrical power distribution, in cathode ray tubes, to generate Xrays and particle beams, to network. The price is calculated as the total cost of transit and losses divided by the sum of losses and high voltage deliveries. In their exploration of cost influential factors, Burns and WeymanJones (1996), Filippini and Wild (2001), and Berg, Lin, and Tsaplin (2005) claim that the following factors are relevant: (a) maximum demand on the system, (b) total number of customers served, (c) types of customer, (d) dispersion dispersion, in chemistry dispersion, in chemistry, mixture in which fine particles of one substance are scattered throughout another substance. A dispersion is classed as a suspension, colloid, or solution. of the customers, (e) size of the distribution network (interpreted as distribution area), (f) value placed upon system security, (g) ground characteristics, (h) climate, (i) length of distribution line, (j) transformer capacity, and (k) overhead/underground network mix. (i)(k) are not relevant to include in a cost function since they are regarded, at least partly, to be endogenous endogenous /en·dog·e·nous/ (endoj´enus) produced within or caused by factors within the organism. en·dog·e·nous adj. 1. Originating or produced within an organism, tissue, or cell. to the utilities, and there are no standard routines for handling a system of equations involving frontier and/or random coefficient models; (f) can also be considered as endogenous because utilities generally can operate within a quality interval without affecting the probability of being subject to regulation and quality might be affected by ownership (Buehler, Gartner, and Halbheer 2006). The variables representing the primary focus of this study, ownership and regulatory regime, are included as dummy variables. Utilities are classified as private if the share held by private investors is >0, that is irrespective of irrespective of prep. Without consideration of; regardless of. irrespective of preposition despite if they are minority, majority, or sole owners. (11) A utility is considered publicly owned if there is no involvement of private investors. Utilities that have changed ownership status during the period of investigation are excluded to avoid problems with unrepresentative Adj. 1. unrepresentative  not exemplifying a class; "I soon tumbled to the fact that my weekends were atypical"; "behavior quite unrepresentative (or atypical) of the profession" transitional behavior. Utilitylevel measures of these variables, except for climate and ground characteristics, are provided by the Swedish Energy Markets Inspectorate. All variables outlined in the paragraph above, except climaterelated indicators, have previously been investigated in the context of electricity distribution. The impact of wind speed on cost is well established among practitioners and can also be illustrated from descriptive statistics descriptive statistics see statistics. , with some historical storms having had significant impacts on outages followed by a direct spillover spill·o·ver n. 1. The act or an instance of spilling over. 2. An amount or quantity spilled over. 3. A side effect arising from or as if from an unpredicted source: effect on cost of repairs. Similar extreme weather conditions have shown that large amounts of wet snow also increase the probability of outages. Variables indicating the yearly frequencies of days with a maximum wind speed above 20 m/s and of days with more than 20 mm of wet snow fallen are constructed. Climate data are collected from 154 weather stations operated by the Swedish Meteorological me·te·or·ol·o·gy n. The science that deals with the phenomena of the atmosphere, especially weather and weather conditions. [French météorologie, from Greek and Hydrological hy·drol·o·gy n. The scientific study of the properties, distribution, and effects of water on the earth's surface, in the soil and underlying rocks, and in the atmosphere. Institute (SMHI SMHI Swedish Meteorological and Hydrological Institute SMHI Sveriges Meteorologiska och Hydrologiska Institut ). The station closest to the center of each distribution area is taken as a proxy for the climate conditions across the distribution area. Data on ground characteristics were collected through a mail survey asking utilities to indicate the present shares of their service areas covered by urban land, forest, agriculture land, water, and remaining ground types. (12) The survey was mailed out in April 2006, and the responses were taken to represent the year 2006 with official county statistics on forest and urban areas used as proxies to derive values for 20002005 and water areas assumed to be constant over the years. The sample used in this study is limited to the utilities returning the survey and restricted by the requirement that a utility must have full data from at least 4 years, including at least 1 year before and one after 2003 when the new regulatory regime was introduced. This generates an unbalanced sample with 493 observations from 74 utilities over the 7 years from 2000 to 2006. The standard procedure in the literature is to place the Z vector in the main cost function of the dual disturbance specifications (see Soderberg 2008 for a literature review), and that is also the strategy adopted here. However, it is conceivable con·ceive v. con·ceived, con·ceiv·ing, con·ceives v.tr. 1. To become pregnant with (offspring). 2. that parts of Z also/rather influence inefficiency, and with regard to the purpose of this study the placement of ownership and regulation will be evaluated in both the main and the inefficiency functions. Hence, the stylized styl·ize tr.v. styl·ized, styl·iz·ing, styl·iz·es 1. To restrict or make conform to a particular style. 2. To represent conventionally; conventionalize. representation of the cost function can be expressed as: C = C(X, [Z.sub.1]) = C(Y, [P.sub.K], [P.sub.L], [P.sub.E], Den, Con, Urb, For, Agri, LowV, Sn_ov20, Ws_ov20, Priv, Reg) (6) and for the dual disturbance models the additional possibility of: u = u([Z.sub.2]) = u(Priv, Reg) (7) with variable definitions displayed in Table 1. A flexible translog form is chosen to model Equation (6) and homogeneity Homogeneity The degree to which items are similar. is achieved by normalizing the cost and input prices by the price of electricity. A homothetic functional form is applied, excluding interactions between input/output variables and remaining variables in the X vector, to reduce multicollinearities. This allows us to write Equation (6) as (with fixed coefficients): [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (8) TABLE 1 Descriptive Statistics Variable Description Mean (SD) Max Min C Total cost ('000 34,448 (27,327) 174,097 2,600 SEK) (a) Y Electricity 225,609 (230,262) 1,198,093 10,864 delivered ('000 kWh) [C.sub.u] Number of customers 11,362 (11,456) 66,422 770 [P.sub.E] Price of purchased 0.073 (0.026) 0.163 0.016 electricity; total cost of purchased electricity divided by total kWh purchased (SEK/kWh) (a) [P.sub.K] Price of capital; 0.104 (0.061) 0.579 0.023 interest plus depreciation divided by value of fixed assets (SEK/SEK) (a) [P.sub.L] Price of labor; 18,495 (897) 20,913 16,900 average total labor cost (SEK/employee) (a) Den Customer density 90.52 (115.40) 473.20 1.49 (customers/ [km.sup.2]) Con Average customer 20,133 (8,399) 83,839 9,737 consumption (kWh/no. of customers) Urb Urban area share11 0.308 (0.319) 1 0 For Forest area share1' 0.392 (0.266) 0.953 0 Agri Agriculture area 0.252 (0.244) 0.887 0 share LowV Low voltage 0.782 (0.153) 1 0.163 electricity share Ws_ov20 Number of days 0.233 (0.965) 8 0 maximum daily wind speed has exceeded 20 m/s Sn_ov20 Number of days total 0.075 (0.350) 4 0 amount of daily wet snow fallen has exceeded 20 mm Priv Dummy variable to 0.12 (0.32) 1 0 indicate whether utility is privately owned Reg Dummy variable to 0.58 (0.49) 1 0 indicate incentivebased regulation (a) Monetary values are deflated with Swedish consumer price index and expressed in year 2000 values. (b) Source: Statistics Sweden, www.scb.se (c) Source: Swedish National Forest Inventory, www.svo.se where T is a linear trend and corresponds to [[epsilon].sub.it]in Equations (1) and (2) and to [[upsilon].sub.it] + [u.sub.it] in Equations (3)(5). In determining whether u in Equation (7) has a heterogeneous mean and/or is heteroskedaslic, preliminary estimations reveal that only the heteroskedastic alternative is estimable es·ti·ma·ble adj. 1. Possible to estimate: estimable assets; an estimable distance. 2. Deserving of esteem; admirable: an estimable young professor. , indicating that the estimation is not able to handle the multicollinearity problem caused by [Z.sub.2] both in the mean and in the variance. (13) Hence,[u.sub.it] has a halfnormal distribution with mean 0 and variance [[sigma].sub.it.sup.2] which can be written as (with fixed coefficients): [mu] = 0 (9) [[sigma].sub.ui.sup.2] = exp([lambda][Z.sub.2it]) = exp([[lambda].sub.0] + [[lambda].sub.1]Priv + [[lambda].sub.2]Reg) (10) It is important to point out that because E[u.sub.it][micro] = [micro]([Z.sub.it])], = [micro] + [[sigma].sub.u] [empty set]([micro]/[[sigma].sub.u]/[PHI phi n. Symbol The 21st letter of the Greek alphabet. PHI, n See health information, protected. ]([micro]/[[sigma].sub.u]with [empty set]and [PHI] denoting probability standard density function and cumulative standard distribution function respectively, E[u.sub.it]] will be >0 even when [micro] = 0. In fact, Greene (2007) shows that E[u.sub.it][micro] = 0] = 0.79788[[sigma].sub.uit]. An increase in [[sigma].sup.2.sub.ui]can therefore be interpreted as an increase in inefficiency. V. ESTIMATION To evaluate the effects from a single versus dual disturbances, a timeinvariant versus a timevariant inefficiency for the dual disturbance and fixed versus random slope coefficients, in addition to the different locations of Priv and Reg for the dual disturbance models, there are nine specification alternatives. This number would increase multiplicatively if the number of random coefficients was allowed to vary, and hence only the primary variables of interest Priv and Reg are evaluated under random properties. Using Limdep 9.0, preliminary estimations reveal that the dual disturbance model with random intercept and fixed slope coefficients for Priv and Reg specified in either Equation (8) or Equation (10) do not provide any unique information and the likelihood function is inestimable in·es·ti·ma·ble adj. 1. Impossible to estimate or compute: inestimable damage. See Synonyms at incalculable. 2. when Priv and Reg are random in both Equation (8) and Equation (10). This reduces the relevant number of specification alternatives to six. We first turn to the preferred specification, that is Equation (5), which has a dual disturbance structure and random slope coefficients to account for a costminimizing behavior and unknown/uncertain heterogeneity. Both versions of Equation (5) are displayed in Table 2 together with the rest of the dual disturbance specifications. With random coefficients in Equation (8), it is suggested that private utilities are significantly more efficient at the frontier (significant at the 1% level) and with random coefficients in Equation (10) we find that the revised incentivebased regulatory regime has significantly reduced the magnitude of the inefficiency (significant at the 5% level) but that the mean frontier is unaffected. Standard deviations for these coefficients are highly significant, which suggests that unobserved/unknown heterogeneity cannot be disregarded dis·re·gard tr.v. dis·re·gard·ed, dis·re·gard·ing, dis·re·gards 1. To pay no attention or heed to; ignore. 2. To treat without proper respect or attentiveness. n. . The costreducing effect from the revised incentive regulation could in fact be even more significant than revealed by this estimation because it is expected that utilities are going through a transition period, and the positive trend coefficient may indicate that utilities have experienced increased costs as a consequence of adapting to the new regulatory requirements. Consequently, these outcomes allow us to accept H1, H2, and H3. TABLE 2 Output from Dual Disturbance Model Estimations Random Random Effects with Effects: Timevariant Inefficiency: Equation (3) Equation (4) Variable Coefficient Coefficient SD Random (SE) (SE) Coeff. (SE) Main cost function (i.e.. Equation [8]) Constant 0.2839 0.2186 *** 0.1226 *** (0.3695) (0.0622) (0.0037) InY 0.9400 *** 0.7841 *** (0.2667) (0.1586) InCu 0.0461 0.2182 (0.2664) (0.1600) In([P.sub.L]/[P.sub.E]) 0.1708 *** 0.1679 *** (0.0324) (0.0156) In([P.sub.K]/[P.sub.E]) 0.1356 *** 0.1514 *** (0.0232) (0.0095) (InY) (2) 0.0997 0.1521 *** (0.1654) (0.0388) (InCu) (2) 0.0199 0.0274 (0.1239) (0.0357) In[P.sub.L]) (2) 0.1967 *** 0.1841 *** (0.0666) (0.0428) (In[P.sub.K]) (2) 0.0463 0.0352 *** (0.0346) (0.0194) InY*InCu 0.1702 0.2351 ** (0.3806) (0.0999) InY * 0.0299 0.0464 In([P.sub.L]//[P.sub.E]) (0.1145) (0.0535) InY * 0.1319 0.1187 *** In([P.sub.K]/[P.sub.E]) (0.1024) (0.0330) InCu * 0.0946 0.0769 In([P.sub.L]/[P.sub.E]) (0.1402) (0.0618) InCu * 0.1500 0.1395 *** In([P.sub.K]/[P.sub.B]) (0.1137) (0.0372) In([P.sub.E]/[P.sub.E]) * 0.4133 *** 0.4029 *** In([P.sub.K]/[P.sub.E]) (0.0701) (0.0410) InDen 0.0540 *** 0.0631 *** (0.0185) (0.0040) In Con 0.3641 0.1944 (0.2595) (0.1591) Low_v 0.0886 0.0551 (0.1222) (0.0350) Ws_ov20 0.0025 0.0040 (0.0102) (0.0037) Sno_ov20 0.0154 0.0176 (0.0190) (0.0112) Fores 0.2599 0.0452 (0.3683) (0.0605) Urb 0.2746 0.1073 ** (0.3808) (0.0566) Agri 0.2393 0.0651 (0.3593) (0.0554) T 0.0076 0.0085 * (0.0054) (0.0047) Priv 0.0412 0.0090 (0.0545) (0.0175) Reg 0.0138 0.0175 (0.0217) (0.0212) Priv * Reg 0.0061 0.0084 (0.0178) (0.0173) Variance of inefficiency, (i.e. Equation [10]) Constant 0.0816 (0.3561) Priv 0.4335 ** (0.2108) Reg 0.1288 (0.2476) [[sigma].sub.v] 0.0669 0.0559 [[sigma].sub.u] 0.2186 0.0593 [lambda] 3.2643 1.0616 Log likelihood 520.18 526.72 Halton draws 200 n 493 493 Random Coefficient: Random Coefficient: Equation (5) Equation (5) Variable Coefficient SD Random Coefficient SD Random (SE) Coeff. (SE) (SE) Coeff. (SE) Main cost function (i.e.. Equation [8]) Constant 0.3331 *** 0.1261 *** 0.3076 *** 0.1331 *** (0.0572) (0.0037) (0.0582) (0.0040) InY 0.8461 *** 0.7784 *** (0.1371) (0.1413) InCu 0.1627 0.2288 (0.1388) (0.1422) In([P.sub.L]/ 0.1488 *** 0.1821 *** [P.sub.E]) (0.0148) (0.0135) In([P.sub.K]/ 0.1529 *** 0.1481 *** [P.sub.E]) (0.0088) (0.0087) (InY) (2) 0.0574 0.2286 *** (0.0375) (0.0373) (InCu) (2) 0.0374 0.0769 ** (0.0337) (0.0343) In[P.sub.L]) 0.1920 *** 0.1631 *** (2) (0.0416) (0.0369) (In[P.sub.K]) 0.0404 ** 0.0303 * (2) (0.0179) (0.0178) InY * InCu 0.1693 * 0.4447 *** (0.0956) (0.0973) InY * 0.0086 0.0634 In([P.sub.L]/ (0.0487) (0.0488) [P.sub.E]) InY * 0.1324 *** 0.1003 *** In([P.sub.K]/ (0.0299) (0.0309) [P.sub.E]) InCu * 0.1452 *** 0.0344 In([P.sub.L]/ (0.0568) (0.0559) [P.sub.E]) InCu * 0.1497 *** 0.0983 *** In([P.sub.K]/ (0.0331) (0.0338) [P.sub.B]) In([P.sub.E]/ 0.3906 *** 0.4234 *** [P.sub.E]) * (0.0405) (0.0390) In([P.sub.K]/ [P.sub.E]) InDen 0.0653 *** 0.0635 *** (0.0038) (0.0037) In Con 0.2634 * 0.2250 (0.1389) (0.1410) Low_v 0.1319 *** 0.0196 (0.0335) (0.0331) Ws_ov20 0.0025 0.0044 (0.0033) (0.0035) Sno_ov20 0.0215 ** 0.0155 (0.0107) (0.0103) Fores 0.1047* 0.1754 *** (0.0559) (0.0590) Urb 0.1133 ** 0.1818 *** (0.0524) (0.0539) Agri 0.0103 0.1171 ** (0.0512) (0.0530) T 0.0077 ** 0.0076 *** (0.0036) (0.0025) Priv 0.0491 *** 0.0428 *** (0.0138) 0.0087 Reg 0.0086 0.0582 *** (0.0140) 0.0041 Priv * Reg 0.0143 (0.0158) Variance of inefficiency, (i.e. Equation [10]) Constant 0.5313 (0.3632) Priv 0.0953 0.7029 * (0.4993) (0.4332) Reg 1.9248 ** 2.1850 *** (0.8464) (0.6074) [[sigma].sub.v] 0.0417 0.0578 [[sigma].sub.u] 0.0694 0.0436 [lambda] 1.6646 0.7546 Log likelihood 539.05 538.22 Halton draws 200 200 n 493 493 *, sig at 10% level; **, sig at 5% level; ***, sig at 1% level. Next, we investigate to what extent variations in assumptions regarding utility behavior and unknown/uncertain heterogeneity influence these conclusions. First, the random effects model with timeinvariant inefficiency with properties according to according to prep. 1. As stated or indicated by; on the authority of: according to historians. 2. In keeping with: according to instructions. 3. Equation (3) is unable to attribute any significant influence from Priv or Reg. The random effects Random effects can refer to:
There are two different specification alternatives for the single disturbance model: one with a random intercept according to Equation (1) and one with random intercept and slope coefficients according to Equation (2). There is little to be said a priori a priori In epistemology, knowledge that is independent of all particular experiences, as opposed to a posteriori (or empirical) knowledge, which derives from experience. about these equations because we believe they are grossly misspecified. The estimation outcomes are displayed in Table 3 with Equation (1) suggesting that private utilities are less cost efficient and that the incentive regulation has no effect. Equation (2) does, however, disagree that ownership has a significant effect on the cost level and it confirms the insignificant influence from the incentive regulation. The conclusion that Priv is significant for Equation (1) when slope coefficients are fixed can only be trusted if we have reason to believe that ownership has a direct influence on cost and that utilities do not minimize cost. However, the significant standard deviation for the Priv coefficient with random properties confirms previous conclusions that the influence from Priv is conditioned on heterogeneity, and it also shows that coefficient signs can change if this heterogeneity is not accounted for. As indicated above, one should generally interpret the results from the single disturbance models with care. It has nevertheless been demonstrated that variations in assumptions regarding utility behavior and unknown/uncertain heterogeneity have substantial effects on our conclusions regarding private ownership and regulatory incentives. TABLE 3 Output from Single Disturbance Model Estimations Random Effects: Equation (1) Variable Coefficient (SE) SD Random Coeff. (SB) Main cost function (i.e., Equation [8]) Constant 0.2744 *** 0.1209 *** (0.0616) (0.0037) InY 0.8453 *** (0.1544) InCu 0.1577 (0.1560) In([P.sub.L]/[P.sub.E]) 0.1701 *** (0.0157) In([P.sub.K]/[P.sub.E]) 0.1465 *** (0.0096) (InY) (2) 0.1574 *** (0.0375) (InCu) (2) 0.0148 (0.0350) (In[P.sub.L]) (2) 0.1977 *** (0.0415) (In[P.sub.K]) (2) 0.0445 ** (0.0192) InY * InCu 0.2124 ** (0.0970) InY * In([P.sub.L]/[P.sub.E]) 0.0570 (0.0541) InY * In([P.sub.K]/[P.sub.E]) 0.1205 *** (0.0327) InCu * In([P.sub.L]/[P.sub.E]) 0.0717 (0.0628) InCu * In([P.sub.K]/[P.sub.E] 0.1466 *** (0.0363) In([P.sub.L]/[P.sub.E]) * 0.4028 *** In([P.sub.K]/[P.sub.E]) (0.0409) In Den 0.0625 *** (0.0041) InCon 0.2612 * (0.1555) LowV 0.0673 * (0.0355) Ws_ov20 0.0037 (0.0039) Sn_ov20 0.0193 * (0.0113) For 0.0490 (0.0612) Urb 0.1100 (0.0574) Agri 0.0868 (0.0564) T 0.0087 ** (0.0044) Priv 0.0394 *** (0.0143) Reg 0.0148 (0.0178) Priv * Reg 0.0091 (0.0139) Log likelihood 525.27 Halton draws 200 n 493 Random Coefficient: Equation (2) Variable Coefficient (SE) SD Random Coeff. (SE) Main cost function (i.e., Equation [8]) Constant 0.1838 *** 0.1114 *** (0.0594) 0.0037 InY 0.8648 *** (0.1388) InCu 0.1548 (0.1401) In([P.sub.L]/[P.sub.E]) 0.1625 *** (0.0162) In([P.sub.K]/[P.sub.E]) 0.1376 *** (0.0094) (InY) (2) 0.1041 *** (0.0397) (InCu) (2) 0.0028 (0.0365) (In[P.sub.L]) (2) 0.1908 *** (0.0447) (In[P.sub.K]) (2) 0.0463 ** (0.0185) InY * InCu 0.1214 (0.1023) InY * In([P.sub.L]/[P.sub.E]) 0.0014 (0.0543) InY * In([P.sub.K]/[P.sub.E]) 0.1134 *** (0.0312) InCu * In([P.sub.L]/[P.sub.E]) 0.1218 * (0.0641) InCu * In([P.sub.K]/[P.sub.E] 0.1290 *** (0.0353) In([P.sub.L]/[P.sub.E]) * 0.4229 *** In([P.sub.K]/[P.sub.E]) (0.0418) In Den 0.0609 *** (0.0040) InCon 0.2092 (0.1393) LowV 0.0452 (0.0342) Ws_ov20 0.0040 (0.0037) Sn_ov20 0.0218 ** (0.0104) For 0.0210 (0.0596) Urb 0.0529 (0.0556) Agri 0.0982 * (0.0544) T 0.0085 ** (0.0035) Priv 0.0155 0.0340 *** (0.0151) (0.0107) Reg 0.0178 0.0479 *** (0.0146) (0.0049) Priv * Reg 0.0117 (0.0162) Log likelihood 538.06 Halton draws 200 n 493 *, sig at 10% level; **, sig at 5% level; ***, sig at 1% level. The remaining coefficient estimates are generally consistent in terms of magnitude and sign over the different specifications and also concur with expectations. It is worth noting that no explanatory ex·plan·a·to·ry adj. Serving or intended to explain: an explanatory paragraph. ex·plan power is found for wind speed and there is only a weak positive contribution from snowfall. A more detailed examination of climate threshold values and possible interaction effects, for example, with share of service area covered by forest, should be fruitful fruit·ful adj. 1. a. Producing fruit. b. Conducive to productivity; causing to bear in abundance: fruitful soil. 2. to consider in future studies. VI. CONCLUSIONS The first conclusion is that under the most appropriate model specification(s), and consistent with theoretical predictions, it is confirmed that the Swedish private utilities are more cost efficient compared to its public counterparts and that all utilities have reduced their cost inefficiencies following the introduction of the stronger cost incentives in 2003. It is apparent that utilities have responded to financial incentives because cost reductions are only documented in cases when utilities gain private benefits (i.e., when owners are strongly motivated by financial performance and when the risk of regulatory intervention is reduced). This sends a clear message to those representing publicly owned utilities and regulatory policy makers because private ownership and a carefully designed regulatory regime can reduce the cost level in the utility sectors. This is consistent with conclusions presented by Kumbhakar and Hjalmarsson (1998) based on conditions in the Swedish electricity sector prior to the significant reregulation of the sector in 1996. It does, however, question the voluminous literature suggesting that ownership is only relevant in combination with other market and utility characteristics (e.g., Aroncena and Waddams Price 2002; Berg, Lin, and Tsaplin 2005; Bhattacharyya et al. 1995) and that incentive regulation does not improve cost efficiency (e.g., Goto and Tsutsui 2008; Aubert and Reynaud 2005). As a second conclusion, it is also demonstrated that different econometric specifications related to assumptions on utility behavior/the design of regulatory regime, and the different treatment of unknown/unobserved heterogeneity, can lead to significantly different outcomes in terms of explanatory power, direction, and magnitude in the estimation of utility cost functions. Specifically, the ambiguous empirical outcomes reported in the literature on how utility cost is influenced by variation in ownership and regulatory regime, are replicated, suggesting that the ambiguities are not only attributed to country and sector characteristics or specific interacting effects. The lesson for future empirical evaluations is that model specification(s) should reflect the conditions having an effect on utilities' actual behavior. This recommendation is easily extendable to other sectors and the use of frontier models and random parameters are likely to be justified in more instances than what the literature suggests because economic optimization together with unobserved heterogeneity are the rule rather than exception in empirical evaluations of economic markets. The issue of how utility ownership (under different regulatory regimes) is related to economic efficiency is by no means "solved" in this paper. 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Journal of Productivity Analysis, 18, 2002, 24153. (1.) Competition in industries involving physical infrastructure is artificial in the sense that it is typically based on regulatory benchmarks according to principles first described by Shleifer (1985). (2.) Kumbhakar and Hjalmarsson (1998) find that private utilities are more cost efficient in the Swedish electricity distribution sector and Saal and Parker (2000) find that stronger cost incentives (in the form of stricter price cap boundaries) improve cost efficiency in the English and Wales Wales, Welsh Cymru, western peninsula and political division (principality) of Great Britain (1991 pop. 2,798,200), 8,016 sq mi (20,761 sq km), west of England; politically united with England since 1536. The capital is Cardiff. water and sewerage sector. (3.) The Swedish water and wastewater utilities are fully owned by municipalities and are required to confer to a lighthanded costofservice regulation, whereas private suppliers are allowed in the Swedish district heating sector without having to submit to economic regulations. (4.) Regulators in Europe often rely on RPIX and price/revenue cap models following Littlechild (1983), and in the United States United States, officially United States of America, republic (2005 est. pop. 295,734,000), 3,539,227 sq mi (9,166,598 sq km), North America. The United States is the world's third largest country in population and the fourth largest country in area. , performancebased regulation has mainly been in the form of price caps or profit sharing profit sharing, arrangement by which employees receive, in addition to their wages, a share of the net profits of a business. The purpose is to give them an incentive to increase their output through enhanced morale, less wasteful use of materials, better care of schemes and the result of agreements between public utility commissions and individual utilities. (5.) Inefficiency has been claimed to be limevariant because of technical progress and continuous organizational learning. In addition, Alvarez, Arias, and Greene (2004) claim that inefficiency could vary even under constant management efficiency. (6.) Publicly owned utilities can be further divided into state companies, municipal companies, municipal utilities, and cooperatives. However, that level of detail does not change the conclusions in subsequent sections, nor docs it provide any additional insights. Hence, this study only contrasts publicly and privately owned utilities. (7.) The cost of the fictitious Based upon a fabrication or pretense. A fictitious name is an assumed name that differs from an individual's actual name. A fictitious action is a lawsuit brought not for the adjudication of an actual controversy between the parties but merely for the purpose of network is determined by number of customers, where customers are located within the service area, energy delivered, and the level of power. Jamasb and Pollitt (2008) provide a more detailed description of the Swedish incentive model. (8.) See Joskow and Schmalensee (1986) for a review of the main regulation models, Coelli, Rao, and Battese (2005) for detailed discussion of the benchmarking techniques, and Jamasb and Pollitt (2001) for a survey of regulatory benchmarking used in the electricity sector. (9.) The Pearson correlation between assets and different capacity measures are generally high with assetsline length having a correlation value of 0.901 and assetstransforming capacity a value of 0.972 (based on statistics from 2007). (10.) The problem with labor statistics reported by utilities is because of nonperfect reporting of labor resources being shared among several utility and/or local government services. (11). The representation of ownership was elaborated with, for example, % of shares held by private investors and dummy to indicate if private investors hold a majority of shares, but the conclusions were not significantly affected by variation in definition. (12.) Every ground type classified as "remaining" could be referred to as either forest or agricultural. (13.) It should be emphasized that there are no economic arguments for where to place Z and that a heteroskedastic specification is just as likely as any other specification. ABBREVIATION WACC: Weighted Average Cost of Capital MAGNUS SODERBERG * * Financial support from Elforsk/Market design is gratefully acknowledged. For important comments and suggestions on a number of earlier versions. I am indebted in·debt·ed adj. Morally, socially, or legally obligated to another; beholden. [Middle English endetted, from Old French endette, past participle of endetter, to oblige to Ted Lindblom, Mans Soderbom. seminar participants at University of Gothenburg, the coeditor (Robert J. Michaels), and an anonymous referee. The usual disclaimer applies. Soderberg: Centre for Regulation and Market Analysis, School of Commerce, University of South Australia South Australia, state (1991 pop. 1,236,623), 380,070 sq mi (984,381 sq km), S central Australia. It is bounded on the S by the Indian Ocean. Kangaroo Island and many smaller islands off the south coast are included in the state. , GPO Box 2471, Adelaide, SA 5001, Australia. Phone 61883020601, Fax 61883027001, Email magnus. soderberg@unisa.edu.au doi: 10.1111/j. 14657287.2010.00209.x 

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