The production inefficiency of US electricity industry in the face of restructuring and emission reduction

Purpose – The paper investigates the production inefficiency of the US electricity industry in the wake of restructuring and emission reduction regulations. Design/methodology/approach – The study estimates a multiple-input, multiple-output directional distance function, using six inputs: fuel, labor, capital and annualized capital costs of sulfur dioxide (SO 2) , nitrogen oxides (NO X ) and particulate removal devices, two good outputs – residential and industrial-commercial electricity and three bad outputs – SO 2 , carbon dioxide (CO 2 ) and NO X emissions. Findings – The authors find that restructuring in electricity markets improves deregulated utilities' technical efficiency (TE). Deregulated utilities with below-average NO X control equipment tend to invest less in these devices, but above-average utilities do the opposite. The reverse applies to particulate removal devices. The whole sample spends more on NO X , particulate and SO 2 control systems and reduces its electricity sales slightly. Increased investments in SO 2 and NO X control equipment do not reduce SO 2 and NO X emissions, but expansions of particulate control systems cut down SO 2 emissions greatly. Stricter environmental regulations have probably shifted the production frontier inwards and the utilities farther from the frontier over time. Practical implications – Restructuring and environmental regulations do not make all utilities invest more in emission control systems. The US government should devise other schemes to achieve this goal. Originality/value – The paper unveils heterogeneous reactions of US electric utilities in the wake of restructuring and emission regulations.


Introduction
Emissions of sulfur dioxide (SO 2 ) and nitrogen oxides (NO X ) from electric generating units (EGUs) and other large combustion sources contribute to the formation of ozone. High concentration of ozone at ground level can exacerbate respiratory diseases and raise susceptibility to respiratory infections. It can also damage sensitive vegetation, causing loss of diversity that may reduce the value of real property (US EPA, 2022). Serious health and ecological hazards of air pollution have brought about remarkable changes in environmental regulations, which began with the Clean Air Act Amendments of 1990 (Aldy et al., 2022). Accordingly, several programs have been established to require power utilities to reduce SO 2 and NO X emissions through cap-and-trade (CAT) systems. These programs set a cap on regional emissions and provide individual emission sources with flexibility in how they comply with emission limits.
It has long been recognized that this approach could coordinate pollution abatement activities highly effectively (Cicala, 2022). Fowlie (2010) argued that preexisting distortions in output markets might hinder the CAT programs from operating efficiently. Restructuring in electricity markets could induce deregulated plants to choose less capital-intensive control technology as compared to regulated or publicly owned plants. Since regulated utilities enjoy a guaranteed rate of return on capital investment, they tend to relatively overcapitalize their control devices. Fowlie (2010) assumed that plant managers would choose a compliance strategy that minimizes a weighted sum of expected annual compliance costs and capital costs. There is, though, implied separability of emission control and electricity generation. It is probably more reasonable to expect that power plant managers would decide on an environmental compliance option based on not only its costs but also other indicators relevant to plant operation. This paper puts those managers' decisions in a broader view by examining production efficiency of US electric utilities in light of multiple inputs and multiple outputs.
To that end, we extend Fu's (2009) dataset by adding annualized capital costs spent on SO 2 , NO X and particulate removal devices. We employ a multiple-input, multiple-output directional distance function [1]. It allows us to avoid assuming separability, which may exclude statistically significant interactions among various outputs, and to compute the partial effects between any pair of endogenous variables. We find that restructuring in electricity markets tends to improve technical efficiency (TE) of deregulated utilities since they operate under the discipline of competitive markets. The absence of rate-of-return regulation is likely to decrease capital investment in NO X control equipment only for utilities that have this equipment below average but increase for utilities that have this equipment above average. The reverse applies to particulate removal devices. However, the whole sample spends more on these two as well as SO 2 control systems and reduces its electricity sales slightly.
There are several important interactions among inputs and outputs. Increased capital investments on SO 2 and NO X control equipment do not reduce SO 2 and NO X emissions, respectively. However, expansions in particulate control systems cut down SO 2 emissions greatly. Moreover, larger installations of NO X and particulate removal devices help curb CO 2 emissions marginally. While residential and industrial-commercial electricity sales are substitutable, SO 2 , CO 2 and NO X emissions are generally complementary. Additionally, the utilities have been shifted increasingly farther from the frontier over time. Inward shifting of the production frontier, as well as declining TE and productivity growth, appears to follow the implementation of stricter environmental regulations.
The remainder of the paper is organized as follows. The next section presents properties of the directional distance function and computation of productivity change (PC). Section 3 reports empirical results and conclusions follow in section 4. JED 2. The directional distance function This section follows Agee et al. (2010). Consider a production technology in which electric utilities combine N nonnegative good inputs, x ¼ ðx 1 ; . . . ; x N Þ 0 ∈ R N þ , to produce M nonnegative good outputs, y ¼ ðy 1 ; . . . ; y M Þ 0 ∈ R M þ . A utility's production technology, S(x, y), is given by Sðx; yÞ ¼ fðx; yÞ : x can produce yg; (1) where S(x, y) consists of all feasible good input and good output vectors. We can extend (1) to include "bad" outputs (e.g. SO 2 , CO 2 and NO X emissions). Letỹ ¼ ðỹ 1 ; . . . ;ỹ L Þ 0 ∈ R L þ denote a vector of L bad outputs produced jointly with y. Following Chambers et al. (1998), the output directional distance function is defined as x; y;ỹ; 0; g y ; Àgỹ Á ¼ sup where P(x) is the set of good and bad outputs that can be produced with inputs x and output direction ðg y ; − gỹÞ ≠ ð0; 0Þ. For a given level of inputs, the output directional distance function measures the increase in good outputs (decrease in bad outputs) in the direction g y ð−gỹÞ in order to move to the frontier of P. Differences between the best practice (frontier) and actual outputs are measures of technical inefficiency in a utility's electricity generation. The measure is equal to zero when the utility is on the frontier of P and greater than zero when the utility is below the frontier of P.
The output directional distance function has the following properties: D1. Translation property: D2. g-Homogeneity of degree minus one: x; y;ỹ; 0; g y ; Àg~y Á ; γ > 0; D3. Good output monotonicity: x; y;ỹ; 0; g y ; Àgỹ Á ; D4. Bad output monotonicity: D5. Concavity: x; y;ỹ; 0; g y ; Àg~y Á is concave in À x; y;ỹ Á ; D6. Nonnegativity: x; y;ỹ; 0; g y ; Àgỹ Á ≥ 05 À y;ỹ Á ∈ PðxÞ: The translation property says that increasing y and decreasingỹ by δ-fold of their respective directions will reduce the directional distance by δ. Equation (4) implies that if Production inefficiency of US electricity sector each direction is scaled by γ, then the directional distance will be scaled by γ À1 . The next two expressions (5) and (6) indicate that the directional distance function of a profitmaximizing utility is monotonically decreasing in good outputs and monotonically increasing in bad outputs. Expression (7) imposes concavity of the output directional distance function. In this paper, we impose D1, which will guarantee D2. We can test for D3 and D4. Normalization after estimation of the directional distance function is needed to make sure that D6 holds.
(1) Quadratic output directional distance function. We use a quadratic function to approximate the output directional distance function. In preliminary estimates, the null hypothesis that the squared input terms and the interaction terms among inputs are jointly equal to zero is rejected. We also reject the null hypotheses that the interaction terms between inputs and outputs are equal to zero and that the interaction terms between restructuring (RE) and annualized capital costs (KSO 2 , KNOX, KTSP) spent on SO 2 , NO X and particulate removal devices are equal to zero. The quadratic form of the output directional distance function is as follows: where d i is a dummy variable for utility i, i 5 1, . . ., F and The composite error « it is an additive error with a one-sided component, μ it ≥ 0, which captures technical inefficiency and statistical noise, ν it , assumed to be iid with zero mean. We set the left-hand side of (9) equal to zero for all observations. To meet the translation property D1, we need to impose the following restrictions: Symmetry also is imposed on the doubly-subscripted coefficients in (9). JED Again, following Agee et al. (2010), the fixed-effect approach is used here by including F utility-specific dummy variables to relax the strong distributional assumptions on both the ν it and μ it , and the unlikely assumption of no correlation between the μ it and the explanatory variables that are required in the random-effect approach. The implicit function theorem allows us to examine the partial effect of any individual variable on another variable. For instance, the effect of a good output on another good output is Finally, the effects of an input on a good output and a bad output are −ðv (2) Measuring TE, EC, TC and PC. This subsection follows Agee et al. (2010). Estimation of utility-specific TE, EC, TC and PC proceeds as follows. Since we want to measure EC, TC and PC in terms of percentage changes, we have to transform output directional distance function measures into Malmquist distance function measures. Following Balk et al. (2008), Malmquist output-oriented distance function measures in period t are In the distance function, e it 5 v it þ u it , which are assumed to be two-sided and one-sided error terms, respectively. Taking logs of (13) and using fitted values from (9) transformed by (12), we get or In order to sweep away the statistical noise, b v it , from the composite error, we follow Cornwell et al. (1990) by regressing b e it on F utility dummies and the interactions of time with utility dummies: where the random error term ζ it is uncorrelated with the regressors. The fitted values,ũ it , of (16) are consistent estimates of u it . As u it needs to be nonnegative, we transformũ it by subtractingũ t ¼ min i ðũ it Þ, which is the estimated frontier intercept, and obtainũ F it ¼ũ it −ũ t ≥ 0. Adding and subtractingũ t from the estimated (14) yields Production inefficiency of US electricity sector Þ þũ t is the log of the fitted frontier shadow distance function in period t. Utility i's TE in period t is defined as EC i,tþ1 is the change in TE or the rate of catching up to the frontier from t to t þ 1, defined as Technical change, TC i,tþ1 , is estimated as the difference between ln b D F;tþ1 0 holding all inputs and outputs constant: TC is interpreted as a shift in the frontier over time. Given EC i,t and TC i,t , we obtain PC (3) Standardizing units. As discussed in Agee et al. (2010), the output directional distance function involves inputs and outputs that have different units. We cannot compare a certain absolute increase in kilowatt hours of electricity to an absolute decrease in tons of NO X emissions. We need to standardize all input and output measures to a zero mean and unit variance, except for dichotomous variables. Then the marginal effect of a variable on another variable is in standard deviations.
(4) Choosing direction. Also as discussed in Agee et al. (2010), the direction is not a parameter that can be estimated. Instead, we can preassign the directions with a broad range of values expressing different assumed value judgments relevant to the tradeoffs between good and bad outputs.

Data
The dataset used in this paper is an extended version of the panel of utilities originally analyzed by Fu (2009

JED
The outputs include two good outputs, residential and industrial-commercial electricity (SALR and SALIC), and three bad outputs (SO 2 , CO 2 and NO X emissions). The inputs initially are fuel, labor and capital. The quantity of fuel is the heat content from all fossil fuels burned. The quantities of labor and capital are defined as the ratios of input expenditures to prices.
We compile three new inputs, namely, annualized capital costs KSO2, KNOX and KTSP spent on SO 2 , NO X and particulate removal devices. Since control equipment can be used for several boilers in a power plant, we classify boilers into groups that share the same removal devices. Then we compute attributes of each group based on primary data for specific boilers from the US Energy Information Administration's Forms EIA-767 and EIA-860. These attributes are plugged into the Integrated Environmental Control Model (IECM) developed by the Department of Engineering and Public Policy at Carnegie Mellon University to obtain KSO2, KNOX and KTSP at group level. Finally, we aggregate them up to the utility level.

Empirical results
We standardize the data and estimate the directional distance function (9). Table 1 presents the function estimates corresponding to three alternative sets of direction vectors, following Agee et al. (2010). In column two with an output direction vector ðg y ; − gỹÞ ¼ ð2; − 1Þ, the translation property requires a two standardized unit increase in the good outputs for every one standardized unit decrease in the bad outputs, holding all inputs constant, in order to move towards the frontier. In other words, ðg y ; − gỹÞ ¼ ð2; − 1Þ weights a decrease in bad outputs twice as much as an increase in good outputs. We focus on the output direction vector ðg y ; − gỹÞ ¼ ð1; − 1Þ shown in column three of Table 1 since we assume equal weights on increases in good outputs and reductions in bad outputs.
Before examining partial impacts among the outputs and inputs, we compute the partial derivatives of the directional distance function with respect to the outputs given in Table 2. They are averages weighted for electricity sales (including residential and industrial commercial) made by utilities [2]. The directional distance function is decreasing in the good outputs (i.e. residential and industrial-commercial electricity sales) and increasing in the bad outputs (i.e. SO 2 , CO 2 and NO X emissions). These results are consistent with the properties D3 and D4 stated above.
In addition, the directional distance function is decreasing with industry restructuring. This variable has an average partial effect of À0.0241. It implies that, in markets where electricity prices are no longer set by state regulators but determined by competitive markets instead, deregulated utilities are closer to the frontier. The discipline of competitive markets improves their performance, as expected. However, the partial effect of restructuring on KNOX is different from Fowlie's (2010) findings (see Table 3). While below-average utilities (with KNOX below average) in deregulated markets tend to invest 20% less on NO X control equipment, above-average utilities (with KNOX above average) tend to invest 50.7% more. The story for KTSP is the opposite. Restructuring induces below-average utilities to spend 2.66% more and above-average utilities to spend marginally 0.87% less on particulate control systems. However, for the whole sample, restructuring increases annualized capital costs for NO X , particulate as well as SO 2 removal devices. Further, as a result of restructuring, these utilities reduce their residential and industrial-commercial electricity sales by 0.06 and 0.87%, respectively.
As power plants face more and more stringent environmental regulations on emissions, they have to switch to "greener" fuels or technologies, install more expensive removal devices, buy emission permits whose overall limits are decreasing, reduce plant utilization or even stop generation. Either compliance strategy means that they operate increasingly farther from the best-practice frontier than in the absence of these restraints. This is reflected by a positive and significant estimate of 0.010 for the time variable.

Production inefficiency of US electricity sector
Variable Coefficient (Standard error)

JED
Regarding partial effects among the outputs, the estimated coefficients of the quadratic function between SALR, SALIC, SO 2 , CO 2 and NO X emissions indicate that these good and bad outputs may be substitutes or complements. Table 4 shows that a 10% increase in residential electricity sales is associated with a reduction of 39.7% in industrial-commercial electricity sales for below-average utilities (with both SALR and SALIC below average) and a reduction of 21.5% for above-average utilities (with both SALR and SALIC above average) [3]. These two good outputs are understandably substitutable since electricity generated is sold for either residential or industrial-commercial usage. CO 2 and SO 2 emissions are also substitutable for two groups of utilities. However, taking into account utilities having one emission below average and the other emission above average, CO 2 and SO 2 emissions are complementary for the whole sample [4]. NO X emissions have a complementary relationship with CO 2 and SO 2 emissions for both groups of utilities and for the whole sample.
We also compute the partial effects of SALR and SALIC on SO 2 , CO 2 and NO X emissions. Larger SALR and SALIC sales typically raise SO 2 and CO 2 emissions, but their impacts on SO 2 emissions vary greatly across two groups. Ten percent increases in SALR and SALIC boost SO 2 emissions from below-average utilities by 16,468 and 5,172 percent, respectively. Meanwhile, SO 2 emissions from above-average utilities rise by 267 and 73%. However, higher SALR and SALIC tend to reduce NO X emissions. Now we consider the partial impacts of the inputs on the outputs in Table 5. Holding other things constant, an expansion in capital generally decreases residential but increases industrial-commercial electricity sales slightly. Increases in fuel and labor lead to small reductions in electricity sales. As these power generating facilities invest 10% more on SO 2 control equipment, their SO 2 emissions decrease only for above-average utilities by 7.4% but Note(s): Direction: g y ¼ 1; − gỹ ¼ −1 Table 2. Partial derivatives of the directional distance function with respect to outputs Table 3. Partial effects of restructuring (percent) Production inefficiency of US electricity sector strikingly increase for below-average utilities by 347.2%. Hence, for the whole sample, SO 2 emissions rise by 85%. The same holds for NO X control equipment, although its partial effects on NO X emissions on both groups are reversed. However, larger KTSP installations cut down SO 2 emissions greatly, especially for below-average utilities. In addition, increases in KTSP and KNOX help curb CO 2 emissions marginally. Table 6 provides estimated technical efficiencies for the direction vector (1, À1) for the good and bad outputs. Technical efficiencies are computed using (18). The weighted-average TE of the 78 utilities in 1988 is 0.87. This measure implies that if the average utility that year were to combine its inputs as effectively as the best-practice utility, then its electricity sales (SO 2 , CO 2 and NO X emissions) would increase (decrease) by about 15% (1/0.87 5 1.15). Between 1988 and 1995, average TE rose from 0.87 to 0.98 but at a decreasing rate. However, after Phase I of the Acid Rain Program came into effect in 1995, the average TE started to decline at an increasing rate from 0.96 in 1996 to 0.93 in 2000. The downward trend reversed in 2001 and then continued its momentum afterward. The short improvement in TE in 2001 is probably attributed to previous adjustments by these utilities to comply with earlier requirements to reduce emissions. By then, several utilities had even stopped their electricity generation. However, this improvement was quickly undermined by stricter environmental regulations. Table 7 displays average PC, TC and EC, which are calculated using expressions (21), (20) and (19). Technical change, which measures the shift in the production frontier, exhibits a pattern of change similar to that of TE. The frontier first shifted outward at a decreasing rate, but began shifting inward in 1994, earlier than the trend decrease in TE. The inward shift was also interrupted in only 2001. The resulting PC, which is the sum of TC and EC, closely resembles them. The average utility tended to experience declining productivity over time. Note(s): Direction: g y ¼ 1; − gỹ ¼ −1 Table 6. Average utility technical efficiencies Table 5. Partial effects of inputs on outputs