# Peruvian Electrical Distribution Firms’ Efficiency Revisited: A Two-Stage Data Envelopment Analysis

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## Abstract

**:**

## 1. Introduction

## 2. First Stage Estimation: DEA Models, Data and Results

_{h}and y

_{h}are the inputs and outputs of the firm under evaluation. The efficiency of the evaluated firm is represented by θ. The constant returns to scale model (CRS) can be modified to assume variable returns to scale (VRS) by incorporating the convexity restriction; this is N1′ λ = 1, where N1 is one of a number of vectors.

## 3. Two-Stage Data Envelopment Analysis

#### 3.1. Brief and Critical Review of the Two-Stage DEA Literature

#### 3.2. Review of the Two-Stage DEA Power Distribution Literature

## 4. Two-Stage Data Envelopment Analysis (DEA): Results

#### 4.1. Two-Stage Drivers

#### 4.2. Alternative Models and Results

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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Variable | Sales (MWh) | Customers (Number) | Workers (Number) | Net Fixed Assets (Thousands of Soles in 1994) | Losses (MWh) |
---|---|---|---|---|---|

Mean | 971,650 | 302,945 | 264 | 434,214 | 96,808 |

Minimum | 33,327 | 19,743 | 19 | 22,784 | 4675 |

Maximum | 7,185,542 | 1,293,552 | 787 | 2,088,524 | 536,922 |

Standard deviat. | 1,553,483 | 280,244 | 188 | 460,151 | 121,545 |

Company | ET CRS | ET VRS | ES | |||
---|---|---|---|---|---|---|

1996 | 2014 | 1996 | 2014 | 1996 | 2014 | |

Edecañete | 1.000 | 0.651 | 1.000 | 1.000 | 1.000 | 0.651 |

Edelnor | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 |

Electro Oriente | 0.632 | 1.000 | 0.638 | 1.000 | 0.991 | 1.000 |

Electro Puno | 1.000 | 0.799 | 1.000 | 0.847 | 1.000 | 0.943 |

Electro Sur Este | 1.000 | 0.915 | 1.000 | 0.916 | 1.000 | 0.998 |

Electro Sur Medio | 0.697 | 1.000 | 0.711 | 1.000 | 0.980 | 1.000 |

Electro Ucayali | 0.838 | 1.000 | 1.000 | 1.000 | 0.838 | 1.000 |

Electro Centro | 0.864 | 1.000 | 1.000 | 1.000 | 0.864 | 1.000 |

Electro Noroeste | 0.780 | 0.963 | 0.784 | 1.000 | 0.995 | 0.963 |

Electro Norte | 0.961 | 0.945 | 0.975 | 0.947 | 0.986 | 0.998 |

Electro Sur | 0.948 | 1.000 | 0.997 | 1.000 | 0.950 | 1.000 |

Hidrandina | 0.572 | 0.868 | 0.623 | 0.993 | 0.918 | 0.874 |

Luz del Sur | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 |

Seal | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 |

Average | 0.878 | 0.939 | 0.909 | 0.979 | 0.966 | 0.959 |

Study | Data | Method | FS Variables | SE Regression Variables |
---|---|---|---|---|

[15] | NDF = 12C = ColombiaP = 1985–2001 | FS: lnput-oriented DEA CRS & VRS modelSE: OLS pooled; Tobit pooled and Tobit random-effects panel regressions | I: Worker in distribution & commercialization (number), Transformer & Substations (number), Network (km); Regional GDP per capita, Installed generation capacityO: Sales (GWh), Customers (number), Area served (Km^{2}) | DVSE: DEA TE CRS & SE scores depending on the model.CVSE: Sales-GWh/Transf; Sales-GWh/lines; Subscribers per Km^{2}; Urban Area (Km^{2}); Industrial/residential sales; Log PPE; Log (sales/PPE); Oper-income/net worth; Loss index; Industry-adjusted loss index; Regulation; Business |

[3] | NDF = 14C = PeruP = 1996–2006 | FS: lnput-oriented DEA VRS modelSE: Tobit random-effects panel regression and Mann-Whitney Test | I: Worker (number), Net Assets (000 Soles), Losses (MWh)O: Sales (MWh), Customers (number) | DVSE: DEA TE VRS scoresCVSE: Investment per client; Low-medium voltage sales ratio; Mountains and Jungle indexes; Reform; DProp. |

[33] | NDF = 12C = UKP = 1996/06–2002/03 | FS: Cost minimization DEA VRS modelSE: Tobit pooled regression | I: OPEX; TOTEX; Duration of interruptions; Losses (GWh)IP: 1 (for TOTEX & OPEX), Willingness-to-pay (Duration of interruptions); Energy price (Losses)O: Customers (number); Network length; Energy delivered | DVSE: DEA ET & EE scores depending on modelCVSE: Weather index I (Minimum temperature, air frost, ground frost and concrete temperature); Weather index II (maximum temperature, thunder, hail land gale) |

[30] | NDF = 73C = USAP = 1994–2003 | FS: lnput-oriented DEA CRS modelSE: GLS estimation with fixed effects. | I: OPEX or TCEX depending on the modelO: Sales (MWh); Customers (number); Network length | DVSE: DEA CRS scoresCVSE: POST-DIVEST = dummy for major divestiture or series of timing dummies POST1, POST2, POST6 for successive years after the particular utility’s major divestiture, depending on the model; POST-MAND = if divesture was mandated; POST-NON = if divesture was not mandated; Residential-total sales ratio |

[29] | NDF = 73C = USAP = 1994–2003 | FS: lnput-oriented DEA CRS modelSE: GLS with random effects. | I: OPEX or TCEX depending on the modelO: Sales (MWh); Customers (number); Network length | DVSE: DEA CRS scoresCVSE: PRE = sets of years before merger; POST = sets of years after merger; GROUP subsets of utilities (buyers vs. sellers, buyers vs. non-merging utilities, etc.); Residential-total sales ratio; Distribution output generated by the utility itself (%); Adjacent dummy (physical proximity of the merging units); Twomergers dummy |

[31] | NDF = 127C = NorwayP = 2004–2007 | FS: DEA VRS model with weight restrictions related to environmental conditionsSE: Tobit regression | I: TOTEX (including the interruptions’ costs)O: Cottage customers (number); Regular customers (except cottages) (number); Energy delivered (MWh); High voltage lines (Km); Network stations transformers (number), Interface Environmental conditions: forest, snow and coast/wind. | DVSE: DEA TE VRS scores CVSE: Firm remaining life span, Size (total cost); Environmental conditions (Forest, Coast and Snow indexes). |

[32] | NDF = 21C = TurkeyP = 2002–2009 | FS: lnput-oriented DEA VRS modelSE: Tobit pooled regression | I: Worker (number); Network length (km); Transformer capacity (MVA); Outage hours per customer; Loss & theft ratio. O: Energy delivered (MWh); Customers (number) | DVSE: DEA TE VRS scores CVSE: Customer density; Customer structure (%); Restructuring; ownership; Loss & theft ratio |

[27] | NDF = 61C = BrazilP = 2003–2009 | FS: lnput-oriented DEA-NDRS modelSE: Simar and Wilson (2007) bootstrapped truncated regression | I: OPEX ($)O: Energy Delivered (MWh); Customers (number); Network length (Km) | DVSE: DEA TE NDRS scores CVSE: MS = Mean Salary; PI = natural logarithm of precipitation index; CI = Complexity index; CA = natural logarithm of consumer per area |

[34] | NDF = 13C = IndiaP = 2005–2012 | FS: Conventional & Boostrap DEA modelSE: FGLS and Pooled OLS regression | I: Model 1: Worker (number); Transformer capacity (MVA), Network (km)Model 2: Worker (number); Total Assests ($)O: Electricity delivered (GWh); Customers (number) | DVSE: Conventional & bias-correctedbootstrap efficiency estimates of DEA depending on model CVSE: Tariff ratio; consumer structure (%); Log of Population density (person per Km^{2}); Ownership dummy; Log of Subsidy; Population density x ownership |

[28] | NDF = 61C = BrazilP = 2015 | FS: lnput-oriented DEA-NDRS model with weight restrictions. SE: OLS and Tobit regresions | I: Mean operational costO: Underground network; Overhead network; High voltage network; Consumers (number); Weighted energy market; Non-technical losses; Consumer-hour interrupted energy.(Mean values were calculated using 2011 to 2013) | DVSE: DEA TE CRS & VRS scores depending on the model CVSE: Density of consumers; Network density; Complexity index; Precipitation index; Lightning rate; Low vegetation index; Medium vegetation index; High vegetation index; Mean declivity index; Proportion of paved roads; Concession area (km^{2}); Average duration of interruptions; Frequency of interruptions; e-factor |

[35] | NDF = 14C = AustraliaP for FS = 2009–2017P for SE = 2017 | FS: lnput-oriented VRS DEA model. SE: Simar and Wilson’s(2007) double bootstrap truncated regression | I: Operating Expenditure; Network capacity; Network length (km)O: Electricity delivered (GWh) | DVSE: DEA TE scoresCVSE: Reliability; Average age of poles; Customers (number) |

Present Study | NDF = 14C = PeruP = 1996–2014 | FS: lnput-oriented DEA VRS modelSE: all model proposed in the literature, including fractional models | I: Worker (number), Net Assets (000 Soles), Losses (MWh)O: Sales (MWh), Customers (number) | DVSE: DEA TE scores CVSE: Investment per client; Low-medium voltage sales ratio; Mountains and Jungle indexes; Reform; DProp |

Variable | TE (VRS) | LV/MV | K/N | Jungle | Mountain | Property | Reform |
---|---|---|---|---|---|---|---|

Average | 0.932 | 2.035 | 1.482 | 0.143 | 0.286 | 0.327 | 0.523 |

Minimum | 0.557 | 0.584 | 0.726 | 0.000 | 0.000 | 0.000 | 0.000 |

Maximum | 1.000 | 6.175 | 4.573 | 1.000 | 1.000 | 1.000 | 1.000 |

Standard Deviation | 0.105 | 1.224 | 0.578 | 0.351 | 0.453 | 0.470 | 0.500 |

Variables | Y_{1} | Y_{2} | X_{1} | X_{2} | X_{3} | Θ | Z_{1} | Z_{2} | Z_{3} | Z_{4} | Z_{5} | Z_{6} | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Users | Sales | Employees | Loss | Capital (K) | Vrs | LV/MV | (K/N) | Mountain | Jungle | Reform | T | ||

y_{1} | users | 1 | |||||||||||

y_{2} | sales | 0.9040 | 1 | ||||||||||

x_{1} | employees | 0.8748 | 0.8318 | 1 | |||||||||

x_{2} | loss | 0.9202 | 0.9534 | 0.879 | 1 | ||||||||

x_{3} | capital (K) | 0.9565 | 0.9376 | 0.8581 | 0.925 | 1 | |||||||

θ | vrs | 0.3213 | 0.2699 | 0.1725 | 0.228 | 0.2178 | 1 | ||||||

z_{1} | LV/MV | 0.0146 | −0.169 | 0.0412 | −0.17 | −0.0269 | 0.1577 | 1 | |||||

z_{2} | (K/N) | −0.091 | 0.0459 | −0.0556 | 0.032 | 0.1104 | −0.5402 | −0.0662 | 1 | ||||

z_{3} | mountain | −0.085 | −0.25 | −0.1391 | −0.252 | −0.1476 | 0.1496 | 0.6736 | −0.1772 | 1 | |||

z_{4} | jungle | −0.297 | −0.2 | −0.2862 | −0.223 | −0.2157 | −0.5118 | −0.1333 | 0.5344 | −0.2582 | 1 | ||

z_{5} | reform | 0.4801 | 0.4266 | 0.4249 | 0.415 | 0.4337 | 0.347 | −0.2449 | −0.1935 | −0.3951 | −0.4271 | 1 | |

z_{6} | t | 0.2686 | 0.2007 | 0.0289 | 0.079 | 0.1742 | 0.227 | −0.145 | −0.367 | 0 | 0 | 0.1443 | 1 |

Variable | Logit | Probit | LogLog | Cloglog | ||||
---|---|---|---|---|---|---|---|---|

Coefficient | APE | Coefficient | APE | Coefficient | APE | Coefficient | APE | |

Constant | 1.99 | 1.28 | 2.01 | 0.946 | ||||

(4.346) | (5.449) | (4.437) | (5.679) | |||||

LV/MV | 0.395 | 0.023 | 0.202 | 0.023 | 0.35 | 0.022 | 0.149 | 0.023 |

(3.204) | (3.006) | (3.527) | (3.293) | (3.106) | (2.864) | (3.988) | (3.802) | |

K/N | −0.502 | −0.029 | −0.31 | −0.036 | −0.419 | −0.026 | −0.293 | −0.045 |

(−2.922) | (−2.915) | (−3.52) | (−3.486) | (−2.626) | (−2.583) | (−4.275) | (−4.188) | |

Mountain | 0.224 | 0.013 | 0.066 | 0.008 | 0.26 | 0.016 | 0.014 | 0.002 |

(0.875) | (0.876) | (0.491) | (0.492) | (0.987) | (0.996) | (0.148) | (0.148) | |

Jungle | −0.322 | −0.019 | −0.167 | −0.019 | −0.298 | −0.019 | −0.134 | −0.021 |

(−1.016) | (−1.012) | (−1.028) | (−1.027) | (−0.982) | (−0.976) | (−1.120) | (−1.12) | |

Trend | 0.031 | 0.002 | 0.013 | 0.002 | 0.029 | 0.002 | 0.008 | 0.001 |

(1.484) | (1.449) | (1.243) | (1.224) | (1.475) | (1.435) | (1.094) | (1.089) | |

Reform | 1.14 | 0.067 | 0.556 | 0.065 | 1.1 | 0.069 | 0.4 | 0.062 |

(4.239) | (4.324) | (4.38) | (4.452) | (4.043) | (4.170) | (4.577) | (4.687) | |

Log-likelihood | −44.884 | −44.617 | −45.026 | −44.329 | ||||

R^{2} | 0.366 | 0.379 | 0.358 | 0.394 | ||||

Bootstrap replications | 1000 | 1000 | 1000 | 1000 |

Variable | OLS | Fixed Effect | Random Effect | Tobit | Simar-Wilson | |
---|---|---|---|---|---|---|

Bootstrap | Bootstrap | Bootstrap | Algorithms #2 | |||

Coefficient | Marginal Effects | Coefficient | ||||

Constant | −0.039 | −0.12 | −0.105 | 0.903 | 0.682 | |

(−1.171) | (−1.543) | (−1.214) | (26.885) | (17.942) | ||

LV/MV | 0.016 | 0.029 | 0.026 | 0.023 | 0.013 | 0.025 |

(2.445) | (1.178) | (1.111) | (2.66) | (2.604) | (3.688) | |

K/N | −0.076 | −0.066 | −0.067 | −0.052 | −0.03 | −0.101 |

(−4.422) | (−3.118) | (−3.858) | (−5.381) | (−4.948) | (−7.276) | |

Mountain | 0.005 | − | 0.015 | 0.01 | 0.006 | −0.038 |

(0.275) | (0.217) | (0.252) | (0.252) | (−1.634) | ||

Jungle | −0.077 | − | −0.047 | −0.042 | −0.024 | 0.004 |

(−2.547) | (−0.526) | (−0.9) | (−0.908) | (0.145) | ||

Trend | 0.002 | 0.002 | 0.002 | 0.002 | 0.001 | 0.013 |

(1.932) | (1.092) | (1.072) | (2.219) | (2.184) | (9.312) | |

Reform | 0.052 | 0.109 | 0.099 | 0.084 | 0.048 | 0.109 |

(3.457) | (1.618) | (1.584) | (4.465) | (4.225) | (5.123) | |

Log-likelihood | 247.941 | 321.310 | − | 343.670 | 276.165 | |

ρ | 0.423* | 0.48 | 0.518 | 0.423 | ||

χ^{2} | 247.941 | 13.976 | 20.512 | 108.715 | 405.517 | |

Bootstrap replications | 1000 | 1000 | 1000 | 100/1000 |

^{2}.

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**MDPI and ACS Style**

Pérez-Reyes, R.; Tovar, B. Peruvian Electrical Distribution Firms’ Efficiency Revisited: A Two-Stage Data Envelopment Analysis. *Sustainability* **2021**, *13*, 10066.
https://doi.org/10.3390/su131810066

**AMA Style**

Pérez-Reyes R, Tovar B. Peruvian Electrical Distribution Firms’ Efficiency Revisited: A Two-Stage Data Envelopment Analysis. *Sustainability*. 2021; 13(18):10066.
https://doi.org/10.3390/su131810066

**Chicago/Turabian Style**

Pérez-Reyes, Raúl, and Beatriz Tovar. 2021. "Peruvian Electrical Distribution Firms’ Efficiency Revisited: A Two-Stage Data Envelopment Analysis" *Sustainability* 13, no. 18: 10066.
https://doi.org/10.3390/su131810066