Heteroskedastic Stochastic Cost Frontier Approach in the Estimation of Cost Efficiency of Tunisian Water Distribution Utilities Tawfik Ben Amor,PhD and Thuraya Mellah, MD Higher School of Digital Economy-University of Manouba LEF A Laboratory- IHEC Carthage Presidency Tunisia Methods Abstract Model I does not have the ability to distinguish between cost inefficiency and unobserved heterogeneity of the firms. Model II is an heteroskedastic frontier model formulated in the following way: For the two model cost inefficiency score for firm i at time t can be defined as: EFF takes values greater than one unless a firm is fully efficient. Economies of output density and economies of scale measure respectively are defined by: The purpose of this paper is to explore if some limitation of conventional stochastic frontier model can be overcome cost inefficiency scores. For that purpose, we use à number of alternative methodologies for comparing firm’s efficiency. We use an original dataset base of Tunisian Water Utility (TWU) that consist of an unbalanced panel of it's district water agencies observations observed over the period 1999-2009. The investigation examined also the Stochastic Frontier Approach (SFA) and the Fixed Effects Model (TFE). Keywords Stochastic Cost Frontier Function Cost inefficiency level Economies of Output Density Economies of Scale . Chart 1. cost inefficiency scores by region . Discussion Economies of output density (EOD) are present for all three types of regions with respect to size. Since EOD > 1, a 1% increase in cost (C) is associated with a more than 1% increase in the amount of water distributed (Q), holding the number of customers (CU) and the size of the service area (AS) constant. It would therefore be beneficial for region’s water if they managed to distribute larger amounts of output to the existing customers within their service areas. EOD are the highest for small utilities, followed by medium-sized utilities and large utilities. Economies of scale are also present in medium-sized District, where they are close to one. This is also an indication that the optimal size of Tunisian water distribution utilities is relatively close to the median point of the sample. The median company (Sousse) corresponds to a region with an annual water supply of 2,047 million cubic meters and 63,65 kilometers of service area size (connection). This model (model II) treats firm-specific time-invariant fixed effects (αi) and time-varying inefficiency (uit) separately and is therefore able to distinguish between the unobserved heterogeneity and inefficiency. Introduction Conventional water resource exploitation in Tunisia is achieving its limits in the near future. Thus, a strategy for managing water demand or rather water conservation has been adopted. This strategy is based on a set of regulatory, institutional, technical, economic measures. This investigation has the purpose of determining the gap between the efficient cost and real cost of Tunisian water distribution utility. Over the period 1999 and 2009. For this subject we use tow cost specification such as: Stochastic Frontier Approach (SFA) and true fixed effect model (TFE) (2005a, b) . For these specifications, we consider that TWU uses three inputs, labour (Pl), capital (Pk) and material (PM). to distribute a single output to a number of customers within its service area of size. The customer size and the area size can be considered as output characteristic variables. The output characteristics are included as explanatory variables to control for the cost differences that occur merely due to the heterogeneity of output. Cost inefficiency Score is the ratio between the actual cost and the efficient cost (minimum) Economies of Output Density measure the reaction of costs to an increase in output, holding the number of customers and the size of the service area constant. Economies of Scale measure the reaction of costs when the output, the number of customers and the area size increase proportionally. It is assumed that customer density and output per customer are held fixed. Models for this study are estimated by Maximum Likelihood Estimates are performed using the Stata10 software. Results By employing the pooled stochastic frontier model (Model I), the average cost inefficiency is estimated to vary between 5% to 130%. Furthermore, the average cost inefficiency based on the true fixed effects model (Model II) is estimated to vary between 3% to 95%. Since EOD > 1, a 1% increase in cost (C) is associated with a more than 1% increase in the amount of water distributed (Q), holding the number of customers (CU) and the size of the service area (AS) constant. The economies of scale (ES) equal the inverse of the percentage change in costs when the output, number of customers and area size increase by 1%. The results show that substantial economies of scale are present in smaller companies (ES > 1). Conclusions In ²²²this paper, we reconsider the estimation of two models such as the stochastic frontier and the “true” fixed-effects stochastic frontier, These models have for purpose to estimate cost inefficiency for the sample of Tunisian water distribution utilities over the 1999-2011 period. From the methodological point of view the empirical results show that conventional stochastic frontier models tend to overestimate cost inefficiency since the inefficiency estimates also contain unobserved heterogeneity, The true fixed effects model seems to be able to distinguish between unobserved heterogeneity and inefficiency but it may underestimate the inefficiency since all time-invariant effects are treated as unobserved heterogeneity. Finally, The estimated economies of scale close to one for the sample mean point indicate that medium-sized utilities closely correspond to the optimal size of water distribution utilities in Tunisia, Large utilities are found to operate at levels where diseconomies of scale are already present, while smaller utilities should be interested in expanding their service areas since this would lead to a decrease in average operating costs Economies of output density is confirmed for all three different types of utilities with respect to the size of the operation, Therefore, franchised monopolies, rather than side-by-side competition, seem to be the most efficient form of production organization in the water distribution utility. Mean Std, Dev, Minimum Maximum Model I 1,583 0,33225 1,5005 1,9705 Model II 1,3986 0,2956 1,287 1,697 Table 1. Estimated cost inefficiency scores EOD ES Model I Model II , Model II Mean 2,66 3,5 1,05 1,2 Std, Dev 0,58 1,08 0,19 0,11 Minimum 1.647 1.98 0,72 0.764 Maximum 3,2 4,71 1,39 1,41 Table 2. Economies of output density (EOD) and Economies of scale (ES). Figure 1. The largest dam in Tunisia: Sidi Salem Figure 2. Share population connected to the drink water in Tunisia.. References Contact Antonioli, B, and Filippini, M, (2001), The use of a variable cost function in the regulation of the Italian water industry, Utilities Policy 10, 181-187, Ben Amor and Goaeid (2011) :“Stochastic Coefficient Frontier Model in the Estimation of Technical Efficiency of Irrigated Agriculture in Tunisia”.  Agricultural Journal 5 (6), 329-337. Ben Amor and Muller (2011) : “Application of Stochastic Production Frontier in the Estimation of Technical Efficiency of Irrigated Agriculture in Tunisia   ”Agricultural Journal 5 (2): 50-56, Medwell Journals Caudill, S.B., J.M. Ford and D.M. 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Mellah,T and Ben Amor,T (2016) ” Performance of the Tunisian Water Utility: An input-distance function approach.: An Input Distance Function Approah” Utilities Policy Volume 38, February 2016, Tawfik Ben Amor & Mellah Thuraya Higher School of Digital Economy, University of Manouba Tunisia Email: tawfikbenamor@yahoo.fr tmellah@yahoo.fr Phone: (216) 26 11 12 13 (216) 24 39 82 10 Home page: