Abstract
This study investigates the role of aligning tariff adjustments and quality incentives in a Price cap regulatory regime. According to theory costs and quality are positively related. If additional resources are needed to improve service quality, a high cost high quality utility could be at a disadvantage when tariffs are adjusted by an X-factor that does not include quality. The regulator of the electricity distribution sector of Brazil has set up a public ranking of utilities according to quality compliance at the same time that a quality component is added to the X-factor, in 2013. We develop a stochastic cost frontier integrating all components of the X-factor to rank the utilities based on this integrated efficiency. Comparing this rank with the regulator’s public rank we argue that the resulting differences highlight the importance of using the same factors to rank and adjust tariffs in the sector. Otherwise, incentives would be misplaced with respect to factors used in cost adjustments. In addition, our findings reveal that the utilities’ cost behavior with respect to quality depends on the volume of energy delivered. We believe these results could be considered by the regulator when setting incentives and considering factors to adjust tariffs.
Appendix 1: Regularity Conditions and Properties of the Cost Function
We proceed to the inspection of regularity conditions of the cost function. A well-behaved cost function is concave in input prices and non-decreasing in outputs. Assuming the cost function is twice continuously differentiable, a necessary and sufficient condition for concavity in prices is a negative semi-definite matrix of the second order partial derivatives of the cost function with respect to prices. In the case of the translog functional form, this is granted by imposing symmetry on the parameters of the interacted input prices (γij = γji for all i ≠ j). Additionally, the price shares are found positive at mean values (Diewert and Wales 1987).
Regarding properties of the cost function, it must be homogeneous of degree one in prices to correspond to a well-behaved production function. This means that for a fixed level of output, total costs must increase proportionally when all prices increase proportionally. This is accomplished by imposing the restrictions specified in Equation (1.1). This implies normalizing input prices and cost by one of the input prices, in this case we use price of materials. That is, cost and input prices are divided by price of materials.
A homogeneous technology is a special case of a homothetic technology when the elasticity of cost with respect to output is constant. A cost function corresponds to a homothetic production technology if and only if the cost function can be written as a separable function in output and factor prices. To test for both, homotheticity and homogeneity, we follow Christensen and Greene (1976) and Diewert (1974) by imposing the restrictions specified in Equations (1.2) and (1.3), respectively at estimation time.
A Likelihood Ratio test accepts the hypotheses of homotheticity and homogeneity with 99% confidence. A homothetic production function implies that the input mix is constant with scale. The function being homogeneous implies that returns to scale are constant with the scale of the firm and the production mix. This implies that in this sector, companies have similar behavior regarding costs within each size group, given that the group variable is included in the model. This result is helpful for the regulator, as introducing changes in the sector could be done considering the size of the companies. After adjusting the cost model for these results, the functional specification used in estimation becomes explicit in Equation (1.4) (As customary when using a panel data, each variable in the equation has a subscript for time and company, but omitted for clarity, with the exception of the intercept).
In Equation (1.4), C is annual operating costs for each utility; Y represents defined output, volume of electricity; P is input price with sub-index i varying for each of the defined input prices; K is the capital stock; Z represents each defined non-discretionary (exogenous) variable which includes the four dummies for the regions and the quality variable Q, therefore m is equal to 5; ε is the error term, and α, β, γ, δ, φ and ω are parameters to be estimated (this is identical to Equation (7) in the main text).
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