Cost Analysis of Water Utilities: A Goodness-of-Fit Approach
Raffiee, Kambiz, Narayanan, Rangesan, Harris, Thomas R., Lambert, David, Collins, John M., Atlantic Economic Journal
The existing studies in the literature on the ownership/efficiency issue of private and public water utilities have presented conflicting findings. These studies are an indirect test of the tradeoff between two sources of inefficiency in private and public water utilities: 1) inefficiency from regulation of private water utilities and 2) inefficiency from attenuation of property rights in public water utilities. Crain and Zardkoohi |1978~ determine that public water utilities have higher costs than the private water utilities. Feigenbaum and Teeples |1983~ and Byrnes, Grosskopf, and Hayes |1986~ find no evidence to reject the hypothesis that public and private water utilities are equally efficient. Both of these studies fail to provide a conceptual framework to justify their findings that private and public water utilities are equally efficient.(1)
In addition to the analysis of the differences in the cost behavior of public and private water utilities, the fundamental question that has to be addressed is whether the cost behavior of individual water utilities is consistent with well-defined principles of cost minimization. Is there any significant difference in the observed cost behavior of private and public water utilities in terms of departure from the cost-minimizing behavior?
This paper presents new empirical evidence on the efficiency/ownership hypothesis by examining the cost behavior of 238 public and 33 private water utilities using the data obtained from a 1989 survey of the water industry conducted by the American Water Works Association (AWWA). Following the Weak Axiom of Cost Minimization (WACM) developed by Varian |1990~, an efficiency index is calculated to determine the percentage difference between the observed cost of production and the optimum cost of production for each individual private and public water utility in the sample. The empirical results provide evidence that private water utilities are more efficient than public water utilities, confirming the broad proposition that alternative institutional arrangements are important in determining the outcome of conduct and performance of economic firms involved.
The outline of this paper is as follows. Section II presents the theoretical framework for deriving the efficiency index following the WACM. The application of the WACM to the 1989 data set from the AWWA and the empirical findings are discussed in Section III. Conclusion of the study is summarized in the final section.
Consider a production process by a firm that generates an observed set of data (|W.sup.i~, |X.sup.i~, |Y.sup.i~) for i = 1,...,n, where |W.sup.i~ is a vector of factor prices, |X.sup.i~ is a vector of factor demands, and |Y.sup.i~ is a (scalar) measure of output. If the firm is minimizing cost, it must satisfy the following condition:
C(|W.sup.i~,|X.sup.i~) |is less than or equal to~ C(|W.sup.i~,|X.sup.j~) for all |Y.sup.j~ |is greater than or equal to~ |Y.sup.i~. (1)
Hence, the cost of the observed production process, C(|W.sup.i~,|X.sup.i~) = |W.sup.i~|X.sup.i~, must be no greater than the cost of any other process, C(|W.sup.i~,|X.sup.j~) = |W.sup.i~|X.sup.j~, that produces at least as much output. This criterion is known as the WACM. This condition is both necessary and sufficient for cost-minimizing behavior. If a data set satisfies the WACM, then it is possible to construct a production function that would generate the observed decisions as cost-minimizing decisions. Discussion on consistency with cost minimization based on the WACM can be found in Varian |1984, 1990~, Diewert and Parkan |1985~, and Afriat |1972~, among others.
In the empirical analysis of consistency with cost minimization, one has to make the distinction between the conventional tests and the goodness-of-fit tests. The major criticism of the conventional tests is that they are based on exact optimizing behavior. …