Scope and scale economies in multi-utilities: evidence from gas, water and electricity combinations

Abstract

Within the recent debate on liberalization of local public services, the paper investigates the cost properties of a sample of Italian public utilities providing in combination gas, water and electricity. The estimates from a Composite Cost Function econometric model (Pulley and Braunstein, 1992) are compared with the ones coming from other traditional functional forms such as the Standard Translog, the Generalized Translog, and the Separable Quadratic. The results highlight the presence of global scope and scale economies only for multi-utilities with output levels lower than the ones characterizing the ‘median’ firm. This indicates that relatively small specialized firms would benefit from cost reductions by evolving into multi-utilities providing similar network services such as gas, water and electricity. However, for larger-scale utilities the hypothesis of null cost advantages is not rejected. Thus, it is possible that the recent diversification waves of leading companies are explained by factors other than cost synergies, so that the welfare gains that can be reasonably expected from such examples of horizontal integration, if any, are likely to be very low.

Acknowledgments

The authors would like to thank L. Benfratello, M. Ivaldi, S. Ostrover, and D. Piacentino for useful comments. We also wish to thank participants at the 29th Annual Conference of the European Association for Research in Industrial Economics (EARIE), Madrid, Spain 5–8 September, 2002 and at the Advanced Workshop in Regulation and Competition – 16th Annual Western Conference, San Diego (CA) 25–27 June, 2003, where earlier versions of this paper were presented. The financial support of HERMES Research Centre (www. hermesricerche.it) is gratefully acknowledged. The usual disclaimer applies.

Notes

See Kim (1987) for the water industry and Salvanes and Tjotta (1998) for electricity.

For other earlier studies on gas-electricity combination utilities, see the references listed in Sing (1987).

The subscript referring to individual observations has been omitted for convenience in the presentation.

Cost-shares are computed as S _r  = (X _r P _r )/C. By Shephard's Lemma X _r  = ∂C/∂P _r , where X _r is the derived demand for the rth input, so that S _r  = ∂ lnC/∂ lnP _r .

In this case zero values for any of the three outputs are substituted by 0.000001.

See Röller (1990a).

Baumol et al. (1982) recommend such a structure because it is able to measure the characteristics of multi-product technologies without prejudging their presence.

In the original specification proposed by Pulley and Braunstein (1992) the composite model includes an additional constant term β₀ and other price-output interactions (Σ _i Σ _r μ _ir Y _i lnP _r ) different from those entering via the output structure. Since the authors encountered problems in the estimation of the complete model, they decided to delete β₀ and the terms involving μ _ir . Following Pulley and Braunstein (1992) and the subsequent studies by McKillop et al. (1996), Braunstein and Pulley (1998) and Bloch et al. (2001), empirical analysis is based on this more parsimonious version as reported in Equation 3.

To be consistent with cost minimization, Equations 1 and 3 must satisfy symmetry (α _ij  = α _ji and β _rl  = β _lr for all couples i, j and r, l ) as well as the following properties: (a) non-negative fitted costs; (b) non-negative fitted marginal costs with respect to outputs; (c) homogeneity of degree one of the cost function in input prices (Σ _r β _r  = 1 and Σ _l β _rl  = 0 for all r, and Σ _r δ _ir  = 0 for all i); d) non-decreasing fitted costs in input prices; (e) concavity of the cost function in input prices. Symmetry and linear homogeneity in input prices are imposed a priori during estimation, whilst the other regularity conditions are checked ex-post.

Pulley and Braunstein (1992) suggest for the PB and SQ specifications to transform both sides of the cost function. In particular, in order to enlarge the set of plausible empirical specifications, they propose to estimate C ^{( ϕ )} = [C(Y, P)]^{( ϕ )} + ψ _C where (ϕ) refers to a Box–Cox transformation. The optimal value of ϕ can be found either (a) by searching over a grid of given ϕ values and judging on the basis of the sum of squared errors (SSE) or (b) by direct estimation, resorting to standard non-linear least squares routines. Using approach (b), the authors found that the optimal value of ϕ was −0.14, while McKillop et al. who relied on the grid-search approach, found that ϕ’s in the range of 0.7–1.3 were balancing relatively high log-likelihood values with the highest degree of satisfaction of regularity conditions. Braunstein and Pulley (1998) and Bloch et al. (2001), on the other hand, did not apply the transform-both-sides procedure but directly estimated Equation 3 which corresponds to setting ϕ equal to zero. By following approach (a) it was found that ϕ = 0.23 was associated with the highest log-likelihood value. Since the estimates were very similar to the ϕ = 0 case (see Section V), the final choice was to adopt the simpler specification of Equation 3.

See Kim (1987).

In our three outputs case, the measure of product-specific economies of scope for the couple (i, j) is identical to the one for the remaining good k (SC _k  = SC _-ij ):

Baumol et al. (1982) have shown that a multi-product cost function characterized by weak cost complementarities over the full set of outputs up to the observed level of output exhibits scope economies.

The final choice to include two inputs only is due to the fact that weighted averages are used to obtain factor prices. The specification of the energy input (i.e. electricity or gas purchased for resale) as a separate factor would have implied strong asymmetries between utilities which are mostly distributors (i.e. gas operators) and utilities that are also active at the production stage (i.e. electricity and water utilities). Such an asymmetry is likely to produce biases in the estimates.

For the GT and PB models, for instance, this leads to the estimation of systems 1–2 and 3–4.

See Greene (1997), Chapters 10 and 15.

The software used for the estimation is LIMDEP Version 7. Since the study is working on a panel data in which each firm is observed over a period of three years, one had to choose whether to add to the model a fixed effect for every year or eventually a time-trend variable. To tackle this issue LR tests were performed after having included in the model the time dummies for 1994 and 1996 or a time-trend variable. At the usual confidence levels, both the null hypotheses of constancy of the intercept over time and of not significant time-trend effect could not be rejected. Thus we opted for a simple regression based on the pooled observations.

The median firm (the point of normalization) corresponds to an hypothetical firm operating at a median level of production for each output and facing median values of the input price variables.

A similar pattern can be observed by looking at the log-likelihood values of the cost and labour-share equations, as well as by comparing their estimated SSE.

See Gasmi et al. (1992), page 286.

In the present case the value of HQ is equal to 0.86.

This resulting statistic is asymptotically normally distributed under the null hypothesis of equal fit. Thus, given a critical value z from the standard normal distribution at some significance level, we cannot reject H₀ if the normalized LR statistic is smaller than z in absolute value. On the other hand, if the normalized LR statistic is smaller (higher) than −z(+z), we conclude that GT(PB) model is significantly better.

The general formula for ‘quasi’-scope economies in the three-outputs case is QSC(ε) = [C(εY _G , εY _W , (1−2ε)Y _E ) + C(εY _G , (1−2ε)Y _W , εY _E ) + C((1−2ε)Y _G , εY _W , εY _E )−C(Y _G , Y _W , Y _E )]/C(Y _G , Y _W , Y _E ).

The estimated PB cost function also satisfies each of the output and price regularity conditions at 90% of the sample data points. More precisely, fitted costs are always non-negative and non-decreasing in input prices (fitted factor-shares are positive at each observation). Concavity of the cost function in input prices is satisfied everywhere in the sample (the Hessian matrix based on the fitted factor-shares is negative semi-definite). Fitted marginal costs with respect to each output are non-negative for 244 observations on 270.

This indicates that combination utilities are benefiting from cost savings arising from sharable inputs such as, for instance, meter reading, billing, accounting and engineering services.

Following Equation 9, the cost savings are to be intended with respect to the sum of the costs incurred by a specialized firm producing good i and a two-products firm producing the other two goods.

The t-ratio of the related parameter, α _WE , is indeed extremely low.

Taking as an example SL _W , this means that adding the supply of water service to the set of existing products (electricity and gas) brings incremental average costs which are not different from marginal costs (see Equation 7).

When one applies the ‘transform-both-sides’ procedure and use the best estimate of ϕ = 0.23 (see note 9) one obtains results very similar to the ones reported above. The only remarkable difference is that global and product-specific economies of scope are significantly different from zero for the ‘median’ firm too.