Cost Efficiency, Urban Patterns and Population Density When Providing Public Infrastructure: A Stochastic Frontier Approach

Abstract

Relying on stochastic frontier analysis we propose a methodology to study the technological characteristics and cost efficiency levels related to the provision of public infrastructure for basic utilities. The methodology assumes a cost minimizing behaviour on the part of public officials when planning the construction of local infrastructure, which is represented by way of a flexible translog cost function. Introducing relevant definitions of scale economies, associated with larger numbers of inhabitants and dwellings, as well as economies of density, brought about by reductions in urban dispersion, we analytically determine the optimal population densities for which average cost is minimized. We illustrate our model with the water cycle sector, including water distribution, sewage collection and cleansing of wastewater, and considering data at the municipality level for the Spanish region of Castilla y León. The obtained results indicate potential cost savings in the form of decreasing average costs, as relevant scale and density economies are present, along with large inefficiency levels. Relevant policy guidelines favouring larger and denser urban sizes are drawn, as the observed cost excess is the result of a general suboptimal urban size in terms of population density, and the negative effects of dispersed settlement patterns.

Acknowledgements

This study was supported by the Spanish Ministerio de Educación y Ciencia within research grant SEJ2006/1482/ECON. We also acknowledge the assistance provided by CYLSTAT, SL, when compiling the LIES database. We are also grateful to the technical departments within different jurisdictional levels (local, provincial and regional governments), that have provided us with all the information on the engineering guidelines for the parametric price database. A previous version of this study has been published as working paper no. 639/2011 of the Working Papers Collection of “La Fundación de Cajas de Ahorros (FUNCAS)”.

Notes

1. Linear homogeneity in provision prices together with crossed effects' symmetry requires, respectively, the following restrictions: and

2. The inefficiency term is normally modelled according to the following distributions: exponential, half-normal, and truncated normal with mean μ. In the empirical section we test these alternative assumptions.

3. The definitions that we present of economies of scale (4) and density (5) correspond to those originally introduced by Panzar and Willig (1977) and adopted by Torres and Morrison (2006), and they are the inverse of those later suggested by Caves et al. (1984, 1985), that in turn are favoured by Bottasso and Conti (2009). Nevertheless, whether the scale and density economies are defined as the inverse of the sum of the elasticities or not does not change any conclusion, but just their numerical interpretation.

4. The Spanish Statistical Office (INE) population cluster defines as a hamlet consisting of at least 10 buildings arrayed in streets or around central squares.

5. See Faludi (2003) for a critical review of the European Spatial Development Perspective.

6. As provision levels and conditions may change with time as services deteriorate or are improved, the inventory is periodically updated. Its importance resides in the fact that it constitutes a dynamic statistical source that can be used to evaluate local provision levels and conditions to allocate the intergovernmental grants. We remark, however, that our analysis solely relies on the quantity variables of the “LIES” survey and therefore does not take account the characteristics related to quality of the infrastructure (whether it is in good, mediocre or bad condition). Therefore, in the context of this limitation, we can explain the reduction in cost due only to quantity (physical) related improvements in the provision of basic infrastructure.

7. These and other individual task prices that we have used to determine unit prices for the remaining provision variables can be looked up in the Castilla y León database of construction prices, Instituto de la Construcción de Castilla y León: www.iccl.es, BPCCL (2004).

8. For this purpose we have gathered information from the technical engineering staff of the provincial governments whose expert opinion on the components and prices of the different civil works—provision variables—is critical. These public works' supervisors plan, organize, oversee, coordinate and review a comprehensive program of public works construction, maintenance and repair of urban infrastructure, including water distribution, sewage collection and cleansing of wastewater.

9. The weight capturing the lithological and geological characteristics of a municipality reflects soil hardness when executing a work. The information provided by the lithological map of Castilla y León, SIEMCALSA (1997) allows us to classify urban areas in 13 distinctive categories and six levels of soil hardness. As for the altitude, we have considered four levels taking as reference for a particular urban area that of its largest population cluster. Finally, when the closest city head of a commercial area coincides with the administrative capital city, the distance can be found in the 1993 Nomenclature produced by the Spanish National Statistical Office, INE (2003), while the distances to alternative commercial cities have been calculated using the information database given by the National Center of Geographical Research, CNIG (2001) and the Commercial Atlas of Spain published by the Spanish savings bank, La Caixa (2000).

10. These weights are commonly used in studies on production of urban utilities, e.g. Coelli and Walding (2005) for water supply, Rubiera (2007) in studies testing central place, hierarchy, and location theories, Deller et al. (1988) for rural low-volume roads, all of which obtain provision prices by means of engineering costs analyses.

11. A methodological discussion summarizing the conclusions of the Camberra group on capital stock measurement, with regard to the concepts of gross, net and productive capital stocks can be found in OECD (2001).

12. The stochastic frontiers are estimated using Stata V.11.

13. Lai and Huang (2010) extend the likelihood ratio (LR) test of Vuong (1989) model selection criterion to the SF models. This test compares a parametric family of the SF model: , with an alternative parametric family of the SF model , where f(y|s; θ_f) and g(y|s; θ_g) represent the conditional probability densities of both models, respectively, d_f and d_g are the dimension of the parameters, θ_f and θ_g are the vector of parameters, and Θ_f and Θ_g are the parameter spaces of the SF models. In our calculations, also programmed with the Stata V.11 software, we contrast the convenience of the truncated normal distribution model , which constitutes the baseline model in Vuong's test statistic, in comparison with the exponential and the half-normal distributions corresponding to . The following two hypotheses are tested: (i) H₀: and are equivalent and (ii) H_f: is better than . To contrast both hypothesis, Vuong's (1989) LR test defines as: where and are the conditional log-likelihood functions and . Under some regular conditions (assumptions A1−A6 in Vuong (1989)), for H₀.

14. Similar conclusions can be found in Filippini et al. (2008), and the literature dealing with service—and not infrastructure—utility production.