Analyzing the spatial allocation of public services with transparent data

Financial Economics
Fiscal Policy - Public and Welfare Economics

It is often argued that public goods and services are provided in order to benefit certain groups of the population. This could be for political- or other reasons. In a recent paper I look at one specific aspect of public services, that is, the spatial distribution. I limit myself to services for which citizens visit the place of service delivery. The goal is to develop a transparent method in order to assess the optimality of the spatial distribution, which can then be used as an input to analyses of e.g. political manipulation.

The paper, “Location-allocation of public services – Citizen access, Transparency and Measurement. A method and evidence from Brazil and Sweden” is forthcoming in Socio-Economic Planning Sciences, and will be presented at the 2016 LACEA meeting.

In Operations Research, and at least since the 1960’s, location-allocation analysis has been available as a tool to calculate the optimal spatial allocation of e.g. warehouses (a private sector problem), or hospitals (a public sector problem, which is our topic). A typical objective is to place a fixed number of units to minimize citizens’ travel distances or travel times (a “p-median problem”). The minimum data needs are disaggregate population data and a distance matrix, with distances or travel times between all points in the population data. Available since long are mathematical theorems, heuristics and modern software that allow us to solve problems that would otherwise be prohibitively difficult or time consuming. As an example, I solve a problem with 10E70 possible spatial allocations. What has happened lately, however, is that real distance (or travel time) data is becoming ever more available, which I discuss at some length in the paper. It is now feasible to construct real distance matrices between, for instance, all municipalities in a country. Over time, databases with all distances between e.g. a municipality sub-district and all other sub-districts in a country, will be feasible. In the paper I use a matrix with 4 million entries. Importantly, the data can be obtained, or will become ever more possible to obtain, without involvement of the public entities being evaluated, through e.g. OpenStreetMap.

In the paper I analyze Citizen Service Centers, called Poupatempo (“Savetime”), in São Paulo, Brazil (and a similar service in Sweden). In a 2008-2011 expansion, 16 new units were built in São Paulo. Comparing the actual locations (black and red in the below figure), to the distance-minimizing allocation of the same amount of units (black and green), one can illustrate both the actual-optimal differences in spatial distribution, as well as the distance reduction that would obtain, had the optimum been implemented.


The analysis can be repeated for a number of public services. A recent example is the work by Corbacho and coauthors (listed below), studying the important question of how distance to a birth registry affects birth registration, and subsequent life outcomes. A methodological contribution of the paper is to suggest a metric of spatial misallocation, which can then be linked to e.g. political variables, a topic we currently study.


Access Paper

Corbacho, A., Rivas, R., 2012A. Travelling the Distance: A GPS Based study of the access to birth registration services in LA and the Caribbean. IDB Working Paper Series 307.

Corbacho, A., Brito, S., Rivas, R., 2012B. Birth Registration and the Impact on Educational Attainment. IDB Working Paper Series 345

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