Who gets what – and how efficiently? Assessing the spatial allocation of public goods

Abstract

Governments frequently face distributive pressures that can lead them to allocate resources along partisan or ethnic lines. Such patterns of distribution can run counter to welfare maximization. It is therefore important to incorporate distributional concerns into the measurement of government performance. This paper outlines a method for doing so, adapting standard techniques for measuring government efficiency. The proposed method’s utility is demonstrated with data from Tanzanian local governments. The application illustrates how failing to take distributional concerns into account can bias the measurement of performance. Assessing how well governments translate resources into outputs that equitably serve their citizens is important for a number of topics in political science, including decentralization, distributive politics, and government fragmentation. It can also inform efforts to promote aid effectiveness. The proposed approach is applicable to a wide range of contexts given the increasing availability of geo-coded data on public goods. Replication files are provided for those wishing to conduct their own analyses.

Introduction

For a number of public goods, spatial distribution matters to determine how well a government is serving its citizens. This is particularly so in contexts where people rely on the state to provide things like access to clean water, roads to take their goods to market, and dispensaries with life-saving drugs. However, governments frequently face distributive pressures that can lead them to allocate goods along partisan or ethnic lines (Burgess et al., 2015; Franck and Rainer, 2012; Golden and Min, 2013). Such patterns of distribution can run counter to welfare maximization. It is therefore important to incorporate distributional concerns into the measurement of government performance. This paper suggests an approach for doing so, adapting techniques from the efficiency literature to assess how well governments translate resources into outputs that equitably serve their citizens.

I begin by introducing standard techniques for measuring government efficiency and then describe how to incorporate distributional concerns. The proposed approach is applicable to a wide range of government-provided goods but is most suited to those intended to benefit a wide swathe of the population on a regular basis, for example, water wells, roads, and dispensaries. An empirical application with data from Tanzanian local governments demonstrates the method’s utility. This example also illustrates how failing to take distributional concerns into account can bias the measurement of government performance.

Assessing how well governments translate resources into outputs that equitably serve their citizens is important for a number of topics in political science. These include decentralization, which many scholars argue should make local government service delivery more efficient than that of higher levels of government (Crook, 2003; Faguet, 2014). Similar arguments are made in the context of government fragmentation (Grossman et al., 2017). The proposed technique allows for more rigorous testing of such arguments. It can also complement existing metrics of corruption and provide insights into the allocation of public goods at varying levels of electoral competition.

Measuring government efficiency

In what follows, I introduce standard approaches to measuring government efficiency, which I adapt to incorporate distributional concerns. In general, the measurement of efficiency compares actual performance of “decision-making units” (DMUs; e.g., firms, countries, or governments) with optimal performance in terms of their ability to translate inputs into outputs. Since the true optimum is unknown, an empirical approximation is needed to generate the “best practice frontier” (Fried et al., 2008). Observations that lie within the frontier are considered inefficient, as this implies that other DMUs use fewer or equal amounts of inputs to generate more or as many outputs.

Scholars have developed a variety of approaches to generate best practice frontiers, and measure deviations from them. The dominant approaches fall into two categories: econometric and nonparametric methods. The econometric approach, also called stochastic frontier analysis, hypothesizes a functional form and econometrically estimates the parameters of that function using the entire set of DMUs. Nonparametric approaches on the other hand use observed combinations of inputs and outputs to generate a piecewise frontier. Many scholars prefer nonparametric approaches, given that the functional form of the production process is frequently unknown, creating the potential for specification biases (Daraio and Simar, 2007).

Two nonparametric methods dominate the empirical literature. The first, data envelope analysis (DEA), connects the efficient entities (those that produce the most outputs with the least inputs) to generate a convex production possibilities set (Charnes et al., 1978). However, scholars have raised both theoretical and empirical concerns with the convexity assumption (Geys and Moesen, 2009). In light of this, many prefer the approach developed by Deprins et al. (1984), which constructs a “free disposal hull” (FDH) efficiency frontier with a staircase shape. FDH identifies exactly one role model for each inefficient producer, where the role model is an actual efficient producer rather than a fictitious combination of efficient producers.

Figure 1 provides a stylized depiction of the efficiency frontiers constructed by DEA and FDH. Each dot represents a hypothetical DMU – the most efficient are those that produce more outputs from fewer inputs (those on the left/top left of the figure). The DEA frontier is shown as a dotted line while the FDH frontier is shown as a solid line. Hence, dots a, b, c, and d are considered to be efficient using the FDH frontier, but dot c is not efficient if the DEA frontier is used. ¹

Figure 1.

Comparison of DEA and FDH.

When it comes to assessing government efficiency, most empirical studies consider total current expenditures by government units as inputs, and various public goods and services as outputs. The outputs in question often do not take spatial distribution into account. However, people tend not to be distributed equally within government jurisdictions. Population density can vary considerably across countries, municipalities, and even villages, as people frequently cluster given geography or access to land and housing. Moreover, politicians do not necessarily attempt to meet the needs of their constituents in an equivalent manner. As noted above, there is considerable evidence of politicians targeting the allocation of public goods and services to identifiable localities or groups. While most studies have examined the targeting practices of central government politicians, scholars have also presented evidence of politically motivated allocations within local government jurisdictions (Carlitz, 2017; Harris and Posner, 2019). It is therefore important to take distributional concerns into account when measuring government efficiency, in order to capture such politicized misallocation.

Incorporating distributional concerns

The method I introduce in this paper builds on standard approaches to measuring government efficiency to incorporate distributional concerns. It is best suited to assess the allocation of government-provided goods that are defined territorially in that they serve a geographically distinct area and people experience the same service regularly. Such goods are also targetable, in that government officials can choose to focus on particular beneficiaries (Batley and Mcloughlin, 2015). Traditional measures of efficiency would compare the amount of money governments spend on such goods to the number of outputs produced. Accordingly, two governments that produce the same amount of output for the same amount of money would look equally efficient, even if in one, all new goods were distributed in a manner that favored certain individuals (e.g., all new wells built outside party officials’ homes), whereas in the other they were more evenly distributed to serve the general population.

In order to capture such differences, I suggest modifying the measurement of output to relate the geographic placement of government-provided goods directly to the distribution of beneficiaries within government jurisdictions. Specifically, I suggest calculating for each government-provided good the proportion of the population that resides within its catchment area. ² One can then incorporate this metric of output into any of the above-mentioned techniques for measuring efficiency in order to compare government spending (or use of other inputs) with improvements in access by the relevant population. ³

Measuring output in this way requires geo-coded data on public goods and services and fine-grained spatial data on population distribution for all government units. There is now a wealth of data on the former thanks to projects such as AidData, OpenStreetMap, and waterpoint mapping initiatives implemented by nongovernmental organizations and national governments (Welle, 2010). Fine-grained data on population distribution also exist for nearly every country in the world and is available from organizations such as WorldPop and the Gridded Population of the World database.

The final data requirement of my approach is shapefiles with polygons corresponding to the boundaries of the relevant government units. ⁴ These are also now widely available, through public databases like GADM and national statistics bureaus. Using software such as ArcGIS, QGIS, or R one can link the geo-coded data on service delivery and population distribution to the relevant government unit, and determine the extent to which people in that jurisdiction have access to the service in question.

One limitation of this approach is that geographic access does not guarantee that someone will benefit from a given good or service (Smiley, 2016). Furthermore, my proposed method does not consider the relative need of different members of the population. Such issues could be considered through more in-depth analysis once an initial assessment has been made. Finally, one might note that environmental factors such as population density and terrain ruggedness can condition the ability of governments to reach the efficiency frontier. These factors can be incorporated through a variety of techniques. In the most widely used method, efficiency scores are estimated in the first stage and then in a second stage the efficiency scores are regressed on the environmental factors (Narbón-Perpiñá and De Witte, 2018). However, the data-generating process through which environmental factors affect efficiency scores is frequently unknown, and statistical inference is complicated due to serial correlation among the estimated efficiencies (Simar and Wilson, 2007). Thus, scholars increasingly prefer conditional efficiency approaches, which are fully nonparametric and include environmental variables in the calculation of efficiency (Daraio and Simar, 2005). ⁵ Alternatively, scholars of transport and urban planning have developed measures of accessibility that compare the actual distribution of transport hubs to the optimal distribution in terms of minimizing travel time (Geurs and Van Wee, 2004; Monzón et al., 2013). This differs from the proposed approach in that the optimum is theoretical, rather than based on what has been observed empirically. The appropriate technique for calculating the efficiency frontier is likely a function of the research question at hand.

Example: Tanzanian local governments

To demonstrate the utility of my proposed method, I examined spending and construction of communal waterpoints (standpipes, handpumps, improved springs) by local government authorities (LGAs) in Tanzania. These authorities, which govern at the district level, bear the main responsibility for water provision and rely heavily on central government transfers. In this regard, Tanzania’s governance arrangements for water provision are similar to many other low-income countries.

Tanzania’s LGAs exhibit considerable variation when it comes to how they spend the resources they receive for rural water provision. Over the first phase (2007–2013) of the Water Sector Development Program (WSDP), a large, multi-donor initiative increased the Tanzanian water sector budget fourfold (World Bank, 2011), some local governments built hundreds of new water points, while others constructed just a handful or none at all.

Even if two LGAs construct the same number of waterpoints for a given amount of money, this can have very different implications for access. The construction of new waterpoints will only translate into improved access to clean water if infrastructure is built in places where people previously lacked access. To illustrate this, I examined data from a recent waterpoint mapping exercise conducted by the World Bank and the Tanzanian Ministry of Water. ⁶ This dataset includes observations of 83,615 public waterpoints serving rural communities in mainland Tanzania. ⁷ Since the waterpoint data is geo-coded, it was possible to see precisely where new infrastructure had been built. I incorporated high-resolution data on the population distribution from WorldPop in order to determine whether new construction is benefiting previously underserved areas.

I present two strategies for calculating efficiency. ⁸ The first, which I term spending efficiency, does not take the spatial distribution of outputs into account. In this case, the input is district-level spending on water infrastructure (2007–2013) and the output is the number of waterpoints built over the same period. ⁹ Next, I estimate a measure of what I term access efficiency, where the input is again spending on water and the output is the percentage point improvement in access, calculated in terms of the LGA’s population residing within 1 km of a waterpoint.

To illustrate the importance of taking space into account, one can compare two districts (Bagamoyo and Mkuranga) in Tanzania’s Coast region. During the first phase of the WSDP, Bagamoyo built 1175 new waterpoints, at an average cost of 1.3 million Tanzanian shillings each (about US$800 using December 2013 exchange rates). Mkuranga constructed 489 new waterpoints during that same period, at an average cost of 2.4 million Tanzanian shillings per waterpoint (US$1,500). Thus it would appear that Bagamoyo is using its money more efficiently. Indeed, Bagamoyo’s spending efficiency score is 0.45 compared with Mkuranga’s score of 0.35.

However, if one looks at where the waterpoints are placed within each district relative to need, a different picture emerges. Figure 2 depicts the waterpoint catchment areas in the two districts, overlaid atop the population distribution (darker areas correspond to more densely populated areas). Panel (a) illustrates the distribution of the 2006 stock of waterpoints (in yellow) in Bagamoyo district. The figure shows that prior to the WSDP, many people resided outside the catchment area of a waterpoint. This is illustrated by the dark portions of the map not covered by yellow shading. Specifically, in 2006, just 18.6% of Bagamoyo’s population lived within 1 km of a waterpoint. Panel (b) shows the catchment areas of new waterpoints, constructed between 2007 and 2013 (in green). Few of the previously dark areas are now covered; rather, much of the placement of new waterpoints appears to be redundant. Indeed, by 2013, the proportion of Bagamoyo’s population residing within 1 km of a waterpoint had only risen to 25%.

Figure 2.

Placement of Water Infrastructure in Bagamoyo over panels (a) 2006 Catchment Areas; (b) New Catchment Areas, 2007-2013 and Mkuranga over panels; (c) 2006 Catchment Areas; (d) New Catchment Areas, 2007–2013.

The situation is very different in Mkuranga. While initial access was somewhat higher (25.5% of the population lived within 1 km of a waterpoint as of 2006), new construction expanded coverage considerably: the green catchment areas depicted in panel (d) now cover many of the dark areas that were uncovered by yellow catchment areas in panel (c). Indeed, Mkuranga saw access increase to 45.8% by 2013. Mkuranga’s more efficient spatial distribution of infrastructure is captured by its access efficiency score of 0.66, which is considerably higher than Bagamoyo’s score on the same metric of 0.27. Table A3 in the Online Appendix shows that a number of districts are characterized by a similar divergence among the different measures of efficiency. ¹⁰

This divergence between spending and access efficiency scores is emblematic of the flawed inferences that may be drawn by only considering efficiency in terms of translating inputs into outputs that do not take spatial distribution into account. Accurately measuring the efficiency with which local governments translate resources into outputs that benefit their citizens is important, given increasing interest in results-based aid and other performance-based initiatives to improve service delivery in Tanzania and other low-income countries (Brinkerhoff and Wetterberg, 2013; Miller and Babiarz, 2013). In such initiatives, aid is disbursed to central or local governments for achieving results of some kind. The results in question are frequently defined in terms of outputs (e.g., construction of new waterpoints by local governments). However, if recipients are only rewarded or punished on the basis of how well they translate aid resources into outputs, without considering how those outputs are distributed within local jurisdictions, results-based aid and related schemes may fail to achieve their aims.

Conclusion

Understanding variation in the efficiency of public service delivery is an important area of inquiry for many topics in political science, including distributive politics, corruption, administrative unit proliferation, and other research areas. It is also a matter of substantive importance, given the increasing amount of resources and responsibilities flowing to local governments following decentralization reforms. However, political scientists have largely refrained from the systematic measurement of efficiency. Moreover, the dominant approaches to measuring efficiency often do not take the spatial distribution of government outputs into account, and thus do not capture the extent to which governments are effectively serving their constituents’ needs. I have therefore proposed a method that builds on standard approaches to measuring government efficiency to incorporate distributional concerns. Replication files are provided for those wishing to conduct their own analyses. The increasing availability of geo-coded data on service delivery makes the proposed approach available to scholars working on a variety of topics.

Supplemental Material

Appendix – Supplemental material for Who gets what – and how efficiently? Assessing the spatial allocation of public goods

Supplemental material, Appendix for Who gets what – and how efficiently? Assessing the spatial allocation of public goods by Ruth D. Carlitz in Research & Politics