EFFICIENCY IN LOCAL PUBLIC INVESTMENT: PROOF OF TIEBOUT HYPOTESIS IN BOLIVIAN COUNTRY

Mónica Meneses Covarrubias ∗ Fernando Michel Ayala Vargas ∗∗ Carlos Meneses Covarrubias ∗∗∗

∗ Master in Sciences of Economics. Graduated from Lovaina-Namur (Bélgica) university. Researcher in the Institute of Social and Economics Studies (IESE)-UMSS. ∗∗ Lic. Fernando Michel Ayala Vargas. System Ingenier. Graduated from San Simon University. Enterprise JALASOFT S.R.L. ∗∗∗ Lic. Carlos Meneses Covarrubias. System Ingenier. Graduated from San Simon University.

1 Introduction

Decentralization has become an increasingly familiar theme in development theory and practice over the past two decades. There is a worldwide trend toward increasing transfer of power, resources and responsibilities to the sub national levels of government. Both federal and unitary countries, whether industrialized or developing are moving toward more fiscal decentralization. This trend towards greater fiscal decentralization that began in 1980’s with many developing countries embarking on the path to devolve more functions to the local jurisdictions, gained momentum during 9o’s. Paul Smoke (2001) asserts that during the 1990s, fiscal decentralization and local government reform have become among the most widespread trends in development (Sharma 2005).

Proponents of decentralization claim a number of benefits for the efficiency and equity of government performance. However, this basic economic rationale for decentralization of the public sector is not quite so simple and compelling as it appears. Some of the more recent literature provides, first, a thoughtful and provocative critique of the traditional view of fiscal decentralization, and, second, some new approaches that reveal its dark side, especially in practice. There is emerging, in short, a broader perspective on fiscal decentralization that raises some serious questions about its capacity to provide an unambiguously positive contribution to an improved performance of then public sector. Oates (2007).

Yet the literature on decentralization has tended to concentrate on theoretical discussions rather than empirical analysis, and few studies have explored the practical consequences of decentralization policies in a quantitative way (Khaleghian, 2003). Many of the proposed benefits of decentralization are open to question, especially in developing countries. The case of it is not an exception to this trend. There exist only a few studies about this topic in this country. One of them is the study of Faguet (2002), who found that the change in the pattern of investment from centralization to a decentralized government has been leaded by the local needs of the population. This paper has centered on the comparison between centralization and decentralization of public good provision as most of the literature that started with Oates (1972)’s seminal contribution. However in this line of investigation the efficient conditions of the decentralization have not been treated.

The aim of these papers relies precisely on the efficiency of local public good provision. In his celebrated paper published a half century ago, Tiebout (1956) argued that although Samuelsonian pure public goods may be underprovided due to consumers’ free-riding incentives in reporting preferences, examples of pure public goods are very rare, and impure local public goods can be provided efficiently (efficiency) by consumers’ revealed preferences through voting with feet (self-selection) and competition among jurisdictions (entrepreneurship) (Konishi, 2007).

As suggested by the work of Tiebout (1956) and as explained by Oates (1972, p. 35), a system of decentralized local governments can achieve allocative efficiency in the provision of local public goods by allowing consumers with different preferences for government spending to reside in different communities (homogeneity within the communities). Instead of having many heterogeneous consumers who are dissatisfied with the quantity of government services offered by a single centralized government, decentralized provision can increase consumer welfare by improving the match between consumers' demands and the services provided.

This paper seeks to assess more formally the relevance of Tiebout hypothesis. Our strategy is to derive a more realistic version of these. We first generalize the Tiebout model and show in a general environment that there is homogeneity across municipality’s demands and heterogeneity across municipalities’ investment. This suggests that Tiebout incentives do not hold because there is no an efficient match between consumer’s demands and the services provided.

To evaluate this prediction, we consider: (i) a sample of Bolivia municipalities (318) in one year (2001). Almost all of our empirical results stand in opposition to the Tiebout prediction of heterogeneity across communities and investments.

It is important to contrast our approach with previous empirical tests of the Tiebout (1956) hypothesis. The present investigation includes de spatial component in looking for the efficiency in the allocation of public goods. Two factors determine this inclusion. The first refers to the definition of local public goods which have the geographic components which is their essential difference respect to the definition of club goods. The second arise because of the proper definition of efficiency in Tiebout hypothesis. Tiebout (1956) himself wrote that: "there is no way in which the consumer can avoid revealing his preferences in a spatial economy. Spatial mobility provides the local public goods counterpart to the private market's shopping trip." Tiebout showed that a quasi-spatial adjustment mechanism (what has since been termed 'voting with one's feet') could, under certain conditions, lead to equilibria that satisfy the efficiency conditions for a local public good (Heikkila, 1995).

No one of the studies dealing with Tiebout hypothesis include the spatial component. Konishi (2007) introduce to his theoretical model spatial considerations; however the spatial model proposed is related to spatial location of each jurisdiction and it is not related to other jurisdictions as in our study.

Moreover, we use a second approach to analyse public investment efficiency of Bolivian local governments, using non-parametric technology. Specifically, we calculate an index of efficiency for two technologies: Free Disposal Hull (FDH) and Data Envelopment analysis (DEA). The objective is to complement the results from Tiebout hypothesis, studying how the local heterogeneous government’s investment is matching the local requirements. The basic idea of the methodology is to compare the use of public resources related to the public services obtained, among the municipalities.

The paper proceeds in several related stages. In section 2 we systematize the literature review, in section 3 we present a description of the methodology, data and specification of the model, section 4 exhibit briefly the results and finally section 5 the conclusion of the investigation.

2 Literature

Early tests of the Tiebout model primarily attempted to evaluate whether fiscal variables affect residential decision of households. The Tiebout hypothesis implies that there is at least partial sorting of individuals in communities based on local public goods. Some studies looked at migration and mobility patterns explicitly, and others focused on indirect tests. These studies investigated primarily whether public spending affected property values (Rubinfeld 1987).

The most prominent approach was introduced by Oates (1969), who studied whether public spending and taxation were capitalized into land values. Oates reasoned that an increase in public spending, with everything else including taxes held equal, should increase property values. The idea is that more public spending would attract more individuals to the community and hence increase the demand for housing in this particular community, resulting in an increase in price. Most of the studies following Oates´s find evidence that capitalization of public spending and taxes is prevalent. Kobayashi and Ribstein (2006). However, critics noted that no such relationship should exist in full Tiebout equilibrium, when taxes equal the price of efficiently provided local government services (Hamilton 1976). Thus, the rejection of the null hypothesis of no relationship between housing prices and fiscal variables indicated that such a Tiebout equilibrium did not exist. Epple et al. (1978).

Kobayashi and Ribstein (2006) distinguish a second set of papers testing the Tiebout theory used sub-county data to examine whether lower mobility costs were associated with greater Tiebout sorting. Gramlich & Rubinfeld (1982) estimated public spending demand functions and found that variance in local spending demand within communities was significantly lower than the statewide variance. This finding is consistent with Tiebout sorting of individuals with similar demands for public spending. Gramlich & Rubinfeld also found that estimated preferences for median voters in urban areas were consistent with actual levels of local government services provided. However, the results were weaker in rural areas, where mobility costs are higher. These results are consistent with local jurisdictions providing the desired level of services in the presence of low mobility costs. On the other hand, Rhode & Strumpf (2003) found that decreased mobility costs over time were not associated with increases in intercommunity heterogeneity in local taxation and service levels, which is inconsistent with Tiebout sorting. This suggests that forces reducing cross-community heterogeneity overwhelmed Tiebout forces over time.

There another studies with the hypothesis of Tiebout as a common theoretical framework to prove the “fiscal descentralization hypothesis”. Among them, Bergstrom and Goodman (1973) provided sufficient assumptions to allow estimation of de-mand functions from community-level data (Mitra, 2004). Their seminal paper spurred a large literature that estimated demand functions by com-bining data on public-good expenditures with community-specific information such as median income levels and demographics Dennis Epple (1999) and Holger Sieg (1999).

Another way to prove the same attempt is explain the variation in local government structure across metropolitan areas by examining the relationship between population characteristics and the number and size of local governments within a metropolitan area. Mitra (2004) have analyzed the relationship between measures of population heterogeneity and the number and size of local governments in U.S. metropolitan areas. The heterogeneity on the population represents the different preferences for government spending to reside in different communities and the number and size of local governments represents the capacity to achieve allocative efficiency in the provision of local public goods in a Tiebout framework. Related studies to this issue are Nelson (1990), Kenny and Schmidt (1994), Martinez Vazquez et al. (1997), Wassmer and Fisher (1997), and Fisher and Wassmer (1998); these researchers have concluded that greater fiscal decentralization occurs when demands for government services of residents within a metropolitan area are more heterogeneous.

An inverse relation of variables is used to tests of homogeneity in which a measure of heterogeneity within jurisdiction (inequality within jurisdiction/inequality between jurisdictions) is regressed on SMSA size, number of municipalities, and other explanatory variables (Eberts and Gronberg,1981). They find empirical confirmation of the Tiebout homogeneity hypothesis by showing that the percentage of within-district inequality decreases with the number of local jurisdictions (school districts) within SMSAs. Munley's (1982) approach is similar in spirit to that of Eberts and Gronberg (1981), in that he also regresses a measure of heterogeneity on, among other variables, the number of local jurisdictions within an area, and he too finds corroboration for the Tiebout 'homogeneity hypothesis'.

There exists a third strand of this literature which has concentrated in theoretical models about the existence of an efficient optimal equilibrium in the allocation of local public goods. Konishi, Le Breton and Weber (1997) examine the existence of a non cooperative equilibrium in a Tiebout local public goods economy with a finite number of consumers with quasi-linear preferences. They show that every Nash equilibrium under a poll tax scheme fails to satisfy a very weak efficiency notion, called intrajurisdictional inefficiency which requires that no formed jurisdiction S could improve the payoffs of all its members by choosing another public project1.

Instead to treat with non-cooperative games as before, Wooders (1999) interpret and extend the Tiebout hypothesis through cooperative game theory: in large economies with relatively small effective coalitions, there are outcomes in the core, that is, there are feasible states of the economy that cannot be improved upon by any coalition. (Note that a coalition may consist of many jurisdictions)2. Moreover, the core has the equal treatment property outcomes in the core do not discriminate between identical individuals, a ‘‘market-like’’ feature 3 . The results discussed depend primarily on one crucial property, small group effectiveness (SGE) (6), dictating that all or almost all gains to cooperation can be realized by coalitions that are small relative to the total population. Cooperative games can represent diverse economic models, including economies where players form multiple, possibly overlapping jurisdictions and those where players are affected by the characteristics of other members of the coalition, their social skills, their education levels, and their productive abilities.

Wooders (1999), provides a proof of Tiebout's conjectures for local public good economies with endogenous jurisdiction structures (partitions of the set of agents into jurisdictions). For small E and large economies, the E-core4 "shrinks" to the core. An E -equilibrium is defined and shown to be in the E –core. The utilities of most consumers are nearly equal to their utilities in a local public equilibrium allocation5. In this paper, it is assumed that there is only one private good and one local public good.

Recent studies show that it is possible the modification of equilibrium in the presence of interjurisdictional externalities. That is the optimal public good production and the optimal jurisdiction size may increase or decrease depending on the spillover strength changes Conley and Dix (1998). Therefore, there is not necessarily an improvement in efficiency by partially internalizing the positive externalities 6.

1 Under a proportional income tax scheme, which implies heterogeneity of income, a Nash equilibria may fail to exist1. However, under a poll tax scheme, with heterogeneity of income, equilibrium always exists. 2 A jurisdiction (or club) is a group of individuals who collectively provide public goods for themselves exclusively (the public goods are local). 3 When the effect of an individual on others is determined by his crowding type (his observable characteristics, including profession, appearance, age, gender, and lifestyle), the core dictates not only that identical individuals are treated identically but also that, in their interactions with others, individuals with the same crowding types are treated equally (2–4). These features all are in stark contrast to the situation with pure public goods (such as radio or national defense), for which relatively small jurisdictions are inefficient. 4 An E-core, similar to the Shapley-Shubik weak E-core.(efficient equilibrium) 5 The local public equilibrium is defined in [14], where it is called a competitive local public equilibrium since prices of private goods are determined competitively. It is a Lindahl equilibrium relative to an appropriate jurisdiction structure. For the purposes of this paper, the most important feature of the equilibrium is that the equilibrium states of the economy are in the core. 6 In the presence of positive externalities, for example, between localities it is not always efficient to consolidate the economy into a small number of more populous clubs producing larger levels of public goods. It holds for both positive and negative spillovers and for spillovers resulting both from public goods production (mosquito eradication programs, and radio and TV broadcasts) and crowding (museums, parks, and zoos) or local public goods. The described results also holds for profit maximizing entrepreneurs which establish clubs and compete to attract members by offering various combinations of public goods levels, club size, and admission fees and for the social planner case.

3 Methodology

In order to test the efficiency of Decentralization in Bolivia, we use Spatial Econometrics techniques. This tools are appropriate in situations when agents’ (or region’s) behaviour reacts to the behaviour of others, i.e. the outcome is dependent on the outcome for neighbours and/or the presence of reaction functions, direct spillovers from neighbours occurring through observed behaviour

Spatial dependence reflects the fundamental theorem of regional science, distance matters. Observations that are near each other should reflect a greater degree of spatial dependence than those more distant from each other. In other words, the strength of spatial dependence between observations should decline with the distance between observations. But Why?, this effects could include Reaction functions, Spillovers, externalities, unobserved similarities between places, Diffusion (disease spread), Common activity in neighbouring areas, Common policy across neighbouring areas, etc

3.1 Data

We consider: (i) a sample of Bolivian municipalities (318) in one year (2001). The investment variable have been transformed in per-capita terms and logarithms transformation have not been considered in this variable because we have values of ceros among them. (ii) The source of the information has been the National institute of statistic in Bolivia (INE) and the observatory of decentralization in Bolivia web page (iii) the investment variable has been desegregated for the three sectors of study: education, health and sanitation

In order to show robustness of the results we utilize two samples. One of them correspond to the all municipalities in the Bolivian country and the other sample is built for the municipalities that are more spatially concentrated in the occident side of the country in order to avoid the influence of high dispersions among municipalities in the oriental side of the country. We also adopt the binary matrix of distances to avoid such a problem.

Figure 1 Scatter of the two samples

Santos MercadoNueva Esperanza 9000000 8400000 CurvaCharazani (Gral.Perez) Santa RosaHumaitaVilla Nueva (Ingavi) BolpebraCobija SanPto.Riberalta Pedro(Conquista) G.Guayaramerín Moreno MocomocoChumaAyataAucapata FiladelfiaPorvenirBellaPuerto Flor Rico Puerto AcostaTacacomaTipuani El Sena PuertoQuiabayaSorata Carabuco San Lorenzo AncoraimesCombaya CopacabanaAchacachi TitoSan YupankiPuerto Pedro Pérez de CoroicoTiquina Puerto Siles BatallasPucarani YanacachiCoripataChulumani San Joaquin TiahuanacuLajaElNuestra AltoPalca IrupanaSe±ora de ExaltacionSanMagdalena Ramon DesaguaderoGuaquiViachaAchocallaMecapaca HuacarajeBaures 8200000 CollanaSapahaquiCairomaLicoma Puerto Villarroel Santa Ana NazacaraCaquiaviriComancheColquenchaCalamarca de PacajesMallaQuimeInquisivi Chimore Santa Rosa CatacoraSantiago Corode MachacaWaldo CoroAyo-Ayo LuribayBallivianYacoIchocaIndependencia SanRurrenabaqueReyes Buenaventura Morochata SantaMinerosGral. Rosa Saavedra 8500000 Apolo San Javier UmalaSica-SicaColquiri (V.Aroma)VintoQuillacolloColcapirhuaTiquipayaCochabambaSacabaColomi PortachueloMontero Pelechuco San Borja Trinidad Charaña SantiagoChacarilla de TapacaríSipeSantivañez TolataSipeSanPunataTiraque Benito (VJQ.Mendoza) SanBuena Carlos Vista CharazaniCurva (Gral.Perez)San IgnacioLoretoSan Andres San PedroEucaliptusCaracollo de Curahuara TarataArbietoClizaTocoVillaTacachiCuchumuelaAraniAlalayVacas RiveroPocona (V. 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Carlos Saavedra(San Juan) YunguyoCruzEsmeraldaHuachacallaEscara de BelenMachacamarca delSantiago de Andamarca de AndamarcaOcuriRavelo Villa MojocoyaPucara Cabezas Charaña ChacarillaSanEucaliptus PedroCaracolloTapacarí deSantivañezArbietoTarataTolataTocoCliza SanPunataCurahuaraVillaCuchumuelaTacachiAraniAlalayVacasPocona Benito Rivero (VJQ.Mendoza) (V.Buena G.Villarroel)WarnesOQUINAWAPailon Vista TodosLaCarangas RiveraSabaya Santos Presto CurahuaraSanSantiagoPapel Pedro Pampa de Tacopaya deDeArqueSicaya CapinotaCarangas ArampampaHuayllamarca AnzaldoTotoraSacabambaTotoraPojoComarapaPorongoSantaCotoca Cruz (Ayacucho) de la Sierra Sucre Yotala TurcoChoquecotaToledoOruroMachacamarcaVillaBolivarSacaca AcasioHuanuniToroVilaMizque VilaToroOmerequeSaipinaPampaMairanaElLa Torno GrandeGuardia San Jose Coipasa PampaSantuario Aullagas QuillacasTinquipayaTacobambaYamparaezVillaTarabuco ZudanezTominaVilla (Tacopaya) Serrano CorqueElPoopo ChoroLlallaguaUnciaCaripuyoChayantaSan PedroAiquilePasorapaMoromoroTrigalQuirusillasSamaipata BelenYocalla de Urmiri Icla (R.Mujia)Padilla PazñaAntequeraPocoataColquechacaPoroma (Bolivar)VallegrandePostrer Valle Robore Puerto Quijarro SopachuyVilla AlcalaGutierrez CarangasYunguyoCruzEsmeraldaHuachacallaEscaraBelen Santiagode Machacamarca delChallapata de Litoral Andamarca deOcuri AndamarcaRaveloPrestoVillaPucara MojocoyaCabezas Salinas de G. Mendoza PotosiChaquiBetanzos El Villar 8000000 TodosLaSabaya RiveraChipaya SantosSantiago deSucre HuariYotala Lagunillas CoipasaPampaSantuario BelenAullagasYocallaTinquipayaTacobamba QuillacasYamparaezVilla deTarabucoIcla Urmiri TominaZudanezVillaPadilla (R.Mujia) Serrano (Tacopaya) Puerto Suarez Tahua Porco Puna Monteagudo Salinas de G.Potosi ChaquiMendozaBetanzosSopachuyVillaEl Villar AlcalaGutierrez Caiza "D" Tarvita (V.Arias)Villa Vaca Guzman LlicaTahua PorcoPuna TarvitaMonteagudoVillaLagunillas (V.Arias)Charagua Vaca Guzman San LucasVilla AzurduyCamiri TomaveCaizaVitichiSan "D" LucasVilla AzurduyCamiri (Thola Pampa)SanCuevo BoyuibePablo de Huacareta 7800000 San PabloCuevoBoyuibe de Huacareta SanColcha"K" Pedro de (V.Martin) QuemesCotagaitaCamargoIncahuasiHuacaya Camargo Atocha VillaCulpina Abecia Machareti Incahuasi Huacaya San Agustin LasTarija CarrerasVilla Montes Culpina UriondoSanEntre Lorenzo Rios Villa Abecia SanMojinete PabloYunchara deTomayapo Lipez (El Puente) San AntonioVillazonPadcaya de EsmorucoCarapariYacuiba LasTarija Carreras UriondoSan Lorenzo Bermejo Tomayapo (El Puente) 7500000 500000 1000000 1500000 2000000 4000007600000 600000 800000 1000000 1200000 x x

3.2 Methodology used: Spatial Econometrics

Spatial econometrics is a subfield of econometrics that deals with the treatment of spatial interaction ( spatial autocorrelation ) and spatial structure (spatial heterogeneity ) in regression models The motive is that two problems arise when sample data has a locational component: 1) spatial dependence exists between the observations and 2) spatial heterogeneity occurs in the relationships we are modeling.

3.2.1 Spatial dependence Spatial dependence in a collection of sample data observations refers to the fact that one observation associated with a location which we might label i depends on other observations at locations j ≠ i. Formally, we might state:

With regard to spatial dependence between the observations, recall that Gauss-Markov assumes the explanatory variables are fixed in repeated sampling. Spatial dependence violates this assumption; this gives rise to the need for alternative estimation approaches as will be explained later.

3.2.2 Spatial heterogeneity The term spatial heterogeneity refers to variation in relationships over space. In the most general case consider that we might expect a different relationship to hold for every point in space. Formally, we write a linear relationship depicting this as:

Where i indexes observations collected at i = 1…..n points in space, Xi represents a (1 x k) vector of explanatory variables with an associated set of parameters βi, y i is the dependent variable at observation (or location) i and

εi denotes a stochastic disturbance in the linear relationship.

Similarly, spatial heterogeneity violates the Gauss-Markov assumption that a single linear relationship exists across the sample data observations. If the relationship varies as we move across the spatial data sample, alternative estimation procedures are needed to successfully model this type of variation and draw appropriate inferences.

3.2.3 Quantifying location in the models

A first task to undertake before asking questions about spatial dependence and heterogeneity is quantification of the locational aspects of our sample data. There are two sources of information on which we can draw.

The location in Cartesian space represented by latitude and longitude is one source of information. This information would also allow us to calculate distances from any point in space, or the distance of observations located at distinct points in space to observations at other locations. The second source of locational information is contiguity, reflecting the relative position in space of one regional unit of observation to other such units. Measures of contiguity rely on the knowledge of the size and shape of the observational units depicted on a map.

From this, we can determine which units are neighbours (have borders that touch) or represent observational units in reasonable proximity to each other. Regarding spatial dependence, neighbouring units should exhibit a higher degree of spatial dependence than units located far apart. A transformation often used in applied work is to convert the matrix W to have row-sums of unity. This is referred to as a standardized first-order" contiguity matrix.

Contiguity weights : Hence, if zone j is adjacent to zone i, the interaction receives a weight of 1. wij = 1/k if j adjacent to i, 0 otherwise; and where k is the number of regions adjacent to region i

Distance weights : Instead, we might know or be able to calculate the distance between central points of all our regions. We might then use the weighting scheme: Wij is a distance-based weight which is the inverse distance between locations I and j (1/d1 ij ) d ij wij = ∑ 1 j dij

The motivation for the standardization can be seen by considering what happens if we use matrix multiplication of C and a vector of observations on some variable associated with the other regions which we label y. This matrix product x* = Wx represents a new variable equal to the mean of observations from contiguous regions.

This is one way of quantifying the notion that xi = f(xj); j ≠ i, denoted before. Hence, if Positive spatial auto-correlation: x and Wx similar; if Negative spatial auto-correlation: x and Wx dissimilar. And if No spatial autocorrelation: x and Wx unrelated

Considering then a linear relationship that uses the relation x= ρ Wx+ ε to explain variation in x across the spatial sample of observations. Where ρ represents a regression parameter to be estimated and ε denotes the stochastic disturbance in the relationship. The parameter ρ would reflect the spatial dependence inherent in our sample data, measuring the average influence of neighboring or contiguous observations on observations in the vector x. If we posit spatial dependence between the individual observations in the data sample x, some part of the total variation in x across the spatial sample would be explained by each observation's dependence on its neighbors.

3.2.4 Spatial Autocorrelation Based on the spirit of the first law of geography: “everything is related to everything else, but near things are more related than distant things” , the Spatial Autocorrelation compute the correlation of a variable with itself through space. It measures the extent to which the occurrence of an event in an areal unit constrains, or makes more probable, the occurrence of an event in a neighboring areal unit. Or, it measure the strength of spatial autocorrelation in a map, or it test the assumption of independence or randomness

If there is any systematic pattern in the spatial distribution of a variable, it is said to be spatially autocorrelated; If nearby or neighboring areas are more alike, this is positive spatial autocorrelation. Negative autocorrelation describes patterns in which neighboring areas are unlike. And finally Random patterns exhibit no spatial autocorrelation; as can be seen in the next figure

Figure 2 diagram for +, - and 0 spatial correlation

Moran’s test This test compares the value of the variable at any one location with the value at all other locations N∑ ∑ WXXXXiji, (− )( j − ) I = i j (W )( X− X ) 2 ∑i ∑ ji, j ∑ i i or:

Where Wij is a contiguity matrix, this test compares the sum of the cross- products of values at different locations, two at a time weighted by the inverse of the distance between the locations. Similarly to correlation coefficient it varies between –1.0 and + 1.0, a high I value indicates positive autocorrelation, or: I >0 → positive spatial autocorrelation I <0 → negative spatial autocorrelation I =0 → no spatial autocorrelation

Geary’s C test Similar to Moran’s I (Geary, 1954), the interaction is not the cross-product of the deviations from the mean, but the deviations in intensities of each observation location with one another

2 [(N− 1)[∑ ∑ WXXij ( i − j ) ] C = i j 2 2(∑ ∑ Wij ( X i − X ) i j

Their values typically range between 0 and 2. If values of any one zone are spatially unrelated to any other zone, the expected value of C will be 1; values less than 1 (between 1 and 2) indicate negative spatial autocorrelation.

This test is inversely related to Moran’s I, and it does not provide identical inference because it emphasizes the differences in values between pairs of observations, rather than the covariation between the pairs. Moran’s I gives a more global indicator, whereas the Geary coefficient is more sensitive to differences in small neighborhoods.

3.2.5 Spatial autoregressive models

This model attempts to explain variation in y as a linear combination of contiguous or neighboring units with no other explanatory variables. This model is analogous to the lagged dependent variable model in time series.

We can also add additional explanatory variables in the matrix X that serve to explain variation in y over the spatial sample of observations.

As we mentioned in last paragraphs, using this kind of models lead to some complications in the use of traditional techniques of estimation; to illustrate the problem with least-squares estimation of spatial autoregressive models, consider applying least-squares to the following model in which would produce an estimate for the single parameter ρ in the model:

, Then

Then, we can show that this estimate is biased and inconsistent

The usual argument that the explanatory variables matrix X in least-squares is fixed in repeated sampling allows one to pass the expectation operator over terms like and argue that E(ε ) = 0, eliminating the bias term. Here however, because of spatial dependence, we cannot make the case that Wy is fixed in repeated sampling. For an observation i, the regressor Wy is a spatially weighted average of other y j values in the sample. But each of these y j s is a spatially weighted of other y values in the data set, including yi . Since yi depends directly on εi , it is clear that the regressor and error term are not uncorrelated, so OLS estimates of ρ are biased and inconsistent. More intuitively: the average neighbouring dep. var includes the neighbour’s error terms, the neighbour’s-neighbours error terms, the neighbour’s- neighbour’s-neighbours error terms and so on….

This also rules out making a case for consistency of the least-squares estimate of ρ , because the probability limit (plim) for the term y´W´ ε is not zero. In fact, Anselin (1988) establishes that:

Given that least-squares will produce biased and inconsistent estimates of the spatial autoregressive parameter ρ in this model, we proceed the estimation through Maximum Likelihood . The estimator for ρ requires that we find a value of ρ that maximizes the likelihood function shown in, by assuming unobservables are normally distributed with no heteroscedasticity, serial correlation etc.

ML is in addition difficult (slow) to evaluate when sample size n is very big, and the Matrix (I - ρ W) must be non-singular (invertible)

Another way to estimate is IV/2SLS estimation of the spatially autoregressive model, Since Wy=ρWWy+WXβ+ε, and since we are assuming that X is uncorrelated with the error term ε, an obvious candidate for instruments is WX, i.e. the spatial lags of the independent variables in the model. The intuition here is that characteristics (X ) of places that neighbour place i determine the outcomes in these neighbouring areas (Wy ), but do not directly affect outcomes in place i (y). To estimate the effect of outcomes in neighbouring places on outcomes in place i (the parameter ρ), we can use the characteristics of neighbouring places as instruments (WX). In IV/2SLS estimation, the neighbouring characteristics generate predictions of neighbouring outcomes that are uncorrelated with the error term for place i.

Although it is easy to estimate, even on big samples and it doesn’t require parametric assumptions about distribution of unobservable factors. Assumes that the neighbouring characteristics WX do not directly affect outcomes y (i.e. error term for i is uncorrelated with neighbouring x), and it is not efficient (precise) relative to ML

3.2.6 The spatial errors model Here we turn attention to the spatial errors model shown below, where the disturbances exhibit spatial dependence, ie unobserved factors in neighbouring places are correlated

y contains an n*1 vector of dependent variables and X represents the usual n*k data matrix containing explanatory variables. W is a known spatial weight matrix and the parameter ρ is a coefficient on the spatially correlated errors analogous to the serial correlation problem in time series models. The parameters β reflect the influence of the explanatory variables on variation in the dependent variable y

Unbiased and consistent estimates of β can be obtained by OLS. But one of the assumptions for consistency of OLS is violated. This assumption says that the error terms must be mutually uncorrelated and of equal variance such that Var (ε)=E[εε′]=σ2I .

The assumption of mutually uncorrelated and equal-variance error is violated. The implication of this is that the usual formula for the variance covariance matrix of the OLS estimator in is wrong, and estimates of the standard errors of the coefficients calculated in this way will be wrong. This will lead to mistaken inferences using standard test procedures. Moreover, if Assumption 3 does not hold, OLS is no longer the most efficient linear estimator available. We could get more precise estimates of the parameters, and unbiased estimates of the their variance covariance matrix. One method is to use Generalised Least Squares or GLS, which modifies OLS to take advantage of our knowledge of the variance covariance structure of the error term. Another approach is to use the method of Maximum Likelihood.

3.2.7 The general spatial model

A general version of the spatial model includes both the spatial lagged term as well as a spatially correlated error structure as shown below

This model is useful if there were evidence that spatial dependence existed in the error structure from a spatial autoregressive model. The estimation is done through Maximum Likelihood too.

3.3 Specification of the model

In this section we attempt to find evidence of the heterogeneity across municipalities controlling for the determinants of the investment within municipalities. According to the Tiebout hypothesis the municipalities offers different local public goods or policy outcome and compete between them in such a way to attract individuals to their jurisdiction. Then the individuals sort to different municipalities according to their diverse preferences. As a result the members of each municipality have the same demands for local public goods and there is heterogeneity across municipalities.

It could be analysed with the following relations:

(i) Invi=+αρ WInv j + β X +∂+ dep δε zon + i

The outcome of the policy outcome or the provision of local public good is represented by the investment of the municipality (Inv). The homogeneous characteristics inside the municipality are represented by X . The heterogeneity between municipalities is measured with the interaction term WInv j which represents the investment of the neighbourhood municipalities multiplied by the matrix of distances from the municipality i to the municipality j. We consider two definition of this matrix: a standaraized matrix with friction (2) in order to weight more heavily municipalities more closed than others and the binary matrix in order to rule out the asymmetry in the size of municipalities.

The rest of the terms in the equations control the differences of the municipalities according to the agro ecologic zone ( zon ) and for the department ( dep ) where are located. Finally εi represents the unobserved factors of the relation.

Another strategy is:

(ii) Invi=+αβγ1 X + WInv j ++∂ dep + δε zon + 1

Invi =+αβλ2 X + WX +∂+ dep δε zon + 2

The aim of this system of equations is to apply instrumental variables in the estimations of the model. It let us to control the problem of endogenous variables between the investments of the municipality i and the investment of the neighbour j. This is another way to test the hypothesis of heterogeneity in the investment across municipalities. The same specification and alternative estimation is present to test the homogeneity of the individual across municipalities.

The specification of the model is fitted to each of three sector considered in the investigation: education, health and drainage.

3.4 Methodology of non-parametric technologies

The parametric methods use lineal programming approach to estimate the technique efficiency. The technique efficiency show the performance of a municipality to produce over the FPP (Frontier of possibilities of production), where it is possible to get maximum output (local services) with the minor cost (local government investment). In contrast, a municipality is technically inefficient related to other, when provide the same or less services with higher investment (input-inefficiency), or when provide less services compared to other municipalities given a level of investment (output- inefficiency). The FPP could have different forms depending of the assumption of the applied models. The DEA and FDH model are the most popular in efficiency studies. The FDH model does not consider the assumption of scale economies and convexity function.

Figure 3 Data Envelopment Analysis (DEA) and Free Disposal Hull (FDH)

The inefficiency is measured as the difference between each point (observation) and the FPP. The x variable (input) is the per-capita local public investment o each municipality. The y variable (output) is the index of Total Municipality Performance (conformed to sub indicators of education, social activity (services to older people), basic sanitation and population) which gives us the level of services provided by the local government.

4 Results

In this section we are going to present the results of the estimations, first we demonstrate the homogeneity of municipalities by spatial correlation measures of the needs; after we demonstrate that there is no relation or pattern in the preferences or investments across municipalities.

Table 1 Spatial Correlation index of the Needs across Municipalities Bolivia SubSample Index Category of Need Variables Coefficient zzz p-value* Coefficient zzz p-value* nbi_2001 0.08 12.248 0.0000 0.517 11.418 0.0000 General idh_2001 0.13 19.582 0.0000 0.501 11.049 0.0000 escol_2001 0.124 18.712 0.0000 0.474 10.464 0.0000 Education tanalfabe 0.209 31.172 0.0000 0.678 14.901 0.0000 Moran's espvida_2001 0.158 23.630 0.0000 0.471 10.386 0.0000 Health mortinf 0.189 28.231 0.0000 0.52 11.465 0.0000 aguaredpct 0.016 2.875 0.0020 0.113 2.779 0.0030 Sanitation alcantarillapct 0.011 2.102 0.0180 0.021 1 0.2790 viviendapct 0.121 18.386 0.0000 0.218 5.014 0.0000 nbi_2001 0.909 -1.626 0.0520 0.55 -8.856 0.0000 General idh_2001 0.996 -0.092 0.4630 0.489 -10431 0.0000 escol_2001 0.947 -1.188 0.1170 0.535 -9.425 0.0000 Education tanalfabe 0.902 -2.055 0.0200 0.297 -14.424 0.0000 Geary's espvida_2001 0.873 -2.765 0.0030 0.509 -9.911 0.0000 Health mortinf 0.872 -2.627 0.0040 0.455 -10.909 0.0000 aguaredpct 1.049 0.278 0.3900 1 -0.285 0.3880 Sanitation alcantarillapct 1.339 1.921 0.0270 1 -1 0.3020 viviendapct 0.673 -3.841 0.0000 0.79 -3.156 0.0010

As shown by the Table 1, there is a positive spatial correlation among the set of variables selected to express the Needs of the Municipalities in Bolivia; a evidence of the Homogeneity of municipalities in Bolivia. In general the Basic Satisified Needs Index is correlated at 13% among the municipalities in the space considering the Moran index, and at 9% considering the Geary measure.

In education also, there is a 12.4% of correlation in the level of schooling across municipalities and 21% considering the analphabetism rate; health needs are correlated at 16% (life expectancy) and 18% (infant mortality).

Table 2 Heterogeneity in Investment in Education across Municipalities W standar friction 2 W binary Bolivia Sample Bolivia Sample Bolivia Sample Bolivia Sample Dep Variable InvEduc_pc eq1 eq2 eq3 eq4 eq5 eq6 eq7 eq8 ruralpct 7.083** 7.320** 7.088*** 7.348*** 7.083** 7.322** 7088 7.320*** (3.398) (3.411) (0.744) (0.823) (3.398) (3.409) (9.52)** (0.820) jovenpct 65.07*** 71.12*** 64.97*** 70.95*** 65.07*** 70.94*** 64967 70.95*** (15.48) (15.70) (3.136) (3.596) (15.48) (15.63) (20.71)** (3.568) logpop2001 8.064 7.435 7.698** 7.214 8.064 7.870 7698 7.914* (4.936) (6.126) (3.687) (4.495) (4.936) (6.116) (2.09)* (4.501) lgconspc -17.89 -16.06 -17.11 -16.25 -17.89 -16.75 -17113 -16.77 (11.72) (13.90) (13.23) (15.81) (11.72) (13.76) (-1.29) (15.76) pobnonativopct -17.68** -21.35*** -17.62*** -21.46*** -17.68** -21.24*** -17619 -21.22*** (7.395) (7.734) (1.761) (2.060) (7.395) (7.697) (10.00)** (2.054) fecund 0.719 -0.734 0.750 -1.040 0.719 -0.743 0.75 -0.718 (3.176) (4.108) (3.965) (4.973) (3.176) (4.070) (-0.19) (4.930) rho -0.00686** -0.0833 -0.00686** -0.0121** (0.00305) (0.0659) (0.00305) (0.00597) WEd01 -0.00500* -0.0256 -0.005 -0.0128 (0.00296) (0.123) (-1.69) (0.00996) _Iidep_2 -140.9* -139.9*** -140.9* -139949 (80.19) (42.11) (80.19) (3.32)** _Iidep_3 -132.3* -8.660 -136.0*** -8.713 -132.3* -3.682 -135967 -3.383 (78.50) (8.514) (41.70) (14.73) (78.50) (9.613) (3.26)** (15.27) _Iidep_4 -134.8* -4.602 -136.5*** -5.569 -134.8* -2.397 -136490 -2.184 (77.71) (7.478) (40.64) (15.66) (77.71) (7.867) (3.36)** (15.76) _Iidep_5 -114.4 9.136 -118.6*** 6.663 -114.4 12.02 -118563 12.40 (77.57) (16.75) (43.36) (21.23) (77.57) (17.34) (2.73)** (21.19) _Iidep_6 -24.23 -25.68 -24.23 -25675 (54.93) (38.57) (54.93) (-0.67) _Iidep_7 -135.0* 2.975 -135.3*** 2.227 -135.0* 3.353 -135307 3.439 (79.04) (8.861) (41.84) (19.37) (79.04) (8.702) (3.23)** (19.29) _Iidep_8 -131.2 28.42 -129.9*** 28.66 -131.2 28.04 -129932 28.00 (80.40) (22.59) (40.56) (19.97) (80.40) (22.45) (3.20)** (19.92) _Iidep_9 -132.8* 11.04 -130.2*** 10.38 -132.8* 9.110 -130189 9.052 (79.41) (13.19) (43.64) (31.57) (79.41) (12.90) (2.98)** (31.46) _Iidzona2_2 -78.98 -74.10** -78.98 -74101 (52.48) (36.41) (52.48) (2.04)* _Iidzona2_3 -23.88 -34.38 -20.47 -33.66 -23.88 -35.24 -20467 -35.36 (16.68) (24.73) (24.21) (63.03) (16.68) (24.96) (-0.85) (62.86) _Iidzona2_4 -13.96 -26.08 -11.59 -26.12 -13.96 -26.72 -11587 -26.76 (14.18) (19.75) (21.08) (26.61) (14.18) (19.86) (-0.55) (26.54) _Iidzona2_5 -137.1* -133.2*** -137.1* -133158 (81.24) (42.71) (81.24) (3.12)** _Iidzona2_6 7.510 9.650 7.774 8.990 7.510 9.002 7774 9.020 (6.507) (6.591) (10.91) (12.48) (6.507) (6.498) (-0.71) (12.37) _Iidzona2_7 -8.874 -3.089 -7.481 -2.618 -8.874 -6.605 -7481 -6.852 (7.349) (7.724) (16.36) (18.12) (7.349) (8.353) (-0.46) (18.37) Constant 183.5 29.14 176.5* 33.69 183.5 30.68 176533 30.38 (124.4) (93.20) (102.5) (114.3) (124.4) (92.25) (-1.72) (113.6) Observations 314 234 314 234 314 234 314 234 R-squared . . 0.784 0.819 0.78 0.820 Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1

Table 2 shows that there is not acceptable evidence on the relation between the Investments in education among municipalities. Eq 1 represents a Spatial lag model of order 1 for the Investment in Education, the value of the coefficient rho (-0.007) is although significative, very small in order to conclude a significative relation: if the weighted Investment in education of the municipalities j increase by one unit, the investment in education in municipality i decrease by 0.007 (Bolivians per capita). Eq 2 repeats the exercise but for the subsample of concentrated municipalities, here the value of the coefficient rho turns on not significant (and the negative sign remains).

In equation3 and 4, instrumental variables methodology is used in the estimation in order to reduce the pitfalls of Maximum Likelihood (as explained in methodology section). In Eq 3 this technique is applied to the overall observations and in equation 4 to the subsample already defined, here the results of the coefficients WED01 are similar to the results with ML (rho), significative at 10% in Bolivia’s sample and not significative in the concentrated sample. Note that the value of the coefficient is still very small and with negative sign.

In equations 5-8 the same exercise is repeated but considering another weighting matrix W, a binary matrix that weight with 1 if they are neighbors and 0 otherwise. Equations 5 and 6 are run by Maximum Likelihood, and equations 7 and 8 by Instrumental Variables, the same pattern holds, coefficients negatives, not significative and very small.

As controls for this specification were used: 1) the proportion of people that lives in rural areas , which have a positive influence on the investment in education in the municipalities, if the proportion of rural persons increase by one unit the investment in education increases by 7 Bolivians percápita 2) the proportion of young people (less than 15 years old), which have a big positive influence on the education spends, if the proportion of young persons increase by one unit the investment in education increases by around 70 Bolivians percápita 3) the size of the municipality (proxied by the log of the total population), it also have a positive influence on the education investment, if the size of a municipality increases by 1% the spend in health increases by 2 Bs percápita 4) the level of wealth (proxied by the log of consume percápita), as can be seen if the proportion of richer persons increase by one percent the investment in education decreases by around 17 Bolivians percápita (note whereas that this result is not statistically significative) 5) Proportion of persons that do not speak spanish in the municipality (persons that speak quechua, aymara, etc), if the proportion of te population that do not speak Spanish increases by one unit, the investment in education decreases by around 17 Bolivians percápita 6) Size of the family (proxied by the fecundity rate in the municipality: number of children per woman), that turned not significative in the models.

It is important to highlight that these controls are variables selected in order to represent the heterogeneity inside the municipality. And that the signs of the most variables and especially of the measures of the relation across municipalities are stable.

Table 3 shows repeat the exercise for the Investment percápita in health; the result is clear, there is not evidence on the relation between the Investments in Health across municipalities. In equation 1 (a Spatial lag model of order 1), the value of the coefficient rho is significative at 10%, if the weighted Investment in education of the neighbor municipalities increase by one unit, the investment in education in the municipality i decrease by 0.17 (Bolivians per capita). In equations 2-8 the value of the coefficients that measure the relation of the investment across municipalities turns on not significant (although the small value and the negative sign remain).

Again, in equations 3, 4, 7 and 8: instrumental variables methodology is used; in equations 1, 2, 5 and 6 Maximum Likelihood procedure is applied. First a traditional standardized matrix W is used (with friction 2) and in equations 5-8 the same exercise is repeated but considering a binary weighting matrix. The results are tested in two samples, all the country and in the concentrated’ municipalities sample.

As controls for this specification were used: 1) the proportion of people that lives in rural areas , which have a negative influence on the investment in sanitation, if the proportion of people that do not live in the urban area increases by une unit the investment in sanitation decreases by 5 Bolivians percápita 2) the proportion of women , which have a positive influence on the health spends, if the proportion of women increase by one unit the investment in health increases by around 7 Bolivians percápita 3) the number of childbirth , which have a very small positive influence on the health spends, if the number of childbirths increase by one unit in the municipality the investment in health increases by around 15 cents percápita 4) the size of the municipality (proxied by the log of the total population), it also have a big positive influence on the health investment, bigger municipalities spend more in education than smaller ones 5) the level of wealth (proxied by the log of consume percápita), as can be seen if the proportion of richer persons increase the investment in health decreases (note whereas that this result is not statistically significative) 6) Proportion of persons that do not speak spanish in the municipality (persons that speak quechua, aymara, etc), if the proportion of the population that do not speak Spanish increases by one unit, the investment in health increases by around 1 Bolivian percápita 7) Analphabetism rate , if the proportion of ignorant people increase the investment in health decrease.

Table 4 shows the results for the Investment percápita in sanitation; the result is again clear, there is not evidence on the relation between the Investments in sanitation across municipalities. Again, in equations 1, 2, 5 and 6 Maximum Likelihood procedure is applied, and in equations 3, 4, 7 and 8 instrumental variables methodology were used. Both, a traditional standardized matrix W is used (with friction 2) and a binary weighting matrix. The results are tested in two samples, all the country and in the concentrated’ municipalities sample.

As controls for this specification were used: 1) the proportion of people that lives in rural areas , which have a negative influence on the investment in health in the municipalities, (although here not significative) 2) the proportion of men , which have a positive influence on the sanitation spends, if the proportion of men increase by one unit the investment in sanitation increases by around 25 Bolivians percápita 3) the size of the municipality (proxied by the log of the total population), it does not have a influence on the sanitation investment, bigger municipalities spend more in education than smaller ones 4) the level of wealth (proxied by the log of consume percápita), as can be seen if the proportion of richer persons increase the investment in sanitation increases by 25 Bs percápita 5) Proportion of persons that do not speak spanish in the municipality (persons that speak quechua, aymara, etc), if the proportion of the population that do not speak Spanish increases by one unit, the investment in sanitation increases by around 25 Bolivians percápita (this result is strange, although not so important, considering it is a control)

Table 3 Heterogeneity in Investment in Health across Municipalities W standar friction 2 W binary Bolivia Sample Bolivia Sample Bolivia Sample Bolivia Sample Dep Variable InvHealth_pc eq1 eq2 eq3 eq4 eq5 eq6 eq7 eq8 ruralpct -0.0520 -0.0525 -0.0492 -0.0683 -0.0624 -0.0655 -0.0630 -0.0657 (0.0947) (0.115) (0.103) (0.119) (0.0969) (0.116) (0.104) (0.118) mujerpct 7.414*** 7.412*** 7.133*** 7.056*** 7.353*** 7.340*** 7.104*** 7.081*** (0.608) (0.398) (0.744) (0.424) (0.592) (0.396) (0.739) (0.422) parto2001 0.00121*** 0.00121* 0.00141*** 0.00147** 0.00125*** 0.00124* 0.00145*** 0.00146** (0.000333) (0.000678) (0.000377) (0.000695) (0.000337) (0.000682) (0.000383) (0.000693) logpop2001 2.162*** 2.158*** 2.079*** 1.962*** 2.098*** 2.044*** 2.031*** 1.997*** (0.692) (0.598) (0.770) (0.683) (0.719) (0.604) (0.770) (0.678) lgconspc -2.707 -2.701 -2.266 -2.353 -2.595 -2.516 -2.430 -2.395 (2.361) (2.189) (3.072) (2.474) (2.354) (2.206) (3.058) (2.472) pobnativopct 0.987** 0.988*** 1.230** 1.246*** 1.001** 1.016*** 1.226** 1.236*** (0.481) (0.310) (0.575) (0.337) (0.476) (0.313) (0.579) (0.338) tanalfabe -0.160** -0.160** -0.125 -0.130 -0.155** -0.156** -0.129 -0.129 (0.0719) (0.0762) (0.0878) (0.0885) (0.0720) (0.0767) (0.0878) (0.0883) Ws21 -0.156 -0.00211 0.000677 -0.00256 (0.157) (0.0775) (0.00221) (0.00625) rho -0.163* -0.0779 -0.000588 -0.00481 (0.0865) (0.0644) (0.00185) (0.00630) _Iidep_2 -35.98*** -35.90*** -34.34*** -34.08*** (8.867) (6.817) (9.001) (6.669) _Iidep_3 -39.78*** -39.70*** -3.029** -2.901 -37.56*** -38.05*** -2.591* -2.735 (8.847) (6.719) (1.348) (2.272) (9.101) (6.545) (1.475) (2.300) _Iidep_4 -35.47*** -35.39*** 2.041 1.893 -33.66*** -33.90*** 2.191 2.049 (9.042) (6.514) (1.976) (2.505) (9.238) (6.370) (2.014) (2.529) _Iidep_5 -37.06*** -37.01*** 0.920 0.197 -35.78*** -36.30*** 0.753 0.484 (9.120) (6.741) (3.264) (3.548) (9.403) (6.782) (3.319) (3.547) _Iidep_6 -19.82 -19.83*** -19.92 -20.21*** (12.62) (6.011) (13.03) (6.076) _Iidep_7 -34.89*** -34.81*** 3.207 3.131 -33.14*** -33.13*** 3.153 3.142 (8.979) (6.722) (2.337) (2.885) (9.145) (6.558) (2.325) (2.882) _Iidep_8 -39.37*** -39.29*** -1.883 -1.870 -37.48*** -37.24*** -1.831 -1.849 (8.374) (6.608) (4.030) (3.162) (8.468) (6.384) (4.067) (3.160) _Iidep_9 -37.24*** -37.15*** -1.239 -0.838 -35.26*** -34.79*** -0.971 -0.904 (9.220) (7.112) (2.378) (4.662) (9.295) (6.890) (2.418) (4.643) _Iidzona2_2 1.117 1.094 0.249 0.921 (5.025) (5.491) (5.225) (5.631) _Iidzona2_3 0.123 0.129 -1.898 -2.080 0.0684 0.510 -2.143 -2.116 (3.716) (3.556) (4.323) (8.990) (3.925) (3.664) (4.378) (8.980) _Iidzona2_4 3.256 3.247 2.590 2.539 2.909 3.190 2.571 2.555 (3.972) (3.175) (4.796) (3.756) (4.091) (3.230) (4.824) (3.752) _Iidzona2_5 -31.26*** -31.22*** -30.49*** -29.95*** (8.687) (6.503) (8.845) (6.548) _Iidzona2_6 3.038* 3.028* 4.064** 3.815** 2.791* 2.809 3.883** 3.848** (1.612) (1.712) (1.799) (1.813) (1.618) (1.710) (1.781) (1.796) _Iidzona2_7 0.727 0.719 1.833 1.647 0.452 0.618 1.492 1.562 (1.605) (2.530) (1.758) (2.641) (1.634) (2.559) (1.771) (2.639) Constant 36.92** 36.81** -4.335 -2.665 34.58** 33.81** -2.744 -2.685 (16.87) (15.99) (20.32) (17.31) (16.73) (15.96) (20.31) (17.21) Observations 314 314 234 234 314 314 234 234 R-squared . 0.881 . 0.909 . 0.879 . 0.909 Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1

Table 4 Heterogeneity in Investment in Sanitation across Municipalities W standar friction 2 W binary Bolivia Sample Bolivia Sample Bolivia Sample Bolivia Sample Dep Variable InvSanitat_pc eq1 eq2 eq3 eq4 eq5 eq6 eq7 eq8 logpop2001 56.01 33.42 135.3 100.0 39.34 46.66 105.6 93.55 (91.03) (96.43) (115.7) (119.8) (90.89) (94.95) (108.2) (117.0) ruralpct -5.468** -5.653*** -5.630** -5.832*** -5.536** -5.566*** -5.787** -5.835*** (2.413) (0.573) (2.303) (0.601) (2.443) (0.556) (2.335) (0.579) pobnativopct 20.88*** 21.21*** 24.59*** 24.98*** 20.95*** 21.07*** 24.95*** 25.13*** (5.696) (1.439) (5.755) (1.603) (5.764) (1.419) (5.865) (1.583) hombrespct 25.14*** 24.52*** 21.29*** 20.51*** 24.90*** 24.81*** 20.60*** 20.28*** (7.514) (1.954) (7.317) (2.161) (7.616) (1.896) (7.503) (2.097) lgvivienda -52.50 -31.13 -132.3 -98.10 -36.15 -43.83 -103.4 -91.70 (90.63) (96.03) (115.3) (119.5) (90.36) (94.73) (107.6) (116.8) lgconspc 18.62** 19.94*** 14.37* 15.34* 18.91** 19.38*** 15.27* 15.72* (7.876) (7.535) (8.341) (8.344) (8.052) (7.453) (8.451) (8.305) rho -0.123 -0.0602 -0.00146 0.00328 (0.0904) (0.0769) (0.00183) (0.00520) WIs21 0.127 0.0386 0.000456 0.00808 (0.175) (0.0808) (0.00238) (0.00598) _Iidep_2 -69.25** -68.39** -69.30** -68.68** (34.68) (31.80) (34.74) (31.60) _Iidep_3 -70.19** -71.69** -3.052 -3.724 -67.58* -71.97** -5.006 -7.266 (34.89) (31.30) (7.748) (10.43) (35.04) (31.56) (7.807) (10.76) _Iidep_4 -74.85** -75.75** -8.170 -9.089 -73.60** -75.82** -9.250 -10.01 (34.34) (30.70) (6.067) (11.08) (34.34) (30.62) (6.081) (11.07) _Iidep_5 -89.77*** -97.54*** -24.92*** -30.02** -90.12*** -94.67*** -29.77*** -32.33** (34.80) (32.92) (9.396) (15.15) (34.49) (32.75) (9.608) (14.88) _Iidep_6 -90.72*** -93.92*** -90.89*** -92.73*** (24.72) (29.12) (24.67) (28.94) _Iidep_7 -65.12* -65.95** -1.247 -1.340 -64.24* -65.93** -1.291 -1.272 (35.57) (31.69) (7.539) (13.79) (35.77) (31.55) (7.426) (13.75) _Iidep_8 -120.2*** -118.7*** -63.36*** -63.83*** -120.0*** -119.3*** -63.79*** -64.00*** (32.89) (30.77) (18.79) (14.02) (32.87) (30.56) (19.13) (13.99) _Iidep_9 -96.71*** -96.96*** -28.62*** -28.77 -97.99*** -96.47*** -28.65*** -28.56 (34.23) (33.08) (7.617) (22.44) (34.31) (32.92) (7.616) (22.38) _Iidzona2_2 -0.937 -2.212 -4.062 -0.782 (38.69) (26.71) (38.81) (26.83) _Iidzona2_3 14.59 14.93 27.30 28.01 13.28 15.22 28.25* 29.00 (13.11) (17.18) (16.73) (43.86) (13.39) (17.24) (16.95) (43.77) _Iidzona2_4 17.23 15.83 29.30 29.72 15.66 16.82 29.79 30.13 (13.58) (15.39) (20.21) (18.40) (13.65) (15.33) (20.39) (18.35) _Iidzona2_5 -95.88*** -97.18*** -98.25*** -95.98*** (33.32) (31.42) (33.38) (31.33) _Iidzona2_6 -2.303 -3.939 -5.065 -6.245 -2.973 -3.148 -5.809 -5.844 (5.501) (8.296) (5.052) (8.831) (5.549) (8.167) (5.165) (8.757) _Iidzona2_7 -11.95** -11.91 -12.32** -11.74 -12.36** -11.79 -11.06* -9.734 (5.930) (12.27) (6.233) (12.92) (6.074) (12.21) (6.151) (12.99) Constant -78.38 -77.82 -114.7** -109.9** -75.71 -78.86 -111.9** -112.1** (66.20) (55.86) (54.24) (49.21) (66.75) (55.64) (53.28) (48.93) Observations 314 314 234 234 314 314 234 234 R-squared . 0.898 . 0.925 . 0.900 . 0.925 Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1

Finally, we observe the results obtained by applying the methodology of DEA and FDH to evaluate the efficiency of the heterogeneous investment of municipalities.

In figure 1, we observe the index of efficiency from the Bolivian municipalities localized in the orient side of Bolivia (applying the DEA methodology). The municipalities with an index of efficiency equal to one, are over the FPP. The other municipalities are localized below the FPP, showing higher inefficiency (levels from 2-10), and most of them presenting a level of inefficiency over three.

In figure 2, we observe the same as before but applying the FDH methodology. That is, the concentration of the more inefficient municipalities at the levels (3-10) and the more efficient ones (l-2), follows the same path as the preceding methodology.

Figure 4 Level of efficiency of the orient side of Bolivian municipalities DEA methodology

Figure 5 Level of efficiency of the orient side of Bolivian municipalities FDH methodology

Following the same explanation, we can observe the efficiency of the municipalities from the occident side of Bolivia (Annex II), in which we observe higher levels of inefficiency. Additionally there are only a few municipalities over the FPP as in the case of the municipalities of the orient side of Bolivia.

5 Conclusions

We showed that the Tiebout hypothesis does not hold in the Bolivian economy. The three sectors of local public investment present heterogeneity across municipalities because they are almost not related to the inversions of the neighbourhoods (only education present very weakly evidence). On the other side we proved that the municipalities are homogeneous among them because of the high signification in the spatial correlations of their demands and principal characteristics. Evidently, the homogeneity of the municipalities and heterogeneity of the inversion do not correspond to the efficient framework designed by Tiebout in which the heterogeneity of the investment is along with heterogeneity of the communities.

In this sense, we were motivated to study if the public investment of the municipalities is matching efficiently the requirements of the population. We could see high levels of inefficiency among orient and occident side municipalities. That is, the input which is the level of public investment does not reach a good level of public services which is represented by the index of Total Municipality Performance (conformed with sub indicators of education, social activity, basic sanitation and population), compared to the reduced efficient municipalities.

In brief, what is relevant and new of this research is the consideration of the spatial dimension to prove the efficiency in the distribution of local public good. It is probably that the municipalities are acting as separated and isolated entities which are revealed by the heterogeneity of the investment, without considering alliances to fulfil the homogeneous demand.

ANEXO I

DEA METHOD Orient side of Bolivia Inefficient DMUs: data table

inefficiency inefficient DMU activity level (λ) DMUs used as reference

9.996784 Ascencion de Guarayos 1.000000 Boyuibe

9.719220 Exaltacion 1.000000 Boyuibe

9.496415 Santa Rosa 1.000000 Boyuibe

9.453052 Humaita (Ingavi) 1.000000 Boyuibe

9.112775 Riberalta 1.000000 Boyuibe

9.045296 Bella Flor 1.000000 Boyuibe

8.456770 San Pedro(Conquista) 1.000000 Boyuibe

8.278543 Santos Mercado 1.000000 Boyuibe 7.883575 Nueva Esperanza 1.000000 Boyuibe

7.651855 Villa Nueva 1.000000 Boyuibe

7.491189 Yapacani (San Juan) 1.000000 Boyuibe

7.473090 Bolpebra 1.000000 Boyuibe

0.434311 Boyuibe 7.390888 San Julian 0.565689 Pucara

7.261602 Pto. G. Moreno 1.000000 Boyuibe

0.441154 Boyuibe 7.196222 Pailon 0.558846 Pucara

7.025236 San Lorenzo 1.000000 Boyuibe

6.938267 San Javier 1.000000 Boyuibe

6.928669 Reyes 1.000000 Boyuibe

6.857165 Charagua 1.000000 Boyuibe

6.752230 Filadelfia 1.000000 Boyuibe

6.620126 San Andres 1.000000 Boyuibe

6.494639 San Borja 1.000000 Boyuibe

6.458485 Santa Ana 1.000000 Boyuibe

0.574878 Boyuibe 6.365495 Santa Rosa 0.425122 Pucara 6.319849 El Sena 1.000000 Boyuibe

6.205264 Baures 1.000000 Boyuibe

0.736159 Boyuibe 6.161166 San Javier 0.263841 Pucara

6.013338 Trinidad 1.000000 Boyuibe

5.952828 Yunchara 1.000000 Boyuibe

5.929828 Guayaramerín 1.000000 Boyuibe

0.478371 Boyuibe 5.925054 Lagunillas 0.521629 Pucara

0.514978 Boyuibe 5.671510 Buena Vista 0.485022 Pucara

0.622840 Boyuibe 5.593160 San Jose 0.377160 Pucara

5.566995 Cobija 1.000000 Boyuibe

5.489614 Puerto Rico 1.000000 Boyuibe

5.470811 Padcaya 1.000000 Boyuibe

5.468748 Santa Rosa 1.000000 Boyuibe

5.357644 Mineros 1.000000 Boyuibe

5.345775 Warnes 1.000000 Boyuibe 5.323633 Porongo (Ayacucho) 1.000000 Boyuibe

5.297793 Carapari 1.000000 Boyuibe

0.533310 Boyuibe 5.288955 San Carlos 0.466690 Pucara

5.150261 Magdalena 1.000000 Boyuibe

0.346491 Boyuibe 5.070916 San Miguel 0.653509 Pucara

5.045677 Huacaraje 1.000000 Boyuibe

5.021119 San Ramon 1.000000 Boyuibe

0.177855 Boyuibe 4.887781 Puerto Siles 0.822145 Pucara

4.879705 Villa Montes 1.000000 Boyuibe

0.746253 Boyuibe 4.870418 San Ignacio 0.253747 Pucara

0.231222 Boyuibe 4.846147 Loreto 0.768778 Pucara

4.812104 Uriondo 1.000000 Boyuibe

0.629575 Boyuibe 4.717166 Concepcion 0.370425 Pucara

0.881857 Boyuibe 4.704273 San Joaquin 0.118143 Pucara

4.605226 San Ignacio 0.103891 Boyuibe 0.896109 Pucara

4.600472 Entre Rios 1.000000 Boyuibe

4.575875 San Matias 1.000000 Boyuibe

0.957097 Boyuibe 4.360236 Rurrenabaque 0.042903 Pucara

0.889988 Boyuibe 4.303162 Puerto Suarez 0.110012 Pucara

4.272993 San Lorenzo 1.000000 Boyuibe

0.358746 Boyuibe 4.184991 Cabezas 0.641254 Pucara

0.198411 Boyuibe 4.139094 Gutierrez 0.801589 Pucara

4.045238 Santa Cruz de la Sierra 1.000000 Boyuibe

0.305979 Boyuibe 4.038383 Gral. Saavedra 0.694021 Pucara

4.015814 Montero 1.000000 Boyuibe

3.928188 Vallegrande 1.000000 Boyuibe

3.782431 Camiri 1.000000 Boyuibe

3.340212 Puerto Quijarro 1.000000 Boyuibe

3.339887 Tarija 1.000000 Boyuibe

3.335026 Robore 0.514312 Boyuibe 0.485688 Pucara

0.675211 Boyuibe 3.171843 La Guardia 0.324789 Pucara

0.525404 Boyuibe 2.892507 Postrer Valle 0.474596 Pucara

0.264130 Boyuibe 2.880525 Portachuelo 0.735870 Pucara

2.854077 Pampa Grande 1.000000 Boyuibe

0.077094 Boyuibe 2.842813 Porvenir 0.922906 Pucara

0.425849 Boyuibe 2.759801 Mairana 0.574151 Pucara

0.276967 Boyuibe 2.576010 OQUINAWA 0.723033 Pucara

0.029557 Boyuibe 2.348980 Cotoca 0.970443 Pucara

0.504471 Boyuibe 2.259401 Comarapa 0.495529 Pucara

0.157677 Boyuibe 2.251113 El Torno 0.842323 Pucara

2.216916 Urubicha 1.000000 Boyuibe

0.293323 Boyuibe 2.055648 El Puente 0.706677 Pucara 0.609959 Boyuibe 1.739674 Saipina 0.390041 Pucara

0.050489 Boyuibe 1.659544 Samaipata 0.949511 Pucara

0.801835 Boyuibe 1.313679 Cuevo 0.198165 Pucara

0.158195 Boyuibe 1.157016 San Rafael 0.841805 Pucara

0.591137 Boyuibe 1.152438 San Antonio de Lomerío 0.408863 Pucara

0.287658 Boyuibe 0.855897 Quirusillas 0.712342 Pucara

0.430022 Boyuibe 0.853985 San Ramón 0.569978 Pucara

0.393186 Boyuibe 0.851304 Moromoro 0.606814 Pucara

0.463652 Boyuibe 0.490431 Trigal 0.536348 Pucara

0.046343 Yacuiba 1.000000 Bermejo

0.038511 Tomayapo (El Puente) 1.000000 Bermejo

FDH METHOD Orient side of Bolivia Inefficient DMUs: data table inefficiency inefficient DMU activity level (λ) DMUs used as reference 9.996784 Ascencion de Guarayos 1.000000 Boyuibe

9.719220 Exaltacion 1.000000 Boyuibe

9.496415 Santa Rosa 1.000000 Boyuibe

9.453052 Humaita (Ingavi) 1.000000 Boyuibe

9.112775 Riberalta 1.000000 Boyuibe

9.045296 Bella Flor 1.000000 Boyuibe

8.456770 San Pedro(Conquista) 1.000000 Boyuibe

8.278543 Santos Mercado 1.000000 Boyuibe

7.883575 Nueva Esperanza 1.000000 Boyuibe

7.651855 Villa Nueva 1.000000 Boyuibe

7.491189 Yapacani (San Juan) 1.000000 Boyuibe

7.473090 Bolpebra 1.000000 Boyuibe

7.261602 Pto. G. Moreno 1.000000 Boyuibe

7.025236 San Lorenzo 1.000000 Boyuibe

6.938267 San Javier 1.000000 Boyuibe

6.928669 Reyes 1.000000 Boyuibe

6.857165 Charagua 1.000000 Boyuibe 6.752230 Filadelfia 1.000000 Boyuibe

6.620126 San Andres 1.000000 Boyuibe

6.494639 San Borja 1.000000 Boyuibe

6.458485 Santa Ana 1.000000 Boyuibe

6.319849 El Sena 1.000000 Boyuibe

6.205264 Baures 1.000000 Boyuibe

6.013338 Trinidad 1.000000 Boyuibe

5.952828 Yunchara 1.000000 Boyuibe

5.929828 Guayaramerín 1.000000 Boyuibe

5.566995 Cobija 1.000000 Boyuibe

5.489614 Puerto Rico 1.000000 Boyuibe

5.470811 Padcaya 1.000000 Boyuibe

5.468748 Santa Rosa 1.000000 Boyuibe

5.461740 San Julian 1.000000 Pucara

5.357644 Mineros 1.000000 Boyuibe

5.345775 Warnes 1.000000 Boyuibe

5.323633 Porongo (Ayacucho) 1.000000 Boyuibe

5.297793 Carapari 1.000000 Boyuibe 5.289048 Pailon 1.000000 Pucara

5.150261 Magdalena 1.000000 Boyuibe

5.045677 Huacaraje 1.000000 Boyuibe

5.021119 San Ramon 1.000000 Boyuibe

4.879705 Villa Montes 1.000000 Boyuibe

4.812104 Uriondo 1.000000 Boyuibe

4.600472 Entre Rios 1.000000 Boyuibe

4.575875 San Matias 1.000000 Boyuibe

4.279257 Santa Rosa 1.000000 Pucara

4.272993 San Lorenzo 1.000000 Boyuibe

4.246364 Puerto Siles 1.000000 Pucara

4.231607 San Ignacio 1.000000 Pucara

4.211365 Lagunillas 1.000000 Pucara

4.045238 Santa Cruz de la Sierra 1.000000 Boyuibe

4.044375 Loreto 1.000000 Pucara

4.015814 Montero 1.000000 Boyuibe

3.928188 Vallegrande 1.000000 Boyuibe 3.927258 Buena Vista 1.000000 Pucara

3.903092 San Miguel 1.000000 Pucara

3.782431 Camiri 1.000000 Boyuibe

3.754955 San Javier 1.000000 Pucara

3.616587 San Jose 1.000000 Pucara

3.601891 San Carlos 1.000000 Pucara

3.522300 Gutierrez 1.000000 Pucara

3.340212 Puerto Quijarro 1.000000 Boyuibe

3.339887 Tarija 1.000000 Boyuibe

3.162808 Gral. Saavedra 1.000000 Pucara

3.159288 Cabezas 1.000000 Pucara

2.990272 Concepcion 1.000000 Pucara

2.880034 San Ignacio 1.000000 Pucara

2.854077 Pampa Grande 1.000000 Boyuibe

2.649412 Porvenir 1.000000 Pucara

2.551417 San Joaquin 1.000000 Pucara

2.290240 Puerto Suarez 1.000000 Pucara

2.284224 Portachuelo 1.000000 Pucara 2.282291 Cotoca 1.000000 Pucara

2.233114 Rurrenabaque 1.000000 Pucara

2.216916 Urubicha 1.000000 Boyuibe

2.202725 Robore 1.000000 Pucara

2.004067 OQUINAWA 1.000000 Pucara

1.933189 El Torno 1.000000 Pucara

1.908413 Mairana 1.000000 Pucara

1.859683 Postrer Valle 1.000000 Pucara

1.849335 La Guardia 1.000000 Pucara

1.570337 Samaipata 1.000000 Pucara

1.542913 El Puente 1.000000 Pucara

1.420147 Comarapa 1.000000 Pucara

0.945458 San Rafael 1.000000 Pucara

0.930311 Saipina 1.000000 Pucara

0.549501 Quirusillas 1.000000 Pucara

0.530510 San Antonio de Lomerío 1.000000 Pucara

0.491552 Cuevo 1.000000 Pucara 0.457399 Moromoro 1.000000 Pucara

0.430984 San Ramón 1.000000 Pucara

0.130212 Trigal 1.000000 Pucara

0.046343 Yacuiba 1.000000 Bermejo

0.038511 Tomayapo (El Puente) 1.000000 Bermejo

DEA METHOD Occident side of Bolivia Inefficient DMUs: data table inefficiency inefficient DMU activity level (λ) DMUs used as reference

73.509219 Tacobamba 1.000000 de Pacajes

67.811964 Ravelo 1.000000 Nazacara de Pacajes

65.811305 1.000000 Nazacara de Pacajes

62.035522 Coipasa 1.000000 Nazacara de Pacajes

53.716235 1.000000 Nazacara de Pacajes

49.917103 San Lucas 1.000000 Nazacara de Pacajes

49.771444 Villa Tunari 1.000000 Nazacara de Pacajes

0.918167 Nazacara de Pacajes 49.356492 Santiago de 0.081833 El Choro

48.070534 San Pedro de Curahuara 1.000000 Nazacara de Pacajes 0.960365 Nazacara de Pacajes 45.484593 Pelechuco 0.039635 El Choro

45.177607 1.000000 Nazacara de Pacajes

44.351596 San Pedro 1.000000 Nazacara de Pacajes

43.033650 Culpina 1.000000 Nazacara de Pacajes

42.974200 Calacoto 1.000000 Nazacara de Pacajes

0.934275 Nazacara de Pacajes 42.272577 Sica-Sica (V.Aroma) 0.065725 El Choro

41.369501 Pocoata 1.000000 Nazacara de Pacajes

40.458382 Pojo 1.000000 Nazacara de Pacajes

39.671698 Sacaca 1.000000 Nazacara de Pacajes

39.450946 1.000000 Nazacara de Pacajes

38.849225 Morochata 1.000000 Nazacara de Pacajes

38.392750 Chuma 1.000000 Nazacara de Pacajes

37.606774 1.000000 Nazacara de Pacajes

37.459673 1.000000 Nazacara de Pacajes

0.950636 Nazacara de Pacajes 36.667120 Puerto Villarroel 0.049364 El Choro

36.509472 Caripuyo 1.000000 Nazacara de Pacajes 36.345700 Tiahuanacu 1.000000 Nazacara de Pacajes

0.839931 Nazacara de Pacajes 36.078715 Malla 0.160069 El Choro

34.823020 1.000000 Nazacara de Pacajes

34.683980 Tarvita (V.Arias) 1.000000 Nazacara de Pacajes

34.661792 Caranavi 1.000000 Nazacara de Pacajes

33.516455 Vitichi 1.000000 Nazacara de Pacajes

33.384803 Poroma 1.000000 Nazacara de Pacajes

33.184085 1.000000 Nazacara de Pacajes

32.620625 Patacamaya 1.000000 Nazacara de Pacajes

32.157201 Arque 1.000000 Nazacara de Pacajes

31.630206 Belen de Urmiri 1.000000 Nazacara de Pacajes

31.263278 Incahuasi 1.000000 Nazacara de Pacajes

30.902047 Tapacarí 1.000000 Nazacara de Pacajes

30.815283 1.000000 Nazacara de Pacajes

30.541184 Cruz de Machacamarca 1.000000 Nazacara de Pacajes

30.384714 Tiraque 1.000000 Nazacara de Pacajes

30.115472 Cotagaita 1.000000 Nazacara de Pacajes 29.989671 Betanzos 1.000000 Nazacara de Pacajes

29.757895 Apolo 1.000000 Nazacara de Pacajes

29.729237 1.000000 Nazacara de Pacajes

29.627300 1.000000 Nazacara de Pacajes

29.476507 Guanay 1.000000 Nazacara de Pacajes

29.140277 Icla (R.Mujia) 1.000000 Nazacara de Pacajes

28.948902 Palos Blancos 1.000000 Nazacara de Pacajes

28.799206 Independencia 1.000000 Nazacara de Pacajes

28.400624 San Pedro De Totora 1.000000 Nazacara de Pacajes

28.172341 1.000000 Nazacara de Pacajes

28.117200 1.000000 Nazacara de Pacajes

28.015677 Toro Toro 1.000000 Nazacara de Pacajes

27.946069 Mizque 1.000000 Nazacara de Pacajes

27.798060 Padilla 1.000000 Nazacara de Pacajes

27.794143 Tinquipaya 1.000000 Nazacara de Pacajes

27.761850 Pocona 1.000000 Nazacara de Pacajes

27.730982 1.000000 Nazacara de Pacajes

27.600455 Tomina 1.000000 Nazacara de Pacajes 27.560820 Sipe Sipe 1.000000 Nazacara de Pacajes

27.499223 Puna 1.000000 Nazacara de Pacajes

27.478633 Machareti 1.000000 Nazacara de Pacajes

27.289657 1.000000 Nazacara de Pacajes

26.873271 Salinas de G. Mendoza 1.000000 Nazacara de Pacajes

26.352423 Villa Azurduy 1.000000 Nazacara de Pacajes

26.174835 Villa Serrano 1.000000 Nazacara de Pacajes

26.160064 1.000000 Nazacara de Pacajes

25.967146 1.000000 Nazacara de Pacajes

0.741947 Nazacara de Pacajes 25.807112 Bolivar 0.258053 El Choro

0.740335 Nazacara de Pacajes 25.637803 Pampa Aullagas 0.259665 El Choro

25.513969 Tacopaya 1.000000 Nazacara de Pacajes

25.469692 Villa Mojocoya 1.000000 Nazacara de Pacajes

25.354239 Ichoca 1.000000 Nazacara de Pacajes

25.095929 Chaqui 1.000000 Nazacara de Pacajes

25.059701 Monteagudo 1.000000 Nazacara de Pacajes 24.888181 1.000000 Nazacara de Pacajes

24.755786 Turco 1.000000 Nazacara de Pacajes

24.254161 Laja 1.000000 Nazacara de Pacajes

24.117312 Vinto 1.000000 Nazacara de Pacajes

23.723565 Santiago de Huari 1.000000 Nazacara de Pacajes

23.297929 Tiquipaya 1.000000 Nazacara de Pacajes

0.834172 Nazacara de Pacajes 23.272376 0.165828 El Choro

23.065027 Uncia 1.000000 Nazacara de Pacajes

22.875433 1.000000 Nazacara de Pacajes

22.838591 Presto 1.000000 Nazacara de Pacajes

22.823669 Colomi 1.000000 Nazacara de Pacajes

22.814603 Chayanta 1.000000 Nazacara de Pacajes

22.745586 Sacaba 1.000000 Nazacara de Pacajes

22.373173 Villa Huanuni 1.000000 Nazacara de Pacajes

0.517792 Nazacara de Pacajes 22.271131 0.482208 El Choro

21.822891 Palca 1.000000 Nazacara de Pacajes

21.754698 San Pablo de Huacareta 1.000000 Nazacara de Pacajes 21.367723 Villa Vaca Guzman 1.000000 Nazacara de Pacajes

21.059108 La Asunta 1.000000 Nazacara de Pacajes

21.025346 1.000000 Nazacara de Pacajes

20.925113 Tupiza 1.000000 Nazacara de Pacajes

20.824560 1.000000 Nazacara de Pacajes

20.755530 1.000000 Nazacara de Pacajes

20.747380 Santiago de Andamarca 1.000000 Nazacara de Pacajes

20.600255 \"Colcha\"\"K\"\" (V.Martin)\" 1.000000 Nazacara de Pacajes

20.450567 San Benito (VJQ.Mendoza) 1.000000 Nazacara de Pacajes

20.089518 \"Caiza \"\"D\"\"\" 1.000000 Nazacara de Pacajes

20.083028 1.000000 Nazacara de Pacajes

19.944014 Pazña 1.000000 Nazacara de Pacajes

19.927028 1.000000 Nazacara de Pacajes

19.687099 Santiago de Callapa 1.000000 Nazacara de Pacajes

19.647132 1.000000 Nazacara de Pacajes

19.304253 Alalay 1.000000 Nazacara de Pacajes

19.217171 Yocalla 1.000000 Nazacara de Pacajes 19.101081 Cliza 1.000000 Nazacara de Pacajes

18.669370 Villa Zudanez (Tacopaya) 1.000000 Nazacara de Pacajes

18.616026 Yotala 1.000000 Nazacara de Pacajes

18.615348 1.000000 Nazacara de Pacajes

18.550314 Quillacollo 1.000000 Nazacara de Pacajes

18.521984 Curva 1.000000 Nazacara de Pacajes

18.396070 Camargo 1.000000 Nazacara de Pacajes

18.325222 Ocuri 1.000000 Nazacara de Pacajes

18.320218 San Buenaventura 1.000000 Nazacara de Pacajes

18.307492 Cajuata 1.000000 Nazacara de Pacajes

0.453386 Nazacara de Pacajes 18.241394 Esmeralda 0.546614 El Choro

18.206361 1.000000 Nazacara de Pacajes

18.144168 Aiquile 1.000000 Nazacara de Pacajes

18.074922 Tacachi 1.000000 Nazacara de Pacajes

18.015643 Colcapirhua 1.000000 Nazacara de Pacajes

17.954992 Uyuni (Thola Pampa) 1.000000 Nazacara de Pacajes

17.885650 Tarabuco 1.000000 Nazacara de Pacajes 17.881517 Santuario Quillacas 1.000000 Nazacara de Pacajes

0.374354 Nazacara de Pacajes 17.780744 Carangas 0.625646 El Choro

17.475846 1.000000 Nazacara de Pacajes

17.335578 San Pedro de Quemes 1.000000 Nazacara de Pacajes

17.320808 Cochabamba 1.000000 Nazacara de Pacajes

17.142349 Omereque 1.000000 Nazacara de Pacajes

17.081930 Anzaldo 1.000000 Nazacara de Pacajes

17.035267 1.000000 Nazacara de Pacajes

17.010236 1.000000 Nazacara de Pacajes

0.732336 Nazacara de Pacajes 17.002597 0.267664 El Choro

16.963338 Villazon 1.000000 Nazacara de Pacajes

16.807315 Sicaya 1.000000 Nazacara de Pacajes

16.796713 Chipaya 1.000000 Nazacara de Pacajes

16.576499 Sucre 1.000000 Nazacara de Pacajes

16.564176 Punata 1.000000 Nazacara de Pacajes

16.403821 1.000000 Nazacara de Pacajes

16.262437 Arani 1.000000 Nazacara de Pacajes 16.050967 Todos Santos 1.000000 Nazacara de Pacajes

0.611229 Nazacara de Pacajes 15.983042 0.388771 El Choro

15.851037 Las Carreras 1.000000 Nazacara de Pacajes

15.724330 Potosi 1.000000 Nazacara de Pacajes

15.603573 Toco 1.000000 Nazacara de Pacajes

15.555160 1.000000 Nazacara de Pacajes

15.522314 Nuestra Se±ora de La Paz 1.000000 Nazacara de Pacajes

15.509758 1.000000 Nazacara de Pacajes

15.208847 Antequera (Bolivar) 1.000000 Nazacara de Pacajes

15.085354 Tomave 1.000000 Nazacara de Pacajes

14.916897 Villa Alcala 1.000000 Nazacara de Pacajes

14.893758 1.000000 Nazacara de Pacajes

14.678936 Desaguadero 1.000000 Nazacara de Pacajes

14.625789 Yamparaez 1.000000 Nazacara de Pacajes

14.185251 Totora 1.000000 Nazacara de Pacajes

13.469628 Vacas 1.000000 Nazacara de Pacajes

13.461129 Poopo 1.000000 Nazacara de Pacajes 0.270928 Nazacara de Pacajes 13.157066 Belen de Andamarca 0.729072 El Choro

0.452410 Nazacara de Pacajes 12.982059 Challapata 0.547590 El Choro

12.852442 1.000000 Nazacara de Pacajes

12.795574 Capinota 1.000000 Nazacara de Pacajes

12.533398 Toledo 1.000000 Nazacara de Pacajes

12.061693 1.000000 Nazacara de Pacajes

11.774078 Tito Yupanki 1.000000 Nazacara de Pacajes

11.515344 1.000000 Nazacara de Pacajes

11.172750 1.000000 Nazacara de Pacajes

0.863036 Nazacara de Pacajes 11.157448 Acasio 0.136964 El Choro

10.995333 Ayo-Ayo 1.000000 Nazacara de Pacajes

10.930222 Villa Rivero 1.000000 Nazacara de Pacajes

10.813100 Villa Abecia 1.000000 Nazacara de Pacajes

10.452798 El Villar 1.000000 Nazacara de Pacajes

10.451887 1.000000 Nazacara de Pacajes

10.431673 Comanche 1.000000 Nazacara de Pacajes 10.360913 1.000000 Nazacara de Pacajes

10.323808 Sopachuy 1.000000 Nazacara de Pacajes

10.175027 1.000000 Nazacara de Pacajes

9.762224 1.000000 Nazacara de Pacajes

0.504994 Nazacara de Pacajes 9.650067 Tolata 0.495006 El Choro

9.341496 1.000000 Nazacara de Pacajes

0.229177 Nazacara de Pacajes 9.188650 Chimore 0.770823 El Choro

9.119491 Porco 1.000000 Nazacara de Pacajes

9.054025 1.000000 Nazacara de Pacajes

8.983458 Choquecota 1.000000 Nazacara de Pacajes

0.849933 Nazacara de Pacajes 8.672593 Tarata 0.150067 El Choro

8.537845 Santivañez 1.000000 Nazacara de Pacajes

7.818224 Sacabamba 1.000000 Nazacara de Pacajes

0.331543 Nazacara de Pacajes 7.695822 Copacabana 0.668457 El Choro

7.642772 Huacaya 1.000000 Nazacara de Pacajes 0.751815 Nazacara de Pacajes 7.288015 Tahua 0.248185 El Choro

7.136842 (Gral.Perez) 1.000000 Nazacara de Pacajes

7.022264 Arbieto 1.000000 Nazacara de Pacajes

6.654199 Pasorapa 1.000000 Nazacara de Pacajes

6.377949 San Agustin 1.000000 Nazacara de Pacajes

6.357910 Corque 1.000000 Nazacara de Pacajes

0.141622 Nazacara de Pacajes 6.264485 Coro Coro 0.858378 El Choro

6.053508 San Pablo de Lipez 1.000000 Nazacara de Pacajes

5.731354 Oruro 1.000000 Nazacara de Pacajes

0.269085 Nazacara de Pacajes 5.533743 Yunguyo del Litoral 0.730915 El Choro

0.776096 Nazacara de Pacajes 5.413667 Ixiamas 0.223904 El Choro

0.325852 Nazacara de Pacajes 5.376374 Escara 0.674148 El Choro

4.692852 Chacarilla 1.000000 Nazacara de Pacajes

0.157448 Nazacara de Pacajes 4.681930 La Rivera 0.842552 El Choro

4.565332 1.000000 Nazacara de Pacajes 0.214096 Nazacara de Pacajes 4.276261 Vila Vila 0.785904 El Choro

3.903724 Cuchumuela (V. G.Villarroel) 1.000000 Nazacara de Pacajes

0.102337 Nazacara de Pacajes 3.712612 Charaña 0.897663 El Choro

3.243467 1.000000 El Choro

2.682813 Waldo Ballivian 1.000000 Nazacara de Pacajes

0.036872 Nazacara de Pacajes 2.142757 Machacamarca 0.963128 El Choro

1.966831 Mojinete 1.000000 Nazacara de Pacajes

1.852907 Atocha 1.000000 El Choro

1.595087 Huachacalla 1.000000 Nazacara de Pacajes

0.016724 1.000000 Nazacara de Pacajes

FDH METHOD Occident side of Bolivia Inefficient DMUs: data table inefficiency inefficient DMU activity level (λ) DMUs used as reference

73.509219 Tacobamba 1.000000 Nazacara de Pacajes

67.811964 Ravelo 1.000000 Nazacara de Pacajes

65.811305 Sabaya 1.000000 Nazacara de Pacajes 62.035522 Coipasa 1.000000 Nazacara de Pacajes

53.716235 Colquechaca 1.000000 Nazacara de Pacajes

49.917103 San Lucas 1.000000 Nazacara de Pacajes

49.771444 Villa Tunari 1.000000 Nazacara de Pacajes

48.070534 San Pedro de Curahuara 1.000000 Nazacara de Pacajes

45.177607 Sapahaqui 1.000000 Nazacara de Pacajes

44.351596 San Pedro 1.000000 Nazacara de Pacajes

43.033650 Culpina 1.000000 Nazacara de Pacajes

42.974200 Calacoto 1.000000 Nazacara de Pacajes

41.369501 Pocoata 1.000000 Nazacara de Pacajes

40.458382 Pojo 1.000000 Nazacara de Pacajes

39.671698 Sacaca 1.000000 Nazacara de Pacajes

39.450946 Colquencha 1.000000 Nazacara de Pacajes

38.849225 Morochata 1.000000 Nazacara de Pacajes

38.392750 Chuma 1.000000 Nazacara de Pacajes

37.606774 Puerto Acosta 1.000000 Nazacara de Pacajes

37.459673 Yaco 1.000000 Nazacara de Pacajes

36.509472 Caripuyo 1.000000 Nazacara de Pacajes 36.345700 Tiahuanacu 1.000000 Nazacara de Pacajes

34.823020 Pucarani 1.000000 Nazacara de Pacajes

34.683980 Tarvita (V.Arias) 1.000000 Nazacara de Pacajes

34.661792 Caranavi 1.000000 Nazacara de Pacajes

33.516455 Vitichi 1.000000 Nazacara de Pacajes

33.384803 Poroma 1.000000 Nazacara de Pacajes

33.184085 Calamarca 1.000000 Nazacara de Pacajes

32.620625 Patacamaya 1.000000 Nazacara de Pacajes

32.157201 Arque 1.000000 Nazacara de Pacajes

31.630206 Belen de Urmiri 1.000000 Nazacara de Pacajes

31.263278 Incahuasi 1.000000 Nazacara de Pacajes

30.902047 Tapacarí 1.000000 Nazacara de Pacajes

30.815283 Puerto Carabuco 1.000000 Nazacara de Pacajes

30.541184 Cruz de Machacamarca 1.000000 Nazacara de Pacajes

30.384714 Tiraque 1.000000 Nazacara de Pacajes

30.115472 Cotagaita 1.000000 Nazacara de Pacajes

29.989671 Betanzos 1.000000 Nazacara de Pacajes 29.757895 Apolo 1.000000 Nazacara de Pacajes

29.729237 Sorata 1.000000 Nazacara de Pacajes

29.627300 Ancoraimes 1.000000 Nazacara de Pacajes

29.476507 Guanay 1.000000 Nazacara de Pacajes

29.140277 Icla (R.Mujia) 1.000000 Nazacara de Pacajes

28.948902 Palos Blancos 1.000000 Nazacara de Pacajes

28.799206 Independencia 1.000000 Nazacara de Pacajes

28.400624 San Pedro De Totora 1.000000 Nazacara de Pacajes

28.172341 Viacha 1.000000 Nazacara de Pacajes

28.117200 Colquiri 1.000000 Nazacara de Pacajes

28.015677 Toro Toro 1.000000 Nazacara de Pacajes

27.946069 Mizque 1.000000 Nazacara de Pacajes

27.798060 Padilla 1.000000 Nazacara de Pacajes

27.794143 Tinquipaya 1.000000 Nazacara de Pacajes

27.761850 Pocona 1.000000 Nazacara de Pacajes

27.730982 Achacachi 1.000000 Nazacara de Pacajes

27.600455 Tomina 1.000000 Nazacara de Pacajes

27.560820 Sipe Sipe 1.000000 Nazacara de Pacajes 27.499223 Puna 1.000000 Nazacara de Pacajes

27.478633 Machareti 1.000000 Nazacara de Pacajes

27.289657 Luribay 1.000000 Nazacara de Pacajes

26.873271 Salinas de G. Mendoza 1.000000 Nazacara de Pacajes

26.352423 Villa Azurduy 1.000000 Nazacara de Pacajes

26.174835 Villa Serrano 1.000000 Nazacara de Pacajes

26.160064 Batallas 1.000000 Nazacara de Pacajes

25.967146 Irupana 1.000000 Nazacara de Pacajes

25.513969 Tacopaya 1.000000 Nazacara de Pacajes

25.469692 Villa Mojocoya 1.000000 Nazacara de Pacajes

25.354239 Ichoca 1.000000 Nazacara de Pacajes

25.095929 Chaqui 1.000000 Nazacara de Pacajes

25.059701 Monteagudo 1.000000 Nazacara de Pacajes

24.888181 Yanacachi 1.000000 Nazacara de Pacajes

24.755786 Turco 1.000000 Nazacara de Pacajes

24.254161 Laja 1.000000 Nazacara de Pacajes

24.117312 Vinto 1.000000 Nazacara de Pacajes 23.723565 Santiago de Huari 1.000000 Nazacara de Pacajes

23.297929 Tiquipaya 1.000000 Nazacara de Pacajes

23.065027 Uncia 1.000000 Nazacara de Pacajes

22.875433 Guaqui 1.000000 Nazacara de Pacajes

22.838591 Presto 1.000000 Nazacara de Pacajes

22.823669 Colomi 1.000000 Nazacara de Pacajes

22.814603 Chayanta 1.000000 Nazacara de Pacajes

22.745586 Sacaba 1.000000 Nazacara de Pacajes

22.373173 Villa Huanuni 1.000000 Nazacara de Pacajes

21.822891 Palca 1.000000 Nazacara de Pacajes

21.754698 San Pablo de Huacareta 1.000000 Nazacara de Pacajes

21.367723 Villa Vaca Guzman 1.000000 Nazacara de Pacajes

21.059108 La Asunta 1.000000 Nazacara de Pacajes

21.025346 Tipuani 1.000000 Nazacara de Pacajes

20.925113 Tupiza 1.000000 Nazacara de Pacajes

20.824560 Puerto Pérez 1.000000 Nazacara de Pacajes

20.755530 Mecapaca 1.000000 Nazacara de Pacajes

20.747380 Santiago de Andamarca 1.000000 Nazacara de Pacajes 20.600255 \"Colcha\"\"K\"\" (V.Martin)\" 1.000000 Nazacara de Pacajes

20.450567 San Benito (VJQ.Mendoza) 1.000000 Nazacara de Pacajes

20.089518 \"Caiza \"\"D\"\"\" 1.000000 Nazacara de Pacajes

20.083028 Chulumani 1.000000 Nazacara de Pacajes

19.944014 Pazña 1.000000 Nazacara de Pacajes

19.927028 Santiago de Machaca 1.000000 Nazacara de Pacajes

19.687099 Santiago de Callapa 1.000000 Nazacara de Pacajes

19.647132 Umala 1.000000 Nazacara de Pacajes

19.304253 Alalay 1.000000 Nazacara de Pacajes

19.217171 Yocalla 1.000000 Nazacara de Pacajes

19.101081 Cliza 1.000000 Nazacara de Pacajes

18.669370 Villa Zudanez (Tacopaya) 1.000000 Nazacara de Pacajes

18.616026 Yotala 1.000000 Nazacara de Pacajes

18.615348 Coripata 1.000000 Nazacara de Pacajes

18.550314 Quillacollo 1.000000 Nazacara de Pacajes

18.521984 Curva 1.000000 Nazacara de Pacajes

18.396070 Camargo 1.000000 Nazacara de Pacajes 18.325222 Ocuri 1.000000 Nazacara de Pacajes

18.320218 San Buenaventura 1.000000 Nazacara de Pacajes

18.307492 Cajuata 1.000000 Nazacara de Pacajes

18.206361 Tacacoma 1.000000 Nazacara de Pacajes

18.144168 Aiquile 1.000000 Nazacara de Pacajes

18.074922 Tacachi 1.000000 Nazacara de Pacajes

18.015643 Colcapirhua 1.000000 Nazacara de Pacajes

17.954992 Uyuni (Thola Pampa) 1.000000 Nazacara de Pacajes

17.885650 Tarabuco 1.000000 Nazacara de Pacajes

17.881517 Santuario Quillacas 1.000000 Nazacara de Pacajes

17.475846 El Alto 1.000000 Nazacara de Pacajes

17.335578 San Pedro de Quemes 1.000000 Nazacara de Pacajes

17.320808 Cochabamba 1.000000 Nazacara de Pacajes

17.142349 Omereque 1.000000 Nazacara de Pacajes

17.081930 Anzaldo 1.000000 Nazacara de Pacajes

17.035267 Mocomoco 1.000000 Nazacara de Pacajes

17.010236 Coroico 1.000000 Nazacara de Pacajes

16.963338 Villazon 1.000000 Nazacara de Pacajes 16.807315 Sicaya 1.000000 Nazacara de Pacajes

16.796713 Chipaya 1.000000 Nazacara de Pacajes

16.576499 Sucre 1.000000 Nazacara de Pacajes

16.564176 Punata 1.000000 Nazacara de Pacajes

16.403821 Llallagua 1.000000 Nazacara de Pacajes

16.262437 Arani 1.000000 Nazacara de Pacajes

16.050967 Todos Santos 1.000000 Nazacara de Pacajes

15.851037 Las Carreras 1.000000 Nazacara de Pacajes

15.724330 Potosi 1.000000 Nazacara de Pacajes

15.603573 Toco 1.000000 Nazacara de Pacajes

15.555160 Licoma 1.000000 Nazacara de Pacajes

15.522314 Nuestra Se±ora de La Paz 1.000000 Nazacara de Pacajes

15.509758 San Pedro de Tiquina 1.000000 Nazacara de Pacajes

15.208847 Antequera (Bolivar) 1.000000 Nazacara de Pacajes

15.085354 Tomave 1.000000 Nazacara de Pacajes

14.916897 Villa Alcala 1.000000 Nazacara de Pacajes

14.893758 Combaya 1.000000 Nazacara de Pacajes 14.678936 Desaguadero 1.000000 Nazacara de Pacajes

14.625789 Yamparaez 1.000000 Nazacara de Pacajes

14.185251 Totora 1.000000 Nazacara de Pacajes

13.469628 Vacas 1.000000 Nazacara de Pacajes

13.461129 Poopo 1.000000 Nazacara de Pacajes

12.852442 Quime 1.000000 Nazacara de Pacajes

12.795574 Capinota 1.000000 Nazacara de Pacajes

12.533398 Toledo 1.000000 Nazacara de Pacajes

12.061693 Collana 1.000000 Nazacara de Pacajes

11.774078 Tito Yupanki 1.000000 Nazacara de Pacajes

11.515344 Eucaliptus 1.000000 Nazacara de Pacajes

11.172750 Arampampa 1.000000 Nazacara de Pacajes

10.995333 Ayo-Ayo 1.000000 Nazacara de Pacajes

10.930222 Villa Rivero 1.000000 Nazacara de Pacajes

10.813100 Villa Abecia 1.000000 Nazacara de Pacajes

10.452798 El Villar 1.000000 Nazacara de Pacajes

10.451887 San Antonio de Esmoruco 1.000000 Nazacara de Pacajes

10.431673 Comanche 1.000000 Nazacara de Pacajes 10.360913 Catacora 1.000000 Nazacara de Pacajes

10.323808 Sopachuy 1.000000 Nazacara de Pacajes

10.175027 Inquisivi 1.000000 Nazacara de Pacajes

9.762224 Quiabaya 1.000000 Nazacara de Pacajes

9.341496 Aucapata 1.000000 Nazacara de Pacajes

9.119491 Porco 1.000000 Nazacara de Pacajes

9.054025 Cairoma 1.000000 Nazacara de Pacajes

8.983458 Choquecota 1.000000 Nazacara de Pacajes

8.537845 Santivañez 1.000000 Nazacara de Pacajes

7.818224 Sacabamba 1.000000 Nazacara de Pacajes

7.642772 Huacaya 1.000000 Nazacara de Pacajes

7.136842 Charazani (Gral.Perez) 1.000000 Nazacara de Pacajes

7.022264 Arbieto 1.000000 Nazacara de Pacajes

6.654199 Pasorapa 1.000000 Nazacara de Pacajes

6.648831 Santiago de Huayllamarca 1.000000 El Choro

6.377949 San Agustin 1.000000 Nazacara de Pacajes

6.357910 Corque 1.000000 Nazacara de Pacajes 6.053508 San Pablo de Lipez 1.000000 Nazacara de Pacajes

5.795824 Pelechuco 1.000000 El Choro

5.731354 Oruro 1.000000 Nazacara de Pacajes

5.476463 Sica-Sica (V.Aroma) 1.000000 El Choro

5.070728 Malla 1.000000 El Choro

4.731914 Carangas 1.000000 El Choro

4.692852 Chacarilla 1.000000 Nazacara de Pacajes

4.609130 Curahuara de Carangas 1.000000 El Choro

4.565332 Llica 1.000000 Nazacara de Pacajes

4.554799 Puerto Villarroel 1.000000 El Choro

4.347196 Belen de Andamarca 1.000000 El Choro

4.121297 Esmeralda 1.000000 El Choro

3.903724 Cuchumuela (V. G.Villarroel) 1.000000 Nazacara de Pacajes

3.863471 Bolivar 1.000000 El Choro

3.841365 Pampa Aullagas 1.000000 El Choro

3.256495 Chimore 1.000000 El Choro

3.243467 Caquiaviri 1.000000 El Choro

2.996924 Achocalla 1.000000 El Choro 2.903051 Coro Coro 1.000000 El Choro

2.727360 Challapata 1.000000 El Choro

2.682813 Waldo Ballivian 1.000000 Nazacara de Pacajes

2.600387 Ayata 1.000000 El Choro

2.301120 Papel Pampa 1.000000 El Choro

1.966831 Mojinete 1.000000 Nazacara de Pacajes

1.904839 Charaña 1.000000 El Choro

1.902686 La Rivera 1.000000 El Choro

1.883057 Copacabana 1.000000 El Choro

1.852907 Atocha 1.000000 El Choro

1.616102 Tolata 1.000000 El Choro

1.595087 Huachacalla 1.000000 Nazacara de Pacajes

1.567144 Machacamarca 1.000000 El Choro

1.478317 Yunguyo del Litoral 1.000000 El Choro

1.292075 Vila Vila 1.000000 El Choro

1.138596 Escara 1.000000 El Choro

0.945722 Acasio 1.000000 El Choro 0.568034 Tarata 1.000000 El Choro

0.487457 Tahua 1.000000 El Choro

0.121350 Ixiamas 1.000000 El Choro

0.016724 Caracollo 1.000000 Nazacara de Pacajes

ANEXO II

Figures of the Level of efficiency from the occident side of Bolivian municipalities DEA methodology

Cochabamba

La Paz

Oruro