Abstract
Decentralization has been put forward as a powerful tool to reduce poverty and improve governance in Africa. This paper will study the existence and identify the nature of spillovers resulting from local expenditure policies. These spillovers impact the efficiency of decentralization. We develop a twojurisdiction model of public expenditure, which differs from existing literature by capturing the extreme poverty of some local governments in developing countries through a generalized notion of Nash equilibrium, namely constrained Nash equilibrium. We show how and under what conditions spillovers among jurisdictions induce strategic behaviors from local officials. By estimating a spatial lag model for a panel data analysis of the 77 communes in Benin from 2002 to 2008, our empirical analysis establishes the existence of the strategic complementarity of public spending in various jurisdictions. Thus, any increase in the local public provision in one jurisdiction should induce a similar variation among the neighboring jurisdictions. This result raises the issue of coordination among local governments, and more broadly, it questions the efficiency of decentralization in developing countries in line with Oates’ theorem.
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Notes
 1.
This author recommends going “beyond the traditional fiscal federalism literature,” which is essentially associated with the competition principle. He argues that to some extent, most developing countries do not meet implicit or explicit assumptions posed by the firstgeneration theory of fiscal federalism (see Oates 2005, and Vo 2010, for comprehensive surveys of this literature).
 2.
For instance, the population in AbomeyCalavi has increased dramatically by 6.96 % between 2002 and 2013, while the population of DassaZoume, a rural commune, grew 1.58 % during the same period.
 3.
Chavis (2010) looks at what impact competition has on the effectiveness of decentralization in Indonesia. The author considers the extent to which the cost per square meter of road project decreases in the number of villages that compete to obtain grants from the central government. The analysis of competition is limited to the number of competitors. No analysis of interactions has been carried out.
 4.
This assumption is linked to our empirical work, as well. Since proximity matrices are normalized, their sum is equal to unity for each \(i\). Thus, we have \(\theta _{ij}=\theta _{ji}\) if, and only if, jurisdictions \(i\) and \(j\) have the same number of neighbors for a proximity matrix based on contiguity.
 5.
We show the absence of scale economies in providing current public spending according to the jurisdiction’s size (measured by the population density, \(\hbox {dens}\)). Both signs of first and second derivatives are positive and significantly different from zero: \({ g}_{i}{=3.751^{**}.\hbox {dens}}_{i} { +}\,{0.001^{***}.\hbox {dens}}_{i}^{2}\). Detailed results are provided in Table 1.
 6.
This condition obviously holds if the function \(v\left( .\right) \) is concave.
 7.
If this last expression is positive, then the game played by each jurisdiction is supermodular and at least one equilibrium exists.
 8.
If we adopt the contraction approach (see Vives 1999), the condition of equilibrium uniqueness involves
$$\begin{aligned} U_{11}^{i}\left( g_{i},\theta _{ij}g_{j}\right) +\left v_{12}^{i}\left( g_{i},\theta _{ij}g_{j}\right) \right <0, \end{aligned}$$which yields that \(\left J\right \) is positive.
 9.
 10.
A generalization to \(n\) jurisdictions is immediate, but it would involve some tedious expressions.
 11.
Human Development Report (Watkins 2007).
 12.
Ethnic fragmentation is defined as the probability that two individuals randomly drawn from one commune are from different ethnic groups.
 13.
Ethnic composition data come from 77 monographs provided by the European Union (“Programme d’Appui au Démarrage des Communes”).
 14.
The first round of municipal elections was held on December 15, 2002, and the second round took place on January 19, 2003, with an average rate of turnout estimated at 70 %.
 15.
Local officials are directly elected by the local population, on the same day for all communes, for a sixyear mandate that is once renewable.
 16.
The average population of the communes is about 90,000 inhabitants.
 17.
Local resources mainly stem from the communes’ own resources (about 70 %). Property taxes and licenses to exercise a trade or profession (patente) represent 90 % of local tax revenues (see Chambas 2010 for a detailed analysis of local fiscal resources in subSaharan Africa, particularly in Benin). Retroceded taxes, which come from transfers of state tax revenue to local governments, account for about 10 % of local resources.
 18.
Assets used to compute this wealth index are numerous: cars, refrigerators, irons, beds, phones, motorcycles/scooters, radios, VCRs, DVD players, ovens/stoves, washing machines, chairs, sewing machines, cell phones, bicycles, televisions, video recorders/VCRs, fans, foam mattresses, computers, internet access, land, home ownership, types of fuel, building materials, etc.
 19.
We generate a random number distributed between 0 and 1 for each commune. The weight assigned between two communes is the difference between its random numbers.
 20.
Weights are normalized so that their sum equals unity for each \(i\) for all weight matrices. This assumes that spatial interactions are homogeneous: Each neighbor has the same impact on the commune.
 21.
An alternative way to deal with endogeneity issue in our context has been proposed by Isen (2014), who relies on regression discontinuity design to test the existence of strategic interaction among local jurisdictions in Ohio. However, contrary to Isen, we have no external event similar to all communes that could be used as approximate random assignment (and the subsequent threshold) and then justify a regression discontinuity design.
 22.
Using a data panel helps to eliminate spatial error dependence arising through spatial autocorrelation of an omitted variable, since the influence of such variables is partly captured in communityspecific intercept terms.
 23.
 24.
 25.
\(T_{t}\) is a sequential numbering of the time periods beginning with the value 1.
 26.
Population density is the number of inhabitants per square kilometer. Per capita expenditures and population density are in log. Per capita expenditures are corrected for inflation.
 27.
We measure trade openness as a ratio of total foreign trade (exports plus imports) to GDP, as it is the one most often used in empirical studies.
 28.
\(E_{t1}\), \(E_{t}\), and \(E_{t+1}\) are dummy variables that take the value 1 the year before, the year of, and the year after the election, respectively, and 0 otherwise.
 29.
The variable takes the value 1 if the local government in jurisdiction \(i\) has the same partisan affiliation as the president in office. Until he stepped down in March 2006, Mathieu Kérékou enjoyed strong support in the north of the country (Alibori, Atacora, Borgou, and Donga), which was considered his fief. When Boni Yayi was elected, he affirmed his desire for political openness. His fiefs are concentrated in the south of the country, in particular, Atlantic, Collines, and Mono. Finally, about 40 % of the departments have shared the same partisan affiliation as the president in office.
 30.
 31.
The lags of at least two earlier periods for weak exogenous variables and three earlier periods for endogenous variables are used as instruments. The lagged dependent variable is instrumented by lags of the dependent variable from at least two earlier periods. We use two lags for endogenous and weak exogenous variables.
 32.
The consistency of the estimator depends on whether or not lagged values of explanatory variables are valid instruments. The criteria for the selection of instruments are found in two specification tests ( Arellano and Bond 1991). With the Hansen test, we test the null hypothesis of the overall validity of the instruments’ orthogonality conditions. The second test concerns the serial correlation of residuals. It examines the hypothesis that the residuals from the firstdifferentiated estimating equation are not secondorder correlated. In our case, both statistics confirm the validity of the instruments used.
 33.
As this coefficient provides an estimate \(\lambda \) varying between 0.411 and 0.629, the result indicates some level of persistence in public expenditure.
 34.
Note that, in their study of the Public Health Sector in Uganda, Akin et al. (2005) provide evidence for the hypothesis that spillover effects cause spending on public goods in one district to reduce spending on public goods in neighboring districts. Local public spending are, in this case, strategic substitutes.
 35.
To understand the sign of the coefficient associated with the election year dummy, one must refer to the election calendar and budget votes. Local elections take place at the beginning of March, and the definitive budget must be adopted before March 31. Therefore, in the year before the elections, decision makers increase current expenditures and decrease them the year after, since the definitive budget is approved.
 36.
Note that we find a positive and significant sign for the parameter associated with the employment rate, which indicates the effect of economic conjuncture. The trend variable remains, as expected, significant and negative. Indeed, per capita public expenditure has decreased by 75 % over the period, despite little growth between 2004 and 2006.
 37.
See the third Census of Population and Housing for 2002.
 38.
Formally, we test:
$$\begin{aligned} G_{it}&= \lambda S_{it1}+\rho ^{\prime }.(A_{jt}\times \hbox {EY}_{t})+\rho ^{\prime \prime }.(A_{jt}\times \hbox {NEY}_{t})+\beta _{1}.D_{it}+\beta _{2}.N_{dt} \nonumber \\&\quad +\,\beta _{3}.O_{ct}+\beta _{4}.PR_{it}+\beta _{5}.\hbox {EY}_{t}+\beta _{6}.\hbox {NEY}_{t}+\beta _{7}.T+\alpha _{i}+\varepsilon _{it}, \end{aligned}$$(14)where \(\hbox {EY}_{t}=E_{t1}+E_{t}\) and \(\hbox {NEY}_{t}=(1(E_{t1}+E_{t}))\).
 39.
In contrast, strategic substitutability raises the question of the existence of a Nash equilibrium.
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Acknowledgments
We thank the National Bureau of Economic Research (NBER), which has funded this project since 2009. We are grateful to the members of the Municipal Development Partnership (MDP) in Cotonou, especially Hervé Agossou, for their warm welcome, their valuable help in collecting data, their fruitful comments, and their discussions. We thank Elias Potek (University of Montreal, Geography Dept.) for his outstanding work in creating geographical maps in record time. We thank Simon Johnson (MIT), who has acted not only as a scientific mentor throughout our researching endeavors, but also as a valuable advisor. We thank OddHelge Fjeldstad (International Centre for Tax and Development) and François Vaillancourt (University of Montreal) for all of their helpful suggestions. We are grateful to Leonard Wantchekon (Princeton University) and the participants at the IREEP (Institut de Recherche Empirique en Economie Politique) conference, the CERDI (Centre d’Etudes et de Recherche sur le Développement International) seminar, and the CIRANO (Centre Interuniversitaire de Recherche en Analyse des Organisations) workshop, where a preliminary draft of this paper was presented in November 2010. Finally, we acknowledge financial support from the NBER Program on African Successes, especially Elisa Pepe for her amazing support throughout this project. Financial supports from the “Programme d’Investissements d’Avenir” of the French government (ANR10LABX1401) and the FERDI (Fondation pour les Etudes et Recherches sur le Développement International) are also warmly acknowledged.
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Appendix
Appendix
Proof of Proposition 1
Considering the unconstrained Nash equilibrium \(\left( \forall i,\text { } g_{i}^{*}\left( \theta \right) =\widetilde{g}_{i}\left( \theta \right) \right) \), the differentiation of (5) with respect to \(\theta _{ij}\) for both jurisdictions yields:
Applying the Cramer rule, we then obtain:
where \(J\) is the Jacoby matrix and its determinant is given by
Generally, the sign of \(\left J\right \) remains indeterminate since it does not rely on the sign of the Hessian matrix of a single optimization problem, as Caputo (1996) asserts. Thus, without additional assumptions about the stability or uniqueness of the Nash equilibrium, for instance, we cannot sign \(\left J\right \).
We obtain then three cases:

(i)
If \(g_{i}^{*}\left( \theta \right) =\overline{g}_{i}\), it is then obvious that \(\frac{\partial g_{i}^{*}\left( \theta \right) }{ \partial \theta _{ij}}=0\) and \(\frac{\partial g_{j}^{*}\left( \theta \right) }{\partial \theta _{ij}}=0\) from differentiation of (5) with respect to \(\theta _{ij}\).

(ii)
If \(g_{j}^{*}\left( \theta \right) =\overline{g}_{j}\) and \(g_{i}^{*}\left( \theta \right) =\widetilde{g}_{i}\left( \theta \right) \), then we have \(\frac{\partial g_{j}^{*}\left( \theta \right) }{ \partial \theta _{ij}}=0\), which yields
$$\begin{aligned} \frac{\partial g_{i}^{*}\left( \theta \right) }{\partial \theta _{ij}}= \frac{\theta _{ij}\overline{g}_{j}v^{\prime \prime }\left( g_{i}+\theta _{ij} \overline{g}_{j}\right) }{\frac{\partial ^{2}U^{i}\left( g_{i},\theta _{ij}g_{j}\right) }{\partial g_{i}^{2}}}, \end{aligned}$$which is positive if the function \(v\left( .\right) \) is convex, or equivalently if local public goods are strategic complements given (6).

(iii)
If \(g_{i}^{*}\left( \theta \right) =\widetilde{g} _{i}\left( \theta \right) \) and \(g_{j}^{*}\left( \theta \right) = \widetilde{g}_{j}\left( \theta \right) \), we obtain from (15)
$$\begin{aligned} \frac{\partial \widetilde{g}_{i}\left( \theta \right) }{\partial \theta _{ij} }\frac{\partial \widetilde{g}_{j}\left( \theta \right) }{\partial \theta _{ij}}&= \theta _{ji}\left( \frac{\theta _{ij}\widetilde{g}_{j}\left( \theta \right) v^{\prime \prime }\left( \widetilde{g}_{i}\left( \theta \right) +\theta _{ij}\widetilde{g}_{j}\left( \theta \right) \right) }{\left J\right }\right) ^{2}\\&\quad \times v^{\prime \prime }\left( \widetilde{g}_{j}\left( \theta \right) +\theta _{ji}\widetilde{g}_{i}\left( \theta \right) \right) U_{11}^{j}\left( \widetilde{g}_{j}\left( \theta \right) ,\theta _{ji} \widetilde{g}_{i}\left( \theta \right) \right) . \end{aligned}$$
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Caldeira, E., Foucault, M. & RotaGraziosi, G. Decentralization in Africa and the nature of local governments’ competition: evidence from Benin. Int Tax Public Finance 22, 1048–1076 (2015). https://doi.org/10.1007/s107970149343y
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Keywords
 Local expenditures
 Developing countries
 Decentralization
 Constrained Nash equilibrium
 Strategic complementarity
 Spatial econometrics
JEL Classification
 D7
 H7
 01