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Expenditure interactions between municipalities and the role of agglomeration forces: a spatial analysis for North Rhine-Westphalia

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Abstract

This paper analyzes municipal expenditures in the light of horizontal fiscal interactions. I investigate total expenditures and a set of non-earmarked expenditure subcategories in the largest German federal state, North Rhine-Westphalia. The empirical analysis is based on a Spatial Durbin Model in a panel for the years 2009–2015. Using a two-regime spatial matrix, I also examine the impact of agglomeration on the intensity of public expenditure interactions, thus testing the hypothesis that an agglomerated region can decrease the amount of public goods without losing mobile factors to the periphery. The findings indicate that significant municipal expenditure interaction effects do exist. The reaction functions also vary for different expenditure subcategories. Unlike spillover effects and fiscal competition, yardstick competition is an insignificant source of potential interactions. Expenditure interaction is fiercer if there is less agglomeration in a municipality. Urbanized and populous municipalities appear to benefit from agglomeration economies, a fact that enables them to spend less. Robustness checks confirm the findings.

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Notes

  1. The unemployment rate, on the other hand, is not available at the municipal level.

  2. Allers and Elhorst (2011) argue that the spatial interaction in an expenditure subcategory could also result from tax interdependence or from spatial interdependencies among other expenditure subcategories. This will again be taken up with reference to several estimations in the section on robustness checks.

  3. Another possible concern that I take up in the section on robustness are municipalities subject to consolidation assistance. In 2011, the NRW state government initiated a program supporting indebted municipalities with extra consolidation assistance. Municipalities receiving such support may be forced to spend less and thus distort the core estimations.

  4. Following Leprince et al. (2005) and Fréret and Maguain (2017), vertical effects (where the spending of a local government depends on expenditure at other levels) are not found to be relevant and are therefore not considered.

  5. Normally distributed error terms in Maximum Likelihood estimations are a strong assumption. However, an advantage of the Quasi Maximum Likelihood estimator is that it does not rely on the assumption of normally distributed error terms. Nevertheless, QML assumes that the error term is independently and identically distributed for all i with zero mean and variance σ2 (Elhorst 2014). Also Lee (2004) shows for relatively large samples that the QML estimator is asymptotically consistent even without a normally distributed error term. That applies to my sample, too.

  6. This bias correction can be applied in municipally fixed and time fixed effect models and is referred to as the transformation approach. The time fixed effects involve the incidental-parameter problem in addition to the individual effects (see Lee and Yu (2010a) for a detailed description). The estimation procedure is performed using the Stata module XSMLE for spatial panel data models via (Quasi) Maximum Likelihood as provided by Belotti et al. (2013). The XSMLE command is used with the “leeyu” option to perform inferences with the log-likelihood based on the transformation approach.

    In addition, I manually adopt the double demeaning procedure proposed by Lee and Yu (2010a) and also estimate the model using XSMLE. This enables me to eliminate time fixed and municipally fixed effects, too.

    Both procedures produce very similar results and can be obtained from the author upon request.

  7. LeSage and Pace (2009) state that even if a relevant variable (even though unobserved or unknown) is omitted, the SDM coefficient estimates are still unbiased.

  8. Note that, due to the fact that the interaction parameter ρ enters the equation non-linearly, the optimization method must be non-linear, too.

  9. There are five district governments in NRW, each having a district president and a regional council determined indirectly via municipal elections. Their tasks can play an important role for municipalities because they enforce municipal regulations, control regional/urban planning and development, and are entitled to issue directives. Their influence may intensify fiscal expenditure interactions among municipalities.

  10. The xk variables are normalized from 0 to 1. The weight is then given by \( w_{ij} = \frac{1}{V} \mathop \sum \limits_{V} \left( {1 - \left| {x_{i}^{v} - x_{j}^{v} } \right|} \right). \).

  11. I also test whether the SDM eliminates spatial autocorrelation of the residuals. To this end, I construct the Moran’s I statistic of the residuals of the total expenditures. This can only be done for each cross-section in the seven years. The Moran’s I shows that the autocorrelation is close to zero in all seven cross-section estimates and significantly different from zero in only two of them, which indicates that the SDM almost completely eliminates spatial autocorrelation of the residuals. The result is confirmed in the other expenditure subcategories.

  12. The argument is that left-wing majorities are in favor of redistribution and stand for a more active role by the state, leading to an increase in public spending (Tellier 2006).

  13. In the literature, different agglomeration indices are applied. I follow inter alia Ciccone and Hall (1996), Charlot and Paty (2010), Briant et al. (2010) and use population density to determine the size of urbanization economies. Localization economies on the other hand measure externalities that indicate attributes of industry (Combes and Gobillon 2015). Other agglomeration indices capturing local urbanization economies include the total sum of salaried jobs in municipality i divided by the area of that municipality (Fréret and Maguain 2017). Applying the latter agglomeration indicator to my model does not significantly change my findings. The results can be obtained from the author upon request.

  14. For a detailed derivation of a simple model of spatial fiscal interactions with agglomeration see Fréret and Maguain (2017).

  15. The model has been calculated using the SPM command written by Atella et al. (2014) in Stata and applying a two-way clustered variance–covariance matrix.

  16. The way I introduce the two-regime matrix has many parallels in the literature, e.g. in the studies by Allers and Elhorst (2005), Elhorst and Fréret (2009), Charlot and Paty (2010), Fréret and Maguain (2017) and others. LeSage and Pace (2011), however, criticize this way of extending spatial regression models although they focus on an SAR-type model. One of their remarks is that the specification relies on the assumption that parts of the combination of different weight matrices vanish, which is only possible if W is zero. They also note that the model acts in a way that contradicts the hypothesis it sets out because it does not take into account the feedback effects of all interacting regions.

    A possible solution that has been advanced in the recent literature but has not yet been completely implemented involves the calculation of a QML model with heterogeneous coefficients (Aquaro et al. 2015).

    Nevertheless, in awareness of these distortions and fully cognizant of the fact that comprehensive solutions are not available, the specifications applied provide an indication of the magnitude of interactions under agglomeration regimes of the kind referred to in the studies quoted.

  17. Since yardstick competition is not responsible for fiscal expenditure interactions in NRW, there is no connection between agglomeration economies and yardstick competition, although Costa et al. (2011) and Costa and Carvalho (2013) suggest the contrary.

  18. Considering the log-likelihood values of models (1–5) it turns out that model 1 outperforms the others. At this point it is important to note that the direction of the effects of agglomeration is the main finding—not the models differing log-likelihood values. The conclusion that agglomerations have an effect on spatial interactions can still be drawn.

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Acknowledgements

I am grateful to Artem Korzhenevych, Georg Hirte, Çilem Selin Hazιr and Alejandro de Castro Mazarro for their valuable comments, support and constructive suggestions. Moreover, I thank anonymous referees for their constructive suggestions and comments.

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Authors and Affiliations

  1. Leibniz Institute of Ecological Urban and Regional Development (IOER), Weberplatz 1, 01217, Dresden, Germany

    Sebastian Langer

  2. Faculty of Business and Economics, Technische Universität Dresden, Helmholtzstr. 10, 01062, Dresden, Germany

    Sebastian Langer

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Appendix

Appendix

See Tables 7, 8, 9, 10 and 11.

Table 7 The expenditure subcategories.
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Table 8 Specification tests for spatial panel 2009–2015
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Table 9 Spatial weight model comparison
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Table 10 Yardstick competition—fiscal expenditure interactions between the municipalities of NRW depending on political majorities
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Table 11 Results including right-wing dummy - Fiscal expenditure interactions between the municipalities of NRW
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Langer, S. Expenditure interactions between municipalities and the role of agglomeration forces: a spatial analysis for North Rhine-Westphalia. Ann Reg Sci 62, 497–527 (2019). https://doi.org/10.1007/s00168-019-00905-2

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