Abstract
The Japanese government provides information on local fiscal performance through the Fiscal Index Tables for Similar Municipalities (FITS-M). The FITS-M categorize municipalities into groups of “similar localities” and provide them with the fiscal indices of their group members, enabling municipalities to use the tables to identify their “neighbors” (i.e., those in the same FITS-M group) and refer to their fiscal information as a “yardstick” for fiscal planning. We take advantage of this system to estimate municipal spending function. In particular, we examine whether the FITS-M help identify a defensible spatial weights matrix that properly describes municipal spending interactions. Our analysis shows that they do. In particular, geographical proximity is significant only between a pair of municipalities within a given FITS-M group, and it does not affect competition between pairs belonging to different groups even if they are located close to each other. This would suggest that the FITS-M work as intended, indicating that spending interaction among Japanese municipalities originates from yardstick competition and not from other types of fiscal competition.
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Notes
This is in contrast to the case where g is spending on a pure public good, where \(\beta = \beta _{j} \forall j \ne i\), which reduces \(\sum _{j\ne i}\beta _{j}\hbox {g}_{j}\) to \(\beta \left( \sum _{j\ne i}g_{j}\right) \) (see Sandler 1992).
With panel data, we may identify \(\beta _{j} \forall j \ne i\) by imposing restrictions on a spatial weights matrix. Such restrictions include symmetry, where \(w_{ij}=w_{ji}\) (Bhattacharjee and Jensen-Butler 2013), and sparsity, where each unit is affected by a limited number of other units only (Ahrens and Bhattacharjee 2015; Bailey et al. 2015). Meanwhile, Bhattacharjee and Holly (2013) consider a specific case that allows us to utilize moment conditions to identify spatial interaction. However, we cannot always justify the use of these restrictions or identifying assumptions (we are plausibly unable to do this for the current case too).
The i-th row of W therefore constitutes a set of spatial weights for the i-th local government.
For this argument, we discuss movements of existing entities across borders and exclude cases where, say, new firms are born in a given location.
Indeed, the choice over such factors is arbitrary in the empirical literature. Case et al. (1993) propose constructing W with \(W_{ij} = 1/{\vert }Q_{i}-Q_{j}{\vert }\), where Q is a relevant socioeconomic variable. Typically, studies utilize the following variables for Q: (i) per capita income (Case et al. 1993; Boarnet and Glazer 2002; Finney and Yoon 2003; Baicker 2005; Caldeira 2012), (ii) population (Case et al. 1993; Rincke 2010), (iii) racial composition (Case et al. 1993; Boarnet and Glazer 2002), (iv) migration and commuting (Figlio et al. 1999; Baicker 2005; Rincke 2010), and (v) partisan affiliation (Foucault et al. 2008).
The expenditure functions assigned to municipalities are identical except that towns and villages do not implement some of the social programs provided by cities and there are some variations among the five types of cities. Prefectures devolve parts of their expenditure functions to the first three types of cities, with the largest degree of devolution to designated cities, followed by core and then special cities. The functions assigned to the special wards are more or less similar to those of ordinary cities, although the Tokyo Metropolitan Government handles a few of the standard municipal functions (firefighting, water supply, and sewage disposal) for the special wards. Populations of designated cities are the largest among municipalities (3.7 to 0.71 million) followed, with some overlap of population ranges, by core cities (0.62 to 0.27 million) and special cities (0.57 to 0.19 million). Populations of the special wards in Tokyo metropolitan area range from 41.8 to 0.04 million.
There are four ranges of n for the ordinary cities \((n< 50{,}000; 50{,}000 \le n< 100{,}000; 100{,}000 \le n < 150{,}000; 150{,}000 \le n)\) and five for towns and villages \((n< 5000; 5000 \le n< 10{,}000; 10{,}000 \le n< 15{,}000; 15{,}000 \le n < 20{,}000; 20{,}000 \le n)\). Meanwhile, the classification with \(s_{2}\) and \(s_{3}\) comprises four categories for the ordinary cities \((s_{2}+s_{3} < 0.95\) and \(s_{3}< 0.55; s_{2}+s_{3} < 0.95\) and \(0.55 \le s_{3}; 0.95 \le s_{2}+s_{3}\) and \(s_{3} < 0.65; 0.95 \le s_{2}+s_{3}\) and \(0.65 \le s_{3})\) and three categories for towns and villages \((s_{2}+s_{3} < 0.80; 0.80 \le s_{2}+s_{3}\) and \(s_{3} < 0.55; 0.80 \le s_{2}+s_{3}\) and \(0.55 \le s_{3})\). The combination of these ranges and categories yields 16 \((4 \times 4)\) groups of ordinary cities and 15 \((5 \times 3)\) groups of towns and villages.
Such information includes within-group per capita averages and their annual changes of revenues by sources (e.g., taxes, transfers, and local bonds), expenses by type (e.g., personnel, personal transfers, and debt services), expenses by objective (e.g., social protection, public health, and public works), and capital expenses by funding sources (e.g., categorical grants, local bonds, and general revenues). The FITS-M also show the shares of these items, some of which can be used as indices for fiscal rigidity (the share of obligatory expenses), fiscal capacity, or self-sufficiency (the share of own revenues). Additional tables offer debt-related indices (e.g., several versions of debt ratio) and employment-related indices (e.g., wage level for municipal employees and per capita municipal employments).
Unlike the spatial Durbin model, Eq. (8) excludes as regressors weighted values of other municipalities’ control variables \(\left( \sum _{j\ne i}w_{ij}x_{k,jt} \forall k\right) \). This exclusion is due to the Nash assumption in the theoretical models of fiscal competition on which we base our arguments. The model assumes that the local government decides its fiscal variable \(g_{i}\) as an optimal response to a given value of \({{\varvec{g}}}_{-i}\) chosen by other governments and not to their controls \((x_{k,j} \forall k\) and \(j \ne i)\) that partially condition \({{\varvec{g}}}_{-i}\).
We do not delineate the exact form of the ML function on which we perform optimization. Readers may easily refer to Yu et al. (2008) and Lee and Yu (2010a, (2010b) to obtain appropriate guidance and explanation in this regard. We base our inference on what Lee and Yu call the “transformation approach.” To actually obtain the estimates, we use XSMLE, a Stata module for spatial panel data model estimation introduced by Belotti et al. (2013). Since XSMLE produces the estimates based on the “direct approach,” we adjust their values so that our inferences can be based on the transformation approach.
All figures are those for FY2010.
At the end of FY2010, there were 1750 municipalities. However, during FY2008 to FY2010, there were 96 instances of municipal mergers. We exclude municipalities that vanished on account of these mergers from the sample. Other than the four largest main islands (Hokkaido, Honshu, Shikoku, and Kyushu) and the Okinawa Islands, we also exclude 51 “island municipalities,” which have no geographical neighbors as they consist of only small islands. Furthermore, we exclude 10 municipalities that were hit by the Great Eastern Japan Earthquake in late FY2010 (i.e., March 2011) and 6 cities that changed their city classification type. These exclusions reduce the size of our sample to 1637.
A number of studies use the contiguity matrix as a baseline spatial matrix (Case et al. 1993; Boarnet and Glazer 2002; Hanes 2002; Revelli 2003, 2006; Geys 2006; Lundberg 2006; Revelli and Tovmo 2007; Werck et al. 2008; Nogare and Galizzi 2011; Bartolini and Santolini 2012; Caldeira 2012; Gebremariam et al. 2012; Costa et al. 2015).
The general form of the ID is the “distance decay” function specified as \(W_{ij} = 1/d_{ij}^{\delta }\), where \(\delta \) is some positive parameter. Evidently, our ID assumes that \(\delta = 1\). (Murdoch et al. 1993; Finney and Yoon 2003; Baicker 2005; Foucault et al. 2008; Caldeira 2012; Akai and Suhara 2013; Costa et al. 2015). Variations of distance decay include distance decay with threshold D, where \(W_{ij} = 1/d_{ij}^{\delta }\) if \(d_{ij} < D\), and zero otherwise (Hanes 2002; Baicker 2005; Solé-Ollé 2006; Gebremariam et al. 2012; Costa et al. 2015).
See the classic discussion by Anselin (1988).
See Case et al. (1993, p. 298) for the benefit spillover model and Brueckner (2003, pp. 180–181) for the resource flow model. Using a specific form of benefit spillover, some studies associate the negative sign of \(\rho \) with free-riding behavior of local governments (Murdoch et al. 1993; Finney and Yoon 2003; Akai and Suhara 2013). However, in the presence of a general form of benefit spillover, we cannot generally determine the sign of the slope of the reaction function.
See Case et al. (1993), Bivand and Szymanski (2000), Boarnet and Glazer (2002), Revelli (2003), Baicker (2005), Dahlberg and Edmark (2008), Foucault et al. (2008), Werck et al. (2008), Ermini and Santolini (2010), Rincke (2010), Nogare and Galizzi (2011), Bartolini and Santolini (2012), and Costa et al. (2015). In addition, a number of empirical studies on tax competition provide analogous results. However, Chirinko and Wilson (2008/2013) show that, after controlling for spatiotemporal aggregate shocks and delayed responses, the reaction function indeed slopes down in tax competition.
The following argument is analogous to the issue of choosing between logarithm and level forms of a dependent variable without estimating the Box–Cox form that nests the former two forms with additional parameters. For a textbook explanation, see Davidson and MacKinnon (1993).
Since q = 11 in our case, the critical values of \(\chi ^{2}\)(11) are 17.3, 19.7, and 24.7 for the 0.10, 0.05, and 0.01 levels of significance, respectively.
In this respect, when models to be evaluated are not nested, we can interpret a model selection with the likelihood dominance criterion (LDC) as a ranking of multiple hypotheses through nonnested hypothesis testing that rules out the possibilities of either rejecting or accepting all models.
Several studies in the literature have indeed employed hybrid weights matrices. In particular, they use the matrices to differentiate the effects of interaction between a pair of localities whose geographical proximity is identical (contiguous). For example, Rincke (2010) adjusts the contiguity matrix with an index of commuting patterns between a pair of localities. Other studies adjust the contiguity index with some form of population-related index (Werck et al. 2008; Nogare and Galizzi 2011; Akai and Suhara 2013; Costa et al. 2015). These weights capture the effect of the adjusting factor (commuting patterns or population characteristics) after allowing for the influence of geographical proximity (contiguity).
Obviously, the standard time effect [\(\tau _{t}\) in Eq. (6)] cannot allow for these temporal effects. We also thought of including the interactions of time and cross-sectional dummies in the model, but this was infeasible since the number of such interactions amounts to the sample size \((N \times T)\).
When K refers to the number of parameters to be estimated in the original (linear) model, the augmented model has \(K +N \times (K + 1)\) parameters to be estimated. Given our sample with \(N = 1637\) and \(T = 3\), this method is simply infeasible since \(K +N \times (K + 1) > N \times T\). Chirinko and Wilson (2008/2013) also suggest a way to reduce the number of the augmented regressors by restricting parameters in the augmented model. However, this still requires \(K +N\) parameters to be estimated. Since we only have \(T = 3\), this may still be too large a number of parameters. Furthermore, as Chirinko and Wilson (2008/2013) report, this restriction necessitates a nonlinear estimation, which may have difficulty converging. Indeed, we did have difficulty in converging with the models that have as augmented regressors the interactions of prefectural and time dummies.
Bailey et al. (2015) note, “Almost all spatial econometric models estimated in the literature assume that the spatial parameters do not vary across the units. ... Such parameter homogeneity is not avoidable when T is very small, but need not be imposed in the case of large panels where T is sufficiently large.”
Given the interactions between time and regional dummies, we now have \(q = 25\). The critical values of \(\chi ^{2}\)(25) are then 34.4, 37.7, and 44.3 for the 0.10, 0.05, and 0.01 levels of significance, respectively.
A recent study by Leduc and Wilson (2015) nicely summarizes recent evidence on the flypaper effect and discusses methodological issues in estimating the effect of central grants.
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We are grateful to Robert Chirinko, Editor-in-Chief, and two anonymous reviewers for their helpful observations and constructive suggestions, which substantively improved the paper. We also thank Mutsumi Matsumoto for his valuable comments. Hayashi acknowledges financial support from the Japan Finance Organization for Municipalities and the Grant-in-Aid for Scientific Research (15H03359) of the Japan Society for the Promotion of Science.
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Hayashi, M., Yamamoto, W. Information sharing, neighborhood demarcation, and yardstick competition: an empirical analysis of intergovernmental expenditure interaction in Japan. Int Tax Public Finance 24, 134–163 (2017). https://doi.org/10.1007/s10797-016-9413-4
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DOI: https://doi.org/10.1007/s10797-016-9413-4