# **Box 4. Fiscal Reaction Functions and Spatial Econometric Models**

Most empirical tests on strategic interaction use spatial econometrics to estimate the slope coefficient of reaction functions which connects each government’s policy choices to the decisions of neighboring governments and to its own socio-economic characteristics (Brueckner 2003; Revelli 2006; Madiès, Paty and Rocaboy 2006). The reaction function slope is nonzero when strategic interaction occurs. Three spatial econometrics issues have to be dealt with before estimating such spatial models (Anselin 1988).

( _i_ ) In order to deal with the definition of neighborhood, we have to arbitrarily specify a weighting scheme which indicates the relevance of other governments in the process of interaction. Basically, the weights capture the location of a government _i_ relatively to other governments _j_ . A variety of weighting schemes are often explored to allow different patterns of spatial interaction. The most common is the simple contiguity weighting scheme in which interaction is supposed to occur among jurisdictions sharing geographical boundaries. Under such a scheme, _wij_ =1 for jurisdictions _j_ that are contiguous to _i_ , and _wij_ =0 if they do not share any border. Another possible weighting scheme takes into account the distance from a given jurisdiction to its competitors as imperfect mobility of capital may be a plausible assumption in such models (Brueckner 2003). Other weighting schemes based on socio-economic characteristics such as population or income can also be used. Finally, each weight matrix is row-normalized prior to estimation so that the aggregation of tax rates consists in a weighted average.

( _ii_ ) Because of strategic interaction, we have to deal with the endogeneity of the jurisdictions’ fiscal choices. Policy decisions are endogenous and correlated with the error term. The resulting spatial correlation means that OLS estimates would be inconsistent. In the literature, two methods are used to tackle this problem. The first one is the maximum likelihood (ML) method. A non linear optimisation routine is then used to estimate the model. The second approach is instrumental variables (IV). The fitted values used as instruments for the competitors’ policy choices are uncorrelated with the error term. OLS then yields consistent estimates of the parameters. As it is easier to implement, this procedure is frequently used. Although consistent, one of the objections to IV estimators of spatial models is that they ignore the Jacobian term and are therefore less accurate than ML estimates (Anselin 1988).

_(_ iii) The possible presence of spatial dependence in the errors is the third issue. Such spatial dependence can arise when the error term includes omitted explanatory variables that are themselves spatially dependent. Uncorrected error dependence may provide spurious evidence of strategic interaction. Several approaches exist in order to deal with this problem. One approach is to use ML to estimate the model, taking account of the spatially correlated error structure (Anselin 1988). Under ML procedure, a second approach based on the robust tests of Anselin, Bera, Florax and Yoon (1996) can be employed to detect spatial dependence. Finally, an easier remedy is to rely on the IV method which generates consistent parameters for the reaction function even in the presence of spatial error dependence (Kelejian and Prucha 1998).

Source: Madiès, Paty and Rocaboy <u>(2006)</u> <mark>spillovers) lead to the same reduced form equation to be estimated (Revelli 2006 presents a survey). By contrast, little is known about the extent and significance of fiscal interaction among local governments in developing countries. The design of fiscal decentralization systems in these countries might drive one to conclude that there is no scope for strategic fiscal interactions among subnational governments but until recently there was little empirical evidence. A number of recent papers, which we now review, examine fiscal and yardstick competition among subnational governments in developing countries. They include papers by Yi Yao 2008; Zhang and Chen 2007; Herrmann-Pillath and Xingyuan 2010 for China; Thomas 2009 for Vietnam; del Granado, Martinez-Vasquez and Simatupang 2009) for Indonesia, de Melo 2007 and Haddad, Porsse and Ribeiro 2006 for Brazil; and finally Foucault and Rota-Grazziosi 2010 for Benin.</mark> 21