Fiscal Federalism, Jurisdictional Competition, and the Size of Government: Appendix Nonspherical Errors and Data Heterogeneity Issues

Government spending models typically feature contemporaneously correlated error structures (Beck and Katz, 1995; Kittel and Winner, 2005; Plümper, Troeger and Manow, 2005). Therefore, most models report panel-corrected standard errors (PCSEs), which also correct for cross-section heteroskedasticity. Another possibility is a unit root in the dependent variable (nonstationarity). I conducted Dickey-Fuller tests on all dependent variables and error terms and, with appropriate specification of lags and time trends, was able to reject nonstationarity for at least one panel in all models at p < 0.1. Finally, unit heterogeneity has been a concern in TSCS research. Country fixed effects (CFEs) will purge any unobserved country-level heterogeneity. However, since fiscal federalism does not change over time in most countries, the CFE model will be a highly inefficient estimator. There is no choice but to trade off risk of bias for efficiency gains by excluding CFEs. Nevertheless, concerns about endogeneity due to omitted variable bias may remain and must be addressed. If fiscal federalism is correlated with unobserved factors not included in the models, it may pick up some of the effects of those variables, leading to biased coefficient estimates. To purge endogeneity, there are several options. The first is simply to include more control variables that may be correlated with both the key independent and dependent variables, which is the approach taken here. The “fixed-effects vector decomposition” approach assumes that time-varying variables are endogenous and should be de-meaned, but that time-invariant variables are exogenous (Beck, 2011; Breusch, Ward, Nguyen and Kompas, 2011; Plümper and Troeger, 2011). The Hausman and Taylor (1981) approach divides time-invariant variables into those assumed exogenous and endogenous and instruments for the latter with the time-varying variables in the model. While fiscal federalism correlates strongly with country area and population and ethnic and linguistic diversity, these instruments are insufficiently powerful to meet the stringent requirements for reduction of bias in instrumental-variables regression (so-called “Stock-Yogo tests” (Stock, Wright and Yogo, 2002)). Note that the inclusion of lagged dependent variables will control for each country’s starting position, picking up considerable cross-country heterogeneity. Including CFEs would make sense only if it were thought that each country had its own time trend.