The Granger-causality between income and educational inequality: a spatial cross-regressive VAR framework

A researcher taking the structural approach, through the use of theory, can obtain restrictions to help pin down parameters and, by estimating the structural parameters of a fully specified model, can simulate the impact of alternatives that have never actually occurred in the data (Holmes 2010). However, a cost of the structural approach is that the researcher must be explicit up-front about the underlying model and the underlying economics. This paper puts emphasis on the importance of interregional externalities which occur through many mechanisms. Therefore, adopting a data-driven model, I do not need to make explicit up-front the underlying mechanisms of interregional externalities. Structural econometric modellers must also add statistical structure in order to rationalise why economic theory does not perfectly explain data and must be able to argue that their model will be invariant to the contemplated change in economic environment (Reiss and Wolak 2007). A data-driven model does not face this problem, because a structural model is not based on an artificial economy. Moreover, I do not use a structural model because causal relations cannot be established a priori (Hume 1748). In the proposed model, I construct a spatial weights matrix (see Sect. 2) which captures externalities. Instead of constructing the spatial weights matrix, some researchers suggest directly entering variables that proxy externalities in the regression model (see Harris et al. 2011). Nevertheless, Corrado and Fingleton (2012) argue that such an approach itself requires strong identifying assumptions and therefore possesses no real advantage compared to employing a spatial weights matrix. Modelling spatial interaction in the economic context means in many cases modelling externalities which are difficult to pin down (Corrado and Fingleton 2012). Overall, the putative advantages do not always mean structural models should be favoured over non-structural models. Reiss and Wolak (2007) say that ‘[t]he advantages of structural models of course do not all come for free. All economic theories contain assumptions that are not easily relaxed. While theorists sometimes have the luxury of being able to explore stylized models with simplifying assumptions, structural econometric modelers have to worry that when they use stylized or simplifying assumptions they will be dismissed as arbitrary, or worse: insensitive top the way the world ‘real works” (page 4290).

Granger-causality is a statistical concept of causality that is based on prediction and its mathematical formulation is based on linear regression modelling of stochastic processes (Granger 1969).

The F tests tend to be the most conservative of a set of analogous tests, such as the likelihood ratio and Wald tests, and are the least sensitive to small sample deviations from normally distributed disturbances (Greene 2003; Hood et al. 2008).

For a review of the ECHP survey see Peracchi (2002).

The successor to the ECHP came in the form of the EU Statistics on Income and Living Conditions (EU-SILC) which was launched in 2003 (Atkinson and Marlier 2010). The EU-SILC differs markedly from its predecessor in two important ways: (a) while the ECHP has the advantage of being input-harmonised, that is of being based on standardised questionnaires common across all of the countries where it was implemented, the EU-SILC is output-harmonised, that is, instead of being based on harmonised questionnaires, the procedure involves the specification of a set of social and economic indicators which should be provided by the new data set, but it is up to each member state to decide how these are to be collected; (b) whereas the ECHP is a panel survey, in which the same individuals were interviewed year after year, the EU-SILC takes the form of a rotating panel, where the individuals are interviewed usually for a maximum of four years, and the sample is regularly refreshed with new members (Iacovou et al. 2012). According to Longford et al. (2010), the EU-SILC ‘provides reliable statistics at national level but sample sizes do not allow reliable estimates at subnational level, despite a rising demand from policy-makers and local authorities’ (page 1). Finally, although the EU-SILC survey domains over the enlarged EU, micro-data that would enable us to identify regions and compare them are available only for a few countries (Longford et al. 2010). For example, no location is indicated in the data for the UK, and it is collapsed to only six categories in Germany (Longford et al. 2010).

Nomenclature of Territorial Units for Statistics (NUTS) provides a single uniform breakdown of territorial units where each member state is subdivided into three administrative units (NUTS I, II and III).

The procedure proposed to measure educational inequality is better than just using the variance for two main reasons. (a) It allows us to compare educational inequality with income inequality, as they use the same disproportionality functions and thus the same indices (i.e. Theil index of income and Theil index of education, or Gini coefficient on income and Gini coefficient on education). More specifically, in the literature on inequality, it is conceptualised as the average disproportionality. Inequality concerns a ‘disproportionate share’, which means a share that is bigger or smaller than the average share of all basic units. The challenge for the inequality literature is to comprehend how to aggregate those basic unit disproportionalities to obtain a measure of overall inequality. As each region has a different distribution of income (resp. education), an index of income (resp. education) inequality that is comparable across regions has to be compiled. The index should be fundamentally based on the principle that income (resp. education) inequality increases as the income (resp. education) ratios deviate from 1.0. Hence, the task in hand is to devise summary measures of income (resp. education) inequality that distinguish more inequality from less inequality (Firebaugh 2003). Conceptualising inequality as the average disproportionality across all basic units implies that the degree of income (resp. education) inequality depends on the average distance of the income (resp. education) ratios \(r_{i}\) from 1.0. Income (resp. education) inequality is unaffected by proportional increases or decreases. Inequality indices \(I\) are expressed in a common form \(I=\frac{1}{N}\sum _{i=1}^N {f(r_{i} )} \), where \(f\) denotes the disproportionality or distance function which captures the mathematical functions for determining deviations of income (resp. education) ratios from 1.0. (b) This procedure was initially used by Thomas et al. (2001) and, more recently, by Tselios (2008) and Rodríguez-Pose and Tselios (2009a).

These results can be provided upon request.