Distribution Dynamics in the US. A Spatial Perspective

Abstract

It is quite common in cross-sectional convergence analyses that data exhibit strong spatial dependence. While the literature adopting the regression approach is now fully aware that neglecting this feature may lead to inaccurate results and has therefore suggested a number of statistical tools for addressing the issue, research is only at a very initial stage within the distribution dynamics approach. In particular, in the continuous state-space framework, a few authors opted for spatial pre-filtering the data in order to guarantee the statistical properties of the estimates. In this paper, we follow an alternative route that starts from the idea that spatial dependence is not just noise but can be a substantive element of the data generating process. In particular, we develop a tool that, building on a mean-bias adjustment procedure established in the literature, explicitly allows for spatial dependence in distribution dynamics analysis thus eliminating the need for pre-filtering. Using this tool, we then reconsider the evidence on convergence across US states. It is quite common in cross-sectional convergence analyses that data exhibit strong spatial dependence. While the literature adopting the regression approach is now fully aware that neglecting this feature may lead to inaccurate results and has therefore suggested a number of statistical tools for addressing the issue, research is only at a very initial stage within the distribution dynamics approach. In particular, in the continuous state-space framework, a few authors opted for spatial pre-filtering the data in order to guarantee the statistical properties of the estimates. In this paper we follow an alternative route that starts from the idea that spatial dependence is not just noise but can be a substantive element of the data generating process. In particular, we develop a tool that, building on a mean-bias adjustment procedure established in the literature, explicitly allows for spatial dependence in distribution dynamics analysis thus eliminating the need for pre-filtering. Using this tool, we then reconsider the evidence on convergence across US states. Keywords

Assessment of the factors influencing competitiveness fostering the country’s sustainability

“…This is a test used to identify the unit root and to confirm that the variables are non-stationary (when a constant average is not maintained because higher estimates are followed by smaller ones and the process becomes unpredictable, constant shock prevails) or stationary (when the low-efficiency hypothesis is accepted) (Asuamah et al, 2016;Gerolimetto & Magrini, 2016).…”

The Effect of Immigration on Convergence Dynamics in the US

“…Differently from this view, Gerolimetto and Magrini (2016) think that spatial dependence is often likely to be a substantive element of the process under study and this, in particular, should be the case when studying economic convergence across regional units. Just to give an example, not only it is well known that the level of per capita income in a US state is correlated to the level observed in neighboring states but, as shown by Rey (2001), also the mobility of the states within the cross-sectional distribution of per capita income is significantly affected by the relative position of geographical neighbors within the same distribution.…”

“…In such instances, spatial dependence appears to embody valuable information on convergence dynamics and adopting a spatial filtering technique represents a controversial strategy (Magrini, 2004) as it may yield misleading results. To address the issue, therefore, Gerolimetto and Magrini (2016) first develop a two-step nonparametric regression estimator for spatially dependent data that moves from the standard local linear estimator and does not require a priori parametric assumptions on spatial dependence as information on its structure is in fact drawn from a nonparametric estimate of the errors spatial covariance matrix. Then, they employ this spatial nonparametric (local linear) estimator in the mean-bias adjustment procedure put forward by Hyndman et al (1996).…”

“…Then, they employ this spatial nonparametric (local linear) estimator in the mean-bias adjustment procedure put forward by Hyndman et al (1996). In the present paper, we adopt the strategy developed by Gerolimetto and Magrini (2016) and therefore enrich the estimate of the conditional density through an estimate of the mean function that, in addition to Hyndman et als' original suggestion, allows also for spatial dependence.…”

“…As anticipated in Section 3.3, this estimate is carried out using the procedure developed by Gerolimetto and Magrini (2016) in which the mean function of the conditional density is obtained using a spatial nonparametric estimator. The results of the Moran's I test on the residuals of the estimate of M(ȳ t ) that substantiate this choice are reported in Table 7.…”