Looking at results across sub periods

Looking at results across sub-periods, note first that the absolute values of β in all sub-periods are larger than those for the entire 1872–2000 period. Thus, the processes of convergence of income per capita anda labor productivity in the different sub-periods were not reinforcing but reversing themselves. It is interesting and somewhat puzzling to compare the β-convergence estimates of income per capita with the Lorenz curves presented in Fig. 6 which showed that the municipal concentration of income per capita reduced significantly from 1872 to 1919, increased from 1919 to 1949, was practically unchanged from 1949 to 1970 and decreased significantly from 1970 to 2000. For the whole GSK2118436 1872–2000, estimations were also disaggregated by main regions – North, Northeast, Center-South, South and Center-West – to get a more detailed picture of geographic patterns of convergence of income per capita and labor productivity. Fig. 6 shows that β estimates are negative and significant for all regions though the samples are relatively small for the North, South and Center-West. In all regions the speed of convergence was a bit faster (absolute values of β were larger) than in Brazil as a whole. That suggests a secular process of regional divergence which was counteracted by a slow process of spatial convergence inside each region. The concentration of import substitution industrialization in the Center-South region of the country and the marked regional contrasts in soil aptitude and agricultural development were, undoubtedly, major factors in process of spatial divergence. Inside the regions, the speed of convergence was faster in the South and in the North Region, but slow in the Northeast. For all regions, however, β estimates are exceedingly low in international perspective.
Urban and rural GDP growth convergence, 1919–2000 OLS results for convergence equation are presented in the first line of Table 1. Adjusted correlation coefficients are small compared to the estimates obtained for 1872–2000. The speed of convergence were negative and significant as attested by the t statistics. Convergence faster for labor productivity than for income per capita, both however extremely low when compared to other countries. The faster convergence of labor productivity is difficult to interpret without further analysis of demographic patterns of growth – dependency ratio, in particular – during this period.
Spatial auto-correlation of convergence Statistics for the spatial auto-correlation of the dependent variables (SACD-ρ) are presented together with the estimates of β-convergence presented in Table 1. Though the spatial auto-correlation is significant, in particular for rural activities, estimations of are for the whole period, 1919–2000, are practically unaffected by their inclusion in the model. The same is true for rural activities in the sub-periods considered, except for 1980–2000. For urban activities, the evidence is blurred by very fact that the lack of convergence in the estimation for the period 1919–1949 introduces problems in the estimation. The second model (SACR) assumes that the residuals of the growth of labor productivity in rural and urban activities are subject to spatial auto-correlation. That is, the determinants of these respective growth processes, though unknown, are supposed to be subject to spatial inertia as in the case of most geographic variables; or else to be subject of spatial contagion through markets, culture, or any other kind of institutional mechanisms. This assumption is confirmed by the pretty high values of the respective SAC-ρ presented in the table. Estimates of in the table show that this assumption modifies the results in a significant way. For the whole 1920–2000 period, values of the speed of convergence, , are now close to 1.1 both in rural and urban activities. Once again, in the international context, this is still a relatively slow speed of convergence.