In addition to this introduction in the second section

In addition to this introduction, in the second section is presented the methodology, the data, its corresponding sources, and the development accounting exercises results, according to the Hall and Jones (1999) methodology. In the third section the results with the human capital proxies that capture its qualitative aspect are presented. In the following section, the results with different proxies for physical capital are exhibited.
Development accounting for the Brazilian states In this section, the development accounting results (or level accounting) of the Brazilian states output per worker are presented. Following Hall and Jones (1999), the accounting method decomposes differences in output per worker into differences in capital-output ratio rather than in capital-labor ratio. Capital-output intensification is associated, according to the Solow model (theoretical reference of this development account exercise), to transitional periods, i.e., when the economy grows at higher rates than technological progress due to shocks in the determinants of long term income per worker or by higher marginal productivity of capital. In the long term, the capital-output ratio most is expected since both variables grow at the same pace. Hall and Jones (1999) highlight two reasons for working with the capital-output ratio decomposition: (i) since, in the steady state, K and Y grow at the same rate, we can infer that the economy is in its steady state when their growth rates are due to technological progress and labor growth; and (ii) if there is an exogenous growth in productivity without changing the investment rate, the K/L ratio will grow over time as a result of an increase in productivity. In this case, part of the capital-labor ratio growth reflects productivity growth which would be attributed to physical capital accumulation, while in Hall and Jones (1999) decomposition this effect is captured only by the TFP term.
A point to be considered when using proxies for human capital in the development accounting exercises is its substantial quality gap among states. If this is the case, a purely quantitative proxy tends to underestimate the human capital gap among the states if those with superior quantity are the same with better quality. In this section, human capital proxies to capture its qualitative aspect are used to observe how the results change.
Another difficulty for carrying out the development accounting exercises for Brazil or for its states is the lack of proper measure of physical capital stock. Due to this difficulty, some authors have made efforts in order to estimate this variable, such as Hofman (1992), who estimated Liquid (solution) hybridization for Argentina, Brazil, Chile, Colombia, Mexico, and Venezuela from 1950 to 1989. Morandi (2011), Morandi and Reis (2004), Pinheiro and Matesco (1989), and Doellinger and Bonelli (1987) had estimated the physical capital stock for the Brazilian economy. Coelho (2006) estimated it for the Brazilian municipalities and Kroth and Dias (2012) for the municipalities of the Brazilian Southern states. Ferreira (2010) estimated the physical capital stock for the Brazilian states. Their estimations were based on the perpetual inventory method, which is very sensitive to the values of the initial year of the Brazilian series. The Brazilian states capital stock estimated by Reis et al. (2005) is available for 1970 and 1980. However, it is not for 1990 and 2000. For this reason, we extended their estimations to 2000 by means of Coelho (2006)’s methodology. The latter calculated the ratio between total private capital , i.e. machinery and equipment plus non-residential and residential capital, and the residential capital for each Brazilian municipality, in 1985 . The author assumed that this ratio remains constant through time and with the IPEA series for the municipalities’ residential capital, Coelho (2006) estimated the Brazilian municipalities’ total capital for 1990 and 2000. IPEA also provides data for residential capital for each Brazilian state in the same years (1990 and 2000). Using the 1985 ratio, we can retrieve the private total capital for 1990 and 2000 (K1,1990 and K1,2000) for each state, according to Eq. (6). This capital stock series is named K1 and it is the proxy used in the previously development accounting exercises. To test how much of our result depends on this proxy, the development accounting exercises were carried out with various alternatives proxies for physical capital, such as: