The third motivation was to improve the empirical estimation

The third motivation was to improve the empirical estimation of the human capital proxy, which is our concern since 2005, and now has a widespread recognition with the study of Hanushek and Wößmann (2007). According to the authors’ knowledge there are no development decomposition studies for the Brazilian states that capture human capital qualitative aspect. To accomplish this aim it was employed a proxy for the Brazilian states human capital elaborated by the Brazilian Institute of Applied Economics (IPEA) available for 1980, 1991 and 2000. This variable was developed based on the annual income expected values associated with education and experience. The advantage in using such proxy is that it already captures the real return of the market for the educational system quality since it is based on the actual wages return. The second proxy was a multiplicative term between years of schooling of the population over 24 years and each state Basic Education Development Index (IDEB) score in 2005. Here is made an assumption that quality and quantity are perfect substitutes since state A with the same quantity as state B, but twice its quality has twice of state B human capital. This assumption is the same as in Lucas (1988) and it seems to be reasonable as a first approximation. The development (or level) accounting exercises were based on Solow (1957) and Hall and Jones (1999), applied to study the INCB028050 of output per worker, production factors and TFP, in the case of the Brazilian states with respect to São Paulo state (reference state). The study employed data available on the censuses years: 1970, 1980, 1991, 2000 and 2010. There are many studies investigating the effects of TFP and factors of production on the evolution of the Brazilian Gross Domestic Product (GDP). Some examples are Alston et al. (2010), Barbosa Filho et al. (2010), Bonelli and Levy (2010), Ferreira et al. (2008), Bacha and Bonelli (2005), Gomes et al. (2003), and Bonelli and Fonseca (1998). However, few development accounting exercises were carried out for the Brazilian states. When introducing the IPEA proxy to capture human capital qualitative aspect, the results are almost the same since it is highly correlated with the pure quantitative human capital proxy. One difference is that the human capital gaps of the Brazilian states in relation to the reference one become smaller over the period. With the second human capital proxy, each state gap in relation to the reference one increases. This is because the states with higher quantities of human capital are precisely those with better quality (higher IDEB mean score). For example, São Paulo state is among those with higher quantity of human capital and it is the one with better quality, according to 2005 IDEB scores. As a result, when this production factor qualitative aspect is considered, a gap reduction of the Brazilian States TFP in relation to the reference state takes place since its quality difference, when it is not considered in the decomposition exercises, ends up being captured by TFP. Even with the inclusion of human capital qualitative aspects, TFP continues as the main variable to account for income differentials among the Brazilian states, which complies with other empirical studies with the Brazilian states data, such as Ferreira (2010), Bonelli and Levy (2010) and Tavares et al. (2001). When using different proxies to measure the physical capital stock, certain regularities are noticed in the results, such as the relative increase in capital-output and capital-labor ratios, from 1970 to 2000. The exception is when it is employed a physical capital proxy based on the Brazilian states industrial electric energy consumption, indicating that it does not accurately captures the productive physical capital in the Brazilian states. The proxy based on the industrial energy consumption may underestimate the productive physical capital of the Brazilian states in relation to the reference state. The most appropriate proxies seem to be those based on the studies of Reis et al. (2005) and on the methodology of Coelho (2006).