Introduction to Modern Economic Growth That is, countries differ according to their technology level, in particular, according to their initial level of technology, A¯j , but they share the same common technology growth rate, g Now using this assumption together with (3.21) and taking logs, we obtain the following convenient log-linear equation for the balanced growth path of income for country j = 1, , N : (3.22) ln yj∗ ¶ ¶ µ µ α β s s k,j h,j + (t) = ln A¯j + gt + ln ln 1−α−β nj + g + δ k 1−α−β nj + g + δ h This is a simple and attractive equation Most importantly, once we adopt values for the constants δ k , δ h and g (or estimate them from some other data sources), we can use cross-country data we can compute sk,j , sh,j , nj , and thus construct measures of the two key right-hand side variables Once we have these measures, equation (3.22) can be estimated by ordinary least squares (i.e., by regressing income per capita on these measures) to uncover the values of α and β Mankiw, Romer and Weil take δ k = δ h = δ and δ + g = 0.05 as approximate depreciation rates for physical and human capital and growth rate for the world economy These numbers are somewhat arbitrary, but their exact values are not important for the estimation The literature typically approximates sk,j with average investment rates (investments/GDP) Investment rates, average population growth rates nj , and log output per capita are from the Summers-Heston dataset discussed in Chapter In addition, they use estimates of the fraction of the school-age population that is enrolled in secondary school as a measure of the investment rate in human capital, sh,j We return this variable below However, even with all of these assumptions, equation (3.22) can still not be estimated consistently This is because the ln A¯j term is unobserved (at least to the econometrician) and thus will be captured by the error term Most reasonable models of economic growth would suggest that technological differences, the ln A¯j ’s, should be correlated with investment rates in physical and human capital Thus an estimation of (3.22) would lead to the most standard form of omitted variable bias and inconsistent estimates Consistency would only follow under a stronger 127