Introduction to Modern Economic Growth primarily by affecting the investment rate (or the schooling rate) Therefore, once we condition on the investment rate and the schooling rate, the coefficients on these variables no longer measure their impact on economic growth Consequently, estimates of (3.11) with investment-like variables on the right hand side are difficult to link to theory (4) Regressions of the form (3.11) are often thought to be appealing because they model the “process of economic growth” and may give us information about the potential determinants of economic growth (to the extent that these are included in the vector Xi,t ) Nevertheless, there is a sense in which growth regressions are not much different than “levels regressions”– similar to those discussed in Section 3.4 below and further in Chapter In particular, again noting that gi,t,t−1 ≈ log yi,t − log yi,t−1 , equation (3.11) can be rewritten as ¡ ¢ log yi,t ≈ X0i,t β + + b1 log yi,t−1 + εi,t Therefore, essentially the level of output is being regressed on Xi,t , so that regression on the form (3.11) will typically uncover the correlations between the variables in the vector Xi,t and output per capita Thus growth regressions are often informative about which economic or social processes go hand-in-hand with high levels of output A specific example is life expectancy When life expectancy is included in the vector Xi,t in a growth regression, it is often highly significant But this simply reflects the high correlation between income per capita and life expectancy we have already seen in Figure 1.6 in Chapter It does not imply that life expectancy has a causal effect on economic growth, and more likely reflects the joint determination of life expectancy and income per capita and the impact of prosperity on life expectancy (5) Finally, the motivating equation for the growth regression, (3.8), is derived for a closed Solow economy When we look at cross-country income differences or growth experiences, the use of this equation imposes the assumption that “each country is an island” In other words, we are representing the world as a collection of non-interacting closed economies In practice, 115