Introduction to Modern Economic Growth a function of certain country characteristics, such as institutional factors, human capital (see next section), or even the investment rate If the true equation is (3.10), in the sense that the Solow model applies but certain determinants of economic growth differ across countries, equation (3.9) would not be a good fit to the data Put differently, there is no guarantee that the estimates of b1 resulting from this equation will be negative In particular, it is natural to expect that Cov (b0i , log yi,t−1 ) < (where Cov refers to the population covariance), since economies with certain growth-reducing characteristics will have low levels of output This implies a negative bias in the estimate of b1 in equation (3.9), when the more appropriate equation is (3.10) With this motivation, Barro (1991) and Barro and Sala-i-Martin (2004) favor the notion of “conditional convergence,” which means that the convergence effects emphasized by the Solow model should lead to negative estimates of b1 once b0i is allowed to vary across countries To implement this idea of conditional convergence empirically, Barro (1991) and Barro and Sala-i-Martin (2004) estimate models where b0i is assumed to be a function of, among other things, the male schooling rate, the female schooling rate, the fertility rate, the investment rate, the governmentconsumption ratio, the inflation rate, changes in terms of trades, openness and institutional variables such as rule of law and democracy In regression form, this can be written as (3.11) gi,t,t−1 = X0i,t β + b1 log yi,t−1 + εi,t , where Xi,t is a (column) vector including the variables mentioned above (as well as a constant), with a vector of coefficients β In other words, this specification imposes that b0i in equation (3.10) can be approximated by X0i,t β Consistent with the emphasis on conditional convergence, regressions of equation (3.11) tend to show a negative estimate of b1 , but the magnitude of this estimate is much lower than that suggested by the computations in Example 3.1 Regressions similar to (3.11) have not only been used to support “conditional convergence,” that is, the presence of transitional dynamics similar to those implied by the Solow growth model, but they have also been used to estimate the “determinants of economic growth” In particular, it may appear natural to presume 112