Economic growth and economic development 158

Introduction to Modern Economic Growth identical homothetic preferences imply that (3.29) XjK XjH = = Akj Kj Ahj Hj − csj − csj N X Aki Ki i=1 N X Ahi Hi i=1 where csj is the share of country j in world consumption (the value of this country’s consumption divided by world consumption) and N is the total number of countries in the world These equations simply restate the conclusion in the previous paragraph that a country will be a net exporter of capital if its effective supply of capital, Akj Kj , exceeds a fraction, here csj , of the world’s effective supply of capital, PN k i=1 Ai Ki Consumption shares are easy to calculate Then given estimates for XjK and XjH , the above system of × N equations can be solved for the same number of unknowns, the Aki and Ahi ’s for N countries If we stopped here, we would have obtained estimates for factor-specific productivity differences across countries from an entirely different source of variation than those exploited before In addition, we would not have a single productivity parameter, but a separate labor-augmenting (or human-capital-augmenting) and a capital-augmenting productivity for each country, which is not an uninteresting achievement However, if we indeed stopped here, we would not know whether these numbers provide a good approximation to cross-country factor productivity differences This is in some sense the same problem as we had in judging whether the calibrated productivity (technology) differences in the previous section were reliable Fortunately, international trade theory gives us one more set of equations to check whether these numbers are reliable As noted above, under the assumption that the world economy is sufficiently integrated, we have conditional factor price equalization This implies that for any two countries j and j , we must have: (3.30) (3.31) Rj Rj = , k Aj Akj0 wj wj = , h Aj Ahj0 144