Economic growth and economic development 143

Introduction to Modern Economic Growth Table 3.1 Estimates of the Basic Solow Model MRW Updated data 1985 1985 2000 ln(sk ) 1.42 (.14) 1.01 (.11) 1.22 (.13) ln(n + g + δ) -1.97 (.56) -1.12 (.55) -1.31 (.36) Adj R2 59 49 49 Implied β 59 50 55 No of observations 98 98 107 The most natural reason for the high implied values of the parameter β in Table 3.1 is that εj is correlated with ln (sk,j ), either because the orthogonal technology assumption is not a good approximation to reality or because there are also human capital differences correlated with ln (sk,j )–so that there is an omitted variable bias Mankiw, Romer and Weil favor the second interpretation and estimate the augmented model, in particular the equation β β ln (sk,j ) − ln (nj + g + δ k ) 1−α−β 1−α−β α α ln (sh,j ) − ln (nj + g + δ h ) + εj + 1−α−β 1−α−β (3.23) ln yj∗ = constant + This requires a proxy for ln (sh,j ) Mankiw, Romer and Weil use the fraction of the working age population that is in school With this proxy and again under the orthogonal technology assumption, the original Mankiw, Romer and Weil estimates are given in column of Table 3.2 Now the estimation is more successful Not only is the Adjusted R2 quite high (about 78%), the implied value for β is around 1/3 On the basis of this estimation result, Mankiw, Romer and Weil and others have interpreted the fit of the augmented Solow model to the data as a success: with common technology, human and physical capital investments appear to explain 78% of the cross-country income per capita differences and the implied parameter values are reasonable Columns and of the table show the results with the updated 129