【正文】 ergence and divergence (31) What means convergence? (32) Unconditional convergence In the face of similar parameters governing evolution, the different initial conditions does not matter. To illustrate Figure in Ray (1998).Convergence is indicated by a strong negative relationship between growth rate of per capita ine and the initial value of per capita ine. log(yt+1) – log (yt) = a + b log(yt) +ε 213 Illustrate the figures below (next pages) Parente and Prescott (1993) studies 102 countries over the period of 196085 and finds standard deviation increasing over time. Does it mean the Solow model is wrong and HarrodDomar model is right? (33) Conditional convergence Unconditional convergence has the assumption that across all countries the level of technical progress, the rate of savings, the rate of population growth and the rate of depreciation are all the same. If these conditions are changed, the steady state should be different for different countries. This leads to conditional convergence. If the rate of savings and population growth rates are different, the ine level would differ and growth rate would be the same. (4) The new growth theories ( endogenous growth theories): Introduction (1) While the Solow model gets some of the predicted correlations correct, how do we reconcile the huge observed differences in per capita ine with the more modest predictions of the model? (2) Can we be satisfied with a theory that only assumes differences in key parameters without explaining these differences? (3) Longrun per capita growth may well be driven by technical progress alone, but this does not mean that technical progress falls on societies like manna from heaven. Human beings, through their conscious actions (and some luck), determine the rate of technical progress, and if this is so, such actions should be part of an explanatory theory, and not simply blackboxed.(4) Finally, do capital and labor, along with the smooth unimpeded flow of technical knowledge, tell the whole story of economic production? (41) Model of human capital and growthContributors: Uzawa [1965], Lucas (1988), Barro [1991], Mankiw, Romer, and Weil [1992].Labor is skilled in production, labor that can operate so phisticated machinery, labor that can create new ideas and new methods in economic activity. It is important to contrast this form of labor with unskilled labor. Augment the Solow model by permitting individuals to “save” in two distinct forms: physical capital and human capital. y = kahla (214)where h stands for human capital and unskilled labor has been omitted for now. First, a fraction s of output is saved, permitting the accumulation of physical capital: k(t + 1) k(t) = sy(t). (215)Another fraction q is saved in a different way: it is used to augment the quality of human capital, so that h(t+1)h(t)=qy(t). (216) Let r denote the ratio of human to physical capital in the long run. Divide both sides of (215) by k(t) and use (214) to note that Likewise, divide both sides of () by h(t) and use () once again to see the growth rate of human capital.Because these two growth rates are the same in the long run (so that the ratio of human to physical capital also stays constant), we must have sr1α= qr α, or simply r = q/s. (217)The larger is the ratio of saving in human capital relative to that of physical capital, the larger is the longrun ratio of the former to the latter. We can now use this value of r to pute the longrun growth rate. so that the longrun growth rate of all the variables, including per capita ine, is given by the expression sαq1α.Implications: (1) It is possible for there to be diminishing returns to physical capital and yet for there to be no convergence in per capita ine. If countries have similar savings and technological parameters, they do grow at the same rate in the long run, but there is no tendency for their per capita ines to e together: initial relative differences will, by and large, be maintained. (2) There is another implication of the overall constancy of returns. Both the rate of savings and the rate of investment in human capital have growthrate effects once again and not just level effects as in the Solow model. Because these decisions affect the growth rate and the pace of growth is determined from within the model and is not simply attributed to exogenous technical progress. (3) Note, however, that the growth effects are related to the constancy of returns to physical and human capital bined. (4) The introduction of human capital also helps to explain why rates of return to physical capital may not high in poor countries as the Solow model predicts. (5) We see that the model predicts no tendency toward unconditional convergence even if all parameters are exactly the same across countries. Unlike the HarrodDomar model, the present theory still maintains the hypothesis of diminishing marginal returns to each input separately.(5a) Conditional convergence after controlling for human capital. By conditioning on the level of human capital poor countries have a tendency to grow faster. (5b) Conditional divergence after controlling for the initial level of per capita ine. By conditioning on countries the initial level of per capita ine, countries with more human capital grow faster. (42) Model of innovation and growthContributors: Romer [1990]. Assume that an economy has a given stock of human capital, which we denote by H. Human capital may be devoted to production (of final goods) or may be employed in a research sector.,