高级宏观经济学chap 1.doc

Lecture 1 The Solow Growth ModelRomer(2001), Advanced Macroeconomics, Chapter 1Blanchard, Olivier J., 2nd edition, Macroeconomics, Prentice Hall曼昆，宏观经济学，人民大学，2000年巴罗，萨拉伊马丁，经济增长，中国社会科学出版社，2000年Some Basic Facts about Economic GrowthAssumptions of One-Sector Growth ModelsThe Dynamics of the ModelThe Impact of a Change in the Saving RateThe Speed of ConvergenceThe Solow Model and the Central Questions of Growth TheoryEmpirical Applications一、 Some Basic Facts about Economic Growth: the stylized facts of growth1. Economic growth through deep time(F2)2. The stylized facts （F3） (F4) (F5)3. international differences in the standard of living(F6)4. The Solow growth model The ultimate objective of research on economic growth is to determine whether there are possibilities for raising overall growth or bringing standards of living in poor countries closer to those in the world leaders. The Solow model is the starting point for almost all analyses of growth. The principal conclusion of the Solow model is that the accumulation of physical capital cannot account for either the vast growth over time in output per person or the cast geographic differences in output per person. The model treats other potential sources of differences in real incomes as either exogenous and thus not explained by the model.( in the case of technological progress) or absent altogether(in the case of positive externalities from capital).二、 Basic assumptions of one-sector growth models1 Input and Output1) Labor-augmenting or Harrod-neutral capital augmenting Hicks-ueutral2) The ratio of capital to output, K/Y, eventually settles down3) Constant returns to scale (first-degree homogeneity) The economy is big enough that the gains from specialization have been exhausted. Inputs other than capital, labor, and knowledge are relatively unimportant.4) intensive form : The amount of output per unit of effective labor depends only on the quantity of capital per unit of effective labor, and not on the overall size of the economy. output per worker5) Assumptions( Inada conditions) The path of the economy does not diverge Cobb-Douglas function2 the evolution of the input into production1) Labor and knowledge grow at constant rates:2) Investment and capital formation三、 The simple dynamics of growth model1 The Harrod-Domar model1) The fixed-coefficients production function2) Saving, investment, and the warranted rate of growth3) Labor force growth:4) The Harrod-Domar condition:2 The Solow model1) Cobb-Douglas function(F7)2) The dynamics of kl One way: actual and break-even investment, k is rising, k is falling, k is constantl The second way: speed3) the balanced growth path (constant)The Solow model implies that, regardless of its starting point, the economy converges to a balanced growth path - a situation where each variable of the model is growing at a constant rate. On the balanced growth path, the growth rate of output per worker is determined solely by the rate of technological progress.四、 The impact of a change in the saving rateThe division of the governments purchanses between consumption and investment goods, the division of its revenues between taxed and borrowing, and its tax treatments of saving and investment are all likely to affect the fraction of output that is invested.1. the impact on output(F24,F25)A change in the saving rate has a level effect but not a growth effect: it changes the economys balanced growth path, and thus the level of output per worker at any point in time, but it does not affect the growth rate of output per worker in the balanced growth path. In the Solow model only changes in the rate of technological progress have growth effects; all other changes have only level effects.2. saving and consumption (welfare)if , if , if , the golden-rule level of the capital stock:Consumption is at its maximum possible level among balanced growth paths. Quantitative Implications1 The effect of s on output in the long run? is the elasticity of output with respect to capital at . Denoting this by If markets are competitive and there are no externalities, is the share of total income that goes to capital on the balanced growth path.A 10% increase in the saving rate (from 20% of output to 22%) raises output per worker in the long run by about 5% relative to the path it would have followed. Significant changes in saving have only moderate effects on the level of output on the balanced growth path.2 The speed of convergence1) One way资本的平均产品。资本报酬递减+Inada条件使 ：所有者的人均收入占人均总收入的份额2) The second wayWhen k equals k*, . A first-order Taylor-series approximation of around k=k* yields: In the vicinity of the balanced growth path, k moves toward k* at a speed approximately proportional to its distance from k*. In addition, one can show that y approaches y* at the same rate that k approaches k*. The half-lifeThe half-life is roughly equal to 70 divided by its growth rate in percent.More exactly, therefore k and y move 4% of the remaining distance toward k* and y* each year, and take approximately 18 years to get halfway to their balanced-growth-path values.Cobb-Douglas函数k, y的收敛速度： Not only is the overall impact of a substantial change in the saving rate modest, but it does not occur very quickly3 D41)2) 绝对收敛与条件收敛（F42）2. 内生增长理论1) AK model (F43)：s，A影响人均增长率；没有趋同。2) 规模报酬递增：(F44)(F45)3) CES function(F46) Case 1 Case 2 Case 3 3. 贫困陷阱（F47）五、 The Solow Model and the Central Questions of Growth TheoryThe Solow model identifies two possible sources of variation-either over time or across parts of the world-in output per worker: differences in capital per worker and differences in the effectiveness of labor. We have seen, however, that only growth in the effectiveness of labor can lead to permanent growth in output per worker, and that for reasonable cases the impact of changes in capital per worker on output per worker is modest. As a result, only differences in the effectiveness of labor have any reasonable hope of accounting for the vast differences in wealth across time and space.If output per worker differs by a factor of X, and the elasticity of output per worker with respect to capital per worker is , log capital per worker must differ by . That is, capital per worker differs by a factor of or .In sum, differences in capital per worker are far smaller than those needed to account for the differences in capital per worker that we are trying to understand. The other potential source of variation on output per worker in the Solow model is the effectiveness of labor.Empirical Applications1. Growth accounting (F38)u Solow residual：（F48,39）It reflects all sources of growth other than the contribution of capital accumulation vir its private return.u Denison(1967): different types of capital and laboru Young(1995): the exceptionally rapid growth of the NICsu Hsieh(1998a): to exam the behavior of factor returns rather than quantitiesu Oliner and Sichel(2000), Jorgenson and Stiroh(2000), Whelan(2000): U.S. productivity growth rebound2. ConvergenceGrowth is whether poor countries tend to grow faster than rich countries.1) The Solow model predicts countries converge to their balanced growth paths2) The Solow model implies that the rate of return on capital is lower in countries with more capital per worker3) If there are lags in the diffusion of knowledge, income differences might tend to shrink as poorer countries gain access to state-of-the-art methods.u Baumol(1986): u De long(1988)3. Saving and InvestmentIn the absence of barriers to capital movements, there is no reason to expect countries with high saving to also have high investment.u Feldstein and Horioka(1980):u Barro, Mankiw, and Sala-I-Martin(1995): There are underlying variables that affect both saving and investment.Furthermore( Delong) 1 The Solow modelSo lets write for the capital-output ratiowhich makes it more clear that the real wage is growing at rate g, and the real return to capital is constant in steady-state growth.In other words, a share of output is going to capital- and is evenly split as the return to capital. 2 Lets look at what happens when we change the parameters of the model: 1) A change in the savings rate s:Lets take =0.5, n=g=0.01, =0.03; s starts at 0.015 and jumps to 0.20.Start at time zero with A0=L0=1Our stesdy-state growth path jumps form z*=3, with Yt growing at 0.02 per year, to z*=4, with Yt growing at 0.02 percent per year-a 33.3% boost to steady-state capital per effective worker and output per effective worker.How fast does this economy converge to its steady state? =0.025 equals 2.5 percent per year. So the 1/e time-the time after the time 0 jump in the savings rate for the capital-output ratio to close the gap to its new steady-state value to 1/e of its initial value-40 years.2) “Level effect” but not a “growth effect”Does consumption rise when the savings rate rises? At the beginning, certainly not. if , then the economy is called dynamically inefficient-consumption could be raised at all future dates by lowering saving today.if , then the economy is said to be at the Golden Rule.If the production function is Cobb-Douglas,This will be positive if and only if: When s is sufficiently low, increases in s increase steady-state consumption.When s hits the magic number of the capital sha