1、Romer, David. 1996,2001. Advanced Macroeconomics. McGraw-Hill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Part A Research and Development ModelsPart B Cross-Country Income DifferencesIf capitals earnings reflect its contribution to output and if its share in total income is modest, then capital
2、 accumulation cannot account for a large part of either long-run growth or cross-country income differences.We will analyze the dynamics of the economy when knowledge accumulation is endogenous and consider various views concerning how knowledge is produced. Knowledge accumulation is probably centra
3、l to worldwide growth, but probably not central to cross-country income differences. Much of the variation in income across countries comes from differences in output for given amounts of physical and human capital. Variations in institutions can cause such differences.Early new growth models focuse
4、d on constant or increasing returns to produced factors, where changes in saving rates and Lecture 3 New growth theoryresources devoted to R3) The saving rate is exogenous and constantttsYK4) Population growth is exogenous0,nLttThe model has tow stock variables whose behavior is endogenous, K and A.
5、1)()1(tLttKt aAaYttnLttsttLtKt AaBAThe model without capital1. the dynamics of knowledge accumulation)1()1(LtttLtt aAYaAYygtLtB?01ttAathe growth of gA: 2)1(ttAtng000LaB1) case 1: (F1,2)That corresponds to the case where knowledge may be helpful in generating new knowledge, but where it is not so hel
6、pful that the generation of new knowledge rise more than proportionally with the exiting stock. 2)1(AtAtt gng 0:*tttA1 Regardless of the economys initial conditions, gA converges to g*A. Technology is growing at a constant rate. : Both A and Y/L grow steadily at rate gA*. Thus *Aygthe economy is on
7、a balanced growth path. A endogenous growth: The long-run growth rate of output per worker is determined within the model rather than by an exogenous rate of technological progress. The long-run growth rate of output per worker is an increasing function of the rate of population growth Worldwide gro
8、wth: higher worldwide population growth raises worldwide income growth. Growth would taper off in the absence of population growth. The effects of n(F3) The fraction of the labor force engaged in R&D(aL) does not affects long-run growth.010ALaBgttnA1* The increase in aL has a level effect but not a
9、growth effect on the path of A. (F4) The limited contribution of the additional knowledge to the production of new knowledge, this increase in the growth rate of knowledge is not sustained.2) Case 2: 1The production of new knowledge rises more than proportionally with the existing stock.010ALaBgtt2)
10、1(AttAt gn Knowledge is so useful in the production of new knowledge that each marginal increase in its level results in so much more new knowledge that the growth rate of knowledge rises rather than falls. Once the accumulation of knowledge begins, the economy embarks on a path of ever-increasing g
11、rowth. The economy exhibits ever-increasing growth rather than convergence to a balanced growth path. (F5,6) The increase in aL leads to an ever-widening gap between the new path of A and the path it would have followed otherwise.(F6)3) Case 3: (F7)100LaBgA0LBagAt ngAtt If population growth is zero,
12、 gA is constant regardless of its initial situation: no matter where it begins, the economy immediately exhibits steady growth0LBagYyAt aL affects the long-run growth rate of the economy (1-aL):the fraction of societys resources devoted to producing goods for current consumption, and aL is the fract
13、ion devoted to producing a good(knowledge) that is useful for producing output in the future(the saving rate) liner growth models : AK model The saving rate affects long-run growth2. the importance of returns to scale to produced factorsThe reason that these three cases have such different implicati
14、ons is that is less than, greater than, or equal to 1 determines whether there are decreasing, increasing, or constant returns to scale to produced factors of productionThe general case1. the dynamics of knowledge and capitalttsYK 11)(tLKtt Aag01ttKtc)(KtAtt gngtKtKt0in (gA, gK) space, the locus of
15、points where gK is constant has an intercept of n and a slope of 1.(F8)tLtKtaB01ttAtcgAtKtt gn)( ttAtg0The set of points where gA is constant has an intercept of nand a slope of (F9)1(1)()(tLttKt aAYttnLttsttLtKt AaBA)1(Kttt gngAtKtKt gn0AtKtAt )1( ttt )1(Whether there are on net increasing, decreas
16、ing, or constant returns to scale to the produced factors depends on their returns to scale in the production function for knowledge.1) Case 1: (F10)1The initial values of gA and gK are determined by the parameters of the model and by the initial values of A, K, and L.100KLcgK1AA)(KttKt gngAttAt )1(
17、00KgYAyng*)(1 The long-run growth rate of the economy is endogenous Long-run growth is an increasing function of population growth and is zero if population growth is zero(growth effects) The fractions of the labor force and the capital stock engaged in R&D do not affect long-run growth(level effect
18、s) the saving rate does not affect long-run growth(level effects)2) Case 2: (F11)10)(1*ngAThe growth rates of both A and K, and the growth rate of output, increase continually.3) Case 3: 100AKAgng n0(F12) n=0(F13): *KA regardless of where the economy begins, it converges to a balanced growth path, b
19、ut we dont know what balanced growth path the economy converges to. Balanced growth path is unique Increases in the saving rate and in the size of the population increase this long-run growth rate Long-run growth is endogenous( and depends on parameters other than population growth), but is not affe
20、cted by the saving rate.A specific example(Romer, 1990): 1,01)(tLttaKYttB0nttsYKYLAgBagThis model provides an example of a situation where long-run growth is endogenous, but is not affected by the saving rate.The nature of knowledge and the determinants of the allocation of resources to R&D1 Four di
21、fferent types of knowledge accumulationSupport for basic scientific researchPrivate incentives for R&D and innovationAlternative opportunities for talented individualsLearning-by-doing2 Learning-by-DoingWhen learning-by-doing is the source of technological progress, the rate of knowledge accumulatio
22、n depends on how much new knowledge is generated by conventional economic activity.All inputs are now engaged in goods production:1tttLAKY0,Btt 1)(1tttS : The long-run growth rte of the economy is a function of the rate of population growth, n : There is explosive growth1 : There is explosive growth
23、 if n I positive and steady 1growth if n equals 0. : 0, sbgsbKbKLBY Ytttttt 1We have another example of a model in which long-run growth is endogenous and depends on the saving rate.Models of knowledge accumulation and the central questions of growth theoryWith regard to worldwide growth, the growth
24、 of knowledge appears to be the central reason that output and standards of living are so much higher today than in previous centuries.With regard to cross-country differences in real incomes, the relevance of the models is less clear.Since technology is nonrival, differences in technology are unlik
25、ely to be important to cross-country income differences. The main source of differences in standards of living is not different level of knowledge or technology, but differences in whatever factors allow richer countries to take better advantage of advanced technology.Income differences across count
26、ries: the contributions of physical capital: nonnegligible important the contributions of Human capital: nonnegligible important the contributions of output for given capital stocks: variations in output for given capital stocks are the most important sourceThere may be underlying forces that are important to all three of these immediate determinants of income per person. Social infrastructure(institutions and policies): the allocation of resources between activities that raise overall output and ones that redistribute it
