Summary of Journals

1. Summary of Journals Jones, C., 1995, “R&D-Based Models of Economic Growth,” Journal of Political Economy,103,759-784. Rebelo S.,1991, “Long-Run Policy Analysis and Long-Run Growth” Journal of Political Economy, 99, 500-521. Aghion, P. and P. Howitt, 1992, “A Model of Growth Through Creative Destruction,” Econometrica, 60, 323-353 Romer, P.,1986, “Increasing Returns and Long-Run Growth”, Journal of Monetary Economics, 22, 3-42.

2. R & D BASED MODELS OF ECONOMIC GROWTH OBJECTIVE • To explain about the Endogenous growth model • To describe that the "scale effects" prediction of many recent R & D-based models of growth is inconsistent with the time-series evidence from industrialized economies. • Proposes an extension of these models that eliminates scale effects but also implies that the long-run growth rate is a function of parameters usually taken to be invariant to government policy. • To explain that growth is driven by technological change that results from the research and development efforts of profit-maximizing agents, with the implication that subsidies to R & D, and perhaps other government policies, may influence the long-run rate of economic growth.

3. The R & D Equation and the Problem of Scale Effects • The R & D-based models in the endogenous growth literature by Romer (1 990), Grossman and Helpman (199la,1991b, 199lc), Aghion and Howitt (1992), • Scale effects definition - an increase in the level of resources devoted to R & D should increase the growth rate of the economy. • “Scale effects" prediction • Y is output, Ais productivity or knowledge, and K is capital. Labor is used either to produce output (L,) or to search for new knowledge (L,). • The source of scale effects is the R & D equation in (2). This equation implies that total factor productivity (TFP) growth will be proportional to the number of units of labor devoted to R & D. • The prediction that the growth rate of the economy is proportional to the size of its labor force is easily falsified as shown in empirical study. Equation 1 and Equation 2

4. MODELS OF ECONOMIC GROWTH Scientists and engineers engaged in R & D and U.S. TFP growth. Source: The number of scientists and engineers engaged in R & D is taken from National Science Foundation (1989) and various issues of the Statistical Abstract of the U.S. Economy. TFP growth rates are calculated using the private business sector data in Bureau of Labor Statistics (1991). "Other S&E" is the sum of scientists and engineers engaged in R & D for France, West Germany, and Japan.

5. Later alternative made on specification of the R & D equation that,assumes that TFP growth depends on the share of labor devoted to R & D rather than on the quantity. This was also was falsified with empirical study as shown below. Example: Share grows from about 0.25 percent in the United States in 1950 to nearly 0.80 percent by 1988, an increase of over threefold. (The evidence from France, Germany, and Japan is similar.) is also inconsistent with the lack of increase in TFP growth rates The model of Romer/Grossman-Helpman/Aghion-Howitt and others are all easily rejected because of this prediction of scale effect associated with R & D based model in the endogenous growth literature.

6. An R & D-Based Model of Semi-endogenous Growth • Model R & D structure is maintain with eliminating the prediction of scale. • A is assignedto be the stock of knowledge or technology in an economy. The change in knowledge A will be equal to the number of people attempting to discover new ideas multiplied by the rate at which R & D generates new ideas: • if there are positive spillovers in the production of knowledge, would be increasing in the level of A. • Parameterizing the arrival rate , we get • F< 0 corresponds to the case referred to in the productivity literature as "fishing out," in which the rate of innovation decreases with the level of knowledge; • F> 0 corresponds to the positive external returns case. • A value of F= 0 represents the useful benchmark of constant returns to scale (zero external returns) in which the arrival rate of new ideas is independent of the stock of knowledge. Equation 4 Equation 5

7. Other consideration includes that a given point in time the duplication and overlap of research reduce the total number of innovations produced by L, units of labor. That is, suppose that it is not , but rather that belongs in the R & D equation. Incorporating this change into (4) and (5) yields the R & D equation: • Where , in equilibrium, but , captures the externalities occurring because of duplication in the R & D process. • the restriction F < 1 and show that this justifiable assumption leads to a model in which a balanced growth path is consistent with an increasing number of persons devoted to R & D Equation 6

8. The Decentralized Model • It is similar to the one in Romer (1990) which stresses the important of profit seeking research in growth process • The economy consists of three sectors, final-goods sector, a collection of monopoly firms and designs discovered by the third sector, the R & D sector. • In the R & D sector, individuals take advantage of the existing stock of knowledge, A, to invent new designs for producer durables and sell these designs to the intermediate sector. • Two aspects of the model that are of particular interest, the derivation of the steady-state growth rate and the share of labor invested in R & D by the decentralized economy. Growth rateequation Share of labor equation

9. Welfare and the Social Planner Problem • Steady-state growth rate in the decentralized model is the same as that in the social optimum, despite the presence of externalities in the R & D sector and monopoly behavior in the intermediate goods sector. • In the social planner formulation, the share of labor devoted to R & D along the balanced growth path is affected by the externalities and the imperfect competition. It differs with the decentralized model with 3 reasons. • First, the presence of an additional " - F" term in the social optimum reflects the incorporation of the externalities to R & D. • When these externaIities are positive, too little R & D is undertaken in the decentralized equilibrium because agents do not take into account the increase in the value of future R & D that their discoveries impart. • Otherwise with F is negative, there may actually be too much R & D in the decentralized equilibrium. • The presence of l < 1 will cause the decentralized economy to overinvest in R & D becauseof the negative externality. Labor share equation

10. The decentralized share of labor in R & D differs from the social optimum because of the monopoly markup over marginal cost in the sale of producer durables to the final sector, reflected by the presence of 1/(1 - a) in equation decentralized model. • This effect causes too little labor to be devoted to R & D along the balanced growth path in the decentralized model. • Decentralized economy underinvests in R & D relative to the social optimum

11. The Transitory Effect of an Increase in R & D Investment • Results in the model above is that a permanent increase in the R & D share does not have a permanent effect on the growth rate. Nevertheless, such a change clearly has a level effect and raises the growth rate along a transition path to the new steady state. • The length of the transition path is likely to depend on the parameter , and the closer is to one, the longer the transition path. • The transition dynamics for output growth involve three components. • The first term reflects the direct transition dynamics that occur when the growth rate of knowledge (or TFP) deviates from its steady-state value. • The second term of equation captures the transition dynamics associated with capital accumulation. • The third term of equation incorporates the interaction between technological change and the marginal product of capital.

12. Growth rates along the transition path. The growth rates represent the response to a permanent increase in the R & D share from 1 percent to 2 percent fort the case of F= .5 and l= .5.

13. Summary • Growth in the economy is tied directly to growth in productivity, which in turn depends on the discovery of new designs through R & D. Individuals are the critical input into the discovery of new designs, and the growth rate of the economy depends crucially on the growth rate of the labor force, an exogenous variable. • As in the Solow model, subsidies to R & D and to capital accumulation have no long-run growth effects in this model, but rather affect growth only along the transition path to the new steady state. • The model differs from the Solow model as the growth rate of the economy turns out to be a function of parameters that are typically thought of as exogenous, growth in this model is endogenous in the sense that it derives from the pursuit of new technologies by rational, profit-maximizing agents.

14. Long-Run Policy Analysis and Long-Run Growth OBJECTIVES • To get know Basic Endogenous Growth Model with reproducible factors • To know the LR effect of tax in the Growth Model • To learn part of the extension Basic Endogenous Model (physical and human capital)

15. Basic Endogenous Growth Model Basic factor of production is : • The economy has two sector production Reproducible factor Example: Physical and human capital Quantity : increase over time Zt Non reproducible factor Example : land Quantity : fix T

16. Growth model gy : growth in income gz : growth in capital a : constant Two properties of the model: : no transitional dynamics (continues growth rate at gy) : only capital factor effect the growth

17. Growth rate with long-run tax effect Conclusion from the growth model • When r i ( increasing on investment tax) lead to lower growth rate. • When r c ( increasing on consumption tax) lead no change on growth.

18. Extension of the Basic Model • Disaggregating Zt into Physical and Human Capital Physical Capital Kt : capital I t : Investment Kt : capital depreciates rate Human Capital Leisure (L) Learning (H) Working (N)

19. Consider one-sector model in which output is produced according to a Cobb-Douglas technology that combine capital (Kt), labor (Nt) and non-producible factors (T). The equation for the growth rate of capital shows that under the standard assumption of CRTS, perpetual growth is unfeasible whenever Nt and T are required to produce output Even if all the resources are devoted to capital accumulation, so that Ct=0, the presence of DRTS to the only factor of production that can be accumulated Kt implies that the growth rate of capital has to converge to zero. Perpetual growth and Nonreproducible Factors.

20. 3. A MODEL OF GROWTH THROUGH CREATIVE DESTRUCTION PHILIPPE AGHION AND PETER HOWITT Develop in which vertical innovations generated by a competitive research sector, constitute the underlying source of growth. Equilibrium is determined by a forward- looking difference equation, according to which the amount of research in any period depends upon the expected amount of research next period. One of the source of this intertemporal relationship is creative destruction. The prospect of more future research discourages current research by threatening to destroy the rents created by current research.

21. A MODEL OF GROWTH THROUGH CREATIVE DESTRUCTIONPHILIPPE AGHION AND PETER HOWITT Romer and Lucas literature on endogenous growth - source of sustained growth in per capita income (accumulation of knowledge) This paper examines industrial innovations which improves the quality of products. Introduces the factor of obsolescence – better products render previous ones obsolete. General character of growth process – progress creates losses as well as gains. Embodies Schumpeter’s idea of creative destruction. The expected growth rate of the economy depends upon the economy-wide amount of research.

22. A MODEL OF GROWTH THROUGH CREATIVE DESTRUCTIONPHILIPPE AGHION AND PETER HOWITT The paper shows that equilibrium in such an economy is determined by a forward-looking difference equation, according to which the amount of research in any period depend upon the expected amount of research in next period. Assumes that individual innovations are sufficiently important to affect the entire economy.

23. A MODEL OF GROWTH THROUGH CREATIVE DESTRUCTIONPHILIPPE AGHION AND PETER HOWITT The amount of research this period depends negatively upon the expected amount next period through two effects: Creative destruction – the payoff from research this period is the prospect of monopoly rents next period. The expectation of more research next period will increase that arrival rate, and hence discourage research this period. General equilibrium effect working through the wage of skilled labor, which can be used either in research or in manufacturing. The expectation of more research next period must correspond to an expectation of higher demand for skilled labor (higher wages expectation) It will reduce the monopoly rents gained through knowledge. Thus the expectation of more research next period will discourage this period by reducing the flow of rents expected to accrue to a successful innovator.

24. A MODEL OF GROWTH THROUGH CREATIVE DESTRUCTIONPHILIPPE AGHION AND PETER HOWITT Growth results exclusively from technological progress, which in turn results from competition among research firm that generate innovation. Research firms are motivated by the prospect of monopoly rents that can be captured when it is patented. But the rents will be destroyed by the next innovation, which will render obsolete the existing intermediate goods.

25. 4.Increasing Returns and Long-Run Growth Paul M. Romer Knowledge is assumed to be an input in production that has increasing marginal productivity. Old assumption (Ramsey, Cass, Koopmans)- the rate of return on investment and the rate of growth of per capita output is expected to be decreasing functions of the level of the per capita capital stock. Wage rate and capital labor ratios are expected to converge. E.g. An exogenous reduction in the stock of capital in a given country will cause prices for capital assets to increase and will therefore induce offsetting increase in investment.

26. Increasing Returns and Long-Run GrowthPaul M. Romer In the absence of technological change, per capita output should converge to a steady state value with no per capita growth. The assumption of diminishing returns to per capita capital in the production of per capita output.

27. Increasing Returns and Long-Run GrowthPaul M. Romer Alternative view of the long run: In a fully specified competitive equilibrium, per capita output can grow without bound, possibly at a rate that is monotonically increasing over time. The rate of investment and the rate of return of capital may increase rather than decrease with increases in the capital stock. Departure from the usual assumption of diminishing returns.

28. Increasing Returns and Long-Run GrowthPaul M. Romer It is an equilibrium model of endogenous technological change in which long run growth is driven primarily by the accumulation of knowledge by forward- looking, profit maximizing agents. (Entrepreneur) In contrast to physical capital that can be produced one for one from forgone output, new knowledge is assumed to be the product of a research technology that exhibits diminishing returns. Given stock of knowledge at a point of time, doubling the input of new knowledge will not double the amount of knowledge produced.(this is called externalities)

29. Increasing Returns and Long-Run GrowthPaul M. Romer 3 elements: Externalities, increasing returns in the production of output and decreasing returns in the production of new knowledge will produce well specified equilibrium model of growth. Historical Origins and Relation to Earlier Work Adam Smith’s story of pin factory Marshall’s distinction between internal and external economies. His concept of increasing returns that are external to firm but internal to an industry further supports this model.

30. Increasing Returns and Long-Run GrowthPaul M. Romer Justified the existence of increasing returns on the basis of increasing specialization and division of labor. It is clear that changes in an organization of production cannot be treated technological externalities. Increased specialization opens new markets and introduces new goods. All producers in the industry may benefit from the introduction of these goods but it is not technological externalities. It departs from Ramsey-Cass-Koopman by assuming that knowledge is capital good with an increasing marginal product. It implies the existence of a maximum feasible rate of growth for per capita output. Over time, the rate of growth of output may be monotonically increasing but it cannot exceed this upper bound. Approach used here relies on the assumptions made concerning the research technology; the diminishing returns in research will limit the rate of growth of the state variable.