NEW GROWTH THEORY. Lecture 7-8

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1 NEW GROWTH THEORY Lecture 7-8 1

2 New Growth Theory (part 1) I. INTRODUCTION In the mid 1980 s, growth theorists raised their dissatisfaction with exogenously driven explanations of long-run productivity growth. They started to develop a number of models which allowed endogenous technological progress. As Romer (1994) describes, endogenous growth distinguishes itself from neo-classical growth by emphasising that economic growth is an endogenous outcome of economic system, not the result of forces that impinge from outside. The determination of long run growth within the model is the reason for the name endogenous growth. The details of these models are beyond the scope of this course. We will attempt to discuss simplified versions of some of them, as follow: 1. The AK model. The key feature of this model is to show how the elimination of diminishing returns to capital can lead to endogenous growth. 2. The model with learning-by-doing. Contrary to the AK model it attempts to eliminate the tendency for diminishing returns by assuming that knowledge creation was a side product of investment. When a firm increases its physical capital it also learns simultaneously how to produce efficiently. 3. The model with intentional knowledge creation. There are two sectors, a goods-producing sector where output is produced and a R&D sector where additions to the stock of knowledge are made. The model takes the fraction of labour and capital used in R&D and the rest of resources are used for production of goods. To understand the distinct contribution of new growth theory, remember the basic problem of the neo-classical model of economic growth: Variable of interest: growth in output per capita In the simple N-C model: diminishing returns to capital, thus capital accumulation cannot generate growth in the long-run. 2

3 Need 'technical change' to grow continuously. But: 1) exogenous in the model - 'manna from heaven' 2) do not know what it is. Let's briefly review: why does steady growth in y require t change? The key variable I want to concentrate on is the growth rate of the capitallabour ratio, k/k. Why? Because y is a function of k and A. It can only grow when either k or A are growing. Remember the fundamental equation of capital accumulation from the second lecture: k sy ( n ) k (1) Thus; k k = s y k - (n + ) (2) We want to know what happens to k/k when k changes. This depends on the difference between sy/k and (n +. We can show this in a diagram: (n + ) is shown by the continuous horizontal line. For sy/k, there are four different possibilities, which depend on the exact nature of the y function. 3

4 Since s is constant, it is y/k that determines how k/k changes as k changes. But note that this ratio is just the average product of capital. The key question now is: will the sy/k curve intersect the (n + ) line, and if so, will it do so from above or below. In the diagram, I have drawn four possible sy/k curves. The first (labelled '1') is downward sloping and intersects the (n + ) line at E 1. The second ('2') is upward-sloping and crosses at E 2. The third and fourth are parallel, one being above ('3') and one being below ('4') the (n + ) line. These four can be interpreted as follows: 1. Here the sy/k curve crosses from above. The slope is negative there is an inverse relationship between k/k and k as k rises the rate of growth of k falls, and vice versa. The point E 1 is a stable equilibrium. This corresponds to the standard neo-classical model without technical change. 4

5 2. Here the sy/k curve crosses from below. The slope is positive there is a positive relationship between k/k and k as k rises the rate of growth of k rises. The point E 2 is an unstable equilibrium - once we are away from it, we will not come back. This corresponds to explosive (or implosive growth), not a model of interest. 3. Here the sy/k curve is parallel. The slope is zero there is no relationship between k/k and k the rate of growth of k is independent of k. There is no equilibrium, only an equilibrium difference, i.e. sy/k > (n +, thus there is continuous positive growth in k (see eq. (2) above). 4. similar to 3., but there is continuously negative growth in k not a sensible model. Thus, key issue: What happens to APK (Average Product of Capital) as k rises? An example: Cobb-Douglas production function In per capita terms: Y = K (AL) 1-0 < < 1 (3) y = k A 1- (4) Now consider the crucial y/k ratio (= APK). y k = 1 k k A 1- = k A 1- = A k 1 (5) This implies that y/k is a decreasing function of k, thus corresponding to case 1 above. Now: We want to consider a simple model of endog. growth which fits the 3. scenarios described above. 5

6 II. THE AK MODEL The key property of endogenous growth models is the absence of diminishing returns to capital. In technical terms this implies: The average product of reproducible inputs must not fall as these inputs increase. The simplest version of a production function without diminishing returns is the AK function: Y = AK (6) where A is a positive constant that reflects the level of technology. Output per capita is y = Ak (7) and the average and marginal products of capital are constant at the level A y k = dy dk = A Now rewrite (7) in growth terms: y y = A A + k k = k k since A is assumed constant. In this particular case the growth rate of y is exactly equal to the rate of growth of k. To derive the rate of growth of k, substitute the expression for y in (7) in (2) above, i.e. k k = s y k - (n + ) = s Ak k - (n + ) = sa - (n + ) (8) 6

7 This is an interesting result. It says that as long as there is positive net investment (i.e. sa > n + ), there will be constant growth in output per capita even in the absence of technical progress (remember: A is fixed). This corresponds to case 3 earlier, and can be shown in a diagram as follows: In this case, the rate of growth of y depends on: A, the state of technology s, the savings rate n, the rate of population growth, the rate of depreciation The key implications are: An economy described by an AK production function can display positive long-run growth without any technological progress. 7

8 Does not predict convergence. The growth rate is independent of the level of y. Countries with identical parameters will grow at the same rate, but if there are initial differences, the ones behind will never catch up. No transitional dynamics (but can be adjusted quite easily to allow for these). Government policy may affect long-run growth through induced changes in A, n, s or. The key parameters themselves may be endogenous. For instance, the savings rate will depend on the rate of time preference and the degree of risk aversion. The rate of population growth may depend on social security systems or education levels. A, the level of technology, may depend on the level of human capital and the allocation of resources between different activities. Problem with AK model: Does not make intuitive sense, because only one factor of production with and production function with constant returns to that factor. Next model: - provides a justification for the AK specification; - shows that AK specification is just a special case of a wider class of models; - shows the extreme sensitivity of the AK model to assumptions about the underlying relationships in the model. 8

9 III. A SIMPLE MODEL WITH LEARNING-BY-DOING Romer (1986) 1 - key paper that revived interest in growth theory - eliminates dim. returns to (the reproducible factor) K by assuming that knowledge creation is a side product of investment. This is similar to Arrow's (1962) 2 model of learning-by-doing. The central idea of learning-by-doing is that, as individuals produce goods, they inevitably think of ways of improving the production process. Improvements in productivity thus occur without any explicit innovations. The accumulation of knowledge is therefore a side effect of conventional economic activity. Here: Will consider a simple model (see Appendix for more complex case) Start off with a standard Cobb-Douglas production function with labouraugmenting 'technical change': Y = K (AL) 1- (9) The simplest case of learning-by-doing is when learning occurs as a side effect of the use of new capital. Then the stock of knowldege is a function of the stock of capital. This relationship can be put in a very simple form as follows: A = K > 0 (10) (see Appendix for more complex version). Substituting (10) into (9)) gives Y = K ( KL) 1- (11) = 1- KL 1-1 Romer, P (1986), Increasing Returns and Long-Run Growth, Journal of Political Economy, Vol. 66, December, pp Arrow, K. J. (1962) The economic implications of learning by doing Review of Economic Studies, 29 (June), pp

10 We saw earlier that the behaviour of the model crucially depends on the APK (average product of capital). Y/K = APK = 1- L 1- (12) Thus APK does not vary with K. We are thus back at case 3 (see section I). Again, consider the growth rate of the capital-labour ratio (eq. (2)): k k = s Y K - (n + ) = s 1- L 1- - (n + ) (13) (where I have used the fact that Y/K = y/k). Here, as expected, k/k is independent of k. See diagram underneath. (sil= s 1- L 1- and d = This is the same diagram as in the AK model. The difference to the AK model here is that k/k is a positive function of L. k/k will be a constant 10

11 only if population growth is zero (i.e. n = 0). If n > 0, then the sy/k function will continuously shift upwards. The AK model is thus a special case of this with zero population growth. A more general model with capital externalities (e.g. learning by doing) which allows for different returns to scale characteristics Consider C-D production function with labour augmenting technical change for firm i: Yi = Ki (BiLi) 1-0 < < 1 (A1) B i is the index of knowledge available to the firm. Now make two assumptions (following Arrow, 1962; Romer, 1986): 1. An increase in a firm's capital stock leads to a parallel increase in its stock of knowledge; i.e. B i is a positive function of K i 2. Each firm's knowledge is a public good that any other firm can access at zero cost. In other words, once discovered, a piece of knowledge spills over instantly across the whole economy; i.e B i =B. These ideas can be put in a simple form as follows: Bi = K > 0 > 0 (A2) and thus the individual firm production function can be written (i.e by substituting (A2) into (A1)) as Yi = Ki ( K Li) 1- (A3) Now aggregate this over all firms (i.e. by multiplying K i and L i by the number of identical firms in the economy), and you get the aggregate production function 11

12 Y = K 1- K (1 - L 1- and thus Y = 1- K +(1- L 1- (A4) We saw earlier that the behaviour of the model crucially depends on the APK (average product of capital). Y/K = APK = 1- K ( -1)+(1- L 1- (A5) How does APK vary with K? This depends on the exponent on k, since ( Y / K) K = [( -1)+(1-1- K ( -1)+(1- L 1- Whether PK is an increasing, decreasing or constant function of K thus depends on whether this exponent (= elasticity of PK with respect to K) is positive, negative, or zero. This, in turns, depends on whether is bigger, smaller or equal to one. To see this, rewrite the exponent, ( + (1- as follows: ( + (1- = -(1- ) + (1- = ( -1)(1- The following are true (since (1- > 0): 1. if > 1 ( -1)(1- ) > 0 increasing returns to capital (increasing returns to scale) 2. if = 1 ( -1)(1- ) = 0 constant returns to capital (constant returns to scale if n = 0) 3. if < 1 ( -1)(1- ) < 0 decreasing returns to capital (decreasing returns to scale if n = 0) 12

13 In case 1, we have explosive growth. In case 2, the production function simplifies to y = 1- kl 1- which corresponds to the model analysed in the text. In case 3, the long-run growth rate of the economy is a function of the rate of growth of population. 13

14 New Growth Theory (part 2) I. A SIMPLE MODEL WITH INTENTIONAL KNOWLEDGE CREATION This is a model in the spirit of Lucas (1988) 3 and Romer (1990) 4. It involves four variables, L (labour), K (capital), A (technology), and output (Y). There are two sectors, a goods-producing sector where output is produced and a R&D sector where additions to the stock of knowledge are made. Fraction a L (a K ) of the labour force (capital) is used in the R&D sector and fraction 1-a L (1-a K ) in the goods-producing sector. Both sectors use the full stock of knowledge, A; since the use of a piece of knowledge in one sector does not preclude the use in the other ( non-rival good), we do not have to consider the division of A between the two sectors. The quantity of output produced is given by Y = [(1-a K )K] [A(1-a L )L] 1-0 < < 1 (1) As usual, this function has constant returns to labour and capital. The production of new ideas depends on the quantities of K and L engaged in R&D activities, and A, A = B[a K K] [a L L] A B > 0,, 0 (2) This production function is not assumed to have constant returns to scale to capital and labour (i.e. it is possible that > 1 or < 1). Obviously, the coefficient determines how cumulative knowledge creation is. If is equal to one, then A is proportional to A. The difficulty with this model is that it has two stock variables (K and A) whose behaviour is endogenous. This makes the analysis more complicated. To proceed, we consider the model without capital. This case shows most of the model's central messages. Thus we get: 3 Lucas, R. (1988), On the mechanics of economic development, Journal of Monetary Economics, Vol. 22, pp Romer, P. (1990), Endogenous Technological Change, Journal of Political Economy, Vol. 98, S71-S

15 Y = A(1-a L )L (3) and A = B(a L L) A (4) In per capita terms: y = A(1-a L ) (5) This implies that rate of growth of y must be equal to the rate of growth of A (assuming a L is constant and determined exogenously): y y = A A = a The growth rate of A, a, is A A = a = B(a LL) A -1 (6) Since B and a L are constant, whether the growth rate of A is rising, falling, or constant, depends on the behaviour of L A -1. We can distinguish between three different cases. Case 1: > 1 a is explosive ( not realistic); Case 2: = 1 constant a if n = 0; (similar results to AK model) if n > 0 explosive a; ( both unrealistic) Case 3: < 1 a converges to a steady-state path steady growth in A and y; steady-state rate of growth is a positive funtion of n This last case can be shown by looking at the rate of growth of a. (6): 15

16 a a = B B + a a L L + n + ( -1)a 0 0 a a = n + ( -1)a (7) This can be shown in a diagram: a a slope = ( -1) = -(1- ) E a The steady state (and stable) equilibrium is where a/a = 0, i.e. at point E. This implies that at E the rate of growth of a is zero, i.e. a is stable. We can work out what determines the equilibrium a, a*, by setting a/a = 0 in equation (7): 0 = n + ( -1)a a* = n 1 (8) This illustrates two points: 16

17 positive population growth is a precondition for steady growth in y; i.e. sustained increases in the population are needed to offset the diminishing marginal returns to additional knowledge (since < 1) the rate of growth will be greater the closer is to one; i.e. the bigger the effect of existing A on the accumulation of A. Thus only case 3 provides a realistic scenario. The problem with it is that it predicts that higher populaton growth leads to faster per capita growth. This is not what one observes; i.e. countries with a higher population growth rate do not in general have a faster rate of growth of y. One can however think of the model as providing an explanation for worldwide economic growth. Interpret A as knowldege that can be used anywhere in the world. Then the model implies that higher global population growth raises worldwide growth. The larger the population is, the more people there are to make new discoveries. NB: The model also implies that the fraction of the labour force engaged in R&D activities, a L, has no effect on growth. This is also due to the fact that < 1. An increase in a L raises a temporarily, but because of the diminishing returns to new knowledge in the process of knowledge creation this cannot have a permanent effect on a (NB: this is exactly the same reasoning as that why an increase in the savings rate has no permanent impact on growth in the neo-classical model). In Lucas (1988), the endogenous variable is called 'human capital', not R&D. The basic structure of his model is, however, similar to the above model. 'Human capital' is accumulated through explicit 'production': a part of individual's working time is devoted to accumulation of skills. The rate of growth of y is then a positive function of the rate of growth of human capital. II. TWO IMPORTANT IMPLICATIONS OF ROMER (1990) AND LUCAS (1988) 1. A competitive equilibrium leads to underinvestment in new technologies (human capital). This is because when an individual firm/worker invests in new technologies (human capital), only the private 17

18 return is taken into account. This implies that the social returns exceed private returns to investment in new technologies (human capital). Since growth is a function of the level of investment in technologies (human capital), growth could be increased by a higher level of investment in these sectors. This leads to the conclusion that government policies (subsidies) are necessary to increase the growth rate to the level of the optimal growth rate (NB: because more advanced techniques are required, we cannot show this result formally here). 2. In the long run the level of y is proportional to the initial stock of new technologies (human capital). This implies that there is no tendency for convergence. III. OTHER IMPORTANT ISSUES 1. Lucas (1988) uses a slightly awkward definition of human capital. It partly resembles learning-by-doing in that it is accumulated on-the-job, but also resembles technology since a given human capital does not vanish when a person dies. In Romer (1990), on the other hand, human capital has a narrower meaning ( skilled labour). 2. The model in Romer (1990) is much more complex than the model presented here. It contains more inputs, and endogenises the allocation of resources (i.e. human capital in the Romer sense) between the goods sector and the technology sector. Some important conclusions from the model are: The growth rate will be affected by the savings rate. Anything that raises s will raise growth. For instance, a fall in the interest rate will raise growth. More human capital raises growth because it speeds up the development of new technologies. The research sector operates under increasing returns to scale. This implies that the marginal product of human capital in research rises as A rises. This leads to an ever increasing share of human capital being devoted to the A sector. If the initial level of H is too small, stagnation may arise. This can be explained as follows. Human capital is required in both the research and the goods sector. The growth rate of A depends on the amount of human 18

19 capital devoted to its production. So in order to produce A, some final goods production/consumption has to be foregone. If the total level of human capital is very low, then any reasonable share of this devoted to the R&D sector may only yield very small marginal increases in A. If there are only small increases in A as a result, we will only get a low return to our investment of human capital in that sector, i.e. a small increase in Y next period as a result of having more A. This is important: it is a little bit like saying that when your income is very low, you may not save any money because the benefit of the extra savings (a little interest earned next period) does not compensate you for the loss of consumption now. Just try and think of the problem as that of a low-level equilibrium trap. Romer himself states that this may explain why there was no growth in prehistoric time, because as anthropologists seem to have argued: 'civilisation, and hence growth, could not begin until human capital could be spared from the production of goods for immediate consumption'. In this respect the appropriate policy response is to subsidise research. Too little human capital will be devoted to R&D ( market failure), since the market wage for human capital will be lower than the social value of human capital. This leads to too low a supply. Trade may be important: By allowing the pooling of human capital, several countries together can achieve a higher growth rate. In other words, the wheel does not have to be reinvented. Similarly an increase in the size of the output market raises the returns to investment in new technologies. IV. KEY RESULTS AND ISSUES IN NEW GROWTH THEORY 1. Key concepts in new growth theory: 1. Increasing returns to scale. 2. Externalities. 3. Human capital. 2. New Growth Theories of the type presented here presents good explanations for global growth. 19

20 3. They may be less good at conceptually explaining cross-country differences. In particular, the question is why A should not convergence across countries. There are two difficulties: - If countries are different because they do not all have access to the same technologies, then the lags in the diffusion of knowledge from rich to poor countries needed to account for observed differences in incomes are extremely long. - Techology is a non-rival good. Its use by one firm does not prevent its use by others. The question then is: why do poor countries not have access to the same technology as rich countries? An alternative explanation is that it is not differences in technology or knowledge, but differences in the ability to use them, that explain persistent differences in standards of living. Also note that if countries are assumed to trade, then differences have to come from factors that are substantially non-tradable (either because this is in their nature, because of costs, or because of restrictions). 4. Alternative explanations: a. Human capital Defined in a narrower sense than Lucas (1988) (i.e. as a rival good): education, training ( investment in human capital is costly). Maybe human capital should be considered as another factor of production. Could explain: - Lack of convergence might be explained by insufficient human capital accumulation. Human capital is not internationally mobile (restrictions to the movement of labour), hence no functioning world market in human capital. - Often observed empirical link between investment and growth. If LDCs want to catch up over time, then they must accumulate human capital. Convergence will be faster the more is saved and invested in both human capital and K. - Lack of international capital flows. Maybe K/L ratio is a poor indicator of productivity, i.e. MPK. If Y=F(K,L,H) then MPK is also a function of H. Combination of low K/L and low H may explain why MPK is actually not higher in poorer countries. 20

21 b. Public Infrastructure Very similar argument to human capital. May help to explain Solow residual. Again, not traded on world markets. Usually financed by public savings. Example: East Germany after reunification. Poor infrastructure was a major reason why foreign investment was so slow to come in. When infrastructure is missing, productivity of all factors will be lower. 5. One important conclusion from all this is that government intervention can affect the growth rate, and may even be desirable, since the competitive (i.e. free-market) equilibrium (rate of growth of y) may be inefficient if externalities are present 21

22 Empirical Studies of Economic Growth We know already There has been substantial growth across most countries. Growth rates have varied considerably between countries. There appears to have been convergence between the richer countries. Only some of the poor countries appear to be catching up with the rich countries. Growth accounting suggests that the 'residual', i.e. the proxy measure of technical change, has an important role in explaining growth over time and differences in growth between countries. In order to evaluate more systematic studies of the empirical evidence, we need to review the main characteristics of the growth models discussed in this course. The neo-classical model Need to distinguish between the steady state and transitional growth rates. In the steady state, the rate of growth of output per capita, gy, is equal to a, the rate of growth of exogenous technology/productivity. People sometimes confuse exogeneity of a with constant a. However, the former does not imply the latter. If it did, then an easy test of the n-c model would be to consider whether gy is more or less constant over time. But we have already seen that gy changes substantially over time. And the brief exercise in growth accounting in lecture 3 showed that industrialised countries have experienced a considerable slowdown in a since the 1970s. During the transition, gy can also be affected by changes in the underlying parameters of the n-c model, such as s, n, or. So any examination of variations in growth rates over the medium run has to take these factors into account. This is partly what growth accounting does. Returning to the steady-state, while gy is not affected by these parameters, the level of y certainly is. One way of assessing the explanatory power of the n-c (Solow) model is to consider y at a particular point of time across 22

23 countries, and examine to what extent differences between countries can be explained by differences in the steady-state parameters. In this framework, one is basically estimating whether cross-country differences in y can be explained by countries having settled on different points (steady-states) of a common production function. Such an analysis was undertaken by Mankiw, Romer and Weil, Quarterly Journal of Economics, May 1992 According to the n-c model, savings and population growth affect output per worker through their impact on K/L. A country that saves more of its output has more capital per worker, and thus more output per worker; a country with higher population growth devotes more of its saving to maintaining its capital-labour ratio, and so has less capital and output per worker. Starting from a simple Cobb-Douglas specification, the following regression specification suggests itself: ln y i = [ln s i - ln (n i + a + )] + i, where i indexes countries, and all the other variables are as usual. The data used is defined as follows: y i = real GDP per person of working age in 1985 s i = average share of real private and government investment in real GDP, n i = average growth rate of the population of working age, The authors set a + equal to 0.05 for all countries. Interpretation of 1 : This is the elasticity of output on the balanced growth path with respect to the savings rate, which should be equal to 1, and is the elasticity of output with respect to capital (= capital's factor share in output). 23

24 For 98 non-oil exporting countries, the estimated results are: ln y i = + [ln s i - ln (n i )], adj. R 2 = Both estimated coefficients are highly significant. Given b 1 = 1.48, the implied equals This value is much higher than anything we get from data on factor shares. Conclusions: These estimates are "not supportive of the textbook Solow model" (p.415). Convergence Convergence is basically about adjustment during the transition to a (new) steady-state. We now need to distinguish between different concepts of convergence. The simplest version of the neo-classical growth model predicts convergence, if countries share exactly the same production function and behavioural parameters. Let's refer to 'absolute convergence' as that implied by identical (in terms of their underlying structure, i.e. parameters) countries which are adjusting to their (common) steady-state. The evidence just considered suggests that there are significant differences in these parameters across countries (otherwise it would not have been able to explain cross-country variations in y). Thus even in their (respective) steady-states, countries will now exhibit differences in y. Convergence in this context is generally called 'conditional convergence'. This concept refers to countries converging to their individual steady-states, i.e. those determined by their specific parameters; there is convergence, but only conditional on those particular values (i.e. if we control for differences in these parameters, we should observe convergence in the original sense). 24

25 As illustration: y 2 * y 1 * f(k) (n + )k s 2 f(k) s 1 f(k) k 1 * k 2 * k Here the two countries differ in terms of their savings rates, and they do not share a common steady-state. Conditional convergence here means that when the two countries are in disequlibrium (i.e. k 1 k 1 * and k 2 k 2 *) they will converge to their respective equilibria. How can the convergence hypothesis be empirically assessed? The general implication is that there should be a negative association between initial y and subsequent growth in y (gy). Thus to formalise this idea in a regression framework: Absolute convergence gy i = y i + i H 0 : 1 < 0 where gy i is growth over a given period, and y i is the initial level of y. This is the type of regression that fits a regression line of the type shown in the first lecture. The evidence strongly suggests no relationship of this type across all countries, as could be expected. 25

26 Conditional convergence Tests for conditional convergence take the specification above, but a number of other variables to capture differences in steady-states between countries. Both types of specifications are, for instance, estimated in Mankiw et al. (1992). Their results are in accordance with the more general literature. There is no evidence in support of absolute convergence (except for the rich countries), but the available cross-country data generally supports the hypothesis of 'conditional convergence'. New growth theory New growth theory provides a variety of suggestions about what actually determines the growth rate of y. It can be seen as an attempt to endogenise a. This course has only looked at a very select class of new growth models. Many more have been developed during the past decade, suggesting a wide variety of factors that can affect growth in y, gy. In the simple AK model, the growth rate was determined by A, s, n and. Anything that shifts either of these will have an effect on the rate of growth of y. The most widely used approach is to run a regression of average growth in y over a period on a number of independent variables which are deemed to affect growth. Prime examples of such variables are trade-policies, government expenditure, and human capital. There have been numerous studies of this type, an example being Barro (1991) 5. The key paper assessing the contributions of empirical studies of this type is Levine and Renelt (1992) The paper is an attempt to systematically assess the significance of the types of variables used in the literature to explain cross-country variations in growth rates. 5 Barro, R. J. (1991), Economic growth in a cross-section of countries, Quarterly Journal of Economics, Vol. 106, pp

27 Why is this important? The main reason is that in regression analysis, the estimated coefficients and standard errors on a given set of variables partly depend on what other variables are included in the regression. This means that certain results may be rather sensitive to the specification of the regression model. Levine and Renelt undertake an analysis of this sensitivity by initially considering a large set of variables. They find that only a small number of variables are actually robustly related to economic growth across countries. These are: Variable Captures Correlation with gy 1 average share of investment in GDP the effect of capital growth positive 2 initial level of income* conditional convergence negative 3 initial secondary school enrolment rate initial human capital positive * robust for period if regression includes human capital; not robust for ; The results of the basic regression including only the robust variables and population growth are gy i = y60 i n i sec i I/Y i R 2 = 0.46 where the underlined coefficients are statistically significant. None of the variables capturing the stance of fiscal policy, trade policy or macroeconomic stability appeared to be robustly related to growth. This clearly shows that previous findings cannot be generalised on the basis of the available data. 27

28 New growth theory and convergence Endogenous growth theory predicts that countries' growth rates should be independent of the past, which implies that there is no automatic mechanism in the models leading to either absolute or conditional convergence. The results in Levine and Renelt suggest that conditional convergence is supported by the data when differences in human capital are controlled for. This can be seen in the attached figure (from Burda and Wyplosz, Figure 5.15, p.125 compare with Figure 5.14 on previous page). The role of human capital Human capital is one of the key variables in many new growth models (e.g. Lucas, 1988; Romer, 1990). In Lucas's model it is the variable which generates the externality necessary for endogenous growth. In Romer's paper it is the key input in the production of new technologies. However, it is also possible to set up a more sophisticated version of the neo-classical growth model, with human capital included as an additional factor or production. This is done in Mankiw et al. (1992) Adding human capital to the neo-classical model (Mankiw, Romer and Weil, Quarterly Journal of Economics, May 1992) Mankiw et al. run a similar regression to the one presented at the beginning of this lecture in the context of the simple neo-classical model, but with the addition of a human capital variable. They proxy investment in human capital by the percentage of the working-age population that is in secondary education (similar to Levine and Renelt, 1992). Adding this variable, they obtain the following results: adj. R 2 = 0.78 (thus the residual is reduced substantially when compared to the simple model) implied physical capital share = 0.31 implied human capital share =

29 These results imply that "adding human capital to the Solow model improves its performance", (p.421) the augmented Solow model comes up with reasonable estimates of the implied elasticities, the implied elasticities suggest that the large factor share attributed to physical capital in the first regression was due to the omission of human capital. These results suggest that the commonly large share of factor returns to labour (approx. 2/3) are in fact partly returns to human capital (which is embodied in the labour input) Conclusions The verdict is still out as to which models perform best empirically. It is very difficult to get a proper handle on endogenous growth models because often either the underlying mechanisms are unobservables, e.g. externalities, or data is not available (especially time-series), or the available data are only a rough proxy of the variables in question (e.g. measures of trade policy, political instability etc.). For these reasons, some authors (e.g. Pack, ; Solow, ) are dismissive of cross-country growth regressions. The evidence on developing countries is also unclear. The World Bank especially has argued for a long time now that trade liberalisation is a key ingredient to successful growth performance. However, as shown in Levine and Renelt (1992), this view is not strongly supported by the evidence. There seems to be a fairly strong consensus on one key ingredient: human capital. Investment in education and training is regarded as a key to growth in industrialised and developing countries alike (only listen to the pronouncements of leading UK politicians). 6 Pack, H. (1994), Endogenous Growth Theory: Intellectual Appeal and Empirical Short Comings, Journal of Economic Perspectives, Vol. 8, No Solow, R. (1994), Journal of Economic Perspectives, Vol. 8, No

30 Overall, the growth process appears to be extremely complex and not easily explained by simplistic models. There are many ingredients, such as institutions (e.g. the state of the legal system) which cannot readily be modelled (see North, , for a discussion of the role of institutions). Maybe an alternative approach would be to closely examine those countries that have been the most overwhelming success stories, such as the East Asian tigers (Hong Kong, South Korea etc.). Young, A. (1992) 9 has examined the economies of Hong Kong and Singapore more closely. Between , average growth in both countries was very similar (approx. 6% p.a.). They share other similarities: Both are ex-british colonies, post-war population mainly consists of immigrant Chinese, have gone through a similar sequence of industries (textiles electronics banking; very rough stylisation), Singapore starting about a decade later. But there are also major differences. Hong Kong: minimal government intervention. Singapore: dominated by government intervention, include. forced savings. Resulting differences most marked with respect to role of capital accumulation. Very high in Singapore, less so in Hong Kong. The effect of this is that the estimated rate of technological progress (1970/1-1990) in Hong Kong has been estimated at 2.3%, while in Singapore at only 0.1%. So Singapore has grown almost entirely through K accumulation. Young argues that this is because Singapore has gone too fast from one industry to the next, leaving insufficient time to learn how to use the releveant techniques efficiently; and, by relying largely on foreign investment, Singapore has not allowed a sufficiently large class of domestic entrepreneurs to develop. The future prospects for Singapore are therefore not so good, if what we said earlier in the course is correct. High investment rates can lead to higher 8 North, D. (1991), Institutions, economic theory and economic performance, Ch. 12 in Institutions, Institutional Change and Economic Performance, Cambridge University Press, pp Young, A. (1992), A Tale of Two Cities: Factor Accumulation and Technical Change in Hong Kong and Singapore, NBER Macroeconomics Annual, pp

31 growth, but not indefinitely. In the long run, productivity growth is essential. 31

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