6.
A paper written by Mankiw, Romer and Weil '' A contribution to the empirics of economic growth'' (1992), hence referred as MRW, performed an empirical
evaluation of a “textbook” Solow (1956) growth model using the Penn World Tables.
MRW discusses the augmented Solow growth model that includes accumulation of human and physical capital, and they perform an empirical evaluation using cross-country data.
MRW find that in the long run steady state, real output per worker by country is positively correlated with savings rate and negatively related population growth rate.
Mankiw et al correctly estimates the direction of the effect of savings and population growth, but tends to over estimate the magnitude of these effects. Therefore they augment the Solow model to include the affects of human and physical capital. This would reduce the affects of savings and populations’ coefficients, hence would not be overestimated.
They find that the augmented solow model fits the cross-country data. Their interpretation that it’s consistent with an augmented solow model depends on the implausible assumption that educational productivity is higher in advanced countries than poor ones.
In section 3 MRW discuss endogenous growth theory and convergence. MRW argues that the solow model does not predict convergence, it predicts only that income per capita in a given country converges to that countries steady state value; conditional convergence.
MRW also discuss the speed of convergence.
MRW’s estimates of the textbook Solow model also implied a capital share of factor
income of about 0.60, which is high compared to the conventional value (based on U.S. data) of about one-third.
They concluded that higher savings rate leads to higher income in the steady state, which in turn leads to a higher level of human capital, even if the rate of human capital accumulation is unchanged. Higher savings raises total factor productivity.
Young has discussed that human capital has played an important role in the rapid growth of some economies. Young looks at the growth rates in East Asia. With the addition of human and physical capital in the augmented model it shows that the growth rate of output has risen and is the result of accumulation of human capital.
In their estimation of the augmented Solow model, MRW assume that α β and g are the same for all countries and that actual output equals balanced growth output. η=0
Their estimation of the text book Solow model assumes that B=0, that is human capital H, does not enter as a separate factor of production.
Additional research by professors at Princeton obtained estimates for the MRW sample period, 1960 - 85, using revised data. The results are similar that was originally found, but with 2 exceptions.
Firstly with the revised data, the over-identifying restriction of the model is rejected for the non OECD country samples. This rejection contrasts with the original MRW findings for the same sample period.
Secondly they find lower estimates of the capital share. It's closer to 0.5 than 0.6
MRW finds, the performance of the augmented Solow model, with human capital, is generally better than that of the textbook version. The augmented model explains a great deal more of the cross-country variation in output per worker; an R2 of 0.59.
With human capital there is a serious problem, equation 3 measures the volume of human capital in terms of income foregone during education – meaning a years worth of schooling would be around 40 times as valuable in Norway (1985 GDP per adult $19723) than in Chad ($462 per adult). This assumption means that MRW is seriously overestimating the difference in stock of human capital per capita.
In the second part of their paper, MRW attempt to estimate directly the speed of convergence to the steady state and to relate their findings to the predictions of the Solow model.
The speed of convergence measures how quickly a deviation from the steady state growth rate is corrected overtime. A rapid convergence rate implies that economies are close to their steady state. MRW finds that convergence is at a rate of 2% indicating that a country is half way to its steady state in 35 years.
Measuring the speed of convergence is a difficult econometric problem, especially in the face of possible parameter heterogeneity and ongoing economic shocks.
A more direct way to study the determinants of long-run growth, is to obtain country-by-country estimates of the growth of TFP.
The MRW framework applies broadly to almost any economic growth model that has a balanced growth path, and that the restrictions specifically imposed by the Solow
model tend to be rejected.
The correlation of variables like the saving rate with long-run output growth rates is inconsistent with the joint hypothesis that the Solow model is true and the economies being studied are in their respective steady states.
The finding that the saving rate and the growth rate of the labour force are correlated with estimated TFP growth is inconsistent with the standard Solow model, even if we do not assume steady states.
7Ai)
Y = A(L)α (K) 1-α
This is the Cobb-douglas production function, where Y equals output and is a function of effective labour AL and capital, K.
The technology variable "A" is said to be "labour-augmenting" or "Harrod-neutral technology shock" – a unit of labour is more productive when the level of "A" is high.
α is a parameter between 0 and 1.
The economic interpretation is saying that labour-augmenting is a function of E, learning by doing effect, K, capital and L, labour.
E is a constant and is a level effect. The higher the E the more productive labour is, and you eradicate diminishing returns to a certain extent. Learning by doing refers to the capability of workers to improve their productivity by regularly repeating the same type of action. The increased productivity is achieved through practice, self-perfection and minor innovations.
K/L is the capital to labour ratio; which simply indicates how much capital is being used by the labour force.
sY = △K + δK
s is the savings rate, which is a fraction between 0 and 1. Y is income for the economy. therefore sY is the amount that is saved by the economy. Solow model assumes a closed economy and by definition a closed economy has savings that equal investment. sY is interpreted as investment made in the economy.
Investment is firstly needed to replace worn out capital. It is also used to increase the stock level of capital. This identity holds at the steady state, where investment equals the change in capital ( △K ) plus the depreciation of capital (δK). When sY is more than △K + δK then the level of depreciation will be high which will then eventually bring the economy to the steady state. On the other hand when sY > △K + δK then capital stock increases because investment exceeds depreciation.
ii) α in these equations are a parameter between 0 and 1. This parameter can be shown to be labour and capital's share of output.
α and 1-α equal 1 the function has constant returns to scale.
The exponents α and 1-α are output elasticities with respect to labor and capital, respectively. Output elasticity measures the responsiveness of output to a change in levels of either labor or capital used in production, ceteris paribus.
iii)
Log and differentiate
Where as its a constant.
The key determinates of this is capital, K, Labour, L, the learning by doing effect, E and technology, A.
Output is a function of effective labour, AL and capital. where effective labour is made up of a variable, A, technology. Technological progress is a function of the learning by doing effect and the capital to labour ratio.
We assume growth in learning- by- doing is zero, therefore technology doesn't grow in time. Hence output solely depends on capital.
iv) Depreciation is the rate at which capital is destroyed. For an economy to grow, depreciated capital must be replaced and additional capital needs to be bought for an increasing growth in population.
Firms have a choice when buying capital, between quantity and quality. Where quality is essentially durability of capital. Durability is inversely related to deprecation. Capital that has high durability will not depreciate quickly.
The assumption of a constant depreciation rate is not well justified. The reasons are because depreciation is due to other factors other than durability.
One reason of depreciation is population growth. An increased population growth increases depreciation. As more of the working population uses capital, there will be more wear and tear. Also capital will be more thinly spread over the number of workers.
We assume there are diminishing returns to durability because providing a rapidly growing population with high quality capital is costly due to forgone consumption.
Another reason for depreciation is increased through technological progress. More rapid technological advances increases the level of output per capita. An example of this would be personal computers. As PC’s have become more advanced old PC’s have become obsolete and useless.
A third reason why a constant depreciation rate is not justified is because of increased savings. Savings accelerates depreciation in an endogenous growth model. With an assumption of diminishing returns to durability, thereby strengthening the positive effects of increased savings and investment on economic growth.
High savings and investment raise the cost of maintaining high quality capital. Higher savings speeds up depreciation because that way growth also speeds up.
v)
In neoclassical growth models, the long run rate of growth is exogenously determined by assuming a savings rate and a rate of technological progress. This does not explain the origin of growth, which makes the Solow model unrealistic.
Y = A(L)α (K)1-a
Is an endogenous growth model, because it incorporates technology into the model. The model endogenizes technology variable into the model. Technology is tied to capital per worker. By using capital, labour learns how to use it better.
E is the learning by doing effect; the bigger the constant the more they are learning and the more efficient the labour face become. Labour will be able to use more capital in the production process and effectively its as if they have grown a third hand, Which can be simple seen as population growth.
Bi)
Y = A(1-b) L
The above function is stating that output, Y is a function of technology, A, the fraction of the labour force in the research and development sector, b and the labour force of the economy that is not involved in R&D.
Expanding out the brackets gives:
Y= AL –Lb
This equation states that output is given by the effective labour in the economy minus the amount of labour force in the R& D sector that produces ideas.
∆ A = BLA
∆A is the rate at which the number of ideas grows. B is a constant, that can be positive or negative which is the rate at which they discover ideas.
If its positive, then ideas in the past raises the productivity of researchers in the present. In this case B is an increasing function of A.
If, on the other hand, it is negative, ideas that are discovered earlier make it more difficult to create ideas in the present. In this case B would be a decreasing function of A.
This reasoning means modelling the rate at which ideas are produced as
B=CA∮
where c and∮ are constants.
∮= 0 indicates that the tendency for the most obvious ideas to be discovered first, exactly offsets the fact that old ideas may facilitate the discovery of new ideas, ie productivity of research is independent of the stock of knowledge.
∮> 0 indicates that the productivity of research increase with the stock of ideas that have already been discovered.
When ∮= 1 is a special case where constant research effort can sustain long term growth.
L is the fraction of people in the research and development sector.
Hence, change in ideas is dependant on the rate at which ideas are generated, the amount of people in R&D and by the number of ideas that have already been produced.
ii)
Y = (A(1-b)L)
Output is a function of capital, effective labour and amount of people in the R&D sector
% both sides by L
Log and differentiate
where 1-b is a constant
This states that output per capita is a function of growth in ideas growth in ideas is a function of B, a constant, A∮, previous ideas thought of in the past and Lbλ the share of researchers in the population.
A new variable has been added. λ
λ is to take into account spillovers and/ or duplication of ideas. It is possible that average productivity of research depends on the number of people searching for new ideas at any point in time.
Duplication of effort is more likely when there are more persons engaged in research.
A way to model this is by Lb λ where 0 < λ < 1
λ < 1 reflects externality associated with duplication.
À = BA∮Lbλ
Divide both sides by A
À / A = (BA∮Lbλ ) / A
À / A = B Lbλ / A 1-∮
g = À / A
log g
g/g = ln B + λ ln Lb – ln A1-∮
g/g = ln B + λ ln L + λ ln b - ln A1-∮
Log and differentiate:
g/g = B/B + λ L/L + λ b/b – (1-∮) À/A
where L/L = n
g/g = 0, B/B = 0, b/b = 0 as we assume share of population that wants to do research is always constant.
g = À/A = λn / 1-∮
g = f(n)
y/y = λn / 1-∮
The rate at which ideas grow is a positive function of n, and is saying that output increases as population grows. As population grows more people in actual terms will be in R&D and will be generating more ideas. Compared to the simple Solow model where, as population increases, output decreases along a balanced growth path.
iii)
Growth in a '' Harrod'' type economy seems to be driven by the learning-by-doing effect.
In this economy the more capital a person uses, he learns by using capital and learns to incorporate an increasing amount of capital to his production process.
The way output grows is the way capital grows. The way capital grows is by the economy saving, and firms borrow money to buy capital and learn to incorporate it into their production process and output increases. As people are learning to incorporate more capital into the production process, more capital is needed per person, which effectively is like population growth.
Hence for growth more capital is needed and the learning by doing effect is contributing to output. Technology is not getting better, people are getting more efficient. The alpha parameter and savings affect the learning by doing effect.
The Romer model takes a different view on the sources of growth. We assume that A/A = g
The Romer model takes a step further to explain how g is determined.
This model states that people are the key input. A larger population generates more ideas and because ideas are non-rivalry, everyone in the economy benefits.
This model, of the engine of growth describes the advanced countries of the world. As poorer countries do not have the right level of human capital or infrastructure to think of new ideas or to implement them.
The result of this model is that growth rate of the economy is tied to the growth rate of the population, but if the number of researchers stops growing, long run growth ceases, according to this model.
There is one special case where constant research effort can sustain long term growth where λ= 1 and ∮ = 1.
Essentially the Romer model puts growth down to population growth and the number of researchers who produce ideas.
Bibliography
Books
Jones. C. Introduction to economic growth. Second edition. W.W Norton and company Ltd (2002)
Mankiw, G. Macroeconomics. 6th ed. Palgrave, (2006)
Journals
Bernake, B. Is growth exogenous? Taking Mankiw, Romer and Weil seriously. National Bureau of Economic Research (2001)
Edwards T. Human capital and the ambiguity of the Mankiw- Romer-Weil model. Loughborogh University (2004)
Felipe, J et al. Why are some countries richer than others? A reassurance of Mankiw Romer Weils test of the neoclassical growth model.
Mankiw, et al. A contribution to the empirics of economic growth. Quarterly journal of economics. (1992)
Porter M and Stern S. Measuring “ideas” production function: Evidence from the international patent output. National Bureau of economic research. (2000)
Young. A Tyranny of numbers: Confronting the statistical realities of the east asian growth experience. The Quarterly Journal of Economics, Vol. 110, No. 3. (Aug., 1995), pp. 641-680.
Zoega G and Gylfasan T. Obsolescence. International macroeconomics. (2001)
Bernake, B. Is growth exogenous? Taking Mankiw, Romer and Weil Seriously. (2001)
Felipe, J. Why are some countries richer than others? A reassessment of Mankiw Romer Weils's test f the neoclassical growth model.
Young, A. Tyranny of numbers. The quarterly journal of economics Vol. 110, No. 3. (Aug., 1995).
Bernake, B. Is growth exogenous? Taking Mankiw, Romer and Weil Seriously. (2001)
Edwards T, Human capital and the ambiguity of the Mankiw-Romer-Weil model. (2004)
Felipe, J. Why are some countries richer than others? A reassessment of Mankiw Romer Weils's test f the neoclassical growth model.
Zoeyga G and Gylfason T. Obsolescene. International Macroeconomics. 2001
