Few issues are as important to a country as the long-term growth and productivity trends
facing their economy. The relative slow-down in the growth rates of the United States
economy since 1973 has worried economists and politicians alike. Many possible causes
have been put forth, though none is fully satisfactory.
Before discussing the theoretical models of growth it would be useful to study the data
on growth that is currently available. As Nicholas Kaldor, in his influential article on
growth ("Capital Accumulation and Economic Growth"; 1961) stated , a theorist ought to
start with the summary of the facts that are immediately available, concentrating
primarily on broad tendencies or "stylized facts." Theories can then be constructed to
explain the facts. Listed below are the stylized facts as mentioned by Kaldor:
1. Output per worker shows continuous growth.
2. Capital per worker shows continuous growth.
3. The rate of return on capital is steady.
4. The capital-output ratio is steady.
5. Labor and capital receive constant shares of total income.
6. There are wide differences in the rate of growth across countries.
In addition to the above, other researchers have found additional features which are
obscure for a wide array of data:
7. Average growth rates show no variations with the level of per-capita income.
8. Growth in trade is positively correlated with income levels.
9. Population growth rates are negatively correlated with income levels.
10. The rate of growth of factors inputs is never large enough to explain the rate of
growth; that is, technical progress is essential to growth.
Angus Maddison, in his book, Phases of Capitalistic Development 1982, lists in great
detail the empirical aspects of growth during the past two hundred years. This study
extends out on the whole Kaldor's main observations. Both output and capital per worker
has shown tremendous growth over time. Even though growth rates have slowed down since
1973, they are at levels still high by historic standards. Similarly, the constancy of
the capital-output ratio is borne out by the statistical data of developed countries.
However, Kaldor's assertion about the constancy of labor and capital shares in total
income has increasingly been disputed. As the figures below show:
COUNTRY INTERVAL SHARE OF CAPITAL (%) REFERENCES
Japan 1913-1938 40 Ohkawa and Rosovsky
1954-1964 31
United Kingdom 1856-1873 41 Matthews, Feinstein and
1873-1913 43 Odling-Smee
1913-1951 33
1951-1973 27
United States 1899-1919 35 Kendrick
1919-1953 25
1929-1953 29
The data suggests that the share of capital has declined from around 40% to 30% over the
course of the century.
Lastly, the great differences in growth rates between countries over time indicates that
there has been no tendency for the convergence in rates of growth, something that the
neo-classical theory would predict.
Having discussed the empirical issues of economic growth, we now turn to the various
theories that have been developed to explain the facts. Perhaps the three most important
theories of growth are:
1. Harrod-Domar model
2. Neoclassical theory of growth
3. Endogenous growth models
The Harrod-Domar model is an offshoot of Keynes' macroeconomic model as stated in the
"General Theory." Indeed, it can be viewed as an attempt to put Keynes' macroeconomic
model of an economy in a dynamic context. From the fundamental relation that investment
must equal saving in a closed economy, leads to the result that the rate of growth of an
economy equals the product of the savings rate and the incremental output-capital ratio.
The equations are:
I ? S
But, DK=I
Also, S=sY (s: savings rate)
Define n=DY/DK (incremental output-capital ratio)
This implies, DK=sY
But, DK=DY/n
Therefore, g?DY/Y=s?n (g?DY/Y: rate of growth of output)
Unfortunately, the Harrod-Domar model has a "knife-edge" property which made it somewhat
unrealistic. This meant that if an economy strayed from its optimal growth path it
either exploded or imploded. This lead to the search for alternative models, the most
famous being the neo-classical growth model, usually associated with the infamous Robert
Solow.
The neo-classical growth model assumes that the economy converges towards a steady-state
rate of growth. Given a neo-classical production function:
Y=A?F(K, N)
Assuming a constant rate of labor force growth (DN/N=n) and no technical progress
(DA/A=0) then in a steady state rate of growth of output (DY/Y) equals rate of population
growth which implies there is no growth in per capita income unless technical progress
takes place.
A critical difference between the Harrod-Domar model and the neoclassical growth model
lies in the effect the savings rate has on growth rates. In the Harrod-Domar model an
increase in the savings rate increases the growth rate. However, in the neo classical
model, an increase in the savings rate increases the per capita income but it does not
result in a permanent (as compared to a temporary) increase in the growth rate.
To summarize, in the neo-classical model the rate of output growth equals the rate of
growth of technical progress (DA/A) and the level per capita output is determined by the
steady-state equation:
sy=(d+n)k
where s: savings rate
y: per capita output
d: depreciation rate of capital stock
n: population growth rate
k: per capita capital stock
While Solow's neo-classical model explains the first five out of the six stylized facts
quite well, it cannot explain the fact that growth rates differ between countries for
long periods of time. This model would suggest convergence in growth rates, something
that does not seem to take place (see table).
To explain this problem, theorists have focused their attention on technical progress
and have made attempts to make the growth rate endogenous (i.e. determined within the
theory). Various endogenous growth theory models, proposed by economists like Robert
Lucas and Paul Romer, have constructed a dynamic model where the rate of growth of output
depends on aggregate stock of capital (both physical and human) and on the level of
research and development in an economy. Many of the models are mathematically complex
but do explain the persistent difference in growth rates between countries and the
importance of research and human capital development in permanently increasing the growth
rate of an economy.
Works Cited
Dornbusch, R. and Fischer, S. Macroeconomics. New York:McGraw Hill, 1994.
Kaldor, N. "Capital Accumulation and Economic Growth" in F.A. Lutz and D.C. Hague
(eds.), The Theory of Capital. New York: St. Martin's Press, 1961.
Maddison, A. Phases of Capatalist Development. Oxford: Oxford University Press, 1982.
Romer, P.M. "Capital Accumulation in the Theory of Long Run Growth." In R. Barro
(ed.) Modern Business Cycle Theory. Cambridge: Harvard University Press, 1989.
Testing Samuelson's Multiplier - Accelerator Interaction Model
The Fundamental Equations Are:
Yt = Ct + It + Go [Go is exogenous] --- Definitional Equation.
Ct = gYt-1 [00] --- Behavioral Equations.
?The model helps to demonstrate how the multiplier and accelerator interact to generate
cyclical fluctuations in the economy.
?g is the marginal propensity to consume (MPC) and a is the accelerator, the marginal
propensity to save (MPS).
?To test the behavioral equations we apply basic econometrics; using the t- statistic to
verify its significance. The first behavioral equation:
Ct = -146.66 + 0.714Yt-1
(1.597) (38.57)
The figures in the brackets are the t- statistics. The higher the value of the t-
statistics the more significant is the value of the parameter. This would suggest that
the marginal propensity to consume 'g' where lagged income is regressed on current
consumption is 0.714. If we chose another behavioral assumption that current is lagged
on current investment then we get the equation:
Ct = -226.18 + 0.711Yt
(6.75) (106.75)
This would suggest that the marginal propensity to consume where current income is
regressed on current consumption is 0.711 which is not very different from the value of
0.714 calculated earlier. So both behavioral assumptions lead to approximately the same
value of 'g'.
?The second behavioral assumption:
It = a(Ct - Ct-1)
where a is the accelerator coefficient. The parameters for the above behavioral equation
are:
It = 623.3 + 0.823(Ct - Ct-1)
(11.259) (1.638)
This would suggest that the parameteric values of the accelerator coefficient is 0.823,
although the relatively low t- statistic value of 1.638 suggests that we cannot place too
much confidence on this parameter.
?Therefore we can state: g = 0.714
a = 0.823.
We also know from Samuelson's model that if ag<1 then the model is stable. From the
value above we see that ag = 0.587 < 1. Hence, the U.S. economy is a stable economy that
experiences cyclical fluctuations.
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