The Solow Swan model of economic growth

1.0 Purpose

Examine facets of the Solow-Swan theoretical account of economic growing and place whether capital accretion has been the cause for growing in the instances of South Korea and Australia.

2.0 The Solow-Swan Model in brief

The theoretical account shows how growing in capital stock ( KM ) and labour ( L ) affect economic growing ( Y ) . It assumes that there is decreasing fringy returns for labor and capital considered individually as inputs and changeless returns to scale when taken together.

Mathematically, this is expressed as:

Y = AK ? L 1-? ( from Cobb-Douglas Production map, where Y= National Income, K=Capital, L= Labour, A= Total Factor Productivity and 0 & A ; lt ; ? & A ; lt ; 1 )

Y = Y/L = AK? L 1-?/L = AK?/L?= Ak?

i.e Y = Ak? ( GDP per worker is a map of Capital accretion per worker )

A is the Entire Factor Productivity map frequently interpreted as ‘technology ‘ or ‘knowledge ‘ .

The above production map is combined with a changeless nest egg rate to foretell that long term growing occurs through capital accretion. Since there are decreasing returns to capital, so economic systems would hit a ‘steady province ‘ where the rate of depreciation of old capital is merely equal to the rate of replacing of capital stock. All economic systems tend to near this steady province in the long tally. ( Solow 1956 )

3.0 Key anticipations of the Solow-Swan theoretical account for empirical confirmation:

1. Is at that place a positive co-relation between the indexs of capital accretion and economic growing as the theoretical account predicts?

2. If growing is so due to capital accretion, so growing will be strongest when the states have begun accretion of capital and will decelerate down as capital accretion advancements. Is this through empirical observation observed?

3. The rate of involvement i.e rate of return on capital should be highest in states with lower labor productiveness ( seen from equation above ) hence capital should flux from higher labor productive states to take down. This would in bend cause faster development of the developing states, and finally convergence. Has this been observed?

4.0 Empirical trial of the Solow-Swan Model

4.1 Choice of Indexs:

The anticipations of the theoretical account are tested by comparing Y/L with first, capital accretion and so, human capital accretion.

For Capital accretion, the undermentioned indexs are chosen:

CO2 emanations ( karat ) : As the degree of industrial activity over the old ages has increased, the CO2 emanations would hold besides increased proportionally. Therefore the degree of CO2 emanations each twelvemonth can be a just index of the sum of capital stock accumulated.

GDP per capita ( changeless LCU ) : The addition in capital stock accumulated will finally interpret into higher GDP, thereby increasing the per capita GDP. So GDP per capita can be a just index of the capital stock accumulated.

Gross Fixed Capital Formation ( changeless LCU ) : this step straight indicates the extent of capital stock accumulated. In the Solow-Swan theoretical account itself, investing is considered a direct determiner of growing.

For Human Capital accretion, the undermentioned indexs are chosen:

Labor Participation rate, female ( % of female population 15+ ) : an increased presence of adult females in the labour force indicates that the position of adult females has improved. Therefore a higher engagement can be said to be a just index that the human capital has grown.

Age dependence ratio ( % of working-age population ) : a higher dependence ratio reflects lower human capital development and frailty versa. This is because, a population with high dependence rates in working population indicates high unemployment every bit good as lower labour productiveness.

Scientific and proficient diary articles: the figure of articles reflects the educational degree and the accomplishment degrees of the general population. The higher the human capital, more will be the demand and supply of scientific articles.

4.2 Consequences of Arrested development:

R2 Value/coefficient for Indicators and Y/L

Indexs

Australia

S Korea

Capital Accumulation ( R2 )

0.866

0.997

CO2 Emission

1.750

1.921

GDP per capita

-4.273

6.384

K*-K ( point estimations )

0.0091

+0.0004

Gross Fixed Capital Formation

-2.059

-2.20

Indexs

Australia

S Korea

Human Capital Accumulation ( R2 )

0.798

0.997

Labor Participation rate

-0.003

0.147

Age Dependency Ratio

-4.85

-0.774

No. of Scientific Articles published

+3.91

0.00002

4.3 Analysis of Consequences: ( Refer enclosed excel sheet )

The graphs for K*-K for South Korea shows that ab initio there was small difference between the steady province and the current province of economic growing. Gradually this spread widened, and in the past decennary this spread has reduced one time once more.

This shows that South Korea has attained its degree of steady province through capital accretion

The graph for K*-K for Australia does non demo any regular form. Alternatively there is a zigzag form along the horizontal axis, with the growing rate holding surpassed the ideal province in some old ages and holding fallen below in others.

This reflects that capital accretion entirely possibly can non explicate the differences in K*-K. the displacements in steady province are possibly caused by some other factor.

Overall, for South Korea there is a really strong correlativity between Capital accretion and productiveness of labor. Australia besides exhibits this relationship, albeit to a somewhat lesser grade.

For Australia, it is seen that the arrested development coefficient for GDP per capita and Y/L is negative. One of the grounds for this could be that the capital per worker rate in the Australian economic system has been well below the long tally equilibrium steady province, hence there would hold been higher returns to capital and hence a lower Y/L value during these periods

Besides, there is a really strong correlativity between the indexs of Human Capital Accumulation and productiveness of labor for both Australia and South Korea.

4.4 Discrepancies of empirical findings with Solow Model:

1. For both states, the GDP growing does non look to be decelerating down with addition in capital stock accretion. The undermentioned two charts depict this fact:

GDP.v. Capital Stock ( AUSTRALIA )

GDP.v. Capital Stock ( SOUTH KOREA )

2. Besides, arrested development consequences between Y/L and Population Growth rate and Gross nest eggs rate of Australia and South Korea, are non consistent with the expected findings from Solow theoretical account.

SUMMARY OUTPUT of Regression of Y/L with Gross nest eggs Rate and Population Growth for South Korea

Arrested development Statisticss

Multiple R

0.927465

R Square

0.860192

Adjusted R Square

0.840219

Standard Error

2.026248

Observations

17

Analysis of variance

df

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F

Significance F

Arrested development

2

353.6524

176.8262

43.06869

1.04E-06

Residual

14

57.47951

4.105679

Entire

16

411.1319

Coefficients

Standard Error

T Stat

P-value

Lower 95 %

Upper 95 %

Lower 95.0 %

Upper 95.0 %

Intercept

69.17444

8.986995

7.697172

2.14E-06

49.89926

88.44963

49.89926

88.44963

Gross Savings rate

-1.01206

0.29757

-3.40108

0.004304

-1.65028

-0.37384

-1.65028

-0.37384

Population Growth

-8.23341

2.262968

-3.63832

0.002686

-13.087

-3.37983

-13.087

-3.37983

SUMMARY OUTPUT of Regression of Y/L with Population growing and Savings Rate of Australia

Arrested development Statisticss

Multiple R

0.83054

R Square

0.689797

Adjusted R Square

0.645482

Standard Error

0.003653

Observations

17

Analysis of variance

df

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F

Significance F

Arrested development

2

0.000415

0.000208

15.56583

0.000276

Residual

14

0.000187

1.33E-05

Entire

16

0.000602

Coefficients

Standard Error

T Stat

P-value

Lower 95 %

Upper 95 %

Lower 95.0 %

Upper 95.0 %

Intercept

-0.00894

0.018525

-0.48261

0.636832

-0.04867

0.030792

-0.04867

0.030792

Population Growth rate

0.001384

0.005547

0.249464

0.806625

-0.01051

0.01328

-0.01051

0.01328

Gross nest eggs rate

0.00467

0.001148

4.066277

0.001156

0.002207

0.007133

0.002207

0.007133

( All Data from WDI,2009 )

From the Solow theoretical account, it would be expected that Y/L is positively correlated with nest eggs rate and negatively correlative population growing rate. However, this is non wholly observed above.

5.0 Theoretical account for empirical observations

Role of Technology So, there appears some other factors at work apart from capital accretion that is increasing GDP growing in malice of addition in capital accretion, and doing deformations in relation of Y/L with population growing rate and nest eggs rate. Solow himself has offered an exogenic factor, i.e engineering. As technological developments and inventions begin to look in the economic system, this moves the steady province up enabling the economic system to maintain sing economic growing without the effects of decreasing returns on capital scene in.

Role of Human Capital Mankiw, Romer and Weil ( Mankiw 1992 ) offered another betterment over the Solow theoretical account. Through their survey, they found that as Solow predicted Y/L was positively correlated with rate of nest eggs and negatively correlated with population growing. However, they found that the portion of physical capital in the entire factor income was really high compared to what was through empirical observation observed in the U.S economic system. This led them to suggest an ‘augmented Solow theoretical account ‘ wherein human capital accretion is besides considered as a factor of production along with capital and labor. From our arrested development informations above, it is already seen that indexs of human capital accretion and Y/L show a really strong correlativity.

Openness of Economy The Solow-Swan theoretical account assumes that it is a closed economic system. However in world, much of South Korea ‘s growing was export driven. Sachs and Warner ( Sachs 1997 ) have argued that states with a broad trade policy will see higher growing. They have defined openness as the absence of non duty barrier, more than 40 % duty rate, and a important black exchange rate market, socialist economic system, and province monopoly of major export. ( Sachs 1997 )

Role of Institutions and Government policies J. Schumpeter has shown the importance of establishments in nest eggs determinations and economic development. They have a direct bearing on the capital accretion in a state. ( Schumpeter 1912 ) Further the regulative clime in the state and institutional norms besides influence growing.

Data Lacks It is besides possible that the above consequences are through empirical observation wrong due to the undermentioned mistakes:

Arrested development has been limited to merely 16 old ages

Inaccuracy of historical informations compared to current informations

Incorrect pick of Indexs.