A Canonical Correlation Analysis of Sectoral Composition of GDP and Development in Asia

This paper identifies the factors that influence percentage contribution of sectors to gross domestic product (GDP) for a group of 32 Asian countries for two cross-section points 1994-96 and 2014-16. Development theories hypothesize that the percentage share of sectors to GDP undergoes transformation with the level of economic development of the country and the degree of competitiveness of its agricultural sector. This paper employed the use of a canonical correlation analysis for 32 Asian countries. This analysis shows that the structural changes in sectoral GDP composition in the selected Asian countries were significantly determined by the factors like employee productivity, employment growth in services sector, rising life expectancy, growth of value added in manufacturing and gross capital formation.


Introduction
Economic development and structural changes in GDP are inter-related.We can see a number of studies related to how the agricultural development is determined by various factors like rural population, life expectancy, foreign direct investment, level of agricultural exports etc.There are studies explaining the growth of service sector in terms of urbanization and per capita income.Similarly, growth of industrial sector is explained in terms of capital formation, foreign direct investment, exports etc. Separate studies on agriculture or industry or services sector are based mainly on multiple regression analysis and excluded the effects of development indicators on the structural changes in the composition of GDP.So this study is based on canonical correlation analysis which is a generalization of multiple regression.In this paper, three response variables are con-

Literature Review
In the economic literature there are two main schools of thought on how sectoral composition and growth interrelate.The neoclassical view holds that sectoral composition is a relatively unimportant byproduct of growth.However, scholars associated with the world bank, including Kuznets [1], Rostow [2], Chenery and syrquin [3], and Baumol et al. [4] posit that growth is brought about by changes in sectoral composition [5].
Lewis theory [6] of economic development explains economic development in terms of structural-change which explains the mechanism of changing structure of underdeveloped economies from subsistence agriculture to more modern and more urbanized.Dual sector theory of Lewis emphasized the importance of agricultural sector in the economy as economic growth progresses.In this theory, industrial sector utilizes the surplus labour in the agricultural sector as its source of growth, along with capital generated by the investment of savings, to expand its production and thus gross output of the economy.As the industrial sector expands in importance, there is a concomitant reduction in the percentage contribution to gross domestic product by the agricultural sector.This growth process thus generally requires the movement of labour from rural areas to the urban areas with a decline of the rural population as a percentage of national population [7] [8].
While recognizing that industrialization is necessary condition for economic DOI: 10.4236/me.2018.92024C. M. Jayadevan development, there are differing views on sequencing of growth in various sectors.Kaldor, has emphasized that the industrial growth leads to the overall growth.He found a positive correlation between the rates of growth of GDP and the rates of growth of manufacturing output in his study of 12 industrially advanced countries during the period 1953-54 to 1963-64.He observed that the rates of economic growth are almost invariably associated with the fast rate of growth of the secondary sector, mainly, manufacturing [9].This phenomenon has been so striking to induce some economists to hypothesize that the manufacturing sector is the engine of economic growth, the so-called "engine of growth argument" [9] [10].Successful industrialization is one aspect of effective development [11].
Wu's study [12] shows that the main determinants of demand for services in India and china are per capita income and urbanization.It is argued that growth of the service sector is determined by several factors such as production specialization, income level and urbanization [13] [14].These factors are interrelated.
As an economy grows, productive activities become more specialized and urbanization accelerates due to the rising level of income.In the meantime, as a result of the increasing specialization of production, firms tend to outsource many service activities such as legal, accounting and security services.Some authors call this process the specialization splintering [15].It is the main source of demand for services from the producers.

Materials and Methods
The main source of data for this study is taken from online statistical database

Empirical Results
Summary Statistics for a group of 29 Asian countries for the period 1994-96 is reported in Table 1.Average share of agriculture in GDP was 23.17%, with a minimum 0.17% and maximum 50.72%.Average share of industry in GDP was 33.92%, with a minimum 15.06% and maximum 59.37%.Average share of services in GDP was 42.91%, with a minimum 19.13% and maximum 66.19%.The highest coefficient of variation is observed for the share of agriculture in GDP (61.68%) followed by the share of industry (29.37%) and the least for the services (25.53%) for 1994-96.
Summary Statistics for a group of 32 Asian countries for the period 2014-16 is reported in Table 1.Average share of agriculture in GDP was 12.73%, with a minimum 0.04% and maximum 33.26%.Average share of industry in GDP was 32.65%, with a minimum 7.2% and maximum 62.12%.Average share of services in GDP was 54.62%, with a minimum 28.54% and maximum 92.73%.1).
The correlation between the variables of sectoral GDP share are moderate, the largest being 0.69 between the share of industrial sector and the share of services sector during 2014-16.Similarly, the correlation between the share of agriculture and the share of services are negative for both periods (Table 2).
Some of the correlations between the development variables are high.High correlations are observed between employee productivity and life expectancy, urban population and employee productivity, urban population and life expectancy, employment in services and employee productivity, and foreign direct investment and the level of exports (Table 3).This is true for both periods.
Generally, the correlations between the variables of sectoral share of GDP and development variables are moderate.The share of agriculture has high negative  3.73, df = (30, 44.70) and p < 0.0001 for 1994-96.On the basis of this, we can reject the null hypothesis that there was no relationship between the variable sets and conclude that there probably was a relationship.Using Wilk's lamda, 1 − λ = 1 − 0.03 = 0.97 = r 2 for the model.All other test statistics are also significant.

Industry
This means that the model is significant.This is true for both periods.
Now that we have tested the hypothesis of independence and have rejected them, the next step is to obtain estimates of canonical correlation.The estimated canonical correlations are reported in Table 6.In general, the number of canonical dimensions is equal to the number of variables in the smaller set; however, the number of significant dimensions may be even smaller.In this example there are three canonical dimensions of which all of them are not statistically significant.For example for 2014-16, the first test of dimensions tests whether all three dimensions are significant (F = 3.78), the next test tests whether dimensions 2 and 3 are significant (F = 1.34).The last test tests whether dimension 3, by itself, is significant (F = 1.21).These results show that only the first canonical correlation is statistically significant.The last two canonical correlations are not significant.The squared values of the canonical variate pairs, found in the squared canonical correlation column, can be interpreted much in the same way as r 2 values are interpreted.We see that 92% of the variation in V 1 is explained by the variation in W 1 .Only the first canonical correlation is very important.This is also true for 1994-96 where 90% of the variation in V 1 is explained by the variation in W 1 (Table 6).variables are held constant (Table 8).Similarly, high positive raw coefficients are observed for share of manufacturing in gdp (0.68) and employment in services for 2014-16.High negative raw coefficient is also observed for industrial employment (Table 8).

Canonical coefficients are shown in
However, for 1994-96, gross capital formation and life expectancy emerged to be significant positive determinants of structural change in GDP.Growth of manufacturing, employee productivity and employment in services were also significant determinants of structural change in GDP for 1994-96.For 2014-16, life expectancy, employee productivity, value added in manufacturing, employment in services and gross capital formation were significant positive determinants of structural change in GDP.However, for 2014-16, the impact of growth of industrial employment was negative on structural change in GDP share.This is also evident from standardized coefficients (Table 8).
The standardized canonical coefficients are reported in Table 7 and Table 8.
The standardized coefficients allow for easier comparisons among the variables when the variables in the model have very different standard deviations.The standardized canonical coefficients are interpreted in a manner as same as to in-terpreting standardized regression coefficients.For example, consider the variable, the employee productivity, one standard deviation increase in employee productivity leads to 0.76 standard deviation increase in the score on the first canonical variate for set 2 when the other variables in the model are held constant for 2014-16.Similarly, for the variable the share of manufacturing in gdp, one standard deviation increase in the share of manufacturing in gdp leads to 0.37 percent increase in the score on the first canonical variate for set 2 when the other variables in the model are held constant (Table 8).
Below are correlations between observed variables and canonical variables which are known as the canonical loadings, which SAS labels as canonical structure.Correlation between the share of agriculture in GDP and their first canonical variable is negative.Similarly, the correlation between the share of industry in GDP and their first canonical variable is positive (Table 9) which is true for both periods.Similar picture can also be drawn from correlations between the sectoral GDP share and the canonical variables of the development measurements (Table 9).
Correlations between the development measurements and the canonical variables of sectoral GDP share are reported in Table 10.Correlation of first canonical variable with employee productivity, urban population, life expectancy, share of employment in service sector, level of export and share of manufacturing in gdp are high and positive for both periods.Similar picture can also be seen in case of correlations between the development measurements and their canonical variables (Table 10).
Royston's multivariate normality test for response data sets fulfilled for the period 2014-16, Mardia's and Royston's multivariate normality test fulfilled for the period 1994-96.
Univariate regression analysis has also been carried out to confirm the results from CCA.The percentage share of value added in agriculture was explained negatively by employee productivity and life expectancy for both periods.This model could explain 67 percent variation in the share of agriculture in GDP (Table 11).Regression results for percentage share of value added in industry shows that gross capital formation was a significant determinant for the change in the share of industry for both periods.However, the growth of manufacturing also found to be significant for 2014-16.The model could explain 50% variation in the share of industry (Table 12).
Regression results for the percentage share of services shows that improvement in life expectancy was a significant positive determinant of expansion of services sector for 2014-16.The model could explain 24% variation in the percentage share of services.However, no variables were found to be significant for 1994-96 (Table 13).

Conclusions
For 1994-96, gross capital formation and life expectancy emerged to be significant positive determinants of structural change in GDP.Growth of manufacturing, employee productivity and employment in services were also significant determinants of structural changes in GDP for 1994-96.For 2014-16, improvement in life expectancy, growth of employee productivity, growth of value added in manufacturing, growth of employment in services and capital formation were significant positive determinants of structural change in GDP.However, for 2014-16, the impact of growth of industrial employment was negative on the structural change in GDP share.
Univariate regression results show that the most important factors responsible for the transformation of agriculture are the growth in employee productivity and increase in life expectancy which transferred more workforce from agriculture to services.It is notable that improvement in life expectancy was the most important factor responsible for the growth of services sector.Growth of gross capital formation and growth of manufacturing are the most driving factors for the growth of industrial sector.
In order to reduce the contribution of agriculture to GDP and increase the share of non-agricultural sector to GDP, especially, for countries such as Nepal, Cambodia, Myanmar, Tajikistan, Pakistan and Afghanistan, policies to increase life expectancy, employee productivity, employment in services sector, size of manufacturing and gross capita formation are required.

Table 1 .
The highest Summary statistics of percentage sectoral share of GDP in Asia.Jayadevan coefficient of variation is observed for the share of agriculture in GDP (70.60%) followed by the share of industry (29.37%) and the least for the services (24.40%).It is notable that the average share of agriculture in GDP has declined from 23.17% in 1994-96 to 12.73% in 2014-16.The average share of industry has decreased slightly from 33.92% in 1994-96 to 32.65%.On the other hand, the aver- non-agricultural sector in GDP is the lowest for Nepal, Cambodia, Myanmar, Tajikistan, Pakistan and Afghanistan.On the other hand, the share of non-agricultural sector in GDP is above 95% for Singapore, Hong Kong, Brunei, Japan, Korea Republic, Russia and Kazakistan (Figure

Table 2 .
Correlations among the response variables.

Table 3 .
Correlations among the development variables.
dimension statistics are presented in Table5.By far the most common method used is Wilk's lamda (λ) as it tends to have the most general applicability.In our example, the model was statistically significant, with a Wilk's lamda of 0.03, F = DOI: 10.4236/me.2018.92024

Table 4 .
Correlations between response variables and predictor variables.

Table 5 .
Multivariate statistics and F approximations.

Table 7 .
Canonical coefficients for the sectoral GDP share variables.
ical variate of set 2 when all of the other variables are held constant.Similarly, for 2014-16, for life expectancy, 1 percent increase in life expectancy leads to 2.96 percent increase in the first canonical variate of set 2 when all of the other DOI: 10.4236/me.2018.

Table 8 .
Canonical coefficients for the development measurements.

Table 12 .
Regression estimates for percentage share of value added in industry.

Table 13 .
Regression estimates for percentage value added in services.