Relationship between GDP, Life Expectancy and Growth Rate of G7 Countries

Increase in life expectancy is a key indicator to gauge the economic development of a country. Enormous studies have been done to test this hypothesis, and the conclusion is still un-decided. This study aims to explore the impact of life expectancy on economic growth in G7 countries via regression approach. Keeping in view the unique population structure of each of these G7 countries, the trend of life expectancy for each country is also observed. Findings of the study indicate that life expectancy in G7 countries increases with constant rate. The increase in life expectancy is accompanied with the increase in Gross Domestic Product (GDP) per capita income. We have also included the population growth rate as another important factor contributing towards GDP. It is worth mentioning here that increase in life expectancy directly affects per capita real income due to higher expenditure on health. Moreover, it is also found that increase in GDP lessens the population growth.


Introduction
In recent years, the increase in life expectancy has become a critical topic in population studies, as it is conditionally dependent on the economic growth and the expenditure on health improvement. According to World Bank report 1998, improvement in life expectancy is strongly linked with per capita income. It is expected that a prosperous country has a strong impact on the life expectancy of its inhabitants. An increase in GDP, normally decrease mortality rates, however, less developed countries experience mortality reduction in clusters of different age groups such as younger or working ages. Kelley and Schmidt (1995) explored that increase in population is neither all good nor all bad for economic growth, both elements coexist. Rodgers (1979) investigated that there exist a relationship between life expectancy, income and income distribution. On contrary, Becker, Philipson, and Soares (2003) suggested no such relationship.
On the other hand, economic growth is a key factor in raising standards of living worldwide and the role of population growth in the enhancement of living standards is a substantial part of it (see Heady & Hodge, 2009). There are abundant literature available which discusses the relationship between economic growth and population growth (Heady & Hodge, 2009). Past research shows that high income countries have relatively low population growth rate (Baker, Delong,& Krugman, 2005). However, significant effects of population growth on economic disparity and on life expectancy are observed.
Various research analysts have investigated empirical evidence which showed that robust population growth enhances economic growth. In contrast, few researchers found reverse evidence to this conclusion. Moreover, there are literatures which reveal that the effects vary with the level of a country's development, the source or nature of the population growth. The other factors that lead to non-uniform impacts on economic growth still need to be probed.
The main objectives of the study are many fold, (1) to observe the dependency of economic growth on population growth and life expectancy. (2) to explore the type of relationship between life expectancy , population growth and GDP in G7 countries which include US, UK, Canada, Italy, France, Germany and Japan.
Literature Review E. Wesley F. Peterson (2017) studied the relationship between population growth and economic growth of high income and low income countries on globe and reviewed the related literature in this context. In their study they found that in low income group, the rapid increase in population will increase the demographic dividend in these countries as the young people become productive adults in future. On contrary, growth rate is low in high income group of countries. However, few countries show negative growth rate indicating that a high percentage of the population consists of elderly people. They investigated relationship between growth rate, growth in per capita output, and overall economic growth using past 200 years data. Their results reveal that low growth rate in high income countries and high growth rate in low income countries may create social and problems.
In the same year Linden, M., & Ray, D. (2017), analyzed health-income relationship spanning period from 1970 to 2010 of 148 countries. They used quantile regression method to find association between health and different income groups. They concluded that in low-income countries' income gradient is quite larger than that of rich countries. Income disparity is measured by Gini criterion which showed that the effect of inequality on health is still remarkable in the least income group of countries. On the other hand became insignificant among highincome group of countries after the year 2000.
Cervellati,&Sunde (2011) tested that the effect of life expectancy on income per capita growth is nonmonotonic. In order to test the hypothesis they used 47 countries data taken from literatures (UN Demographic Yearbook, Maddison(2003)). Their result supports the previous findings on causal effect of life expectancy on income per capita growth. Furthermore, they concluded that improvement in life expectancy might affect the income growth indirectly as well as increases the probability of observing the demographic transition.
In 2002, Hasan explored long-run association between Growth rate and Per Capita Income of Bangladesh. His result exhibited that growth rate and GDP were cointegarted in long-run. Furthermore, a bidirectional relationship also exists between growth rate and GDP (Hasan,2002). In another study (Hasan, 2010) examined the relationship between population and per capita income of China using Granger causality method. Empirical analysis, shows the existence of negative long-run causal relationship of per capita income with population growth and shortterm association between growth and per capita income. In addition to this, he used neoclassical and endogenous growth models which indicated that per capita income growth tends to lower the population growth.
Schnabel &Eilers (2009) explored that the life expectancy has a nonlinear influence on wealth. They followed research of Preston's study, in which life expectancy and GDP had a curvilinear relationship. They also used least asymmetrically weighted squares which led to combine P-spline curves. Different smoothers were applied on a large data set of different countries. Furthermore, their developed models were used to estimate changes in life expectancy of individual countries with the passage of time.

Model Selection and Data Analysis
The data of GDP (per capita income) and Life Expectancy of G7 countries are taken from World Bank web site www.world bank.com. The data spans a period from 1960 to 2017. All countries GDP are taken into USD. All the GDP's are in billion (13 or more digits) so each country's GDP is divided by billion to ease the analysis procedure.
The model we have used for the analysis is a multiple linear regression model in two variables. The general form of the regression equation is described as; Where C is a constant, 'b 1 'is the coefficient measuring the effect of life expectancy on GDP and 'b 2 ' is the coefficient measuring the effect of population growth rate on GDP. The model (1) is further modified for the two group ofG7 countries. One group, in which population growth is positive and another in which population growth is negative for some period of time. Log-Log Regression equation (2)     Italy, Japan and UK has also negative growth rate for some specific period. When graphs of life expectancy and growth rate ( Figure 2&3) are compared it is found that growth rate of Canada has prominent place although it has high and low peaks.  Figure 2. Population growth rate is highest in Canada(1.28) followed by US(1.04), the minimum value of population growth rate is observed for Germany(0.23).  Table 2 reports the regression coefficients when GDP is regressed on life expectancy and population growth rate. The coefficients of life expectancy are highly significant in each of seven countries with positive coefficients. The coefficients of population growth rate are significant in Canada, France, Germany, Italy and Japan and are insignificant for UK and USA. It is also found that all countries except UK have negative coefficients (in significant). The high values of coefficient of determination R 2 indicate fairly good fit to each of G7 countries. The findings in Table 2 are further confirmed by computing the correlations between the three variables of interest.

Conclusion:
This study aims to study the GDP (per capita income), population growth rate and life expectancy of G7 countries. Studies showed that high income group countries lead to increase in the life expectancy. Increase in life expectancy means a large number of elderly people which may cause overburden on economy of the country. Empirical analysis shows that Japan has highest average GDP and life expectancy. But the growth rate of Canada is high among all G7 countries, this may be due to a large proportion of immigrants. The findings of the study agree with the existing empirical studies, which say that countries in the higher income group have low population growth accompanied by higher life expectancy (see Table1). This phenomenon is a special feature of G7 countries which is quite unnatural as the population structure in each of these seven countries is away from what is called the healthy structure of population.

Future Studies:
The current study is carried out only for G7 countries having common trends regarding GDP and life expectancy. However the same study may yield different results if done for developing and under developing countries.