# ECONOMETRIC

ECONOMETRIC: AN ANALYSIS OF THE EFFECT OF INCOME ON LIFE INSURANCE
What is the causal relationship in the journal or working paper? Please state the cause and effect variables.

Cause- Gross national income per capita, life expectancy, youth dependency population, long term interest rates, life insurance as share of entire insurance market, fertility rate.

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Effect- Premiums per capita of life insurance
What is the correlation between the cause and effect variables?
There is a positive correlation between gross national income per capita and premiums per capita of life insurance.

There is a positive correlation between life expectancy and premiums per capita of life insurance
There is a positive correlation between youth dependency and premiums per capita of life insurance.

There is a positive correlation between elderly dependency and premiums per capita life insurance
There is a positive correlation between life share insurance of market and premiums per capita of life insurance.

There is a negative correlation between fertility rate and premiums per capita of life insurance.

Please state and explain the data type used in the journal or working papers?
Cross-sectional data because the data is from random sample. The data was taken from OECD online database.

Discuss whether or not the zero conditional mean assumption (?|? = 0) applies to the econometrics model? What are other factors that you can think of that may influence the ‘effect variable’?
For the simple regression model, zero mean conditional assumption is violated as there is a correlation between x, explanatory variables and µ, mean of unobserved factors.
Based on the multiple regression model zero conditional mean assumption xu=0 is applied to the econometrics model. This is because there is no correlation between x and µ.

Other factor that may influence premiums per capita of life insurance is lifestyle because when people performing low-risk activities, premiums of life insurance per capita increase. Another factor is occupation because for high-risk level of profession it will influenced premiums of life insurance per capita.
Comment on the sign and magnitude of the estimated coefficient of the explanatory variables.

For the multiple regression model(restricted), the explanatory variables are gross national income per capita, life expectancy, youth dependency population, long term interest rates, life insurance as share the entire insurance market and fertility rate.

The higher the gross national income per capita, the higher the life insurance of premium per capita. This will cause the positive sign of the parameter, ?1>0. 1% increase in gross national income per capita will increase life insurance of premium per capita by 1.6842431%.

When the life expectancy is higher, the life insurance of premium per capita also higher because as people live more longer, they are expected to invest in life insurance. So, this cause the positive sign of parameter ?2>0. One unit increase in life expectancy , will increase life insurance of premium by 10.57662%.

Higher youth dependency population affect the life insurance of premium per capita to be higher. So, the sign of parameter ?3>0, positive sign. One-unit increase in youth dependency population will increase life insurance premium by 28.53542%.

When long term interest rates are higher, the life insurance of premium per capita will lower because due to higher interest rate may influence individuals to invest in another place other than in life insurance. So, cause the negative sign of parameter ?4<0. Increase of long term interest rate by one unit, will decrease life insurance premium per capita by 6.14672%.

The higher the life insurance share of market, the higher the life insurance premium per capita. So, cause the positive sign of parameter ?5>0. One-unit increase in life insurance share of market, will increase life insurance premium per capita by 2.71333%.

When fertility rate is higher, the life insurance of premium per capita lower because
One-unit increase in fertility rate, decrease the life insurance premium per capita by
Are these explanatory variables statistically significant?
In Multiple Regression for unrestricted, has 10 independent variables. The value of d.f is 46. Each of the variables are tested with different significance level: 1%, 5% and 10% and use two-tailed test.
For variable gross national income per capita and life share insurance of market, it is tested with 1% significance level. The value of t-stat is 3.16 and 4.64 respectively.
For life expectancy and youth dependency, it is tested with 5% significance level. The value of t-stat is 2.10 and 2.24 respectively.

For long term interest rate and fertility rate, it is tested with 10% significance level. The value of t-stat is 1.82 and 1.8.
These shows that we able to reject null hypothesis and these variables are statistically significant.

For employment rate, health expenditure, elderly dependency ratio and household net saving variables we fail to reject null hypothesis at any significance level. So, we use F-test and the value of F-statistic is 0.7602 and the critical value is 2.574. This prove that these are not jointly statistically significant.
In Multiple Regression Model for restricted, has 6 independent variables.

For gross national income per capita, youth dependency and life share insurance of market, it is tested with 1% significance level. The value of t-stat is 4.09, 4.05 and 5.60 respectively.

For life expectancy, long term interest rates and fertility rate, it is tested with 5% significance level. The value of t-stat is 2.11, 2.38 and 2.5 respectively.

These variables are able to reject null hypothesis and statistically significant.

Would you say the explanatory variables explain much of the variation in dependent variable?
For Multiple Regression 1, R-squared is 0.8094, this show that 80.9% of variation in premiums per capita of the explanatory variables which considered a large variation.

For Multiple Regression 2, R-squared drop to 0.7968 as there is omitted variable, this show that 79.7% of variation in premiums per capita of explanatory variables which also considered a large variation. Hence, we can conclude the explanatory variables explain a lot of variation in dependent variable.

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