Before any conclusions can be made and in order to provide a more comprehensive analysis on the relationship between the infant mortality rate and government expenditure on health, regression analyses should be performed on both Canada and the U.S. to define the coefficient of determination. Generally, the higher the value of R-squared, the better the model fits the data. Although the infant mortality rate tends to decrease as total GDP increases, only 7.3% of the variation in the infant mortality rate for Canada can be explained by government expenditure on health. The remaining 92.7% is unexplained. On the other hand, when computing R-squared for the United States with the infant mortality rate as the dependent variable and government expenditure on health as the independent variable, we derive a percentage of 84.7%. This signifies that 84.7% of the variation in the infant mortality rate is explained by the variation in government expenditure on health. Only 15.3% is unexplained.
If we perform these same analyses, but use the life expectancy as the dependent variable, we obtain the following results: For Canada, 22.3% of the variation in life expectancy is clarified by the variation in government expenditure on health. For the United States, 89.3% of the variation in life expectancy is explained by the variation in government expenditure on health. Through these percentages, it is determined that the infant mortality rate per 1,000 live births and the life expectancy data better fit the model for the United States. The high value of R-squared simply measures the strength of these relationships.
Upon further examination of Canada’s residuals for both infant mortality rate and life expectancy, it appears that autocorrelation has occurred, increasing for life expectancy and decreasing for infant mortality. Following are two graphs depicting these outcomes.
Following is a graphic depiction of the residuals for the United States with life expectancy as the dependent variable. The plot of these residuals versus time indicates independence; however, there appears to be negative first-order autocorrelation (Keller 637).
These assumptions could be confirmed through performing a Durbin-Watson statistic; however, confirmation is not necessary. In order to increase the validity of these models, for both Canada and the United States, it is necessary to ensure that the error variable is normally distributed with a constant variance and that the errors are independent of each other (Keller 603). First, we are going to introduce another independent variable, consumer expenditure on health goods and medical services. Second, we’ll also need to include an independent variable that has a time-ordered effect on the dependent variable. The simplest solution would be to record the number of years since the data were collected. For example, in this case, the third independent variable = 1,2,…, 18 (Keller 641).
After incorporating these variables into the model with infant mortality rate as the response variable, we can determine that the conditions for the error variable have been satisfied. The first graph indicates that there is no heteroscedasticity. The second graph shows independence.
94.1% of the variation in the infant mortality rate is explained by the three independent variables, while only 5.9% remains unexplained. Similarly, the United States has a coefficient of determination of 97.3%. Only 2.7% remains unexplained.
Using life expectancy as the response variable has an even higher R-squared. For Canada, 99% of the variation in life expectancy is explained through these three variables. For the United States, it is 98.1%.
While these outcomes help to determine the relationship of the dependent and independent variables, what other useful information can be extrapolated from this data? What other comparisons can be made between a nationalized and privatized healthcare system besides the obvious comparisons previously established in this paper? In order to do this, the same independent variables will be used, government expenditure on health, consumer spending on health goods and medical services, and time. However, infant deaths will be used as the response variable instead of the infant mortality rate per 1,000 live births.
Using infant deaths as the dependent variable produces similar coefficient of determinations for both Canada and the United States. The relationship between infant deaths and government expenditure on health for Canada is positively related. As the infant death rate increases, the government expenditure on health increases on average by 0.016863. Although, this assumes that consumer expenditure on health and time are held constant. More specifically, for each additional 100 infant deaths, the government expenditure on health increases by 1.69%. Consumer expenditure on health is also positively related to infant deaths. Consumer expenditure on health goods and medical services increases by 4.65% for each additional 100 infant deaths. Once again, this is assuming that the other independent variables are held constant.
Performing this same regression except for the United States, we derive slightly different numbers. The major difference is that infant deaths and government expenditure on health are negatively related. For each additional 100 infant deaths, government expenditure decreases by 3.62%. Results for consumer expenditure on health goods and medical services are slightly higher than Canada. For each additional 100 infant deaths, consumer expenditure increases 4.87%.
Over the years as total GDP has increased and government expenditure on health has increased, the infant death rate has decreased faster in Canada than the United States. Over the 18 year sampling period, on average, the government expenditure on health in the United States was 21% of total government expenditure. Canada’s government expenditure on health, on average, was 4.5% of total government expenditure. Determining the inefficiencies of the United States government expenditure on health is beyond the scope of this paper; however, the higher infant death rate can be partially attributed to an inverse relationship it has to government expenditure on health.
Regression analyses for Canada and the U.S. have been performed using the same independent variables, but life expectancy at birth has been substituted for the response variable. In this particular case for Canada, for each additional 1,000 days or 2.74 years that a person lives, government expenditure on health decreases by 0.015%. Contrary to this number is consumer expenditure on health which increases by 0.159% for each additional 1,000 days. This is assuming that the other two independent variables are held constant.
Compare these figures with the United States. For each additional 1,000 days that a person lives, the government expenditure on health decreases by 0.006%. Consumer expenditure on health increases by 0.002%. Once again, these percentages assume that all other independent variables are held constant.
Overall, government expenditure on health with respect to life expectancy decreases for each additional day that a person lives, but it decreases at a higher percentage in Canada than the United States. Interestingly, consumer expenditure on health goods and medical services increases more for each day a person lives in Canada than in the United States. This fact helps to partially explain why the average life expectancy is higher in Canada than the United States. The government expenditure on health does not promote life expectancy in either country.
In conclusion, the Canadian government spends a smaller percentage on health than the United States yet Canadians enjoy a lower infant death and infant mortality rate per 1,000 live births. Canadians can also expect a longer lifespan. After accounting for autocorrelation, the coefficient of determination in each regression analysis explained over 95% of the variations between the dependent variable and the independent variables. The lower infant death rate in Canada is partially explained through a positive relationship with government expenditure on health. To an extent, the higher life expectancy in Canada is attributable to an increase in consumer expenditure on health goods and related medical services. A more complete analysis needs to be conducted in order concretely determine whether a nationalized healthcare system provides better quality of care and is more efficient than a privatized system. This analysis did show that the Canadian healthcare system is more efficient with its resources and that consumer expenditure on health related services has an effect on the outcome of infant deaths and life expectancy in both the United States and Canada.
Works Cited
Euromonitor International. November 11, 2008. http://www.portal.euromonitor.com/passport/magazine.aspx.
Keller, Gerald and Brian Warrack. Statistics for Management and Economics. Belmont: Thomson Learning, 2004.
Mankiw, N. Gregory. Macroeconomics. New York: Worth, 2007.
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