Relationship between life expectancy and various factors
Many factors have been proved to be related to the life expectancy of people. This paper examines the relationship between the geographical position people live, their genders, per capita GDP and their life expectancy, using the cross-state data in the United States in 2000. In our research, controlling for per capita income and the gender, we find that the geographical position people live in are strongly correlated how long they can live: life expectancy in Hawaii exceeds that in Southern America by as much as four years. Also, based on our research, the females in the States typically live longer than males by five years. These coefficients are significant.
Academics and medical experts have long been curious about what factors will affect the local life expectancy and health. Academics hold different opinions towards this question. Some scholars, using a cross-country, time-series data on health and income per capita, showed that wealthier countries tend to be healthier (Lant Pritchett and Lawrence H. Summers)  ; some scholars suggest that particular air pollution may be a potential causes for decrease in life expectancy (Jaakko Nevalainena and Juha Pekkanen)  ; some scholars have found some diseases correlated with life expectancy, such as Obesity (A. Peeters, J.P. Mackenbach, L. Bonneux)  . However, previous research does not answer the simple question that when the productivity and per capita income is high enough, what is the effect of per capita income on life expectancy. Also they fail to analyze how people living in different geographical positions with comparable income differ in their life expectancy. This is what this paper will focus on.
In this paper, we use the state-level data of 2000 from the U.S. Census Bureau and examine the relationship between life expectancy and various factors, including geographical position, gender and local economic conditions, which are denoted by per capita income. Using an OLS method, we found that the gender and geographical positions strongly correlated with life expectancy. Females in average lives five years longer than males, given other conditions; life expectancy of residents in Hawaii in average is 4 years longer than that of residents in Southern American, including Florida, Georgia, North Carolina, South Carolina, etc. This difference may due to the availability of new medical techniques, the various life styles of different places and the sanitation conditions, which we will not go into the details in this paper.
According to our research, the per capita income is not a significant factor affecting the life expectancy across states in the United States, which is contrary to the previous research done by Lant Pritchett and Lawrence H. Summers as mentioned before. Our research shows that in developed countries, the per capita income may not be an important factor in determining the life expectancy, which means the marginal effect of income on life expectancy diminishes.
2 Data and institutional background
Life expectancy, by its definition, is the expected (in the statistical sense) number of years of life remaining at a given age  . The "life expectancy" in this paper refers to the number of years remaining at birth.
Our analysis is based on linked 2000 state-level data from multiple sources. Data on the state-level life expectancy (of female and male) are provided by the U.S. Census Bureau  , whose mission is to "serve as source of data about the United States' people and economy"  .Data on the per capita income of all states is from the website of Information Please  , which is part of Pearson, an integrated education company. The data was computed by Information Please using mid-year population estimates of the Bureau of the Census.
To examine the effects of factors other than age and per capita income, we consider the geographical location of people. Intuitively, where people live determines their life style, their diet and the climate around, thus affecting the life expectancy. To figure this effect, we include the geographical location in to our model. However, due to the lack of data, we divide states into 8 groups. They are: Alaska; Hawaii; New England, which includes Connecticut, Maine, Massachusetts, New Hampshire, Rhode Island, Vermont; Midwest, which includes Illinois, Indiana, Iowa, Kansas, Michigan, Minnesota, Missouri, Nebraska, North Dakota, Ohio, South Dakota, Wisconsin; West, which includes California, Colorado, Utah, Washington, Wyoming; Middle, which includes Delaware, DC, New Jersey, New York, Pennsylvania; South, which includes Alabama, Arkansas, Florida, Georgia, Kentucky, Louisiana, Mississippi, North California, South California, Tennessee, Virginia, West Virginia; Southwest, which includes Arizona, New Mexico, Oklahoma, Texas.
We introduce 7 dummy variables to denote these 8 categories. If an observation belongs to a certain category, we denote it with 1, else we set it 0.
Our aim in this paper is to examine the effects of genders, per capita income and geographical location on life expectancy. Among these factors, per capita income is measured by the 2000 US Dollar, while the life expectancy is measured in unite of years.
We employ OLS linear regression model to estimate the marginal effect of various factors on life expectancy. Suppose the statistical average years remaining at birth in a certain state is measured by y, and the explanatory variables are vector x. Assume that life expectancy, y is a linear function of our independent variables x, or y=α+xβ+ε, where βis a vector of coefficients andεis assumed to be conditional independent of x and has a expected value of 0, x is a vector of variables assumed to affect life expectancy. Intuitively, per capita income should have a positive coefficient while the female dummy variable negative.
There, using these assumptions and measures, our main hypothesis is as follows.
Hypothesis1: an increase in per capita income should be accompanied with an increase in life expectancy.
Hypothesis2: being a female means longer life expectancy.
Hypothesis3: Living in different part of the United States brings about a different life expectancy.
4.1 Descriptive statistics
Table 1 provides summary statistics for the main variables in our study. As we can easily figure out from Table 1, the life expectancy of female is much greater than that of males. All the common statistics of females, including mean, maximum, minimum and mean, outperform the males' by more than 5 years. Besides, the variation of life expectancy of males among different states, measured by standard deviation, is larger than the females' by about half a year. This fact, to some extent, confirms peoples' guess that due to more variations in life styles, males' life expectancy changes more violently than females'.
Another fact that we should notice in table 1 is that the great range of per capita income. Ranging from 20856 to 40870, per capita income of different states has a standard deviation of 4512, which accounts for 20% of the mean. Such a great variation suggests that the coefficients may have a relatively small coefficient.
Figure 1 is a Box plot of life expectancy for both Male and Female. Visually, we cannot find significant different in variation between these two categories. Most of the observations fall in the "right" area apart from one observation of male which is significantly below the "right" area. This observation is the D.C. Since our purpose is to measure the effects of geographical location on life expectancy, we don’t' have a good reason for deleting this observation from the dataset. As a result, we will keep this sample point and run the regressions.
4.2 Regression results
Table 2 provides the regression results for life expectancy, controlling for geographical locations, genders and per capita income. The first set of results in the table use per capita income in 2000, while the second use that of 1999.
As we can see from the first column of table 1, using Southwest part of the United States as the base, the dummy variables Hawaii, South, Female are significant under 1% significant level and Middle is significant under 5% significant level. The coefficient of Female is 5.2, which means being a female increases life expectancy by about 5 years, controlling for geographical locations. This accounts for about 7% of life expectancy of males. The difference in life expectancy between male and female may due to their distinct living style. In the United States, men tend to work to support the family, while a large proportion of women remain being a house wife. Higher pressure for men, as well as their more exposure to working place accident, public place crime and unhealthy habit, like smoking and drinking, may contribute to their lower life expectancy. When it comes to geographical location, living in Hawaii is with no doubt better for healthy than in southern American. The difference between these two districts may be due to the climate, the living style or some omitted variables, for example, people who like swimming and sailboat may prefer to live in Hawaii. This habit, in turn, makes them healthier than people in other places. Our research has shown that after controlling for per capita income, life expectancy in different parts of the states is different. This suggests a further research on why they differ in life expectancy.
When it comes to per capita income, as we can see, in the first column we introduce per capita income of 2000 as explanatory variable, while in the second column we use that of 1999. Neither of these two coefficients is significant, which means in developed countries, income might not be a determinant factor that affects state-level life expectancy. Notice that we are not saying income is not important for individuals who are less fortune, but for statistical average of large sample size, its effects are offsets by the people who are extremely rich.
Since it is a cross-sectional dataset, we need to test whether heteroskedasticity exists. Figure 2 are the plot of residuals versus genders. Roughly speaking, the distributions of residuals of both genders seem alike. To confirm this point, we conducted Breusch-Pagan test and the results are presented in Table 3. The chi square is 3.02, which means this is significant under a 10% interval and a weak heteroskedasticity may exist. To exclude this effect, we then conducted weighted OLS regression, and the regression results are similar to that in table1. We present it in table 4.
In this paper we examine the effects of geographical location on life expectancy, controlling for gender and per capita income. Our research finds that living in different places does contribute to the different in the life expectancy. A more detailed research may be needed to find out why.
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