Do Lower Birthrates Lead to Longer
Lives?
Hint: Yes, No, Maybe, I don’t know,
Can You Repeat the Question?
Hello and welcome to my blog. Why am I starting a blog? Excellent question hypothetical reader. I sometimes like to do little projects. This blog is mainly so that I have a reason not to half-ass said projects. Also I like economics, science, math, a good debate, among other things and would like to share my interests. I hope that people will enjoy my blog and maybe learn something, but mostly it is just a way for me to motivate myself and organize my thoughts. Anyways enough with introspective explanations and on to what this post is about.
One of the
things that struck me was this graph showing life expectancy and births per
woman.
I thought
this was very interesting, but I immediately questioned whether there was
causation. There seem to be many things that are
associated with births per woman that might explain the correlation. For
instance as economies grow less people work in agriculture and there are more
job opportunities for young women, so women generally have less children. I
think there are also reasons why there might be causation. Families with fewer children might be able to dedicate more time, care and money on each
child. The success of each child might also seem to be more important. I have
heard of families only being able to afford to send one child to school and therefore
sending the child they think is the most likely to succeed.
What do you do when you have
multiple theories that might explain a phenomenon? You turn to
mathematics of course, in this case regression analysis. The great thing about
regression is that it can help us understand how much of an effect a certain
factor has independent of other factors. Regression can get complicated, but I
think the basic idea is actually pretty simple. First you figure out which
variable is the one that is being changed by other factors, in this case life
expectancy. Then you figure out what variables are affecting it. The variable
that is being changed is called the dependent variable and the others are
called independent variables. Then you arrange the variables in an equation so
that the independent is equal to a constant plus each variable multiplied by a
coefficient, or multiplier.
Dependent =
constant + (coefficient)*(indepent1) + (coefficient)*(independent2)
The coefficients are a measure of how strong of an effect the
independent variables have on the dependent. For instance, if you wanted to
know how education affects income, just looking at a graph of the two variables
might lead to false conclusions if other variables have an effect as well.
Perhaps you think parents’ income and age also have an effect. If you made a
regression with those variables you might end up with something like this
(numbers are made up).
(Thousands
of dollars a year)
Income= 20 +
.8(Years of Education) + .1(Parents’ income) + .05(age)
This would indicate that an extra
year of education leads to an $800 increase in income. If the coefficient was
negative then an increase in the variable would cause a decrease in the
dependent. The constant, 20, shows what the dependent, in this case income,
would be if all the other variables were zero. Usually this does not make sense
and is not important. In this case it would indicate newborn babies make 20
grand a year.
We know that our dependent is going
to be life expectancy and that one of the independents is births per woman, but
what other factors affect life expectancy? I thought the main factor for life
expectancy would be the quality of healthcare, so I got statistics from the
World Bank on GPD per capita, health expenditure as a percent of GDP, and
access to improved sanitation facilities. Before I talk about the
results, I would like to emphasize that I am an amateur at best. Making a
regression is easy, doing it the right way is really, really hard. I am doing
it the easy way. To do the regression I used PSPP, a free version of SPSS, and
got these results
Life Exp= 58.7 –(3.06)(Births) + (0)(GDP/Cap) –(.22)(Heal
Exp)+ (.13)(Sanitation)
This
does not make sense. GDP has no effect on life expectancy and increased health
spending shortens life spans. At first I was extremely confused. I tried doing
a regression with just GDP/capita as the independent and it was still zero. I
considered giving up on the whole thing. Then I realized a one dollar increase
in GDP would have a miniscule effect on life expectancy. I redid the regression
with GDP per capita divided by 1000 and things started to make more sense.
Health expenditure still came out negative when sanitation was included. Maybe
this is an indication that increases in healthcare spending are not used
wisely. More likely there are certain tests you are supposed to do about the
relationship between the variables that I don’t think I can do with PSPP. I am
guessing something about how sanitation and health expenditures are related is
messing everything up. I wish I could use a program that was actually designed
to do regression like Eviews, but they cost hundreds of dollars, and if wishes
were horses we would all be eating steak.
I decided that access to sanitation was a better indication of health
and came up with the following sensible equation.
Life Exp=67.49 –(3.07)(Births) +(0.1)(GDP/Cap Thousands)
+(0.13)Sanitation
According
to my results a decrease of one in the number of births per woman leads to an
increase in life expectancy of 3 years. This is more than I thought it would
be. I thought increases in GDP and healthcare were the main reason there was
such a high correlation, although I would once again like to emphasize I do not
have confidence in my own results. I do not think the percent of the population
with access to improved sanitation facilities is a very good way of accounting
for quality of healthcare. Many countries have 100% or very close. What is my
conclusion? I don’t really have one. That wasn’t the really the point of this.
The point was just to practice using regression and to look at an issue from a
different perspective.
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