Wednesday, September 26, 2007

When Information Isn't Informative: Plus Some Notes on Demographics



Does anybody see a problem with the graph on the left?

Here is another graph of the same information (with a few extra years tacked on at the end and the US population added as reference). Do they look at all similar?



















The first graph is terribly misleading because the abscissa/x-axis is nonuniformly scaled. I'm not sure more than two consecutive tick marks have the same scale. I've redone this graph using a uniformly scaled abscissa to show true trend. China for some reason cuts their graph off just before their population is projected to begin shrinking. Maybe its just that I'm an engineer, but this sort of wacky scaling drives me up the wall. The benefit of a graph is that it can convey alot of information intuitively. For that reason, if people aren't careful, uneven scaling can be very misleading. This above graph almost makes it look like China had a lull in population growth that has started to pick up again at a rather dramatic pace. This is not the case at all, as the second figure shows. It doesn't take very long to look this information up and create one's own graph. You would think that a reporter would be educated enough to do something like this, especially when they are working for the BBC and not merely some local rag.
http://news.bbc.co.uk/2/hi/asia-pacific/7000931.stm

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Update/Supplementary Material
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The question came up as to why there is such a lag between when fertility rates drop below replacement levels and when population begins declining. Because population growth is the sum of fertility rates and death rates, there is a lag due to the human lifespan. However, this lag is exacerbated because factors associated with more rapidly declining fertility rates are also associated with increased lifespans, namely increased urbanization and development.

The typical age/sex population distribution for an undeveloped country looks like a pyramid. There are lots of children and relatively few adults. However, as fertility rates decline and lifespans increase, the pyramid begins to morph into a rectangle. Zimbabwe, like most underdeveloped countries has recently begun to reduce its population quite dramatically. One can see that 25 years ago, population was still growing exponentially, but great reductions in fertility rates have come since then. One thing that has surprised demographers over the last 25 years is the rapid pace at which fertility rates have declined in the developing world. They have declined much more quickly than they did in the developed world. Now, the population distribution histograms of even underdeveloped countries like Zimbabwe are starting to morph into the rectangle shape indicative of stable population.

Italy is an example of a country that has experienced the transition from increasing population to decreasing population. Instead of transitioning to a rectangle, they are in the process of transitioning to an inverted pyramid. Not only is population growth an exponential function, but population decline is exponential as well. Unless they can reverse this trend in fertility rates or increase their immigration rates, their population will decrease exponentially to a fraction of what it is today.

The US and China are both countries that are in between the pyramid and rectangle stages. The difference between the US and China is that China has experienced more drastic fertility rate reductions and is beginning to transition into the inverted pyramid stage like Italy. However, the US is beginning to look more like the rectangle with a relatively stable population distribution by age and sex. These plots are also interesting, because they can highlight the sex ratio disparities in countries like China and India.

These plots become even more fascinating when one compares one country today to the same country +/-50 years. I think a short course in demograhics should be required for policy makers dealing with plans like social security and medicare, that take from today's worker to pay for today's retirees benefits instead of investing the money.

One last note because the figures ended up being rather small. The horizontal axis is population with zero in the middle and female population in blue increasing to the left and male population in red increasing to the right. Each horizontal red and blue line represents a histogram of the population for a specific age category. The age categories are 5 year age spans proceeding from 0-5 years old on up to 95-100 years old. I'm sure there's a much simpler way to explain this, but I'm tired and it escapes me right now.

Zimbabwe


Italy


China


US


Source for my Population Graphs: Population Division of the Department of Economic and Social Affairs of the United Nations Secretariat, World Population Prospects: The 2006 Revision and World Urbanization Prospects: The 2005 Revision, http://esa.un.org/unpp, Wednesday, September 26, 2007;

5 comments:

Kevin said...

MB,

Nice catch. Maybe engineers are more prone to notice it, but I'd hope everyone would be perturbed by it.

The graph appears to be intentionally misleading since it ends at 2032 which matches the predicted point of reversal which would be evident even with its chaotic X-axis scale (11, 18, 8, 10, 5, 27). However, the message of the article directly contradicts the graph which might suggest that some incompetence is also in the mix.

From the article:
"""Chinese officials say the current fertility rate is between 1.7 and 1.8 births per woman, well below the 2.1 births needed to keep the population at a stable level.

Overseas experts dispute this figure; they say the fertility rate is even lower and stands at 1.5.
"""

If this is accurate, then why isn't it reflected in either graph's data by a current decline in population? Since 2.1 would represent perfect replacement and a zero slope, anything less than that should be a negative slope, right? What am I missing? Immigration?

Kevin

MamasBoy said...

Kevin,

Great point. It takes a long time for population levels to catch up with fertility levels. Growth is the net birth rate minus the net death rate. There is an inherrant lag in changes because of people die many years after they are born. This lag is exacerbated in an environment of increasing healthcare quality and lifespans. Typically, the birth rate decreases with increased development and urbanization. This also tends to increase the life expectency. Countries like Russia, with decreasing lifespan expectancies, experience this decrease sooner than others.

I will try to post some more pictures in the main body of the post that illustrate this better.

MB

Kevin said...

MB,

Wow! What an amazingly detailed response to my humble question. :) Thanks!

Neat Histograms. Did you use Excel? From a distance, they look symmetrical but the difference between male and female populations is interesting as it's presumably reflective of generational events and mortality differences. It would be neat if there were a vertical line indicating the difference (though please don't spend any more time on my account :)).

Thanks for pointing out my mistake in missing the lag between the birth of the child and the death of the parents as represented by the fertility rates. It seems obvious now. :) I accounted for net growth by comparing the fertility rate to the stable fertility rate, but the result was proportional to a sort of generational growth rate rather than instantaneous growth rate.

The BBC should hire you. :)

Kevin

MamasBoy said...

Kevin,

Yes, I used excel. I can e-mail the file to you if you are interested in playing with it. I actually already did what you suggested, but don't want to take the time or room to print them off as *.jpg's and post them. Drop an e-mail and I'll get them to you: fullFirstName.lastName@gmail.com. Mark has it, if you forget my name.

MB

Kevin said...

e-mail sent. Thanks. :)