Another in our long series of teaching aids
from Maxim Pinkovskiy and Xavier Sala-i-Martin via Brad DeLong
Am I correct in observing that a curve that is wider and flatter is representing a growing gap between the lower and higher socioeconomic strata? Or conversely, a taller and narrower curve means that wealth is distributed more equitably? I’m not sure if I’m interpreting the graphic correctly – I’m trying to see if this verifies the common observation that “Chinese are getting richer, but the gap between the rich and the poor is widening.”
That’s right, I’m quite sure. It’s also worth noting that the total area under the curve has grown, as the population has grown. I’m really struck by the flat top of the most recent curve: it’s really strong evidence of the growing gap, I think (not an economist, obviously), that there isn’t a real bulge in the middle.
apologies for the post-jack but any scholarly reaction to the founding of the republic movie?
[…] This post was mentioned on Twitter by Wesley Tanaka and billsharedfeed, Barrett Parkman. Barrett Parkman said: China's income distribution and growth in bell curves. http://bit.ly/ctGPQl […]
No. The abscissa is on a log scale and represents money, presumably an annualized income in US dollar terms. However no dimension is attached to the ordinate, so what it represents is unclear, although it should represent a distribution density. The scale on the ordinate is therefore relative; it is also a linear scale. What the reporters are trying to show is that the data presented follow closely to what is known as a log-Normal curve. For most of the distributions shown, they are also mono-modal, with the exception of the red curve and possibly the brown curve, where bimodal characteristics could be seen. The data shows that on a log scale, the separation between the “higher” and “lower” ends between the curves is fairly constant; although when translated to a linear scale, the gap would grow exponentially. The data also shows that the proportion of what you call the lower and higher socioeconomic strata (and anything in between) is fairly consistent, after all it follows a Normal Distribution when the log scale is taken into account. You can therefore carry out the usual statistical analyses on the data and make predictions as though it were a Normal Distribution, but taking into account of the log scale. The beauty of the research is that you can predict what the income distribution is like in a 100 years time, or for any time in the future, because it is likely to follow a log-Normal curve. All you need to do is to shift the curve to the right over time. The area underneath the graph represents the total income of a population within the specified range, so when integrated over the whole range (theoretically from + to –infinity) represents the total income of everyone in the country added together. This number would again be a relative figure because the ordinate is on a relative scale. Given that the curves consistently move to the right over time, the total area underneath the curve as time progresses would grow exponentially, as the abscissa is on a log scale. At a guess, I should think the shape of an income (gross income before tax) distribution should also be log-Normal for most other countries.
The flat (flattish) top of the 2006 curve is not evidence (strong or weak) of a growing gap. On the contrary, it shows that for some reason there is a higher than expected proportion of the populationâs income aggregating around the mean income, ie narrowing of the gap. The beauty of the Normal Distribution is that a theoretical distribution could be calculated with only two pieces of statistics- the mean and the standard deviation of the population. It would be interesting to see what shape curve would be generated using the mean and standard deviation of the 2006 data, and see visually where deviations from the ideal model occur. Looking at the curve, I would say the true mean is skewed towards the right of this âflatâ top, and that the distribution to the left (the lower in income) of the mean had been âliftedâ resulting in more people than expected to have a higher income. Was this the result of a government policy around this time? For example were subsidies or extra money such as grants or social benefits paid to certain group of people. Also looking at the income gap (by purely visual means), of say between the 5th percentile and 95th percentile, I would say the difference is somewhere between 2 to 3 orders of magnitude for all the curves, which I would say is not all that different to what you would expect for any other country.
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