Saturday, May 31, 2014

Why the FT comment on Piketty's weighting does not make sense.

Actually, I think weighting does not work. If you want to get the top 1% share for Europe (or any combination of countries), you cannot just weight the top shares; you would have to put the two or more datasets together, rerank all individuals or families by their per capita or per family wealth (use exchange rates to convert the wealth), and then get the share. Obviously, you cannot do that with the data Piketty has, so the only way is to do something is unweghted averaging.

Shares behave like Ginis; they are not convex measures. If you have a rich country with Gini=0, and a poor county with a Gini=0, when you put them together you do not get Gini=0, but a positive Gini. Think of the shares the following way. Let everybody in country A be wealthier than in country B and the two of the same population size. Then the information about top 1% share of wealth in country B is really worthless: these guys will not make it into top 1% share when you put the two countries together. You cannot weigh their top share by anything meaningful to get the result. In other words, does the top 1% share in Tanzania have any impact on the global top 1% share, if the richest 1% of people in Tanzania are at the global median? Obviously not.

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