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Economists often like to use the “90-10 ratio” as a way to s…

Economists often like to use the “90-10 ratio” as a way to summarize the variability, the diversity, the inequality of outcomes that exist in a dataset. The 90-10 ratio is the 90th percentile value divided by the 10th percentile for a particular variable. It’s a useful alternative to the standard deviation, though both have their place. The 90-10 ratio almost always eliminates the extreme outliers from the data, which are often data errors or special cases anyway, so it helps us to focus on the big issues. Also, it’s just clear what the number means.  For the Penn Data you used in the Solow Homework, the 90-10 ratio for GDP per capita is 25 (not 25%, 25x!), and the 90-10 ratio of capital per worker is 55 (not 55%, 55x!). Use productivity levels accounting to report how much incomes per capita differ solely due to differences in capital per worker if alpha has the conventional value of 1/3. Be within 1 of the correct answer. Just answer with a number, no “X” and certainly not a “%”.  You can think of this as a ceteris paribus exercise if you like: “If countries all had the same TFP, and only differed in capital per worker, the 90th percentile of countries would have incomes per capita ____ times as rich as the 10th percentile of countries.” You’ll get the right answer that way, and it’s a useful approach.  But really, as a productivity accounting exercise, what you’re doing is answering this question: “If I explained all differences in income as either caused by differences in TFP or by differences in capital per worker, what’s the effect of this 55X difference in capital between the 90th and the 10th percentile of countries on the 90-10 income ratio?”