I’m not sure if this is typically done, but suppose my data point is in 2013 JPY and I want to express in 2016 USD. Do I apply CPI to express data in 2016 JPY, and then apply exchange rate to 2016 USD? Or do I apply exchange rate to obtain 2013 USD first, then apply CPI to bring forward to 2016 USD? Or is this all redundant?
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$\begingroup$ Depends on what you are trying to do. Please elaborate. $\endgroup$– GiskardCommented Jan 18, 2017 at 15:31
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$\begingroup$ @denesp - To add to the description under the question: This is strictly for the purpose of intellectual analysis and not for practical purposes. I have insurance claims data for companies in Japan from 2010-2016. I'd like to understand the shape of the loss per claim (severity) vs. limit (sum insured) curve and then compare this curve visually to those from other countries. Obviously, the companies will not transfer their portfolio, but without converting to USD and adjusting for inflation (some countries I'm analyzing such as Mexico experiences serious inflation) I can't compare the curves. $\endgroup$– jkoeCommented Jan 18, 2017 at 21:33
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$\begingroup$ "Applying CPI" means multiplying by the relevant price index. "Applying the exchange rate" means multiplying by the exchange rate. A basic property of multiplication is commutivity: changing the order in which multiplications are performed does not affect the outcome. So it doesn't matter which you do first. $\endgroup$– UbiquitousCommented Jan 21, 2017 at 9:07
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NO, it is not redundant. Controlling for nominal effects gives you a better picture, and makes more sense on a theoretical level. To transform assets into USD use
$\textit{asset}_{USD}=\frac{s_t P_{t,JPY}}{P_{t,USD}} \textit{asset}_{JPY}$
where the fraction is the real exchange rate, $P_t$ is the respective price level and $s_t$ the nominal exchange rate.
Alternatively, you can work with differences
$\Delta rer =\frac{\Delta s_t \pi_{t,JPY}}{\pi_{t,USD}}$.
Note that the real exchange rate is far from perfect, but it is common practice in macroeconomics. Also, it does not matter which transformation you do first, as its purely multiplicative.
