# How are PPP, nominal exchange rates and inflation related?

This Forbes article discusses how changes in the market exchange rate can be used to estimate an inflation rate thanks to the principle of purchasing power parity (PPP).

Can someone distill this process a little better? I can follow the steps mentioned in the article, but the underlying principles are still not clear to me.

## 1 Answer

Let $$P$$ denote the price in the home country, $$E$$ represent units of domestic currency used to buy one unit of foreign currency, and $$P^{*}$$ represent the price level in the foreign country. Now, PPP implies that: $$P=EP^{*}$$ In other words, prices when expressed in the same currency are equalized across countries. Log-differentiate and take changes and obtain: $$\hat{P}=\hat{E}+\hat{P}^{*}$$ where hats denote changes. Rearrange, and find that: $$\hat{E}=\hat{P}-\hat{P}^{*}$$ In other words, the changes in exchange rate inform one of relative changes in price levels (inflation). This is what is know as relative PPP

• Thank you for this. Is this 'relative' PPP, the PPP that is approximated by The Economist's Big Mac index? – StatsScared Feb 17 at 22:49
• Relative PPP just expresses PPP in changes. From what I understand, the Big Mac Index still express prices in levels. – ChinG Feb 18 at 16:00