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

CC BY-SA 4.0
2020-02-17T22:49:33.327Z
Thank you for this. Is this 'relative' PPP, the PPP that is approximated by The Economist's Big Mac index?
StatsScared
CC BY-SA 4.0
2020-02-18T16:00:42.467Z
Relative PPP just expresses PPP in changes. From what I understand, the Big Mac  Index still express prices in levels.
ChinG
CC BY-SA 4.0
2020-02-16T00:05:09.133Z
2020-02-16T00:05:09.133Z
ChinG
<p>This <a href="https://www.forbes.com/sites/stevehanke/2018/04/25/the-ins-and-outs-of-venezuelas-hyperinflation-spotlights-on-the-imf-and-the-financial-press/#444db604103c" rel="nofollow noreferrer">Forbes article</a> 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).</p>

<p>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.</p>

<macroeconomics><inflation><exchange-rates><international-economics><purchasing-power-partity>
How are PPP, nominal exchange rates and inflation related?
StatsScared
# How are PPP, nominal exchange rates and inflation related?

(Asked by: username_0 on 2020-02-15)

This [Forbes article](https://www.forbes.com/sites/stevehanke/2018/04/25/the-ins-and-outs-of-venezuelas-hyperinflation-spotlights-on-the-imf-and-the-financial-press/#444db604103c) 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.

**Tags:** macroeconomics, inflation, exchange-rates, international-economics, purchasing-power-partity


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## 1 answers

### Answer by username_1 on 2020-02-16. Score: 1 | Accepted 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**

> **Comments:**
> **username_0**: Thank you for this. Is this 'relative' PPP, the PPP that is approximated by The Economist's Big Mac index?  
> **username_1**: Relative PPP just expresses PPP in changes. From what I understand, the Big Mac  Index still express prices in levels.  

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