# What are the main causes of disparity between nominal and PPP exchange rates?

(I'm not a student of economics and I have no idea about correct terminology and things. ) I've seen the acronym "PPP" in various places for a long time, but it's only recently I became curious enough to actually read up on it. I find it quite bizarre that there can be such dramatic variations between the PPP-adjusted value of a currency and its nominal value in the currency market.

Taking two major examples that caught my attention on the IMF page https://www.imf.org/external/datamapper/PPPEX@WEO/

For China, the "Implied PPP conversion rate" is 4.26 while the nominal rate (from the internet) is 6.47, which is about 1.5x the PPP rate. For India, the PPP rate is 22.38 while the nominal rate is 73.5, over 3x the PPP rate. Indeed it seems to be the case for many countries that the PPP rate is "lower" (less currency units per USD) than the nominal rate. (Actually, it might be fun to download the dataset and make a full comparison -- I might do that.)

Why is this? I racked my (non-economically-trained) brain and could not find a logical explanation.

There is nothing bizarre about disparity between market rates and PPP. If you do not impose any assumptions on the economy they should not even be equal (but can be under certain assumptions), mathematically PPP is given by:

$$S_{PPP}= P_H/P_F$$

where $$S$$ is the PPP exchange rate, $$P_H$$ price level at home and $$P_F$$ price level abroad.

On the other hand nominal exchange rate will be given by:

$$S = q \cdot P_H/P_F$$

where you have extra term $$q$$, which is real exchange rate and this term might not be always 1.

Following Krugman et al International Economics: Theory and Policy Ch 16 there are several reasons for discrepancy:

On the side of PPP

1. PPP is based on a law of one price. This is the idea that a good should have the same price everywhere (after going through exchange rates) because if an apple costs more in neighboring country all sellers would try to sell the apple there and all buyers would want to buy apples in the country with lower price, and this behavior will push prices to be equal.

However, in real life law of one price is violated because there are trade barriers or transportation costs. If transporting an apple from your country to your neighbor cost \$5 then \$5 price differential is sustainable even under perfect competition.

2. The PPP also assumes markets are competitive, but imperfect competition and differences in market power between countries can lead to sustained price level differentials.

3. Probably the most mundane reason is that CPI data (from which PPP is frequently calculated) do not always use the same baskets of goods. Moreover, the consumption patterns are also often different so even if they would use the same basket of goods it would not perfectly work out.

On the side of nominal exchange rate

1. Nominal exchange rates are very volatile. As discussed by Krugman et al in chapter 31, people typically can't observe economic fundamentals that determine $$q \cdot P_H/P_F$$ or even just the $$P_H/P_F$$ and statistics is always reported with lags and measurement errors (in fact, speaking from experience, even a year old statistics can often be later revised). So people in the economy have to base their behavior on their expectations of what economic fundamentals are. That is always difficult and will lead to speculation that fuels nominal exchange rate volatility, thus in a short run nominal exchange rate can often be temporary over or undervalued. Also, due to changes in expectations, which can happen quickly, nominal exchange rate is quite volatile.

The above being said while PPP will rarely equal exchange rate it is sometimes used to see if a currency is over or undervalued, since nominal exchange rate seems to fluctuate around PPP (with sometimes being shifted bit up or down depending on what effect the issues discussed above have). You can see this from the picture below which was again taken from Krugman et al pp 395. However, there is not much basis for thinking they will be equal except for the few points where the graphs happen to cross.