International Finance Theory and Policy
by Steven M. Suranovic

Finance 30-7

# PPP and Cross-Country Comparisons

Probably the most important application of PPP exchange rates is in making cross country comparisons of income, wages, or GDP. Suppose that we would like to compare per capita GDP between two countries, say the US and China. In 2004, GDP in the US was approximately \$12 trillion; in China GDP was about 16 trillion yuan. With a population in the US of 290 million people, per capita US GDP works out to \$41,400 per person. China's population was approximately 1.3 billion people in 2004, so their GDP per capita works out to 11,500 yuan per person. However, we can't compare these two per capita figures since they are in different units, dollars and yuan. Thus, we need to convert units, either turn dollars in to yuan or yuan into dollars.

The simplest approach to make this conversion is to use the spot exchange rate that prevailed in 2004, which was 8.28 yuan per dollar. Converting yuan to dollars yields a per capita GDP for China of \$1,390. Note that at \$41,400 per person, US per capita GDP is almost 30 times higher than China's.

However, there is a problem using this method. One thing that is quickly recognized by Americans when they travel in and around China is that many goods and services seem considerably cheaper than they are in the US and that's because they are less expensive. From a Chinese traveler's perspective, US goods would seem considerably more expensive. The implication is that although US GDP per person is 30 times higher, that income may not purchase 30 times more goods and services because the prices of US goods and services are so much higher when converted at the current exchange rate. Since presumably we are comparing per capita GDPs to compare how "well-off" people are in one country relative to another, these per capita figures will not accurately reflect these differences.

A solution is found in the purchasing power parity theory (PPP). When prices for similar goods differ as described in the previous paragraph, we would say the US dollar is overvalued with respect to the yuan and with respect to PPP. At the same time we would say the yuan is undervalued vis-à-vis the dollar. One way to reach comparable (or equalized) values of goods and services between the countries is to apply the PPP exchange rate. The PPP exchange rate is that exchange rate that would equalize the value of comparable market baskets of goods and services between two countries.

For example, the estimated PPP exchange rate between the US dollar and yuan in 2004 was 1.85 yuan/\$. If this exchange rate had prevailed between the countries, the prices of US goods would seem, on average, to be approximately equal to the prices that prevailed in China. Now, if we use this exchange rate to make the conversion to dollars of GDP per capita in China, then we will get a number that reflects the purchasing power of Chinese income in terms of the prices that prevail in the US, that is, in terms of prices that are equalized between the countries.

Thus, if we take China's GDP per capita of 11,500 yuan, and convert to dollars with the PPP exchange rate, we get, \$6,250 per person. The units derived in this expression would typically be called "international dollars." What this means is that 11,500 yuan will buy a bundle of goods and services in China that would cost \$6,250 if purchased in the US at US prices. In other words, 11,500 yuan is equal to \$6,250 when the prices of goods and services are equalized between countries.

The PPP method of conversion is a much more accurate way of making cross country comparisons of values between countries. In this example, although China's per capita GDP is still considerably lower than in the US (\$6,250 vs. \$41,400), it is nonetheless four and a half times higher than using the spot exchange rate (\$6,250 vs. \$1,390). The higher value takes account of the differences in prices between the countries and thus better reflects the differences in purchasing power of per capita GDP.

The PPP conversion method has become the standard method used by the World Bank and others in making cross country comparisons of GDP, GDP per capita, average incomes and wages. For most comparisons concerning the size of economies or standards of living, using PPP is a more accurate method and can fundamentally change our perception of how countries compare. To see how, consider the following Table constructed from World Bank data. It shows a ranking of the top 10 countries in total GDP converting to dollars using both the current exchange rate method and the PPP method.

 GDP Rankings 2004 (billions of \$) Rank Using current exchange rate Using PPP exchange rate 1 US \$ 11,667 US \$ 11,628 2 Japan \$ 4,623 China \$ 7,124 3 Germany \$ 2,714 Japan \$ 3,774 4 UK \$ 2,140 India \$ 3,362 5 France \$ 2,002 Germany \$ 2,326 6 Italy \$ 1,672 UK \$ 1,832 7 China \$ 1,649 France \$ 1,744 8 Spain \$ 991 Italy \$ 1,621 9 Canada \$ 980 Brazil \$ 1,483 10 India \$ 692 Russia \$ 1,408

The US remains at the top of the list using both methods. However, several countries rise up in the rankings. China rises from the 7th largest economy using current exchange rates to the 2nd largest using PPP. This means that in terms of the physical goods and services produced by the economies, China really does produce more than Japan, Germany, the UK and Italy. PPP conversion gives a better representation of the relative sizes of these countries.

Similarly, India rises from 10th rank to 4th. Brazil and Russia move up into 9th and 10th rank respectively. At the same time, Japan, Germany, the UK, France and Italy move down in the rankings. Spain and Canada move down off the list.

For those countries whose GDP rises in value when converting by PPP, (China and India), their currencies are undervalued with respect to the US dollar. So using the current exchange rate method underestimates the true size of their economies. For the other countries, their currencies are overvalued to the dollar and so their GDPs converted at current exchange rates give an overestimate of the true size of their economies.

International Finance Theory and Policy - Chapter 30-7: Last Updated on 1/25/06