# Nominal, Real and PPP GDP

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1 Nominal, Real and PPP GDP It is crucial in economics to distinguish nominal and real values. This is also the case for GDP. While nominal GDP is easier to understand, real GDP is more important and used widely, not least for calculating the growth rate of an economy and comparing the economies of different countries. It is therefore important to understand how real GDP is calculated and how it is related to nominal GDP. As an example, let us suppose that one country, say the United States, produces three final products: Food, Cloth and Automobiles. Table 1 illustrates how this hypothetical country s nominal and real GDP are derived. In the top two sections, the price and quantity of each good produced in 2010 and 2011 are provided. With this information in hand, it is straightforward to calculate nominal GDP in 2010 (15,600 dollars) and 2011 (21,600 dollars). Table 1 Calculation of Nominal and Real GDP Price (2010) Quantity (2010) alue Food ,000 Cloth ,400 Automobile ,200 Total ,600 Price (2011) Quantity (2011) alue Food ,200 Cloth ,000 Automobile ,400 Total ,600 Price (2010) Quantity (2011) alue Food ,500 Cloth ,000 Automobile ,800 Total , Rate of change (%) Nominal GDP 15,600 21, Real GDP 15,600 17, GDP Deflator We choose 2010 as the base year for calculating real GDP. The third section of Table 1 multiplies the price of each good in 2010 by the volume of its sales in alues in the rightmost column are the revenues that producers of each good would have earned in

2 had its price remained unchanged since The sum of these values, 17,300 dollars, is called the real GDP for 2011 measured in 2010 dollars, or the real GDP for 2011 with the base year As should be clear from this explanation, real GDP is nominal GDP that is adjusted for price changes and tells us how much the volume of a country s production has changed since the base year. Lastly, the bottom part of Table 1 calculates GDP deflators. The GDP deflator is defined as the ratio of nominal GDP to real GDP and tells us how much the country s general price level has changed since the base year. In our example its value for 2011 is 1.249, suggesting that the average price of goods has risen by 24.9 percent between 2010 and Now let us assign the following notations to the values derived in Table Nominal GDP Real GDP Y (= ) Y General price level P P GDP deflator S (= P /P = 1) S (= P / P ) With these notations, the definition of the GDP deflator for 2011 can be written as which is equivalent to the following relationship: S, (1) Y Y S. (2) When one variable is a multiple of another two variables, its rate of change is roughly equal to the sum of the rates of change in the other two variables. 1 Therefore (2) implies or % change in % change in Y % change in S, (3) Nominal econnomic Real economic inflation rate. growth rate growth rate (4) 1 It should be noted that this relationship holds only approximately. In Table 1, the sum of the rates of change in Y and S is 35.8% while that in is 38.5%. However, this approximation is fairly accurate when the rates of change in Y and S are less than several percentage points. 2

3 Figure 1 Growth Rates of the US and Japanese Economies (%) (a) United States GDP deflator Real GDP Nominal GDP (%) (b) Japan GDP deflator Real GDP Nominal GDP -6-8 (Source) IMF, International Financial Statistics. Figure 1 plots the three variables in (3) for the United States and Japan. In both countries, the growth rate of real GDP exhibits cyclical fluctuations each lasting for a few to several years. In Japan, moreover, the average growth rate fell noticeably in the early 1990s, with several 3

4 years of negative growth since then. While the inflation rate measured by the GDP deflator has always been positive in the United States, Japan has also been suffering from mild deflation since the middle of the 1990s. The method of Table 1 can be applied not only to different years in the same country but also to different countries in the same year. As an example, Table 2 provides hypothetical information on the prices and quantities of goods produced in the United States and Japan in The top section is identical to that of Table 1 and computes the United States nominal GDP. The second section calculates Japan s nominal GDP in the same year, which turns out to be 2,160,000 yen. Table 2 Calculation of the PPP GDP and the PPP Exchange Rate Dollar price (USA) Quantity (USA) Dollar value Food ,000 Cloth ,400 Automobile ,200 Total ,600 Yen price (Japan) Quantity (Japan) Yen value Food 8, ,000 Cloth 8, ,000 Automobile 8, ,000 Total - - 2,160,000 Dollar price (USA) Quantity (Japan) alue Food ,500 Cloth ,000 Automobile ,800 Total ,300 USA Japan Nominal GDP 15,600 2,160,000 PPP GDP in dollars 15,600 17,300 PPP exchange rate The third section computes Japan s GDP using the dollar prices in the United States, in parallel with what is done in the corresponding part of Table 1. The result of this calculation, 17,300 dollars, is called Purchasing Power Parity (PPP) GDP. The bottom section conducts the same calculation as that of Table 1. Here we divide Nominal GDP not by real GDP but by PPP GDP, and call the resulting value the PPP exchange rate. 4

5 What do the PPP GDP and the PPP exchange rate represent? To answer this question, let us first give each value in Table 2 the same notation as that of the corresponding value in Table 1. Here we call the United States as the base or reference country, just as we took 2010 as the base year in Table 1. USA Japan Nominal GDP PPP GDP Y (= ) Y Price level P P PPP exchange rate S (= P /P = 1) S (= P / P ) Given its definition, Japan s PPP GDP denotes the nominal GDP that the country would have generated if the price of each good had been the same as in the United States. Then it follows that Japan s (the yen s) PPP exchange rate, S, represents the ratio of Japan general price level to that of the United States, just as S in Table 1 was the ratio of the price level in 2011 to that in Notice, however, that P and P are now measured in different currencies. Let us suppose that we are interested in the relative volume of output in Japan and the United States. Since and are measured in different currencies, these values are not directly comparable. If the market exchange rate in 2010 is 1 dollar = E yen, / Japan s nominal GDP in dollars. Then one may be tempted to compare E represents and. E (5) This comparison is not appropriate, however. Just as real rather than nominal GDP should be used when calculating the growth rate of an economy, PPP GDP, not nominal GDP, is the right yardstick with which to assess the relative size of two or more economies. Given the above notations, the comparison between Y and Y is identical to and, S S (6) which is also equivalent to the comparison between and. P/ P (7) By looking at (5) and (7), we notice that these two comparisons are equivalent only when E P / P. Although this relationship rarely holds in practice (see below), the PPP exchange rate is precisely the exchange rate that does satisfy this relationship: 5

6 P S. (8) P Why S is called the PPP exchange rate can be understood by rewriting (8) as S P P US price in Yen Japan's price in Yen (9) or P US price in \$ P. (10) S Japan's price in \$ These equations tell us that S represents the exchange rate at which the price levels of Japan and the United States coincide with each other, that is, the exchange rate at which one dollar and the equivalent amount of yen have the same purchasing power. In Table 2, S = When the actual exchange rate is lower than this value (e.g., E = 100), Japan s price level is higher than in the United States. It also implies that using (5) instead of (7) would overstate the relative size of the Japanese economy to the US economy. Now let R stand for the ratio of the actual exchange rate to the PPP exchange rate. This value is the real exchange rate, one of the most important variables in international finance. R can be expressed alternatively as R E E E P P, (11) S P / P P P / E which states that the real exchange rate is merely the relative price levels of the two countries. Figure 2 plots the real exchange rate of the domestic currency against PPP GDP per capita (PPP GDP divided by population) for a large number of countries. Since the base country is the United States, the real exchange rate of the dollar is 1 by definition. The real exchange rates of most other currencies are larger than 1, suggesting that the price levels of these countries are lower than that of the United States. It is also evident that the real exchange rate is associated negatively with per capita GDP, implying that the price level tends to rise as a country becomes more affluent. Why this is the case will be analyzed when we study international finance more closely. 6

7 Figure 2 Real Exchange Rates and Income Levels in India 2.0 R 1.5 China 1.0 Japan USA ,000 10, ,000 PPP GDP per caputa (2005 dollars) (Source) World Bank, World Development Indictors ( The upper panel of Figure 3 compares nominal GDP and PPP GDP for a sample of countries. Although the United States is the world s largest economy in terms of both nominal and PPP GDP, China is catching up rapidly, particularly in terms of PPP GDP. The Indian economy also looks much larger in terms of PPP GDP than in nominal GDP, due primarily to its relatively low price level. Lastly, the lower panel of Figure 3 compares the same countries nominal and PPP GDP per capita. PPP GDP per capita has much smaller cross-country variation than does nominal GDP per capita, suggesting that the latter exaggerates real income gaps among countries. Japan s PPP GDP per capita is substantially smaller than its nominal GDP per capita, reflecting the fact that its price level is high even in comparison with other countries at similar income levels. For example, while its nominal GDP is only marginally smaller than that of Singapore, its PPP GDP per capita is less than 60% of that of Singapore. One reason behind Japan s high prices is its regulations on imports of certain agricultural goods, a topic that will be explored in Chapters 5 and 6. 7

8 18,000 16,000 14,000 12,000 10,000 8,000 (billion dollars) Figure 3 Nominal and PPP GDP in 2012 (a) GDP 6,000 4,000 2,000 0 Nominal PPP 120 (thousand dollars) (b) GDP per capita Nominal PPP (Source) See Figure 2. 8

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