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)
Food
Cloth
Automobile
Total
Quantity (2010)
50
80
60
-
100
80
70
Quantity (2011)
80
80
80
-
7,200
8,000
6,400
21,600
Quantity (2011)
50
80
60
-
Value
90
100
80
2010
Nominal GDP
Real GDP
GDP Deflator
Value
90
100
80
Price (2010)
Food
Cloth
Automobile
Total
5,000
6,400
4,200
15,600
Price (2011)
Food
Cloth
Automobile
Total
Value
2011
15,600
15,600
1.00
21,600
17,300
1.25
4,500
8,000
4,800
17,300
Rate of change (%)
38.5
10.9
24.9
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 2011. Values in the
rightmost column are the revenues that producers of each good would have earned in 2011
1
had its price remained unchanged since 2010. 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 2010. 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 2011.
Now let us assign the following notations to the values derived in Table 1.
2010
V*
Nominal GDP
*
Real GDP
GDP deflator
V
*
Y (= V )
General price level
Y
*
P
*
2011
P
*
*
S (= P /P = 1)
S (= P / P*)
With these notations, the definition of the GDP deflator for 2011 can be written as
S
V
,
Y
(1)
which is equivalent to the following relationship:
V  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
% change in V  % change in Y  % change in S,
(3)
or
 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 V 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
Figure 1 Growth Rates of the US and Japanese Economies
(a) United States
14
(%)
GDP deflator
12
Real GDP
10
Nominal GDP
8
6
4
2
0
-4
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
-2
-6
-8
(b) Japan
14
(%)
GDP deflator
12
Real GDP
10
Nominal GDP
8
6
4
2
0
-4
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
-2
-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
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
2010. 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)
Food
Cloth
Automobile
Total
Food
Cloth
Automobile
Total
Quantity (USA)
50
80
60
Yen price (Japan)
8,000
8,000
8,000
-
Quantity (Japan)
90
100
80
Quantity (Japan)
50
80
60
-
90
100
80
-
USA
Nominal GDP
PPP GDP in dollars
PPP exchange rate
5,000
6,400
4,200
15,600
-
Dollar price (USA)
Food
Cloth
Automobile
Total
Dollar value
100
80
70
15,600
15,600
1.00
Yen value
720,000
800,000
640,000
2,160,000
Value
4,500
8,000
4,800
17,300
Japan
2,160,000
17,300
124.86
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
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
Nominal GDP
PPP GDP
*
V
*
Japan
V
*
Y (= V )
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 2010. 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 V* and V are measured in different currencies, these values are not directly
comparable. If the market exchange rate in 2010 is 1 dollar = E yen, V / E represents
Japan’s nominal GDP in dollars. Then one may be tempted to compare
V * and
V
.
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
V*
V
and ,
*
S
S
(6)
which is also equivalent to the comparison between
V * and
V
.
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
S
P
.
P*
(8)
Why S is called the PPP exchange rate can be understood by rewriting (8) as
S  P* 
(9)
P
Japan's price in Yen
US price in Yen
or
P*
US price in $

P
S
.
(10)
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 = 124.86. 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*



,
S P / P*
P
P/E
(11)
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
Figure 2 Real Exchange Rates and Income Levels in 2012
3.0
India
2.5
2.0
R
China
1.5
1.0
USA
Japan
0.5
100
1,000
10,000
100,000
PPP GDP per caputa (2005 dollars)
(Source) World Bank, World Development Indictors
(http://data.worldbank.org/data-catalog/world-development-indicators).
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.
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Figure 3 Nominal and PPP GDP in 2012
(a) GDP
18,000
(billion dollars)
16,000
14,000
12,000
10,000
8,000
6,000
Nominal
PPP
Nominal
PPP
4,000
2,000
0
(b) GDP per capita
120
(thousand dollars)
100
80
60
40
20
0
(Source) See Figure 2.
8