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Unformatted text preview: 46 Chapter 2 The Measurement and Structure of the National Economy 2.4 Real GDP, Price Indexes, and Inflation All of the key macroeconomic variables that we have discussed so far in this
chapter—GDP, the components of expenditure and income, national wealth, and
saving—are measured in terms of current market values. Such variables are called
nominal variables. The advantage of using market values to measure economic
activity is that it allows summing of different types of goods and services. However, a problem with measuring economic activity in nominal terms
arises if you want to compare the values of an economic variable—GDP, for
example—at two different points in time. If the current market value of the goods
and services included in GDP changes over time, you can’t tell whether this
change reﬂects changes in the quantities of goods and services produced, changes
in the prices of goods and services, or a combination of these factors. For exam—
ple, a large increase in the current market value of GDP might mean that a country
has greatly expanded its production of goods and services, or it might mean
that the country has experienced inflation, which raised the prices of goods and
servrces. Real GDP Economists have devised methods for breaking down changes in nominal vari
ables into the part owing to changes in physical quantities and the part owing to
changes in prices. Consider the numerical example in Table 2.3, which gives pro
duction and price data for an economy that produces two types of goods: com
puters and bicycles. The data are presented for two different years. In year 1, the
value of GDP is $46,000 (5 computers worth $1200 each and 200 bicycles worth
$200 each). In year 2, the value of GDP is $66,000 (10 computers worth $600 each
and 250 bicycles worth $240 each), which is 435% higher than the value of GDP in
year 1. This 43.5% increase in nominal GDP does not reflect either a 43.5% increase
in physical output or a 43.5% increase in prices. Instead, it reflects changes in
both output and prices. Table 2.3 Production and Price Data Percent change from Year 1 Year 2 year 1 to year 2
Product (quantity)
Computers 5 10 +100%
Bicycles 200 250 +25%
Price
Computers $1,200/computer $600/computer —50%
Bicycles SZOO/bicycle $240/bicycle +20%
Value
Computers $6,000 $6,000 0
Bicycles $40,000 $60,000 +50%
Total $46,000 $66,000 +43.5% 2.4 Real GDP. Price Indexes, and Inflation 47 Table 2.4 Calculation of Real Output with Alternative Base Years Calculation of real output with base year =Year 1 Current
quantities Baseyear prices Year 1
Computers $1,200
Bicycles $200 II [I ll Year 2
Computers 10 $1,200
Bicycles 250 $200 II II II Percentage growth of real GDP = ($62,000 — $46,000)/$46,000 = 34.8% Calculation of real output with base year =Year 2 Current
quantities Base—year prices Year 1
Computers $600
Bicycles $240 $3,000
548.000
$51,000 II II II Year 2
Computers 10 $600
Bicycles 250 $240 $6.000
$60,000
$66,000 Percentage growth of real GDP 2 ($66,000 — $51,000)/551,000 = 29.4% How much of the 43.5% increase in nominal output is attributable to an increase
in physical output? A simple way to remove the effects of price changes, and thus to
focus on changes in quantities of output, is to measure the value of production in
each year by using the prices from some base year. For this example, let’s choose
year 1 as the base year. Using the prices from year 1 ($1200 per computer and $200
per bicycle) to value the production in year 2 (10 computers and 250 bicycles) yields
a value of $62,000, as shown in Table 2.4. We say that $62,000 is the value of real GDP
in year 2, measured using the prices of year 1. In general, an economic variable that is measured by the prices of a base year
is called a real variable. Real economic variables measure the physical quantity of
economic activity. Specifically, real GDP, also called constantdollar GDP, measures
the physical volume of an economy’s final production using the prices of a base
year. Nominal GDP, also called current—dollar GDP, is the dollar value of an econo
my’s final output measured at current market prices. Thus nominal GDP in year 2
for our example is $66,000, which we computed earlier using current (that is, year 2)
prices to value output. What is the value of real GDP in year 1? Continuing to treat year 1 as the base
year, use the prices of year 1 ($1200 per computer and $200 per bicycle) to value
production, The production of 5 computers and 200 bicycles has a value of
$46,000. Thus the value of real GDP in year 1 is the same as the value of nominal 48 Chapter 2 The Measurement and Structure of the National Economy GDP in year 1. This result is a general one: Because current prices and baseyear
prices are the same in the base year, real and nominal values are always the same
in the base year. Speciﬁcally, real GDP and nominal GDP are equal in the base year. Now we are prepared to calculate the increase in the physical production from
year 1 to year 2. Real GDP is designed to measure the physical quantity of pro—
duction. Because real GDP in year 2 is $62,000, and real GDP in year 1 is $46,000,
output, as measured by real GDP, is 34.8% higher in year 2 than in year 1. Price Indexes We have seen how to calculate the portion of the change in nominal GDP owing to
a change in physical quantities. Now we turn our attention to the change in prices
by using price indexes. A price index is a measure of the average level of prices for
some specified set of goods and services, relative to the prices in a specified base
year. For example, the GDP deﬂator is a price index that measures the overall level
of prices of goods and services included in GDP, and is defined by the formula real GDP 2 nominal GDP/ (GDP deflator/ 100). The GDP deﬂator (divided by 100) is the amount by which nominal GDP must
be divided, or “deﬂated,” to obtain real GDP. In our example, we have already
computed nominal GDP and real GDP, so we can now calculate the GDP deflator
by rewriting the preceding formula as GDP deflator = 100 X nominal GDP/real GDP. In year 1 (the base year in our example), nominal GDP and real GDP are equal,
so the GDP deﬂator equals 100. This result is an example of the general principle
that the GDP deflator always equals 100 in the base year. In year 2, nominal GDP
is $66,000 (see Table 2.3) and real GDP is $62,000 (see Table 2.4), so the GDP deﬂa—
tor in year 2 is 100 X $66,000/$62,000 = 106.5, which is 6.5% higher than the value of
the GDP deﬂator in year 1. Thus the overall level of prices, as measured by the GDP
deﬂator, is 6.5% higher in year 2 than in year 1. The measurement of real GDP and the GDP deflator depends on the choice of
a base year. Box 2.2 demonstrates that the choice of a base year can have important The Computer Revolution and ChainWeighted GDP The widespread use of computers has revolutionized in the United States devoted to computers quintupled
business, education, and leisure throughout much of between the mid19805 and the mid19908,* while com
the developed world. The fraction of the real spending puter prices fell by more than 10% per year on average.’r 'See Joseph Haimowitz, ”Has the Surge in Computer Spending Fundamentally Changed the Economy?” Federal Reserve Bank
of Kansas City Economic Review, Second Quarter 1998, pp. 27—42. *These prices are for computer and peripheral equipment in Table 1 of Stephen D. Oliner and Daniel E. Sichel, ”Computers
and Output Growth Revisited: How Big 15 the Puzzle?" Brookings Papers on Economic Activity, 2: 1994, pp. 273—317. (Continued) The sharp increase in the real quantity of computers
and the sharp decline in computer prices highlight the
problem of choosing a base year in calculating the
growth of real GDP. We can use the example in Tables 2.3 and 2.4,
which includes a large increase in the quantity of com—
puters coupled with a sharp decrease in computer
prices, to illustrate the problem. We have shown that,
when we treat year 1 as the base year, real output
increases by 34.8% from year 1 to year 2. However, as
we will see in this box using Table 2.4, we get a sub
stantially different measure of real output growth if we
treat year 2 as the base year. Treating year 2 as the base
year means that we use the prices of year 2 to value
output. Specifically, each computer is valued at $600
and each bicycle is valued at $240. Thus the real value
of the 5 computers and 200 bicycles produced in year 1
is $51,000. If we continue to treat year 2 as the base year,
the real value of output in year 2 is the same as the
nominal value of output, which we have already calcu—
lated to be $66,000. Thus, by treating year 2 as the base
year, we see real output grow from $51,000 in year 1 to
$66,000 in year 2, an increase of 29.4%. Let’s summarize our calculations so far. Using year 1
as the base year, the calculated growth of output is
34.8%, but using year 2 as the base year, the calculated
growth of output is only 29.4%. Why does this differ
ence arise? In this example, the quantity of computers
grows by 100% (from 5 to 10) and the quantity of bicy
cles grows by 25% (from 200 to 250) from year 1 to year 2.
The computed growth of overall output—34.8% using
year 1 as the base year or 29.4% using year 2 as the base
year—is between the growth rates of the two individual
goods. The overall growth rate is a sort of weighted
average of the growth rates of the individual goods.
When year 1 is the base year, we use year 1 prices to
value output, and in year 1 computers are much more
expensive than bicycles. Thus the growth of overall
output is closer to the very high growth rate of comput
ers than when the growth rate is computed using year 2
as the base year. Which base year is the ”right” one to use? There is
no clear reason to prefer one over the other. To deal
with this problem, in 1996 the Bureau of Economic 2.4 Real GDP, Price Indexes, and Inflation 49 Analysis introduced chainweighted indexes to mea
sure real GDP. Chainweighted real GDP represents a
mathematical compromise between using year 1 and
using year 2 as the base year. The growth rate of real
GDP computed using chainweighted real GDP is a sort
of average of the growth rate computed using year 1 as
the base year and the growth rate computed using year
2 as the base year. (In this example, the growth rate of
real GDP using chain—weighting is 32.1%, but we will
not go through the details of that calculation here): Before the Bureau of Economic Analysis adopted
chainweighting, it used 1987 as the base year to com
pute real GDP. As time passed, it became necessary to
update the base year so that the prices used to compute
real GDP would reﬂect the true values of various goods
being produced. Every time the base year was changed,
the Bureau of Economic Analysis had to calculate new
historical data for real GDP. Chain—weighting effectively
updates the base year automatically. The annual growth
rate for a given year is computed using that year and
the preceding year as base years. As time goes on, there
is no need to recompute historical growth rates of
real GDP using new base years. Nevertheless, chain
weighted real GDP has a peculiar feature. Although the
income—expenditure identity, Y = C + I + G + NX,
always holds exactly in nominal terms, for technical
reasons, this relationship need not hold exactly when
GDP and its components are measured in real terms
when chainweighting is used. Because the discrepancy
is usually small, we assume in this book that the
income—expenditure identity holds in both real and nom
inal terms. Chainweighting was introduced to resolve the
problem of choosing a given year as a base year in cal
culating real GDP. How large a difference does chain
weighting make in the face of the rapidly increasing
production of computers and plummeting computer
prices? Using 1987 as the base year, real GDP in the
fourth quarter of 1994 was computed to be growing at a
5.1% annual rate. Using chainweighting, real GDP
growth during this quarter was a less impressive 4.0%.
The Bureau of Economic Analysis estimates that com
puters account for about threefifths of the difference
between these two growth rates.H iFor discussions of chain—weighting, see Charles Steindel, ”Chain—Weighting: The New Approach to Measuring GDP," Current
Issues in Economics and Finance, New York: Federal Reserve Bank of New York, December 1995, and "A Guide to the NTPAS,”
on the Web site of the Bureau of Economic Analysis, ww.bea.gov/bea/an/nipaguid.htm. *” These ﬁgures are from p. 36 of J. Steven Landefeld and Robert P. Parker, ”Preview of the Comprehensive Revision of the
National Income and Product Accounts: BEA’s New Featured Measures of Output and Prices,” Survey of Current Business, July 1995, pp. 31—38. ...
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 Fall '10
 Nordhaus
 Macroeconomics

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