Chain-Weighted GDP Worked Example
(corrected version of pg. 35 in text)
One problem with traditional “real GDP” calculations is that, since it values all goods at base year
prices, it looks like prices never change. As time goes on, goods whose prices go down (and
quantities usually go up) are still weighted by the old prices, and consequently get too much weight
in later years’ GDP calculations. The goods don’t require a large expenditure share, but if they are
valued at base year prices, it would look like a speciously high share of GDP. Let’s do the example:
YEAR EXPENDITURE PRICE QUANTITY (real)
Computers Trucks Computers Trucks Computers Trucks
1 100 106 $1.00 $1.00 100.0 106.0
2 105 98 $.80 $1.05 131.3 93.3
3 103 104 $.60 $1.10 171.7 94.5
4 99 100 $.40 $1.15 247.5 87.0
Notice that since Expenditure = Price*Quantity, real quantities are just Expenditure/Price. Often
you start with quantities and prices and then derive expenditures; but you can’t do that with
computers like you can with oranges, because although an orange in 1981 is the same as an orange
in 2005, a computer is not – it’s harder to count up “quantity” in two different years. So, to get an
idea of “quantity”, the best thing is to look at total expenditure and divide it by the price level.
It’s simple to calculate real investment (a component of real GDP) in year 1, the base year:
Yr. 1 Real Investment = (100 computers)*($1) + (106 trucks)*($1) = $206
Now, usual calculation of real investment in year 2 would take year 2 quantities and value them at
base year prices:
Yr. 2 Real Investment = (131.3 computers)*($1) + (93.3 trucks)*($1) = $224.60
Similarly, for years 3 and 4:
Yr. 3 Real Investment = (171.7 computers)*($1) + (94.5 trucks)*($1) = $266.20
Yr. 4 Real Investment = (247.5 computers)*($1) + (87.0 trucks)*($1) = $334.50
Look at what happened – computers represent 74% of real investment in year 4. However, this is
unreasonably high since they represent less than half of actual investment expenditures that year!
Why did this happen? Computers have gone down in price, but valuing them at high prices from
long ago makes them look much more important than they actually are.
The “investment deflator” that’s given is the same as the GDP deflator. To calculate it, first
compute nominal investment (current year investment at current year prices):
Yr. 2 Nominal Investment = (131.3 computers)*($.80) + (93.3 trucks)*($1.05) = $203
Yr. 3 Nominal Investment = (171.7 computers)*($.60) + (94.5 trucks)*($1.10) = $207
Yr. 4 Nominal Investment = (247.5 computers)*($.40) + (87.0 trucks)*($1.15) = $199
The “investment deflator” is (Nominal Investment) / (Real Investment)
Yr. 2 Investment Deflator = 203/224.60 = .904
Yr. 3 Investment Deflator = 207/266.20 = .778
Yr. 4 Investment Deflator = 199/334.50 = .595
