Daniel l. Rubinfeld

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96 Part 2 Producers, Consumers, and Competitive Markets
Chapter :3 Consumer Behavior 97
fixed-weight index Cost-ofliving
index in which the
quantities of goods and services
remain unchanged
Paasche index: The amount of money at current-year prices that an individual
requires to purchase the bundle of goods and services chosell ill the ClIlTellt
yellr diyided by the cost of purchasing the same bundle in the base year.
Both the Laspeyres (U) and Paasche (PI) indexes are fixed-weight indexes:
The quantities of the \'arious goods and services in each index remain
unchanged .. For the Laspeyres index, however, the quantities remain unchanged
at bllse-year levels; for the Paasche they remain unchanged at currellt-yenr levels.
Suppose generally that there are t\VO goods, food (F) and clothing (C). Let:
P Ft and PC! be current-year prices
PH and PC/; be base-year prices
F t and C t be current-year quantities
F/> and C/> be base-year quantities
'vVe can write the two indexes as:
that arose "when long-term comparisons of real GOP were made using fixedweight
price indexes (such as Paasche and Laspeyres) and prices were rapidly
changing.
Economists ha\'e known for years that Laspevres cost-of-livinG indexes over-
• • b
state inflation, Hovve\'er, it was not until the enerO'v price shocks of the 1970s
b. '
the more recent fluctuations in food prices, and the concern surroundinG
federal deficits ,that dissatisfaction with the Laspeyres index grew. It ha~
been estimated, tor example, that a failure to account for chanO'es in computer-
. b
buying patterns 111 response to sharp decreases in computer prices has in recent
years caused the ~PI to overstate the cost of living substantially. As a result,
the U.s. Bureau ot Labor Statistics has been vvorking to make improvements to
the CPL ll
Just as the Laspeyres . index will overstate the ideal cost of livinG the Paasche
~
will understate it because it assumes that the individual vl'ill buy the current
year bundle ill the base period. In actuality, facing base year prices, consumers
would ha\'e been able to achieve the same level of utility at a lower cost by
changing their consumption bundles. Because the Paasche index is a ratio of the
cost of buying the current bundle divided by the cost of buying a base-year bundle,
overstating the cost of the base-year bundle (the denominator in the ratio)
will cause the index itself to be oyerstated.
To illustrate the Laspeyres-Paasche comparison, let's return to our earlier
example and focus on Sarah's choices of books and food. For Sarah (who went
to college in 1990), the cost of buying the base-year bundle of books and food
at current-year prices is Sl,720 (100 lbs. X S2.20/lb. + 15 books X S100/book).
The cost of buying the same bLUldle at base-year prices is $500 (100 lbs X $2/lb. +
15 books X S20/book). The Laspeyres price index, LI, is therefore
100 X $l,720/S500 = 344, as reported previously. Likewise, the cost of buying
the current-year bundle at current-year prices is $1,260 (300 lbs. X $2.20/lb. +
6 books x $100/book). TIle cost of buying the same bundle at base-year prices is
S720 (300 lbs X S2/lb. + 6 books X $20/book). Consequently, the Paasche price
index, PI, is 100 X $1,260/$720 = 175. As expected, the Paasche index is lower
than the Laspeyres index.
In recen~ years, tl:ere has been g:'owin publ~c concern about the solvency of
the SOCIal Secunty system. At Issue IS the tact that retirement benefits are
linked to the Consumer Price Index. Because the CPI is a Laspeyres index and
can thus overstate the cost of li\·ing substantially, Congress has asked several
economists to look into the matter.
A commission chaired by Stanford University professor Michael Boskin
COl:duded t,hat, !~le CPI overstated inflation by approximately 1.1 percentage
p0111ts-a slgruhcant amount given the relatively low rate of inflation in the
United States ~ rece,nt yearsY According to the commission, approximately 0.4
percentage P0111tS ot the 1.1-percentage-point bias was due to the failure of the
Laspeyre~ price index to account for changes in the rnix of consumption of the
products 111 the base-year bundle. The remainder of the bias was due to the failure
of the index to account for the growth of discount stores (approximately 0.1
percen,tag~ .points)" for improvements in the quality of existing products, and,
most slgn~hc~ntly, tor the introduction of new products (0.6 percentage points),
If the bla,s 111 the CPI were to be eliminated, in \",·hole or in part, the cost of a
number of tederal programs would decrease substantially (as would, of course,
the corresponding benefits to eligible recipients in the proGrams). In addition to
Social Security, affected programs include federal retirem:nt programs (for railroad
employees and military veterans), Supplemental Security Income (income
support for the poor), food stamps, and child nutrition. According to one study,
a 1-percentage-point reduction in the CPI would increase national savinO's and
thereby reduce the national debt by approximately $95 billion per veal' i~1 veal'
2000 dollarsY - -
chain-weighted price index
Cost-of-living index that
accounts for changes in quantities
of goods and services,
Chain-Weighted Indexes
Neither the Laspeyres nor the Paasche index provides a perfect cost-of-living
index, and the informational needs for the ideal index are too great. 'vVhat is the
best solution in practice The US. government's most recent answer to this diffi­
~ult question ca~e in 1995, when it adopted the use of a chain-weighted price
mdex to deflate Its measure of gross domestic product (GOP) and thereby obtain
an estimate of real GOP. Chain 'weighting \vas introduced to overcome problems
II
Planned changes to the CPI are described b\' the Bureau of Labor Statistics in "Consumer Price
Indexes: Oven'ie\\' of the 1998 revision of the 'Consumer Price Index," (at
and 111 the Federal Resen'e Bank of San Francisco Economic Letter No. 99-05
12r-1' 1
!. IC 1ael J Boskin, Ellen R Dulberger, Robert J Gordon, Z\"i Griliches, and Dale W Joro-enson "The
CPI 78-93. Con l1111SSlOn: ." F':I" 11K mgs anc :I R ecammell . d ations," Americall Ecollomic RCl'ic[{' 87, No.2 " (May ' 1997):
13Michael F Bryan and Jagadeesh Gokhale, "The Consumer Price Index and National Sa\'inc