Beyond the CPI:
An Augmented Cost of Living Index (ACOLI)
William D. Nordhaus
Yale University and NBER
P.O. Box 208268, New Haven, CT 06520-8268
nordhaus@econ.yale.edu
February 1, 1999
Abstract
This note examines an augmented cost of living index (ACOLI) for
the purpose of accounting for “augmented consumption” in real-income
measures. Well-being includes not only conventional consumer purchases
but also goods and services provided by employers, by mandated social
regulations, and by tax-financed public goods. Because augmented
consumption is often provided in ways that raise prices but not market
incomes, deflating with conventional price indexes may understate real
income growth. An exploratory application of the ACOLI approach to the
United States during the 1960 - 1997 period suggests that the consumer
price index (CPI) has grown about 19 percent faster than the ACOLI. This
correction would reduce the estimated cost of living increase by 0.47
percent per year over the last 37 years.
Keywords: consumer price index, public goods
William D. Nordhaus is Professor of Economics, Yale University, P. O. Box 208269,
New Haven, Connecticut 06520-8268 (email: nordhaus@econ.yale.edu). This paper was
stimulated by a discussion with Zvi Griliches and comments of the participants in the
NBER Productivity Program Meeting, April 1996. The author is grateful for suggestions
by participants in that meeting, the Editor, and three anonymous referees. The electronic
file is ACOL020199.wpd.
Forthcoming: Journal of Business and Economic Statistics, April 1999. Vol 17, No. 2
Beyond the CPI: February 1, 1999
Page 2
The United States is currently undertaking a searching inquiry into measuring “the
cost of living.” Ideally, the cost of living would compare the minimum expenditure
necessary to maintain the representative consumer at the same level of well-being at
different time periods or sets of prices. As implemented by the consumer price index
(CPI) with some recent exceptions, the U. S. measures the cost of living as an index of
the price of a fixed basket of purchased goods and services in different time periods. It is
widely recognized that the CPI has numerous flaws, such as substitution bias and
inadequate correction for new goods and quality change. In this note, I address the
question of whether too-narrow a definition of consumption may also distort our
measures of real income.
The question arises because the U. S. and other nations have begun moving
beyond traditional measures of national output to include nonmarketed consumption
(housework, services of government capital, environmental services, etc.) into their
national accounts. The idea is to measure “augmented consumption,” which includes all
consumption along with consumer purchases of marketed goods and services. Rough
estimates indicate that augmented consumption will be at least twice as large as
conventionally measured personal consumption expenditures. The major categories of
augmented consumption are included in Table 1.
Should we also move beyond the traditional definition of the cost of living to
calculate the price of augmented consumption? I call such a measure the “augmented cost
of living index,” or ACOLI. There are many important questions that would be addressed
by an ACOLI. Such an index would correct for defects in the current conceptual
definition of the CPI and would include the price of nonmarket and public goods. For
example, an augmented measure would take into account the rapid growth in the
consumption of health services financed by employer-financed fringe benefits; these enter
into costs and prices but not into wages or incomes. An ACOLI would also capture the
fact that some price-raising taxes or regulations have corresponding benefits and may not
really raise the cost of living. The purpose of the present paper is to provide a conceptual
definition of an extended cost of living index and to provide an exploratory application of
the concept to include a limited number of goods and services.
Beyond the CPI: February 1, 1999
Page 3
1. Analytical Background
The basic idea behind the ACOLI is to measure how much consumer satisfaction
in private and public goods can be bought with market incomes at different times and at
the prices and taxes of those different periods. We often, for example, measure real
wages as the ratio of money wages to the CPI. The difference between the ACOLI and
traditional cost-of-living indexes is that the ACOLI includes certain goods and services
that are provided by firms or governments and whose costs enter into market prices.
A simple example is a benefit tax. Suppose the government builds a free bridge
that is financed by gasoline taxes. The gasoline tax will raise prices and the CPI, and this
will be counted as a decline in real wages and real incomes. (For this analysis, I assume
that all cost-raising measures are fully shifted to product prices. This is inessential to the
analysis, however, and different shifting assumptions are discussed below.) The
counterpart of the tax is the benefit provided by the bridge. If the incremental benefits of
the bridge just equal its incremental costs, then the apparently lower post-bridge real
income will attain the same level of economic well-being as the higher pre-bridge real
income. Hence, in terms of augmented income there is no rise in the cost of living. We
would also not measure this as a cost-of-living increase if the bridge were built by a
private firm; in this case, it would be a new good.
The conceptual basis for an ACOLI extends the standard Konüs cost-of-living
measure to include taxes along with nonmarket and public goods and services. A
comprehensive survey is contained in Diewert (1983). In this extension, because of the
spillover effects of taxes and public goods, we should recognize that there are multiple
households and firms. The basic setup is the following. Assume that there are H
households, h = 1,..., H, and J private goods and services, denoted by the vector x.
Denote q as the vector of pretax market prices or nonmarket shadow prices attached to
each of the private goods. J is the vector of taxes, so that the prices facing households are
p = q + J. G is the vector of public goods.
The preferences of household h are represented by the continuous utility function
u = F (xh, G). We can represent the expenditure function of household h as E h(p,G,u h*),
where uh* is the reference level of maximum attainable utility level for the reference
expenditure level. We then define the price index for individual h as the ratio of
expenditures necessary to maintain the reference utility level for the two periods, as
defined in (1):
h
h
Beyond the CPI: February 1, 1999
(1)
Page 4
P h(p1, p0 ; G1, G0 , u h*) = E h(p1 , G1 ,u h*) /E h(p0 , G0 ,u h*)
The major new element in this specification as compared to the standard one is that it
incorporates public goods and taxes into the expenditures, prices, and utilities.
The next step is to obtain a price index for all consumers. This can be
accomplished in a number of ways. One approach, due to Pollak (1981) and Diewert
(1983), is to calculate the expenditures necessary to keep all households at a reference
level of the Bergson-Samuelson social welfare function.
In this approach, let W = F(u1, ..., uH) be the social welfare function, while W* =
F(u1*, ..., uH*) is the reference level of social welfare that is to be maintained. We then
define the augmented cost of living index (ACOLI) as the ratio of the expenditures
necessary to attain the reference level of social welfare (W*) with the new prices and
public goods (p1 , G1 ) relative to the expenditures necessary to attain W* at the original
levels (p0 , G0 ):
(2)
P( p1 , p0 ; G1, G0 ,W*) =
E h( p1 ; G1 ,W*) / E h( p0 ; G0 ,W*)
In (2), P is the augmented cost of living index for all households. This price index can be
implemented in any of the standard ways (Laspeyres, Paasche, Fisher, superlative, etc.).
By “expenditures” we mean the expenditures of market incomes.
The main feature of the ACOLI is to recognize that price-raising elements which
lead to increased levels of public goods, or private goods not purchased by consumers
may raise conventionally measured price indexes such as the CPI while leaving the
ACOLI unchanged. This is an important point because some measures will lower the
measured standard of living as calculated with the CPI while leaving utility and therefore
the ACOLI unchanged.
2. Examples of ACOLI Adjustments
Some examples where the ACOLI would be conceptually preferable to
conventionally measured price indexes are the following. For these examples, we assume
that all households are identical except for position in the life cycle.
Beyond the CPI: February 1, 1999
Page 5
CSocial regulation. Many government regulations raise costs and prices to
consumers or producers. The counterpart of these higher prices is more stringent levels of
environmental, health, and safety regulations. For example, a Department of
Transportation regulation might require an airbag, which would raise the price of the car;
or an EPA regulation might require reducing sulfur emissions, which would raise
electricity prices. In these cases, the higher costs and prices are in effect purchasing
private or public goods (automobile safety and reduced health damage from pollution).
Current practice is generally to treat regulatory measures as price increases rather than as
quality changes and therefore to pass them through into higher price indexes. The
ACOLI, by contrast, would treat these higher prices as quality changes in the purchased
goods. It is interesting to note that mandated environmental and safety requirements in
automobiles actually are removed from the CPI and are treated in the way that we
propose in this discussion.
CEmployer-provided fringe benefits. Many consumption goods are provided by
firms as tax-free fringe benefits to consumers. Suppose that firms provide their workers
with employer-financed medical care that is worth one-dollar-of-utility per dollar-of-cost.
It is assumed that these costs would be passed on into higher prices, and therefore raise
the CPI. However, the higher prices would simply be a reflection of the fact that the
medical care was being paid for by the firm rather than the worker. In this case, the
ACOLI would treat the price-raising fringe benefit as a purchase of a service rather than
as a price increase. (For simplicity, this paragraph assumes that the these fringe benefits
are passed on in higher prices. The point applies equally well if the costs are shifted
backwards to workers and result in lower wages. In this second case, measured real
wages will be lower than without the fringe because the numerator of the real wage (W/P)
declines. In the forward-shifting case, the denominator increases. In either case, the
measured decline in the real wage or real income would be a biased measure of economic
welfare because it omits the value of the fringe benefit.)
CSocial insurance taxes. Say that employment taxes are levied and the revenues
from those taxes provide public pensions or medical care for retired workers. In the
simplest case, assume that the benefits are actuarially fair, so that the present value of
benefits corresponds to the present value of employees’ taxes. Here again, costs and
prices will rise, but there are offsetting consumption or future-income benefits. For social
security pensions, public savings would be replacing private savings and these measures
are in reality financial transactions that raise prices. The ACOLI would treat social
insurance as a financial transaction rather than a cost-raising item and would therefore
Beyond the CPI: February 1, 1999
Page 6
omit these costs from the ACOLI. (As was discussed in the parenthetical point in the last
paragraph, it is assumed that social insurance taxes are shifted forward, but the bias in the
CPI would be the same if they were shifted backward. Also, we assume that property
taxes are shifted forward, and the discussion about shifting applies equally to these taxes.
Finally, note that income taxes do not drive a wedge between market factor costs and
product prices, so no adjustment in the ACOLI is necessary for income taxes.)
These examples share a common point. We want to compare the expenditures
needed to attain a given level of economic welfare with and without the price-raising
measure. But these higher prices are in reality nonmarket transactions which provide
health services, environmental protection, or future pensions. In other words, what appear
to be price increases are actually purchases of goods, services, or assets by entities
outside the household sector. Because there are (in these idealized cases) no changes in
utility, the augmented cost of living index in (2) is unchanged even though the CPI
increases. These measures lower conventionally measured real incomes (nominal
incomes divided by the CPI) but leave consumer well-being unchanged.
The major difficulty with actually measuring the ACOLI arises because we have
very poor measures of the benefits of many of the expenditure or mandated cost
programs. In the case of private expenditures, we feel confident (probably, too confident)
that the increment to consumer welfare is one dollar per dollar of additional expenditure.
For public goods or transfer programs, this linkage is much more indirect; we cannot be
confident that the benefit from a mandated regulation, a social insurance program, or an
employer-provided fringe benefit will be on a one-for-one basis with the expenditures.
Whether the goods are worth 100 cents on the dollar is particularly questionable for
mandated private goods like health care or appliance standards; for public goods like
smallpox vaccinations or air-pollution regulation, the benefit-cost relationship is
controversial but could bias our ACOLI calculations either upward or downward.
3. Narrow v. Broad ACOLIs
There are two different approaches to calculating an augmented cost of living
index. The first, which is a “broad ACOLI,” includes the augmented items in
consumption and income and then recalculates a price index for augmented consumption.
A second approach, which is called a “narrow ACOLI” and followed here, strips the
augmented items out of consumption and then calculates the price of narrow or “stripped”
Beyond the CPI: February 1, 1999
Page 7
consumption. The first approach would be preferable, but we do not have the data to
implement it, so this paper follows the second approach.
For this section, we separate total consumption into two parts. For simplicity,
“private” consumption is defined as those items that are bought by consumers (cars,
pizzas, shoes, etc.). “Public” consumption are those that are purchased by sectors other
than consumers. Public consumption comprises primarily the three areas discussed above
— government-provided goods, fringe benefits, and tax-financed social insurance.
The derivation of the ACOLI can be explained as follows. Suppose that C1 and C2
are the quantities of private and public goods, p1 is the market price of the private good,
and q1 and q2 are the “true” prices of the two goods. We cannot directly observe either of
the “true” prices of the two goods or the quantity of the public good, but we can observe
p1, C1, q1C1, and q2C2 . The crucial assumption is that the public good is paid for by a tax
which increases the price of the private good. Hence the spending on the private good is
given by:
(3)
p1C1 = q1C1 + q2C2.
In other words, total spending on the private good covers both the cost of the private good
and the cost of the public good.
We would like to calculate a price index that covers both consumption goods (the
broad ACOLI), but this is not possible with the given information. However, by using
existing data we can derive the true price of the private good, and this is the narrow
ACOLI. The narrow ACOLI (q1) can be derived from (3):
q1 = p1(1+ q2C2 /q1C1)-1
which gives
(4)
)log(q1) = )log(p1) - )log(1 + q2C2 /q1C1) Ñ )log(p1) - )( q2C2 /q1C1)
In other words, the rate of change of the narrow ACOLI can be calculated by correcting
the measured price index to reflect the change in the share of the public good in total
consumption spending. Table 2 shows the ratio of augmented to stripped consumption
[(q1C1+ q2C2 )/q1C1]. As shown in equation (4), the change in this ratio provides an
Beyond the CPI: February 1, 1999
Page 8
estimate of the bias from measuring real wages or real income using the CPI to deflate
market incomes.
What is the difference between the narrow and the broad ACOLIs? If the
augmented items (q2C2) have a dollar-of-benefit per dollar-of-cost, then the narrow
ACOLI will to a first-order approximation be a good price index for both narrow and
broad consumption. However, to the extent that the benefit-cost ratios for expenditures on
augmented consumption diverge from unity, the narrow ACOLI will only provide an
accurate measure of real income in terms of narrowly defined consumption. In this case,
the trend in total consumption will not be adequately captured by the narrow ACOLI
correction. Augmented consumption will be growing faster or slower than the ACOLI
measure indicates depending upon whether the benefit-cost ratio of the omitted items is
above or below unity.
To summarize, the augmented cost of living index (ACOLI) is the appropriate
price index or deflator to apply to market incomes for calculating economic well-being,
where well-being includes not only privately purchased goods and services but also those
goods and services provided by price-raising, non-household expenditures. The narrow
ACOLI provides an appropriate price index for private consumption in all cases and an
appropriate price index for augmented consumption only in the case where the benefitcost ratios for public goods and fringe benefits are equal to unity.
4. Illustrative Estimates of the ACOLI Adjustment
How important is the difference between the ACOLI and the CPI or other
conventional price indexes? This question is a major policy issue, yet there is apparently
no empirical research on this topic. The answer is of considerable importance in light of
the ongoing debate about the bias in the CPI as well as the more general debate about
appropriate indexes to use for indexing federal programs. To illustrate the quantitative
importance, I will provide order-of-magnitude estimates of the difference between the
CPI and an ACOLI over the last four decades.
For this example, I correct conventional cost of living indexes for four biases as
follows: (1) Social insurance taxes are considered to be financial transfers rather than
price-increasing taxes. (2) Employer-provided fringe benefits are assumed to provide
consumer goods and services on a dollar-of-utility per dollar-of-cost basis; hence, the
higher prices induced by the increased costs are assumed to purchase an equivalent value
Beyond the CPI: February 1, 1999
Page 9
of consumption. (3) Indirect business taxes are assumed to be benefit taxes which
increase the quantity of public goods on a dollar-of-benefit per dollar-of-cost basis. (4)
Mandated costs from social regulation are assumed to purchase public goods or publicly
mandated private goods on a dollar-of utility per dollar-of-cost basis. Clearly, each of
these assumptions need further research, and there are particularly tricky issues involving
the valuation of tax-free fringe benefits, forced saving, and the benefits of public goods.
To examine the effect of augmenting the concept of consumption, we look
primarily at conventional consumption and “stripped” consumption for the years 1960
and 1997 and years in between. To compare conventional measurement of real income or
real wages with measures of augmented real income, we subtract all four items listed in
the last paragraph from consumption, which gives us “stripped consumption” (that is,
stripped consumption is consumption less the four price-raising items which do not
decrease consumer utilities). We then calculate the growth of the ratio of conventional
consumption to stripped consumption.
In addition, for comparative purposes, I have made the calculation of stripped
income for both net national product and for national income (which is national output
calculated at factor prices). These alternative concepts provide an estimate of a deflator
for all market incomes instead of only for wages.
The sources of the data from the national income and product accounts are the
following: Social insurance taxes are “employer contributions for social insurance.”
Employer-provided fringe benefits are “other labor income.” Indirect business taxes are
that item. Pollution abatement spending is taken from Department of Commerce, Survey
of Current Business, various issues. The cost of personal pollution abatement
expenditures on motor vehicles is subtracted from the total to reflect the correction of the
CPI for mandated pollution abatement spending. An additional correction should be made
for mandated automobile safety equipment, but no estimates are available for that cost.
Non-pollution social regulation includes nuclear power, occupational safety, highway
safety, pharmaceuticals, equal opportunity, and consumer products. The estimates for
1988 are from Robert Hahn, “The Costs and Benefits of Regulation: Review and
Synthesis,” Yale Journal on Regulation, vol. 8, 1991, pp. 233-287. For 1988/89,
pollution abatement is $88.5 billion while non-pollution social regulation is $38.3 billion.
I calculate the cost of non-pollution social regulation for other years by assuming that the
ratio of total social regulation to pollution abatement expenditures is constant.
Beyond the CPI: February 1, 1999
Page 10
Table 2 shows the results, and the detailed calculations are provided in Table 3.
The results indicate that an augmented cost of living index shows dramatically different
results from a standard price index. The total upward bias over the period 1960-97 is 19
percent. This indicates that stripped consumption grew 19 percent more rapidly than
conventionally measured consumption. The upward bias was around 0.47 percent per
year. The bias will differ for different price indexes depending upon the definition of
consumption. For example, the price index for personal consumption expenditures (PCE)
in the national income and product accounts include employer provided fringe benefits in
consumption, so that part of the bias would not be present when applying the PCE price
index to an income figure that include the employer fringes. On the other hand, no price
index makes the ACOLI correction for indirect business taxes or public goods.
Table 2 also shows the breakdown of the bias among the four components. Threequarters of the bias is due to fringe benefits and contributions to social insurance, with
one-quarter due to social regulations and very little to indirect business taxes. Table 3
shows the breakdown by sub-periods. The bias was substantial in all sub-periods except
during the Reagan administration, during which the bias was actually negative. In the
most recent period, from 1989 to 1997, the bias was very close to that of the entire
period.
There are a number of reservations that apply to this calculation. A great deal of
further refinement is necessary to put an ACOLI on a sound theoretical and empirical
framework. More work needs to be done on estimating each of the components of the
ACOLI correction and on determining whether these fringe benefits and public goods in
fact deliver benefits on a dollar-of-benefit per dollar-of-cost basis. There are traditional
index-number issues involving differences in the ACOLI for different groups as well as
the substitution induced by tax and price changes. The shifting assumptions need more
refinement.
These numbers should be put in the context of the findings of the Boskin
Commission, which estimated that the upward bias in the CPI from index-number
problems, outlet bias, and quality change was in 1996 1.1 percent per annum. It is striking
that over the last quarter century conventional price indexes may have overestimated the
true cost of living by a total of 0.47 percent per year because of the omission of fringe
benefits and mandated public goods. This number is a significant fraction of current
estimates of the bias of the CPI.
Beyond the CPI: February 1, 1999
Author's footnote:
Page 11
Beyond the CPI: February 1, 1999
Page 12
Table 1. Categories in “Augmented Consumption”
Private goods
Marketed
Purchased by households (food, clothing)*
Purchased by other sectors (health care, pension plans)**
Nonmarket
Goods and services (leisure, housework)
Other (longevity, improved health status)
Publicly provided private goods
Market (bridges, town beaches)***
Nonmarket (crime, drugs, personal safety)
Public goods
Environmental, health, and safety (pollution abatement expenditures, FDA
certification)***
Science and technology (space exploration)
Note:
*Items with one asterisk are consumer expenditures covered by the CPI.
**Items with one or two asterisks are in personal consumption expenditures in the
national income accounts.
***Items with one, two, or three asterisks are in the ACOLI concept measured here.
Beyond the CPI: February 1, 1999
Page 13
Table 2. Estimated Bias to Inflation Corrected by Using
Augmented Cost of Living Index, 1960-1997
A. Total Difference between ACOLI and Standard Price Index
Output
Measure
Ratio of conventional to
stripped measure of output
1960
Net national product
National income
Consumption
1.172
1.059
1.264
1997
1.293
1.179
1.504
Ratio
1.104
1.114
1.190
Bias in inflation rate,
1960-97
(in basis points
per year, average
annual rate)
27
29
47
B. Contribution of Different Components for Consumption ACOLI
Component
Amount of Bias, 1960-97
(basis points per year)
Contributions to social insurance
Supplements to wages and salaries
Social regulations
Indirect business taxes
15
17
12
3
Total
47
For derivation, see Table 3. The calculation of the contribution of the components
in part B is a geometric mean of the individual indexes or contributions calculated
from consumption and stripped consumption as a base.
Source: For derivation, see Table 3. The calculation of the contribution of the components
in part B is a geometric mean of the individual indexes or contributions calculated from
consumption and stripped consumption as a base.
Beyond the CPI: February 1, 1999
Page 14
Table 3. Data Underlying Calculation of ACOLI
1960
Output measure
Net national product
National income
Consumption
1970
1981
1989
1997
Ratio of conventional to stripped measure of output
1.172
1.059
1.264
1.235
1.110
1.378
1.290
1.175
1.471
1.290
1.180
1.433
1.293
1.179
1.504
Bias in conventional price indexes (basis points per year)
1960-70 1970-81 1981-89 1989-97
53
40
-0
3
48
52
5
-1
87
60
-33
61
Net national product
National income
Consumption
Underlying data (billions of dollars)
1960
1970
1981
1989
1997
Gross national product
529.8
1042.0
3150.6
5452.8
6922.4
Net national product
473.2
935.0
2762.1
4827.4
7192.2
National income (NI)
429.8
840.6
2501.4
4397.3
6649.7
Consumption
332.2
648.1
1941.3
3594.8
4867.5
1960-97
27
29
47
Corrections to obtain the augmented social cost of living:
Employer contributions
to social insurance
Other labor income
Social regulations
Price additions to NI
12.6
34.3
146.8
280.4
408.4
11.2
0.0
23.8
32.5
16.6
83.4
153.0
72.5
372.3
273.1
117.3
670.8
416.6
186.8
1011.8
Indirect business taxes
Price additions to NNP and C
45.5
69.3
94.3
177.7
249.3
621.6
414.7
1085.5
619.4
1631.2
403.9
406.0
262.9
757.3
757.2
470.4
2140.5
2129.1
1319.7
3741.9
3726.5
2509.3
5561.0
5637.9
3236.3
NNP less price additions
NI less price additions
C less price additions
Sources: All data except non-pollution social regulation from U.S. Commerce Department,
Survey of Current Business, various issues. See text for description of transformations. Data
on non-pollution social regulation for 1988 are from Robert Hahn and scaled to other years
assuming the ratio of total to pollution abatement is constant over time. Personal expenditures
on pollution abatement for motor vehicles are subtracted from social regulation to reflect the
adjustment in the CPI.
Beyond the CPI: February 1, 1999
Page 15
References
Diewert, W. E. (1983), “The Theory of the Cost-of-Living Index and the Measurement of
Welfare Changes,” in W. E. Diewert and C. Montmarquette, eds., Price Level Measurement,
Ottawa, Statistics Canada, 163-239.
Pollak, Robert A. (1981), “The Social Cost of Living Index,” Journal of Public Economics,
15, 311-336.