The Effect of Household Characteristics on HouseholdSpecific Inflation Rates: An Application to Trends in

Child Poverty and Educational Real Wage Differentials

by
Todd Idson, Columbia University
Cynthia Miller, Princeton University
Discussion Paper Series No. 695

The Effect of Household Characteristics on Household-Specific Inflation Rates: An

Application to Trends in Child Poverty and Educational Real Wage Differentials

Todd Idson
Columbia University
and
Cynthia Miller
Office of Population Research
Princeton University

August 1994
We would like to thank David Bloom for helpful suggestions.

Abstract

This paper investigates the effect demographic-specific inflation rates on the measured
well-being of two population groups - families with and without children, and families with
different educational attainment. Our major findings are (1) families with children generally
experienced lower inflation rates between 1969 and 1985 than did families without children, yet
calculated trends in child poverty are not significantly affected by the use of group-specific price
indexes, and (2) inflation rates decreased monotonically with the education of the household head
throughout this period, so that real education wage differentials (calculated using educationspecific price indexes) widened more than nominal education wage differentials. This last
finding indicates that the relative economic well-being of the less educated has declined by a
greater extent than would be inferred from trends in nominal education wage differentials.

I. Introduction
Household composition, in addition to prices and income, has been found to be an
important determinant of household expenditure patterns. The number and age composition
of children in the household, for example, have consistently been found to influence patterns
of household demand, even when analyzing the consumption of fairly aggregate commodity
groupings. The incorporation of demographic variables into analyses of consumer demand
dates back at least to Barten (1964), who attempted to use the effects of household
composition on demand to derive price elasticities from cross-sectional data. More recently,
researchers have incorporated household composition into demand analysis as a means to
estimate the cost of children and the allocation of household income between children and
adults (Espenshade 1984, Deaton, et. al. 1989, Lazear and Michael 1988). Results from this
research indicate that, in addition to the number and ages of children, the age, race and
education level of the household head also influence expenditure patterns.
While the fact that demographic variables influence consumption patterns is
interesting in its own right, this paper is concerned with one potential consequence of varying
expenditure patterns. In particular, given that relative prices are typically not constant,
variation across households in expenditure patterns might generate variation in the rate of
inflation experienced across households. Thus, measuring price increases with an overall
price index, such as the Consumer Price Index (CPI), will understate inflation experienced
by some households, and overstate that experienced by others.1 Suppose, for example, that
relatively poor and less educated households spend a greater share of their budget on food

The need for individual price indexes might also arise if households face different prices for
similar consumption bundles. In this study, however, we focus on differences in inflation arising only
from differences in consumption patterns and use the same array of prices for all households.

than the average household and that food prices rise more rapidly than the prices of other
goods. The actual distribution of purchasing power would then trend toward greater
inequality than the distribution calculated from an average price index based on an average
market basket of goods. Deflating an income series by the CPI would act, in this case, to
understate trends in income inequality and poverty relative to what would be the case if
income were deflated by group-specific CPI's that were based on group-specific expenditure
patterns.
Much of the earlier work on group-specific price indexes focused on differential rates
of price increase by income class (see Deaton and Muellbauer 1980, Chp. 7). More
recently, Michael (1979) calculated household-specific price indexes using data from the
1960-61 Consumer Expenditure Survey and finds that although rates of inflation do vary with
several household characteristics, the relationships are not consistent across time periods.
Bridges and Packard (1981) construct a price index for elderly individuals using a market
basket that more accurately measures the spending patterns of the elderly. They find that
their calculated index increased somewhat more rapidly than the overall CPI during the
1970's.2
This paper addresses the effects of using group-specific price indexes, versus an
economy-wide price index, on the measurement of certain social indicators. We focus on
two trends that have received increased attention in recent years: trends in child poverty and
trends in educational real wage differentials. The economic status of children has
2

Other applications include (i) the effects of variations in the cost of living across SMSA's on
estimates of rates of return to schooling (Izraeli, 1983), and (ii) the effects of using inter-urban
variations in cost-of-living to calculate the effects of real AFDC benefits on regional differences in the
size of the AFDC population (Cloutier and Loviscek, 1989).

deteriorated substantially since the early 1970's. In 1990, 20 percent of all children lived in
families with income below the poverty line. Thus any significant distortions in measured
trends in child well-being due to the use of an inappropriate price index seem particularly
pertinent at this time. The policy implications of these considerations arise on a macro level,
as policymakers may be responsive to measured trends in child poverty, and on a micro
level, given that eligibility for many transfer programs is income-based. Additionally, some
transfers that benefit children, such as food stamps and Supplemental Security Income, are
adjusted for inflation.

We will assess the policy importance for child poverty of using

group-specific indexes by using data from the Consumer Expenditure Surveys to construct a
price index for families with children. We will then determine whether the use of an
economy-wide price index leads to an under- or overestimate of the number of children
living in poverty.
Another significant trend in well-being that has taken place over the past two decades
is the marked increase in earnings inequality. This increase, in turn, has been driven in part
by the rise in the returns to education (Katz and Murphy 1992). In particular, the relative
earnings of more educated workers have steadily risen since the early 1970's. Thus we will
also construct price indexes for families by the education level of the family head in order to
see if overall education wage differentials overstate or understate trends in real educational
wage differentials and hence changes in the welfare of families with different education
levels.
In this study differences in price indexes between families will be based solely on
variation in expenditure patterns, or market baskets, across these families. Whether these

observed differences in consumption patterns between specific demographic groups are

sufficiently large to warrant the creation of separate price indexes for each group is an
empirical question and one that we examine below.
The remainder of the paper is organized as follows. Section II discusses the
calculation of the price index and the data used. Section III presents a descriptive analysis of
estimated price indexes across household types. Section IV presents trends in child poverty
rates using group-specific price indexes, and Section V presents trends in real wages by
education level. Section VI concludes.

II. Data and Methodology

The price index is fundamental in the construction of trends in well-being, such as
real income and poverty rates. The poverty rate in a given year, for example, is calculated
by comparing a family's income in that year to the official poverty threshold. This threshold
was created in the mid-1960's and has been updated for inflation each year using the
Consumer Price Index (CPI).
The CPI, however, is calculated based on the consumption patterns, or market basket,
of the average urban household. Given that the prices of goods generally change at different
rates, households with consumption patterns different from the average are unlikely to
experience the rate of inflation indicated by the CPI.
The construction of any price index requires the application of an appropriate weighting
scheme to an array of prices. The weights in this case represent the relative importance of
an item in the consumer's budget. The Consumer Price Index, for example, is a Laspeyres

index:

where
Pit is the price of item i in period t, Pi0 is the price of item i in period 0, and Qr is the
quantity consumed of item i in base period r.
In practice, changes in the CPI from time t to time t + 1 are computed by multiplying,
or updating, the expenditure on item i, P^Q^ by the price ratio Pit+i/Pif The index then is
the sum of these item expenditures (at prices in t+1) over the sum of the expenditures at
prices in period t:

...

S/v^
j

=_f

(2)

Thus, the CPI is called a "fixed quantity" index because the quantity weights remain constant
while the expenditure weights change as prices change.
Alternatively, if we define the expenditure weight for item i using base period prices
as:

Wifi =

then an index of price change from the base period to period t can be calculated as:
where the weights in the base period are normalized to sum to 1. Similarly, the price change

(4

>

from period t to period t + 1 can be calculated as:

p

(5)

In order to apply weights, Wj, that reflect the current spending patterns of consumers
the Bureau of Labor Statistics (BLS) revises the index every 10 to 15 years using expenditure
weights from the most recent Consumer Expenditure Survey. Expenditures are divided into
over 250 categories and the procedure outlined above is used to calculate the CPI.
The data we use to calculate expenditure weights and ultimately, price indexes, are
from the 1960-61 Consumer Expenditure Survey and the 1972-73 Survey of Consumer
Expenditures (CES). The 1960-61 survey contains fairly detailed information on the
spending patterns of 13,728 families. The available public use tape contains expenditure data
broken down into over 90 categories. We follow the procedure used in Michael (1979) and
obtain data for 55 expenditure items covering approximately 95 percent of total consumption
expenditures.3 While the official CPI is calculated using expenditure weights from an urban
subset of the 1960-61 sample, we use the entire sample in our analysis, as it is not possible
to exactly identify the urban sample used by the BLS. The 1972-73 survey contains
expenditure data for 19,975 families. From the Detailed Interview Survey, we use data on

following Michael's reasoning, we did not include home purchase because of the extreme
lumpiness of this expenditure. The discrepancy between the 90 CES items and our 55 items reflects
the disaggregate nature of the CES data. Our expenditure item "women's clothing," for example, is
the sum of four separate components of women's clothing listed in the CES. All but eight of the 90
expenditure types were incorporated one of the 55 items. No published price data were available for
these remaining eight items.

over 1600 expenditure items to calculate 57 expenditure weights and a price index for each
of the 9869 families surveyed in 1972. These 57 expenditure items, covering approximately
86 percent of total expenditures, were constructed to correspond to the 55 items from the
earlier survey.4
We use data from both consumer surveys in order to match the construction of the
actual CPI as closely as possible, which facilitates comparison between the two indexes. The
BLS revised the CPI in 1964 by using weights obtained from the 1960-61 survey and again
in 1978 by using weights obtained from the 1972-73 survey. We use weights from the 196061 CES to calculate price indexes for 1968-1977, and weights from the 1972-73 CES to
calculate price indexes for 1978-1985.
After constructing weights for each expenditure item for each family, we then
calculate an index for each family by applying detailed price data for each item, obtained
from published BLS documents, to each expenditure weight5. The method described above
was used to update the index each year. An effort was made to match the price item as
closely as possible to the expenditure item (see Appendix 1 for a list of the expenditure items
and the corresponding prices used). Although the CPI during most of this time period was
relative to the base year 1967 (i.e., 1967=100), the limited availability of detailed price data

The fact that these 57 items account for less than 95 percent of total expenditure reflects the
more detailed nature of the 1972 data and the the difficulty in assigning each of the 1600 expenditure
items to one of the 55 categories. The items "tuition" and "school books" were added to the total
because price data became available for these items during the later years.
5

For the years 1968-76 we used average annual price indexes for each item. These data were
obtained from editions of the Monthly Labor Review. For the years 1977-85 we used an average of
prices for "All Urban Consumers" in June and and October of each year, since no annual average was
published.

led us to create the earlier series using 1968 as the base year. Comparison between the two
indexes can be made by examining the percentage change in each index from year to year.
Figure 1 shows that on average, over all families, our index matches price changes in the
actual CPI fairly well through 1977, and less so after that time.6 A strict correspondence
between our index and the CPI, however, is not necessary for the analysis that follows. Our
interest lies in the difference between an "average" and a group-specific index. Some part of
the difference between our group-specific index and the official CPI are undoubtedly caused
by different methods of calculation.

III.

Price Indexes by Family Characteristics

Table 1 presents selected expenditure weights for families with and without children7

and for families by the education level of the head. Families with children spend a
somewhat higher share of their budget on food, clothing, home furnishings, and
transportation. Most of these differences are statistically significant. More dramatic
differences, however, are found across educational categories. Families for which the
household head is relatively less educated spend a greater share of their budgets on food at

''There are several potential explanations for why our price index does not increase as rapidly as
the CPI during the later years. First, as noted above, we only capture 86 percent of total expenditure
in the 1972 CES. Second, the BLS stopped pricing a few items after 1977. For the 1968-77 period,
for example, the price of "clubs/hobbies" was proxied by the price of "film developing" while for
1978-85 it was proxied by the price of "photographic equipment and supplies." While the above
factors may introduce error into our index, the most probable reason for the discrepancy between our
series and the official series relates to the relatively rapid increase in the price of housing after 1977.
Thus, our exlusion of home purchases as an expenditure item would cause our index to lag behind the
CPI during these years.
families with children are defined as families with children under age 18 in the household.
8

home and food away from home. Additionally, more educated families tend to spend a
greater budget share on entertainment and clothing. These findings with respect to the
effects of children and education level on food and clothing expenditures are generally
consistent with those found elsewhere (see Lazear and Michael 1988).
These results establish the necessary, though not sufficient, condition that differential
rates of price increase for different commodity groups might generate variation in the rates of
inflation experienced among families with and without children and among families that are
headed by college versus high school graduates.
Table 2 reports our estimates of inflation experienced by specific family types,
calculated as described above. The price index, hereafter referred to as PI, for families with
children has remained consistently lower than the indexes for all families and for families
without children.8 (We also find that over the entire period prices have risen for black
families with children by somewhat less than for white families with children.) In order to
give some indication of the dollar differences these indexes generate, we have taken the mean
income in 1985 of families with children (approximately $28,000) and deflated this amount
by each index. The resulting real incomes are found in the last row of Table 2. Using the
overall index we obtain a real income of $10,223, whereas using the index for families with
children we obtain $10,371. Thus, the small differences between the two indexes generates
only a 1.4 percent difference in estimates of real income.
As with the differences in expenditure patterns, the most dramatic differences in the

Note that all prices changes are relative to the base year 1968, so that a higher index doesn't
actually mean that prices from one year to the next have increased more rapidly, but rather is
indicative of rates of price increase over the entire time period.

price index are across educational levels. Since the early 1970's, the PI for families whose
head is a college graduate has remained below the index for families whose head is a high
school graduate. After deflating $28,000 by the index for more educated families, we obtain
real income of $10,496, a figure that is 2.7 percent higher than real income obtained using
the overall index.
The differences between the PI for families with children and families without
children represents the "gross" effect of children on the PI, and the effect we will use to
determine the policy importance of using group-specific price indexes to calculate trends in
child poverty. Nevertheless, we remain interested in how the index varies with other
household characteristics, some of which may be correlated with the presence of children.
Thus, by using a multivariate framework, we can determine the effect on the index of
children "net" of other factors. We might also determine to what extent other variables are
driving the observed relationship between children and the price index.
Tables 3.1 and 3.2 report regression estimates of the relationship between the PI and
family characteristics. The dependent variable is the calculated PI for each household. The
analysis is done for each year from 1969 to 1977 using the 1961-62 CES sample, and from
1978-85 using the 1972 CES sample. Observations with missing information were deleted
from the samples. We use two different specifications to account for the the presence of
children: (1) a dummy variable for whether the family has any children, as shown in Table
3.1, and (2) three dummy variables capturing the age distribution of the children (the omitted
category is no children), as shown in Table 3.2. Panels (A) of Tables 3.1 and 3.2 present
univariate results that roughly correspond to the patterns found in Table 2, namely the PI is

10

consistently lower for families with children than for families without children, and it is
relatively lower over most of the period for families with young children.
Panels (B) of each table control for a number of additional family characteristics (see
Appendix 2 for variable means). We now find that the effect of children on the PI reverses
sign from negative to positive (except for the effect of all children in the family being older
than six years, which remains negative but becomes insignificant). Note that in the full
specification we have controlled for family size, so that the effect of children does not derive
from the fact that households with children have more members. In Table 3.1 the PI for
families with children is higher than that for families without children from 1975 onward.
Thus, the results indicate that once we control for other family characteristics that may be
associated with the presence of children, children serve to increase the price index. Further
analyses revealed that the factor responsible for the negative univariate effect of children on
the PI is the age of the family head. As the regression coefficients indicate, the PI for
younger families is typically lower than that for older families, a finding that is consistent
with the results of Bridges and Packard (1981), and younger families are clearly more likely
than older families to have children under age 18 in the household.9 When we characterize
the presence of children by their ages, (Table 3.2) the results indicate that the positive effect
of children on the PI derives solely from the effect of younger children, with the youngest

In order to further illustrate the effect of kids in families with different aged heads, price indexes
were predicted for families by the age of the head using the coefficients from the regression for 1985
(Table 3.1) and the means from the 1972-73 CES sample. We then used this index to convert the
$28,000 mean income in 1985 to real income in 1968 dollars for families with different aged heads,
with and without kids. These calculations indicate that real family income is lower by $61.8 if the
family head is 20 years old and kids are present, and by $60.6, $59.2, and $57.5 if the family head
is aged 30, 40, and 50, respectively.
11

children having the greatest impact. This result is consistent with the idea that younger
children alter the family consumption bundle more dramatically than do older children.
Several of the other variables are also significant. The PI is higher for lower income
families, a result that is consistent with earlier findings (Muellbauer 1974, Williamson 1977).
Urban families experienced higher Pi's through the early 1970's, but lower Pi's from 1973
onward. These results for the early 1970's are similar to the effect of urbanicity found in
Michael (1979). Finally, black families face lower Pi's than nonblack families, a pattern that
is consistent over the entire time period. Michael also finds that nonblack families
experienced higher price changes over the 1967-1972 period.
As we mentioned above, for our calculations of trends in child well-being, our
ultimate interest lies only with the average differences between the PI for families with
children and those without children. We conclude from the results in Table 2 (and panels
(A) of Tables 3.1 and 3.2) that over the period 1968-85 inflation increased less rapidly for
families with children than for those without children. Thus, if we calculate "real" income
using price indexes in Table 2 we would expect that poverty rates for children would be
lower when using the group-specific price index than when using an average index. We
address this issue in the following section.

IV. Child Poverty Rates

The percentage of children living in poverty has increased steadily since the early
1970's. In 1990, 20 percent of all children lived in families with income below the poverty
threshold, compared with 14.2 percent in 1973 (U.S. Census 1992). Additionally, and

12

equally alarming, poor children have become poorer; the distribution of children below the
poverty line has steadily shifted leftward over the same time period (Miller 1993). As
mentioned above, the accurate measurement of the welfare of families with children is
relevant to the implementation of policy. The price index also affects the updating of certain
transfers that benefit children and the measurement of real income by which many families
qualify for means-tested benefits.
Table 4 reports trends in child poverty rates calculated from the March Current
Population Surveys and using the PI for families with children and the average PI for all
families. The indexes were used to update the relevant poverty threshold for each family
from its value in 1968.10 The estimates in the first row for each year are calculated using
the average PI for all families as obtained from the CES. The estimates in the second row
are based on the average PI for CES families with children. Estimates in the last two rows
use the characteristics of families in the CPS for that particular year. In order to calculate
the poverty rate in the fourth row, for example, we use the coefficients from Table 3.2 to
predict a PI for each family in the CPS. Thus each family's poverty threshold is inflated by
a family-specific PI. For estimates in the third row, we average the predicted Pi's over all
CPS families and apply this "average" index to all families. The relevant comparisons,
therefore, are between the estimates in rows one and two, and between those in rows three
and four. The calculations based on the Pi's predicted from the characteristics of the CPS
families can be thought of as incorporating changes in the distribution of children across

10

We deflated each poverty threshold back to its 1968 value by using the ratio of the current year
CPI to the CPI in 1968.
13

households and how this distribution has changed since the CES survey year. For example,
the 1981 CPS estimates account for the increase in the percentage of children living in
female-headed families between 1972 (the CES survey year) and 1981.
As noted above, we see that poverty rates for children calculated using the PI for
CES families with children (row 2) are, as expected, consistently lower than the rates
calculated using the overall PI (row 1). The differences, however, are never more than onetenth of a percentage point. Thus, although price increases experienced by families with and
without children are significantly different statistically, the magnitude of this difference
seems insufficient to affect the measurement of child poverty in a way that is significant from
a policy point of view. The results using the CPS samples are similar to the those using the
CES, with one exception ~ using an overall PI rather than family-specific Pi's seems to
understate child poverty in 1976. During the 1980's, however, using an average PI
overstates child poverty rates. In general, the differences are quite small, although in 1981
the overstatement was about nine percent on average.
Although differences in inflation rates might not be sufficiently large to affect the
measurement of poverty rates for children, the application of family-specific price indexes, as
done using the CPS samples and coefficients from Table 3, may have more subtle effects on
the distribution of income. Since our focus is on poor children, Table 5 reports alternative
estimates of the distribution of children below the poverty line, using the overall versus the
family-specific PI. As noted above, this is an important measure of child well-being, given
that poor children have become poorer over time. The results indicate that using an average
PI understates only slightly the percentage of children in poverty who live below 50 percent

14

of the poverty line. The difference is greatest in 1981 (.414 compared with .392). As with
the results in Table 4, however, using the different indexes has only a modest effect on this
measure of children's economic status.
Thus, although we documented statistically significant differences in the price index
between families with children and families without children, the magnitude of these
differences suggested that the effect of using an average versus a group-specific price index
to calculate real income would be minimal. As expected, we find only small differences in
estimates of child poverty using the two different indexes. On the other hand, the magnitude
of the PI difference between educational categories suggests that the effect of using an
average index compared with a group-specific index may be more pronounced for the
measurement of real income by education class.11 We examine this effect in the next
section.

V. Educational Real Wage Differentials

One of the most significant shifts that has occurred in the U.S. labor market since the
mid-1970's has been the widening of earnings differentials between more- and less-educated
males (e.g., between college graduates and either high-school graduates or high-school
dropouts). Recent research has documented the widening of education-earnings differentials
using a variety of data sets and measurement approaches (see, for example, Blackburn,

11

The declining relative earnings of families with less educated household heads might also
contribute to a decline in the economic status of children if children were disproportionately
concentrated in such households. Data from the Current Population Survey (Fuchs, 1986) indicate
that in 1984, 25 percent, 37 percent, and 38 percent of all children lived in families in which the head
of the household did not complete high school, completed only high school, and completed some or
all of college, respectively. Note, however, that our analysis incorporates such effects.
15

Bloom, and Freeman 1990; Mincer 1991; Katz and Murphy 1992; and Juhn, Murphy, and
Pierce 1993), and has also explored a variety of potential explanations for this shift.
In order to further investigate the impact on measured social trends of using
group-specific price indexes, including the welfare implications for the groups in question,
we will investigate the extent to which changes in overall education wage differentials
correspond to changes in real educational wage differentials. If real educational wage
differentials have increased by more (less) than nominal differentials, then the observed
widening in nominal educational wage differentials understate (overstate) the decline in
welfare of less educated individuals relative to those with more education.
Looking at the last two columns in Table 2, we see that high school graduates
experienced higher rates of price increases than college graduates. Table 6 reports
regression estimates of the relationship between price changes and the educational attainment
of the family head. We see that prices increased more slowly for the more educated (with a
monotonic increase with education level that is consistent across the years),12 and that these
patterns persist when we control for a variety of demographic factors.
In Table 7 we report estimates of real educational wage differentials as calculated
from the CPS using an average price deflator, and education-group specific deflators. Panel
(A) shows trends in real average weekly earnings by education group, where column (1)
employs the average PI and column (2) uses the relevant educational-specific PI.13 Panel
(B) then uses these values to calculate patterns in relative earnings by educational group and
12

This result is consistent with Michael's finding (1979)

13

The relative weekly earnings differentials reported in panel (B) correspond very closely to
estimates based on hourly wages (see Murphy and Welch 1992, Table V, last column).
16

investigates how the calculation of real earnings differentials is affected by the use of groupspecific price indexes. As noted in many studies, we see in columns (1) of Panel (B) that the
returns to education have risen over time. Moreover, when we deflate these figures by
group-specific indexes the calculated wage differentials are somewhat larger. For example,
the real dollar difference in 1984 between weekly earnings for college and high school
graduates is $82.75 using an overall index and $89.52 using group-specific indexes. The
earnings difference between college graduates and those with less than a high school
education increases from $122.22 using the average index to $133.34 using group-specific
indexes.
Thus, while it has been well documented that the dispersion of nominal wages across
education groups has increased since the early 1970's, our estimates using groups-specific
price indexes reveal that the dispersion of real wages has increased by a somewhat greater
amount. The relative welfare of the less (more) educated has decreased (increased) by more
than nominal wages indicate. However, although the difference between the estimates using
group-specific versus average indexes is greater for educational real wages than for child
poverty, the educational results are still relatively modest.

VI. Conclusions
This paper has investigated the distribution of inflation rates across different family
types, with particular focus on the effects of these differences on the measured well-being of
two populations - children and workers of varying education levels. We find that families
with children experienced lower inflation rates than families without children over the period

17

1968-1985. Results from a multivariate analysis suggest, however, that children per se do
not skew consumption patterns in the direction of commodity groups that have experienced
less rapid price increases. Rather, this result follows from the fact that families with
children tend to be younger on average than other families, coupled with the fact that
younger families experience lower inflation rates. In fact, holding the age of the family head
constant, children seem to alter consumption patterns in a way that produces relatively higher
rates of inflation for families with children. Nevertheless, when we use group-specific price
indexes to calculate trends in real income we find that the resulting estimates of child poverty
are not significantly different from estimates obtained using an overall price index.
We additionally looked at the distribution of inflation by the educational attainment of
the family head. We find a consistent pattern across the years of a monotonic decrease in
the price index as the education of the family head increases, and that this result is invariant
to controls for other attributes of the families in question. Using education-specific price
indexes to calculate trends in real educational wage differentials, we find that the oft-cited
increase in nominal educational differentials understates trends in real educational earnings
differentials. Hence, the welfare of families with less education, relative to those with more
education, has declined more than would be inferred from patterns in nominal educational
wage differentials. The average annual earnings difference in 1984 between college educated
workers and workers without a high school diploma, for example, was $6356 using an
overall index and $6934 using a group-specific index. Thus, using an overall price index to
deflate earnings underestimates the earnings difference between these two groups by about 10
percent.

18

While we do find that the rate of inflation varies across household types, these
differential rates of price increase are not large enough to generate substantial differences
between real income calculated using an average versus a group-specific index. We should
reiterate, however, that our method of calculating separate indexes relies solely on variation
across family types in expenditure shares. It is almost certainly the case that different
families also face different prices for similar goods. Nevertheless, the evidence at this point
does not warrant replacing the CPI with group-specific price indexes.

19

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Deaton, Angus, and John Muellbauer. 1980. Economics and Consumer Behavior. Cambridge
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Espenshade, Thomas. 1984. Investing in Children: New Estimates of Parental
Expenditures. Washington, D.C.: The Urban Institute Press.
Fuchs, Victor. 1986. "Why are Children Poor?" NBER Working Paper #1984.
Izraeli, Oded, "The Effect of Variations in Cost of Living and City Size on the Rate of
Return to Schooling," Quarterly Review of Economics and Business, vol. 23, No. 4,
Winter 1983: 93-108.
Juhn, Chinhui, Kevin Murphy, and Brooks Pierce. 1993. "Wage Inequality and the Rise in
Returns to Skill." Journal of Political Economy, vol. 101, No. 3, June: 410-442.
Katz, Lawrence and Murphy, Kevin. 1992. "Changes in Relative Wages, 1963-87: Supply
and Demand Factors." The Quarterly Journal of Economics, February, 35-78.
Lazear, Edward P., and Robert T. Michael. 1988. Allocation of Income Within the
Household. Chicago: University of Chicago Press.
Michael, Robert T. 1979. "Variation across Households in the Rate of Inflation," Journal of
Money, Credit, and Banking, vol.11, no.l, February: 32-46.
Miller, Cynthia. 1993. The Changing Economic Status of Children. Unpublished Ph.D.
dissertation. Columbia University, Department of Economics.

Mincer, Jacob. 1991. "Human Capital, Technology, and the Wage Structure: What Do Time
Series Show?11 National Bureau of Economic Research Working Paper No. 3581.
Muellbauer, John. 1974. "Prices and Inequality: The United Kingdom Experience."
Economic Journal, 84: 32-55.
Murphy, Kevin and Finis Welch. 1992. "The Structure of Wages." The Quarterly Journal of
Economics, vol. 107, No. 1, February: 285-326.
U.S. Bureau of the Census, Current Population Reports, Series P-60, No. 181, "Poverty in
the United States: 1991." U.S. GPO, Washington, D.C., 1992.
Williamson, J. 1977. "Strategic Wage Goods, Prices, and Inequality." American Economic
Review, 67(2): 29-41.

Table 1: Selected Expenditure Weights for Families

With children

Without children

1961

1972

1961

1972

Food at home

.237

.217

.222

.213

Food away from home

.046

.047

.058

.046

Rent

.061

.084

.092

.134

Interest on Mortgage

.030

.049

.012

.016

Clothing

.096

.082

.067

.062

Home furnishings

.055

.055

.045

.044

Private Transportation

.131

.199

.109

.181

Entertainment*

.036

.030

.030

.024

Head's education is
high school or less

Head's education is
some college or more

Food at home

.241

.238

.187

.169

Food away from home

.050

.043

.058

.054

Clothing

.080

.063

.087

.079

Entertainment*

.030

.022

.043

.037

Source - Consumer Expenditure Surveys: 1960-61 and 1972-73.

NOTES: 'Includes spectator admissions, participants sports, clubs dues and reading.
1. All differences between families with children and families without children for the same year
are significant at the 5 percent level. The only insigificant differences are "Food at home" and
"Food away from home" in 1972. All differences by education of the family head are also
significant at the 5 percent level.

\2

Table 2: Price Indexes for Demographic Family Groups

With
Kids

No
Kids

Black,
With
Kids

Non
Black,
With
Kids

Head of
family is
a high
school
graduate

Head of
family is
a college
graduate

Year

All

1969

104.88

104.91

104.86

104.81

104.92

104.93

104.94

1970

110.43

110.36

110.50

110.17

110.38

110.47

110.55

1971

114.58

114.23

114.95

114.02

114.26

114.52

114.63

1972

118.16

117.66

118.70

117.61

117.66

117.96

118.03

1973

126.12

125.63

126.65

126.05

125.59

125.58

125.22

1974

140.40

140.01

140.83

140.27

139.98

139.61

138.43

1975

152.06

151.50

152.68

151.71

151.48

151.05

149.63

1976

160.67

159.74

161.68

159.71

159.74

159.68

158.26

1977

170.27

169.05

171.59

168.98

169.06

168.99

167.25

1978

179.86

178.12

181.26

178.00

178.13

178.84

175.42

1979

198.42

196.60

199.88

195.34

196.75

197.48

192.50

1980

221.65

219.71

223.19

216.63

220.07

220.75

214.57

1981

239.43

237.24

241.18

234.02

237.61

238.27

231.58

1982

249.61

246.72

251.92

244.44

246.99

248.05

241.70

1983

256.21

253.00

258.77

251.28

253.20

254.65

248.56

1984

265.08

261.39

268.02

260.29

261.52

263.24

257.38

1985

273.88

269.96

277.02

268.88

270.08

272.07

266.76

$28,000

10,223

10,371

10,107

10,413

10,367

10,291

10,496

NOTES: (1) Calculations are based on expenditure weights for consumer units from the
CES (CES 1960-61 for the years 1968-77 and CES 1972-72 for the years 1978-85). Price
data for 1969-85 were obtained from the Monthly Labor Review. See section II for a
description of the methodology. (2) All inflation rates are relative to the base year 1968.
(3) The last row converts $28,000 in 1985 dollars to real 1968 dollars using each
corresponding index (a value of $10,223 is obtained using the overall index).

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Table 4: Poverty Rates For Children by Select

Family Characteristics
FemaleHeaded

Kids < 6

.120

.533

.192

.415

.119

.531

.190

.161

.412

.118

.527

.189

.168

.427

.123

.541

.194

CES, all

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.445

.145

.529

.226

CES, with kids

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.441

.144

.527

.224

CPS, all

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.441

.144

.527

.225

CPS, individual

.172

.407

.131

.490

.206

CES, all

.201

.467

.154

.542

.236

CES, with kids

.199

.462

.153

.538

.234

CPS, all

.199

.462

.153

.539

.234

CPS, individual

.196

.453

.150

.531

.225

Not
All

Black

Black

CES, all

.164

.418

CES, with kids

.162

CPS, all
CPS, individual

1976

1981

1985

NOTES: Calculations based on the CPS - 1977, 1982 and 1985. Poverty
thresholds for each family from the CPS were updated using each index
above. Family income was then compared with each of these thresholds,
giving four estimates of child poverty. "CES, all" refers to the average
index over all CES families. "CES, with kids" is an average index for all
CES families with children. "CPS, all" is an average of a predicted price
index for each CPS family, while "CPS, individual" is a predicted, familyspecific index.

QIs

Table 5: The Distribution of Children Below Poverty

Percent of poor
children with
family income:

< 50% of poverty

50-75% of poverty

75-100% of poverty

CPS, all

.304

.334

.372

CPS, individual

.312

.316

.383

CPS, all

.392

.299

.309

CPS, individual

.414

.290

.297

CPS, all

.442

.282

.275

CPS, individual

.446

.282

.272

1976

1981

1984

NOTES: Calculations based on the CPS - 1977, 1982 and 1985. Poverty thresholds for each
family from the CPS were updated using each index above. Family income was then compared
with these thresholds, giving the ratio of the family's income to the poverty level. "CPS, all"
is an average of a predicted price index for each CPS family, while "CPS, individual" is a
predicted, family-specific index.

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Table 7: Real Educational Wage Differentials

(A) Average Weekly Earnings
High School
Dropouts (XTHS)

1976

(1)
152.79

1977

(2)

High School
Graduates CHS)
(2)

College or Greater

(COL)
(2)

181.73

(1)
251.67

255.50

187.15

188.57

253.36

257.94

150.53

187.70

188.59

246.83

254.42

147.50

144.51

179.49

180.22

238.90

246.78

1981

143.47

140.41

180.12

181.00

247.91

256.30

1983

145.35

142.38

180.24

181.34

259.22

267.19

1984

147.83

144.79

187.30

188.61

270.05

278.13

151.60

(1)
180.61

152.47

151.04

1979

153.58

1980

(B) Weekly Earnings Differentials

HS/LTHS
1976

(1)
118.21

1977

(2)

com THS

119.87

(1)
164.72

122.75

124.85

1979

122.22

1980

(2)

COL/HS
(2)

168.54

(1)
139.34

140.59

166.17

170.78

135.38

136.79

125.28

160.72

169.02

131.50

134.91

121.69

124.71

161.97

170.77

133.10

136.93

1981

125.55

128.91

172.80

182.54

137.64

141.60

1983

124.00

127.36

178.34

187.66

143.82

147.34

1984

126.70

130.26

182.68

192.09

144.18

147.46

NOTES: Average weekly earnings are calculated as total annual earnings

divided by number of weeks worked. Values are in 1968 dollars for white
men, age 25-64, full-time employees. Under each heading the first column is
deflated by the average PI for all CES families, the second column is deflated
by the relevant educational specific PL
SOURCE: March Current Population Survey (various years)

Appendix 1: Expenditure items and Prices

Expenditure Item from the

Consumer Expenditure Survey
food at home
food away from home
alchohol
tobacco
rent
interest on mortages
property taxes
property insurance and other
repairs and replacements
owned vacation home
solid & petroleum fuels
gas and electricity
water and sewerage
telephone and telegraph
other household services
household supplies
household textiles
furniture
floor coverings
appliances
housewares
insurance on furnishings
other home furnishings
clothing, men
clothing, boys
clothing, women
clothing, girls
footwear, men
footwear, women
footwear, children
clothing, children under 2
clothing materials
clothing upkeep

1968-77 Price Indexes used from BLS.

Listed only if it does not correspond
exactly to expenditure item. (1978-85
index used, if different from 1968-77.)

property insurance premiums

homeownership
fuel oil and coal

liscensed day care service, preschool

child (average of postage, moving, and
appliance and furniture repair)
average of housekeeping supplies, e.g.
laundry soaps, paper napkins and toilet
tissue
furniture and bedding
average of dinnerware and flatware (tableware)
property insurance premiums
table lamps (lawn equipment)
slacks, wool (shirts)
average of boys apparel items
dresses
average of girls apparel items
shoes, street
shoes, street, pump
shoes, oxford
diapers (apparel, infants and toddlers)
yard goods (sewing materials)
drycleaning, men's suits and women's
dresses (laundry and drycleaning)

Expenditure Item

Price Index used, if different

automobile purchase

automobile purchase, new

gasoline, motor oil, etc.

tires and tubes
repairs and parts
auto insurance
auto registration & other
public transportation
hospitalized illness

gasoline

physicians services
dental services
eye care
drugs and medicines
medical appliances, supplies
personal care services
personal care supplies
television
radio, phonograph
spectator admissions
participant sports
club dues, hobbies
reading
music*
tuition+
school books+

auto repairs and maintenance

hospital service charges (hospital and

other medical services)
physician's fees (services)
dentist's fees (services)
examination, prescription and dispensing
of eyeglasses (eyeglasses)
adhesive bandages, package (nonprescription
medical equipment and supplies)
personal care, toilet goods
tv sets, portable and console
average of radios, tape recorders and
phonograph records (sound equipment)
movie admission, adult (entertainment services)
bicycle, boys (bicycles)
film developing, color (photographic supplies
and equipment)
newspapers (reading materials)
piano lessons, beginner
tuition and other school fees
school books and supplies

* obtained for 1960 weights, but not for 1972.

+ obtained for 1972 weights, but not for 1960.
NOTES: (1) All prices are relative to the base year of 1967 (i.e., 1967=100). Price items that
changed base years during the period 1968-1985 were converted to 1967=100. (2) Price data were
obtained from editions of the Monthly Labor Review. (3) In 1983 the BLS changed the way it priced
housing. As a consequence, property taxes, mortgage interest rates and property insurance have not
been priced since 1983. We updated property taxes and mortgage interest rates for 1983-85 by
assuming that they increased by the same percentage as the new "homeownership costs" series.
Property insurance was assumed to increase by the same percentage as the series "household
insurance."

3\

Appendix 2: Variable Means - CES samples

1960-61

1972-73

Families with children

.52

.44

Black

.09

.10

Age of head

47.5

47.6

Education of head < HS

.53

.41

Education of head = HS

.26

.31

Education of head > HS

.21

.28

Female headed family

.17

.20

Family size

3.2

2.9

Family income

6328

11150

Urban

.64

.62

13380

9243

Source: CES - 1960-61 and 1972-73. Sample weights were used.

3%