AN LLNV‘ESIIGATEO‘EI GF D'IFFERERCES IN
INCOME ELAS'I‘ECITEES OF DEMAND
F09. F009 IN HOUSES-{GLUE OF
DIFFERENCE SHZE AND (QMPOSITION

Thesis for II"; Degree of M. S.
MICHIGAN STATE UNIVERSITY

Robert Omar: Herrmann

1961

    
  

  

LIBRARY

Michigan State
University

 

“——

ABSTRACT

AN INVESTIGATION OF DIFFERENCES IN INCOME
ELASTICITIES OF DEMAND FOR FOOD IN HOUSEHOLDS
OF DIF F ERING SIZE AND COMPOSITION

by Robert O. Herrmann

The few past studies of the income-expenditure elasticities of
demand for food in United States households of differing size and type
found evidence of significant differences in elasticities between house-
hold types- Certain other studies, however, indicated that the significance
of these differences might be, at most, small. . The existence of such
differences has important implications for analyses of the demand for
food, for research and theory construction in economic development
and for the estimation of age-sex specific equivalence scales from house-
hold food consumption data. Work in these areas generally has proceeded
on the assumption that the differences in income elasticities for-food
between household types are not significant and that a single income
elasticity may be employed as representing the behavior of all types of
households. Because of the importance of this assumption in the choice
of research methods and techniques in these areas, it was feltthat an
investigation of the significance of the differences in income elasticities
of demand for food between household types would prove worth-while.

. In the course of testing the hypothesis that the differences in income
elasticities between household types are significant, it was necessary
first to examine the relationship between certain concepts of consumption
theory and the concepts which have been employed in empirical analyses
of household exPenditures. It also was necessary to specify precise
definitions suited to the purposes of this study for some of these empirical

concepts. . The concepts and classifications which resulted were

Robert O. Herrmann

instrumental in developing the household types for which income elasticities
for food were estimated. The economic and statistical significance of the
differences in income elasticity for food which were found to exist between
household types were then evaluated.

The study is based on observations selected from the urban portion
of the United States Department of Agriculture's 1955 Household Food
Consumption Survey. Income-expenditure elasticities, of demand 'for food
for home consumption were estimated for twenty-six household types of
varying age-sex composition and ranging in size from one to five persons.
‘ Income elasticities for each household type were estimated with four
functional forms:

(1) Y: a+b1X1+bzX2+u

(2) log Y

(3)‘ Y: a+b1 logX1+ bZXz+u

a+b1 logX1+bzlogXZ+u

a-blji'I'bzXz‘I’u

(4) log Y

Where Y is total weekly expenditure for food for home consumption, X1 is
1954 disposable income after Federal and State taxes and X2 is total
meals served to members of the household during the week.

, The elasticities estimated by equations (1), (Z) and (3) were considered
generally reliable. The elasticity estimates obtained with equation (4) were
unsatisfactory for household types which contained households which reported
zero or low incomes. . Ninety-five percent confidence intervals were
estimated for the elasticities obtained with equations (1), (Z) and (3).
Household types with confidence intervals which did not overlap those of
another household type were considered to have income elasticities which
were significantly different.

- Although statistically significant differences were found to exist
between the elasticities of different household types, it was felt that such
differences were of little importance unless they could be shown to be

economically significant also. The differences which were found to exist

Robert O. Herrmann

would be of little economic significance in a period in which incomes

were stable and population composition changed little. . An illustrative
projection of the demand for food was employed to show that the differences
are, however, sufficient to be significant in a period like the present in
which incomes and population composition are changing rapidly.

The results indicate that the assumption of a single income elasticity
for all household types which has been employed in most recent demand
projections is not warranted. The magnitude of the errors introduced by
this assumption depends on the size of the changes in the distribution of
household types which occur during the period covered by the projection
and on changes in the distribution of income between household types.

. The results also indicate that the techniques employed by J. - A. C. Brown
and by S. J. Prais and H. S. Houthakker to estimate consumption "
equivalence scales from British household food consumption data, may
not be useful for recent United States data, because of the assumption of
a single income elasticity for food for all household types which these
techniques require.

The results suggest that some of the recent changes in historical per
capita food consumption series which have been laid to changes in. "tastes"
may be due, in fact, to changes in the distribution of household types and
in the age-sex composition of the population. .However, a full evaluation
of the effect of changes in population composition on per capita food con-

sumption requires substantial further study.

- AN INVESTIGATION OF DIFFERENCES IN INCOME
ELASTICITIES OF DEMAND FOR FOOD IN HOUSEHOLDS
OF DIFFERING SIZE AND COMPOSITION

BY

Robert Omer Herrmann

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

- MASTER OF SCIENCE

Department of Agricultural Economics

1961

/»‘” 27‘ I»?
. ~ .‘f \‘nl

/ .2 /'/ I, ft :, "

ACKNOWLEDGMENTS

The author wishes to express his thanks to the many peOple who
assisted and advised him in the course of this study.

Dr. James T. Bonnen gave advice as well as inspiration and
encouragement throughout the course of the study. The author wishes
both to acknowledge his debt and express his gratitude to Dr. Bonnen.

Dr. Harold F. Goldsmith, formerly of this Department, gave
important assistance in developing the concepts which underlie the study
and gave painstaking attention to the preparation of the punched cards
which were employed in the analysis.

The author wishes to thank Dr. L.. L. Boger and the Department
of Agricultural Economics for their financial assistance, for the use of
departmental facilities and for their forbearance during the unusually
long gestation period of this project.

The author is indebted to Dr. Robert L. Gustafson for his advice
and for the preparation of the notes which are the basis for the procedures
employed in estimating the confidence intervals of the income elasticity
estimates. The author is also indebted to Dr. L. V. Manderscheid and

'Dr. James D. Shaffer, whose suggestions clarified the presentation at
several critical points.

***************

ii

TABLE OF CONTENTS

CHAPTER

I. INTRODUCTION . . . .................

Studies Giving Direct Evidence of Differences in the
Income Elasticity for Food Between Household
Types ................ , .....

Indirect Evidence of Differences in Elasticities
Between Household Types . ..........

Implications of Differences in Income Elasticity
Between Household Types in the Forecast of
the Demand for Food . . . .........

Implications of Differences in Income Elasticity
Between Household Types for Economic
Deve10pment .................

Implications for Consumption Research of Differ-
ences in Income Elasticity Between Household
Types ......................

Scope and Objectives of the Study .........

II. PROBLEMS IN THE ESTIMATION OF ELASTICITIES
FOR HOUSEHOLDS ..................

The Individual and the Household in Consumption
Theory .................... .
Assumptions Required for the Estimation of Income
Elasticities ..................
Methods of Obtaining Households with Similar Engel
Curves ........... . ....... ..
The Use of Individual Types in Grouping Households
with Similar Engel Curves . ..........
The Types of Individuals in the Household ......
The Combination of Individual Types to Obtain
Household Types ................

III. THE HOUSEHOLD TYPES ................

Criteria for the Selection of the Set of Household
Types for Which Elasticities are—to be
Estimated . . . . . ..............

iii

Page

ll

14

16
19

22

22

25

26

3O
3O

43

47

47

TABLE OF CONTENTS - Continued

CHAPTER

Identifying the Unit of Inquiry . ...........
. Households Included Within the Household Type
Classifications .................

IV. THE ECONOMIC VARIABLES AND EXPRESSIONS OF
THEIR RELATIONSHIP ............... - .

The Variables of Economic Theory .........
Empirical Variables .................
Economic Expressions of the Relationship Between

Income and Expenditure. . . . ........
Regression Equation Forms .............
Forms of the Variables ...............

V . ANALYSIS ........................

The Variable and Equation Forms Employed . . . .
The Household Types Analyzed . ..........
Analytical Process ..................
The Income Elasticity Coefficients .........
Methods of Testing for Differences Between, Elas-
ticity Coefficients ...............
The Significance of the Differences Between the
Elasticities of Different Household Types

VI. CONCLUSIONS ...................

The Economic Significance of‘the Results. .. . . . .

Justification for Acceptance of the Hypothesis . . .

Further Studies Needed ............
BIBLIOGRAPHY .......................

APPENDIX ...........................

iv

Page

51

57

63
63
64

72
73
83
85

85
88
89

104
108

112

119

119
127
128
131

139

LIST OF TABLES

TABLE Page

1. 1 Income Elasticities of Demand for Food in Urban
United States Households of Differing Size, 1950
B. L. S. Survey . .................... 3

l. 2 Income Elasticities of Demand for Food in Urban

United States Families of Differing Size and Composi-

tion, 1935-36 B. L. S. Survey ............. 6
1. 3 Income Elasticities of Demand for Food in United

States Households of Differing Size and Composition

for Wage-Earner and Low-Salaried Families in Urban

Industrial Centers, 1901 B. L. 5. Survey ....... 8

1.4 United States Census Series B Projections for 1965 of
Number of Households by Age of Head . . . . ..... l4

2. 1 Recommended Daily Calorie Intake by Age and Sex. . . 34

2. 2 Estimated Cost of One Week‘s Food by Age-Sex Cate-
gories, April 1959 .................. . . 36

2. 3 Calorie Intakes by Age and Sex, Groton Township Study 37

2. 4 Consumption Scales for Individual Types. Recent
United States and British Studies ............ 41

3. 1 Numbers of Households Excluded from the Household
Types Constructed by This Study . . .......... 61

4. 1 Average Weekly Food Expenditures in Urban House-
holds of Two or More Persons, by Region, 1955. . . . 68

4. 2 Income-Expenditure Elasticities and Marginal Pro-
pensities to Consume for Certain Engel Curve Forms. 81

5. 1. Description of the Household Types Analyzed . . . . . 90

LIST OF TABLES - Continued

TABLE

5.10

Regression Estimates for the Linear Equation Form . .

Regression Estimates for the Double-Log Equation
Form ................. . . . .......

Regression Estimates for the Semi-Log Equation Form

Regression Estimates for the Log-Inverse Equation
Form ..... . . ............. . ......

Estimated Income Elasticities ..............

Ninety-five Percent Confidence Intervals for the
Elasticities Estimated by Linear 'Equations .......

Ninety-five Percent Confidence Intervals for the
Elasticities Estimated by Double-Log Equations

Ninety-five Percent Confidence Intervals for
Elasticities Estimated by Semi-Log Equations . .

Number of Household Types With Elasticities Signifi-
cantly Different From the Elasticity of a Particular
Household Type . . . . . . . . . . . ...... . .

Illustrative Projections of 1966 Average Weekly Food
Expenditure for Certain Types of Urban Households by
the Naive Model Under Two Alternative Assumptions
About Income Elasticities . ..... . .........

Distribution 0f Husband-Wife Households by Number of
Related Children Under 18, Selected Years 1940-60 . .

vi

Page

94

97

99

101

106

114

115

116

117

122

125

LIST OF FIGURES

FIGURE Page

3.1 Groups Associated with Home Food Consumption . . . . 55

vii

LIST OF APPENDIC ES

APPENDIX Page

I . The 1955 Household Food Consumption Survey Sample 139

viii

CHAPTER I

INTRODUCTION

Economists have long sought to control for the effect of household
size and composition on food expenditure in estimating the relationship
between income and the demand for food. Most past studies have concen-
trated their efforts on eliminating these effects from the data. The actual
nature of the effects of household size and composition on food expenditure
has seldom been considered.

A Large numbers of studies of income-expenditure elasticities for
food have been made in which various adjustments have been used to
eliminate size-consumption effects. Only a few studies have been made
of the income elasticities of households of differing size and age-sex

1 Such studies as have been made seem to indicate that

composition.
important differences may exist between the income elasticities for food
of different sizes and types of households. The existence of such differ-
ences would suggest that aggregative measures of income elasticity for
food are perhaps an oversimplification. Differences in income elasticity
for food between household types would have important implications not
only for the estimation of short and long run demand for food and thus for
national policy, but also would be of concern in economic development.
Furthermore, such differences would have important implications for the
choice of techniques to be employed in the estimation of consumption
equivalence scales.

1A compilation of recent studies of the income elasticity for food
is given in Theodore W. Schultz, The Economics of Agriculture (New York:
McGraw-Hill, 1953), pp. 60-61. Size-composition effects have been
eliminated or ignored in all of the studies included.

 

Let us first examine the evidence of such differences in past studies
and then consider more fully the implications of the existence of such dif-

ferences for several areas of economic study.

Studies Giving Direct Evidence of Differences in the Income
Elasticity for Food Between Household Types

 

 

The few past studies of the income elasticity for food in United States
households of differing size and composition which have been made have
distinguished only a few general household types or have distinguished on
the basis of household size alone. The most recent of these studies of
the elasticity of food expenditures with respect to income for households of
different types uses the least detailed household type classification and
distinguishes types only by size.1 The study byMargaret Reid, the results
of which are given in Table 1. 1, was based upon 1950 Bureau of Labor
Statistics data for urban families. The results show marked differences
in the elasticities of the different household size types, especially for food
for home consumption. - In the size-types studied the elasticity coefficient
increases with the size of the household in all but one instance.

The results for one person households, showing a high elasticity
for all food including alcoholic beverages and a very low elasticity fer food
for home consumption differ from the general pattern for the other house-
hold sizes. This difference was explained as arising from the large number
of males in the upper income range of the one person households who'ate
all of their meals out. , Despite the nature of the household type classifi-
cation employed, which Miss Reid herself recognized as crude, the results
of this study indicate that the differences between the income elasticities

of households of differing size may be significante.

 

f

lMargaret G. Reid, "What We DO-Know and Do Not Know About Food
Consumption of American Families, " Journal of Farm Economics, XL,
No. 5 (December 1958), 1309. '

 

Table 1, 1 - Income Elasticities of Demand for Food in Urban Uzgited States
Households of Differing Size, 1950 B.. L. S. Survey

 

 

 

All Food Including Food for Home
.Household Type Alcoholic Beverages Consumption
One person .577 .061
2 persons .476 .291
3opiersons . 482 . 319
4 persons ' I .500 , . -328
5 persons .577 i .426
6 or more persons . 607 A .486

 

a .
'Margaret G. Reid, "What We Do and Do Not Know About Food Consump-
tion of American Families, " Journal of Farm- Economics, XL, No. 5
(December, 1958), 1309.

 

Four income elasticities for different family sizes were estimated
from data collected in the 1948 U.S. D.A. survey of thefood consumption
of urban households.1 The income elasticities obtained using a double log

equation form,

logY=a+blogX+u (1.1)

where Y is expenditure for food and X is income after Federal income tax,

were:
2 person families . 46
3 person families . 35
4 person families , . 38
5 and over person families . 37

 

lFaith Clark, Janet Murray, Gertrude S. Weiss, and Evelyn Gross-
man, Food Consumption of Urban Families in the United States--With an
Appraisal of Methods of Analysis, U. S. Department of Agriculture,
Agriculture Information Bulletin No. 132 (Washington: U. S. Government
Printing Office, 1954), pp. 36-37.

 

 

Although the household type classifications of this study are also broad,
the results give further evidence of the existence of differences in elasticity
between household types, the difference between the elasticities of the two
person families and the larger families being especially marked.

The next most recent study of differences in elasticities for food in
different types of households was made by R. G. D. Allen, using data on
the household expenditures of wage-earner and clerical families in the

Eastern and Midwestern United States. 1

The data was part of that collected
by the Bureau of Labor Statistics in their 1935 survey of urban family
expenditures. The elasticities obtained were estimated using the linear

equation form

Y=a+bX+u (1.2)

where Y is expenditure on food, and X is household income. While this
equation form may be satisfactory for estimating elasticities in groups in
which the range of income is small, logarithmic equation forms generally
are preferred at the present time.2 The results obtained by Allen (Table
1. 2) Show fairly marked differences in the elasticity of demand for food
within each city and class group studied. There are also important dif-
ferences in the elasticities of the same household type between the different
city and class groups. Elasticities estimated with the linear equation form
are equal to the product of the regression coefficient and the ratio of mean
income to mean expenditure on food, when the elasticity is evaluated at

the means of income and expenditure. The differences in the elasticities

for a given household type in the different city and class groups are due

1R. G. D. Allen, "Expenditure Patterns of Families of Different
Types, " Studies in Mathematical Economics and Econometrics, ed. 0.
Lange, F. McIntyre and T. O. Yntema (Chicago: University of Chicago
Press, 1942), pp. 190-207.

 

2The Choice of functional forms for the estimation of elasticities
will be discussed in Chapter Four.

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both to the differences in the regression coefficients obtained, and the
differences in the ratio of mean income to mean expenditure, between
groups. While the household types distinguished are more homogeneous
than those of Miss Reid's study, the age of the data employed in the study
and the use of the linear equation form limit any current use of Allen's
results.

The only other study of income elasticities for different household
types is primarily of historical interest now, since the data used are from
the 1901 Bureau of Labor Statistics survey of household expenditures of
wage-earner and low-salaried families in urban industrial centers. The
results for the food expenditure portion of this study by H. Gregg Lewis
and Paul H. Douglas are given in Table 1. 3.1 They show no clear pattern
of change with increasing size. The results for equation forms two and
three do illustrate the decline in the elasticity of demand for food with
increased income within a household type. This decline in the elasticity
of demand for food is similar to the results which would be expected for
- Engel curves of the shape usually hypothesized.

The income elasticities obtained in these four (studies are the extent
of information now available on the income elasticities of demand for
food in different types of United States households. These studies indicate
without much question that differences in elasticities existed in the past
and that these differences apparently have persisted over time. They can,
however, tell us little about the nature of current differences in income
elasticities. The usefulness of these studies is limited by the household
type classificationsemployed, the equation forms used to estimate the
elasticities as well as by the age of the data itself. The changes in living
patterns, eating habits, real incomes (and in food products which have
occurred since even the most recent of these studies make a more current

and detailed study of the problem desirable.

 

lH.‘ Gregg Lewis and Paul H. Douglas, "Studies in Consumer Expendi-
tures (1901, 1918-19, 1922-24), " The Journal of Business, XX, No. 4,
Part 2 (October, 1947), 20-21.

 

Table 1. 3 - Income Elasticities of Demand for Food in United States
Households of Differing Size and Composition for Wage-Earner
and Low-Salaried Families in Urban Industrial Centers, 1901
B. L. S. Surveya

 

 

 

Total
Family b c (1
Household Type Income Equation 1 Equation 2 Equation 3

Couple, no children $ 250 . 57 . 54 . 64
750 . 57 .52 .50
1250 . 57 . 38 . 43
Couple, one child 250 . 55 . 53 . 52
under 14 750 .55 .54 .54
1250 . 55 . 41 . 53
Couple, two children 250 . 60 . 59 . 58
under 14 750 .60 .52 .53
I 1250 . 60 . 31 . 48
Couple, three children 250 .65 .60 .69
under 14 750 .65 .62 .60
1250 .65 .49 . 52
Couple, four children 250 . 56 . 41 . 39
under 14 750 . 56 . 58 . 57
1250 . 56 . 53 . 61
Couple, five ‘children 250 . 64 . 51 . 79
under 14 750 .64 .65 .59
1250 .64 .60 . 37
A11 families 250 .61 .57 .61
750 .61 . 57 .56
1250 . 61 .41 . 52

 

aH. Gregg Lewis and Paul H. Douglas, "Studies in Consumer Expenditures
(1901, 1918-19, 1922-24), " The Journal of Business, XX, No. 4, Part 2
(October, 1947), 20-21.

 

a + b log X, where Y is expenditure and X is

quuation 1 form: log Y
income.

CEquation 2 form: Y = a + bX + cXZ.

quuation 3 form: log Y = a + b log X + c (log X)z.

Indirect Evidence of Differences in Elasticities
Between Household Types

 

 

In addition to the four studies just discussed there is further evidence
of differences in food expenditure behavior with family size and composition.
Thomas N. Moss, in considering the effects of size of income, household
size, age and education of housewife and the occupation of the household
head on food expenditures, found that size of family and income were the
only two of these factors associated with significant variations in per capita
expenditures.1 George R. Rockwell, Jr. , has derived an elasticity of
expenditure for all food with respect to household size which is independent
of the effects of income.2 He found the size elasticity of demand for urban
households for all food and beverages to be . 41. The income-expenditure
elasticity for the same group was . 27. These two studies of United States
households indicate that changes in size, as well as changes in income
have an important effect on household food expenditures and provide
indirect evidence of the existence of important differences in income
elasticity between households of different size and composition.

The differences in the income elasticities of the household types in
the United States studies discussed seem to indicate that important differences
do exist in the food eXpenditure behavior of different household types. The
existence of differences in income elasticities between households of dif-
ferent size and composition is supported by J. L.. Nicholson's findings in
his study of 1937-38 data on expenditures by British working-iclass house-
holds. 3 In his study, Nicholson classified households into four types,

 

1Thomas N. Moss, "Some Relationships of Selected Socio-Economic
Factors to Food Consumption and Expenditures, Lansing, Spring, 1950"
(unpublished Ph.D. dissertation, Department of Agricultural Economics,
Michigan State College, 1952), p. 141.

zGeorge R. Rockwell, Jr. , Income and Household Size: Their Effects
on Food Consumption, U. S. Department of Agriculture, Marketing Research
Report No. 340 (Washington, U.S. Government Printing Office, 1959), p. 51.

 

 

3J. L. Nicholson, "Variations in Working Class Family Expenditure, ?'
Journal of the Royal Statistical Society, CXII, Series A, Part IV (1949), 370.

 

10

couples with no children and couples with one, two or three children all
under 14. Each household type was cross-classified into three income
classes (total expenditures were used as an estimate of income) and in-
come elasticities were estimated for food, other household budget items
and certain food groups for each of the 12 household type-intome
class cells. Income elasticities, in general, were found to increase
with household size within an income class, and were found to decline
with increasing income within each household type. The maximum range
of the income elasticities within an income class was in the lower income
class, where elasticities increased from .69 to . 92 as household size
increased. Income elasticities were also found to vary substantially within
each household type with increases in income, the maximum range was
in the households with one child where income elasticities decreased
from . 98 to . 30 as income increased.

, Other British and European studies, however, have concluded that
no differences in income elasticities exist between household types, or .
that these differences are not of major importance. J. A. C. Brown
concluded from his study of 1951 British data that there is no significant
difference in income elasticities between household types. 1 Brown did
note, however, that "there is a tendency for households containing adults
and adolescents only to show greater elasticities than those containing

"3

children and infants. The rationing and price controls still in effect at

the time of the study may have affected some households more than others3

 

1J. A. C. Brown, "The Consumption of Food in Relation to House-
hold‘Composition and Income, " Econometrica,. XXII, No. 4 (October 1954)
452-54. ‘

zlbid., p. 454.

 

3J. A. C. Brown, "The Consumption of Food in Relation to Household
Composition and Income: An Analysis of Postwar British Budgets, "
abstract of paper presented before Innsbruck meeting of Econometrics

Society, August 31-September 2, 1953, and discussion, Econometrica,
XXII, No. 1,f(January, 1954), 107.

 

11

and may perhaps have reduced the differences in elasticities between
household types. Brown's findings seem to be supported by an FAO evalu-
ation of the income elasticities for total food by size types determined
in ten different studies, chiefly Eur0pean. 1 In only two of the ten studies
were the elasticities of the size types found to be significantly different.
In the other eight cases a single aggregate elasticity developed by summing
the individual type elasticities weighted inversely to their variances, was
preferred. These eight aggregate elasticities were statistically more
efficient and unbiased as compared to the .overall elasticities computed
without distinguishing household types, however.

Further study of the income elasticity of demand for food in house-s
holds of different size and age-sex composition would be of interest if
only because of the disagreements which do exist on the subject and for
comparison with past studies in order to gain some historical perspective
on changes in the demand for food. The question of the existence of dif—
ferences in income elasticities between households of different size and
composition has an importance which goes beyond these considerations
because of its bearing on several other types of economic problems.
The implications of the existence of differences in income elasticities of
demand for food between household types for some particular areas of

economic study will be considered in the next three sections.

Implications of Differences in Income Elasticity Between
Household Types in the Forecast of the Demand for Food

 

 

If consumer behavior is related to such demographic variables as
age and household size and composition, changes through time in the

distribution of these variables may produce important changes in total

 

1Economic Commission for Europe, Committee on Agricultural
Problems, in cooperation with United Nations Food and Agriculture Organi-
zation, Income Elasticity of the Demand for Food-Household Survey
Analysis, prepared by L.. M. Goreux (Rome: United Nations Food and
Agriculture Organization, 1959),. p. 39.

 

12

economic behavior. If, for example, continuing differences in behavior
exist between households of different size and composition, then changes
over time in the distribution of household types may produce economically
significant changes in aggregate consumer behavior.

5 Recent projections of the demand for food have not considered the
possible effects of changes in population composition. The possible effects
of these changes have been ignored or dismissed or the forecasts have
been made on the basis of per capita consumption trends in which changes
in population composition are implicit. Schultz in forecasting the demand
potentials for United States farm products, considered the effects of popu-
lation increases at some length, but did not take up the possibility of
changes in the structure of demand with changes in population composition.l
James T. Bonnen, in considering the probable relation of agricultural
production to consumption needs in 1965, forecasts the demand for food
from projections of per capita consumption rates and thus does not deal
with the effects of changes in population composition which are implicit in
changes in per capita consumption.2 Rex F. Daly, in 1956, projected the
demand for food on the basis of anticipated increases in real income and
the income elasticities of the major farm products, dismissing the possible
effects of changes in population composition:

Some trends in the age composition and regional distribution of
population may modify the effect of population on demand for farm
products. But the uptrend in numbers of both younger and older
persons, the decline in farm population, and regional shifts in
population are not expected materially to influence total demand. 3

 

lSchultz, pp. 24-27, 30-43.

' 2James T. Bonnen and William A. Cromarty, "The Structure of
Agriculture, " Agricultural Adjustment Problems in a Growing Economj,
ed. Earl O. Heady, Howard G. Diesslin, Harald R. Jensen,: and Glenn
L. Johnson (Ames: Iowa State College Press, 1958), pp. 117-18.

 

3Rex F. Daly, "The Long-Run Demand for Farm Products, "
Agricultural Economics Research, VIII, No. 3 (July, 1956), 77.

 

13

In a more recent study, Daly laid observed changes in consumption chiefly
to changes in real income and relative prices but granted that changes in
per capita consumption were due in part to other factors, such as nutri-
tional and medical advances, food fads, changes in supply and population
shifts.‘

The nature of therelation of economic behavior to demographic
variables has particular importance because of the substantial changes in
population composition and household numbers which have been projected
for the next two decades.2 U. S. Census Bureau Series B projections
forecast a 45 percent increase in the number of households between 1958
and 1980, an absolute increase of 22 million. An 11. 3 percent increase in
the number of households is projected for the 1958-31965 period (see Table
1.4). The greatest percentage increase during the 1958-1965 period is
expected to be for households with heads under age 25. The next greatest
increase is expected to be in households with heads age 55 and over; this
latter group is expected to increase by 17. 2 percent in the seven year
period. The number of households with heads of intervening ages is
expected to increase by only 5 percent.

Another important change projected for 1958-1980 is the increase of
42 percent in the number of families headed by women. The number of
women living alone or with non-relatives is expected to increase by 72
percent during this period. The number of households with female heads

will thus increase about proportionately with the increase in total households,

 

1G. T. Barton and R. F. Daly, "Prospects for Agriculture in a Grow-
ing Economy, " Problems and Policies of American Agriculture, published
under sponsorship of Iowa State University Center for Agricultural Adjust-
ment, (Ames: Iowa State University Press, 1959), pp. 29-39.

 

2U. S. Bureau of the Census, "Illustrative Projections of the Number
of Households and Families: 1960 to 1980, " prepared by David M. Heer
and Paul C. Glick, Current Population Reports, Series P-ZO, No. 90
(Washington: Bureau of the Census, December 29, 1958), pp. 1-10.

 

14

while the number of households maintained by women living alone or with
non-relatives will increase substantially more rapidly than the total
number of households. The number of households headed by men living
alone or with non- relatives is expected to increase by only 31 percent in
the twenty year period. The proportion of suchhouseholds will thus

decline in relation to total households.

Table 1.4 - United States Census Series B Projections for 1965 of Number
of Households by Age of Heada

 

 

Age of Head (years)

 

 

 

All Under 55 and
Households 25 25 to 54 Over
March 1958 (thousands) 50, 402 2, 393 31, 239 16, 770
July 1965 (thousands) 56,076 3,635 32, 793 19,648
Absolute Increase 5, 674 1, 242 1, 554 2, 878
1958-1965 (thousands)
Percentage Increase
1958-1965 11.3 51.9 5.0 17.2

 

aU. S. Bureau of the Census, "Illustrative Projections of the Number of
Households and Families: 1960 to 1980, " prepared by David M. Heer and
Paul C. Glick, Current Population Reports, Series P-ZO, No. 90
(Washington: Bureau of the Census, December 29, 1958), p. 3.

 

Implications of Differences in Income Elasticity Between
Household Types for'Econor'nic Development

Historical evidence shows that in the course of economic develop-
ment the age distribution of the pOpulation undergoes several changes.
As incomes and population increase in the initial stages of development the
age distribution changes under the effects of the changes in fertility and

age-sex specific mortality which take place. Death rates decline most in

15

the youngest age groups and as the ratio of young to old increases, the
ratio of the labor force to the total population falls. Average income tends
to fall as the proportion of the population which is not in the labor force
increases. However, if the increases in average income do, for some
reason, continue, Leibenstein holds that sooner or later declines in

1 The economic burden of dependency is thus decreased

fertility will set in.
and the pressure on average income is eased. At some point this new

shift in population will make escape from a Malthusian equilibrium easier,
with increased average incomes making some savings possible.

Marked changes in demand associated with these shifts in population
composition may either inhibit or aid in economic progress. . More infor-
mation is needed as to what the extent of these changes may be. If the
needs of the increased proportion of children in the population are small,
the effective pressures on average income in the earlier stages of develop-
ment may be smaller than are usually supposed.

Changes in population composition with resultant changes in consump-
tion may also have an important effect on the economies of developed nations.
There is evidence that in more mature economies consumption may be as
important a determinant of income and growth in income as investment is.
Thus, an understanding of the sources of changes in consumption behavior
is as important in constructing a theory of economic growth for mature
economies, as it is for analyzing the problems of countries in the early
stages of development. The differences in economic behavior which are
associated with demographic characteristics may well be one important
source of changes in consumption behavior during the course of economic
development in both underdeveloped and mature economies.

The changes in population composition which occur during economic
development can also be viewed as changes in the distribution of household

types. There is, in fact, a good case to be made for considering these

 

lHarvey Leibenstein, A Theory of Economic-Demographic Develop-
ment (Princeton: Princeton University Press, 1954), pp. 95-96.

 

16

changes in such a way when studying consumption problems. Since
individuals consume as a member of a household unit rather than separately,
it seems more useful to consider changes in the distribution of the house-
hold types in which consumption behavior is centered than to consider only
the changes in the age-sex composition of the pOpulation. Studies of dif-
ferences in income elasticities of demand for food in different household
types for a more mature industrial society, such as the United States,
should give some clues as to the possible importance of differences in
elasticities between household types in both mature and developing societies,
and should also provide useful information on the possible influence of

changes in the age-sex composition of the population on United States growth.

Implications for Consumption Research of Differences
in Income Elasticity Between Household Types

 

 

In addition to the implications of differences in income elasticities
between household types in forecasts of the demand for food and economic
development problems, the existence of differences in elasticities between
household types also has important implications for the choice of analytical
methods in consumption research.

Two recent British studies, in which consumption equivalence scales
measuring the relative food needs of different types of individuals were
estimated, used methods which required the assumption of the same income
elasticity of demand in all household types. In their analysis of 1937-39
British household budgets S. J. Prais and H. S. Houthakker used one
equation of the form

Xm‘h = AZKini (1. 3)

to obtain the equivalence scale coefficients, Ki» for the i types of individuals

which they distinguished, where X is household expenditure on food, m is

17

income per member and ni is the number of individuals of the i-th type

in the household.1 Coefficients A and h are constants, h is the income
elasticity for food. Since only the ratio of the Ki was required, the con-
stant term A was kept on the right hand side. The Ki were estimated by
first selecting the value of h which maximized the correlation between

the composite variable on the left-hand side and the determining variables
ni on the right—hand side. The Ki corresponding to the value of h selected
were then calculated. The other equation employed was of the semi-

1ogarithmic form

X
(c + log m)

 

= szini (I. 4)

a/b. The procedure used was

where b and c are constants, with c
similar to that for equation (1. 3) except that in this case it was the
variable c for which various values were inserted until the one which
maximized the correlation of the left-hand side and the ni was found.
Equation (1. 3) thus requires the assumption that income elasticity h is
constant across household types, just as equation (1.4) requires the
assumption that parameter c is constant across household types.

J. A. C. Brown, in estimating equivalence scales for total food
expenditure from 1951 British data, first calculated the income elasticities
for each of the sixteen household composition types which he distinguished,

using a double-logarithmic equation of the form

h ' d
X = Pkm k (Eni) k (1.5)

where X is household food expenditure, m is net household income, ni

1S. J. Prais and H. S. Houthakker, The Analysis of Family Budgets
("University of Cambridge, Department of Applied Economics Monographs, "
No. 4; Cambridge: Cambridge University Press, 1955), pp. 134-42. See
also, 5. J. Prais, "The Estimation of Equivalent Adult Scales From
Family Budgets, " The Economic Journal, LXIII (December, 1953), 799-
802.

 

 

18

the number of individuals of the i-th type in the household and Pk: hk,
and dk are constants to be estimated for each of the 16 household types,

hk being the income elasticity of the k-th household type.l

After testing
the homogeneity of disturbances, Brown used an F test for differences
between the sixteen partial elasticities. The differences were found to be
significant at the five percent level, but not at the one percent level for
the observations gathered between June and August and insignificant at
both levels for those gathered between September and December.

On the basis of these tests, Brown accepted the hypothesis that the
elasticities were equal. It will be noted that in order to be able to accept
the hypothesis of equality for the first group of observations, Brown found
it necessary to go to the one percent level of significance. The probability
of rejecting a true hypothesis, a Type I error, is thus only one perEent.
The use of the one percent level, however, makes the probability of
accepting a false hypothesis (Type 11 error), high. The probability of
Type ‘11 error appears not to have been examined by Brown. Because of
the test employed the probability of Type 11 error was undoubtedly high,
since the smaller the level of significance used, the greater is the prob-
ability of a Type II error. Thus there is some question as to whether the
hypothesis of equality should be accepted and whether Brown was justified
in doing so.

After accepting the hypothesis that the partial elasticities did not
differ between household types, Brown proceeded to estimate the equivalence
scale coefficients using the common income elasticity estimate. The esti-
mates of the equivalence coefficients obtained by Prais and Houthakker
and by Brown thus depend on whether the assumption of constant elasticity
across household types is a‘valid one or not. Since Prais and Houthakker
did not examine elasticities within household types before proceeding on

the assumption of their constancy and because of the nature of the test for

 

1Brown, Econometrica,. XXII, No. 4 (October, 1954), 444-60.

 

19

differences used by Brown, there would seem to be reason to question
the methods used and the usefulness of these methods in any future
studies of a similar nature. Unless income elasticities can be shown to
be the same for all household types the use of these methods of deriving
equivalent scales cannot be supported on a priori grounds because of the

assumption of constancy which they require.

Scope and Objectives of the Study

 

The first goal of this study was to clarify the relationship between
certain concepts of consumption theory and the concepts which have been
employed in empirical analyses of household expenditures and to Specify
more precise definitions for some of the empirical concepts. The con-
cepts and classifications which resulted were instrumental in the develop-
ment of the household types for which income-expenditure elasticities of
demand for food for home consumption were estimated. The second goal
of the study was to determine the statistical and economic significance of
such differences as were found to exist in the income elasticities of house-
holds of differing size and age-sex composition. One of the particular
goals in this connection was to determine whether the assumption of a
single income elasticity for all household types, which was employed by
Brown and by Prais and Houthakker in their estimations of equivalence
scales, would be warranted for recent United States data.

~ In Chapter II, certain theoretical problems which arise in applying
existing consumption theory are considered. These problems are a result
of the formulation of consumption theory on the basis of individual rather
than household behavior. Problems involved in grouping households into
types which satisfy the requirements of theory for estimating income
elasticities are also discussed. - In the next chapter, the actual consumption

unit whose behavior is under consideration is specified more closely.

20

The individual household observations included within the set of household
types employed are also discussed. These observations are drawn from
the urban portion of the 1955 U.S.D.A. Household Food Consumption
Survey.

The empirical variables which have been found to influence consump-
tion behavior and the variables of consumption theory are discussed in
Chapter IV. The different regression equation forms which have been
employed in the estimation of elasticities are also considered.- In Chapter V,
the process of analysis is related, and the elasticities estimated are pre-
sented. Methods of testing income elasticities for significant differences
and the results of one such test for the elasticities estimated in this study
are presented. In the final chapter, the economic significance of the
results is considered in an attempt to determine whether household classifi-
cations by age-sex composition are useful or necessary in the study of
food consumption behavior. The final chapter also examines the justifi-
cation for the acceptance of the hypothesis that economically and statistically
significant differences exist in the income elasticities for food of house-
holds of differing size and age-sex composition.

An attempt was made to hold this study to matters central to the solu-
tion of the problem. Of necessity, many important related considerations
were examined only in part. Problems such as are involved in the per-
manent income hypothesis, the existence of an economic life cycle and
others were considered only briefly as they relate to the problem.

No attempt was made to refine further or improve upon existing, methods

of estimating elasticities, nor was the question of the usefulness of elasticities
in comparison with other possible expressions of relationship between
economic variables considered.

It is felt that those interested chiefly in the empirical results of this
study may prefer to refer to Chapter V immediately. They can thus omit

the discussions of the concepts and classifications which underlie the

21

analysis and the discussion of the choice of functional forms and variables,
whichare contained in Chapters II, III, and IV. . Those who are interested
in the development of the concepts underlying the analysis as well as in its
empirical results will probably prefer to read the chapters in the order

in which they are presented.

CHAPTER II

PROBLEMS IN THE ESTIMATION OF ELASTICITIES
FOR HOUSEHOLDS -

The Individual and the Household in Consumption Theory

 

The usefulness of consumption theory in the study of observed behavior
has been limited to some extent by its formulation as a theory of the behavior
of the individual. Empirical studies, however, have, of necessity, focused
on the household, the unit in which individual consumption occurs, rather
than on the individual himself. The result of this difference between theo-
retical formulation and empirical practice has been a certainconfusion
about Whose behavior is being studied.. Empirical investigators have pro-
ceeded in the general belief that observations of household behavior may be
regarded as the behavior of the "individual" of economic theory, rather
than as the combined behavior of a group of separate individuals. Consump-
tion studies which discuss theory have generally used a theory of individual
behavior, observed household behavior, and then. made statements about
individuals on the basis of these observations of a group. However, as
Cochrane and Bell have pointed out, we should not regard the individual
as the basic decision-making unit of consumption, paralleling the position
of the firm as the decision-making unit on production side of the market. 1
The confusion in this matter is exemplified in the use of the term "theory
of the household" in referring to theories of the economic behavior of the

individual .

 

1Willard W.. Cochrane and Carolyn S. Bell, The Economics of
Consumption (New York: McGraw-Hill, 1956), p. 13.

 

 

22

23

The reasons for the development of economic theory on the basis of
individual behavior probably lie in the origins of economics within
philosophy and in the physiological and psychological bases which have been
assumed to underlie individual behavior. Despite the individual and sub-
jective nature of these bases, early utility theorists presumed that utilities
could be compared between individuals. The idea of comparability lost
favor as utility theory developed and the individual basis of the assump-
tions became more clearly recognized. Marshall notes Jevons' error in
comparing the utilities of the members of a trading body and corrects him,
stating that the things which the body gives up "represent equal purchasing
power to all its members, but very different utilities. "1 But Marshall
himself advances the proposition that the marginal utility of money is
greater for the poor than for the rich, 2 tempting one to raise questions
about starving misers and spendthrift office boys. . Pareto seems to have
recognized the individual basis of his theory and has distinguished between
theories which compare the sensation of an individual under different con-
ditions and theories in which the sensations of two different individuals
are compared.3 The shift from utility to indifference analysis permitted
the elimination of statements about the intensity of desire for a particular
commodity and substituted a scale of preferences instead. This scale
was clearly recognized as the "given wants" of a single individual.4
Although theoretical emphasis has shifted from the physiological, psycho-

logical and introspective views of utility in which utility was regarded as

 

1Alfred Marshall, Principles of Economics (8th ed; London:
Macmillan and Co. , 1947), p. 818.

Timid” p. 95.

 

3Vilfredo Pareto, Manuel d'Economie Politique, trans. Alfred
Bonnet (2d ed.; Paris: Marcel Giard, 1927), pp. 148-149.

 

4’J. R. Hicks, Value and Capital (2d ed.; London: Oxford University
Press, 1950),. pp. 18-19.

 

24

an introspective magnitude, the ordinal preference scale which has
succeeded it must also be regarded as uniquely individual.l

Recent theories of consumer behavior which have been developed
on psychologically based assumptions consider behavior as arising out
of the individual's perceptions of his own needs, his perceptions of reality
and his own subjective system of valuations, and are likewise uniquely
individual in basis. 7‘ Studies such as Bilkey's, 3 which have deveIOped out
of these theories, have leaped from a theory of individual behavior to
empirical study of household behavior without considering the intervening
steps which may be involved, in the same manner that other studies of
consumer behavior of more traditional form have jumped from utility
and indifference theories of individual behavior to empirical studies of
household behavior.

We can relate empirical studies of household behavior to received
theory if we can assume that the concepts of utility and indifference
analysis may be applied to households as well as to individuals. - Implicit
in such an assumption is the assumption of the existence of a common
utility function or set of indifference curves for each group of individuals
composing a household. Such an assumption can be made only if we
postulate a certain unanimity of preference4 or authoritarian allocation

of the group's resources. With the assumption of a common household

 

1Paul A. Samuelson, Foundations of Economic Analysis (Cambridge:
Harvard University Press, 1958), p. 91.

 

i zSee for example Joseph Clawson, "Lewin's Vector Psychology and
the Analysis of Motives in Marketing, " Theory in Marketing, ed. Reavis
Cox and Wroe Alderson (Chicago: Richard D- Irwin, 1950), pp. 51-56.

 

' 3'Warren J. Bilkey, The Basic Relationships in Consumer Expendi-
ture Behavior, ("Harvard Studies in Marketing Farm Products, " No. 4-H;
Cambridge: Harvard University, 1951)..

 

I 4‘H. S. Houthakker, "The Econometrics of Family Budgets, "
Journal of the Royal Statistical Society, CXV Series A Part I (1952), 2..

 

25

utility function or set of indifference curves, however, the way is cleared
for the proper use of such theoretical concepts as income elasticity in

the study of household as well as individual behavior.

Assumptions Required for the Estimation of
Income Elasticities

 

 

In estimating the income elasticity of a household, it is necessary
first to estimate the Engel curve or regression of food expenditure on
income. The product of the slope of this regression line and the ratio of
income to food expenditure at a particular point on the line equals the
income elasticity for food at the particular point. - In consumption theory
such a line is estimated by observing the food expenditure of a single
household as income is varied through successive levels, with all other
factors influencing food expenditure held constant. The empirical estimate
of the Engel curve of a household is at best only a crude approximation
of the Engel curve of theory because of the methods required for its
estimation.

Cross-sectional income elasticities, such as were estimated in
this study are derived from observations of the food expenditures and
incomes of different households at a particular point in time. The assump-
tion is made that the regression fitted on the expenditures of different
households at differing levels of income approximates the expenditure
behavior of a single household at these successive levels of income.

It is assumed that the influences affecting food expenditure, other than
income, are the same for all of the households observed.

- In the estimation of an empirical Engel curve, the observations
which are employed should be those from households which could be
expected to have similar Engel curves if we were able to observe their

entire curve. . Observations of households with widely differing tastes

26

or- food requirements cannot be regarded as observations for the esti-
mation of the same Engel curve. For example, the food expenditures of
a single individual and a household of five can be expected to differ widely
at all levels of income, because of differences in food requirements if
for no other reasons. Observations of these two households are more
properly regarded as estimates of two different Engel curves rather than
a single one.

Some method of eliminating differences in expenditure behavior
due to differing food requirements is needed if observations from house-
holds of differing size and composition are to be regarded as estimates of
points on a single Engel curve. The use of households which differ in
size and composition in the estimation of a single Engel curve appears
warranted in two instances. The first is when the effects of differences
in size and composition on behavior have been eliminated in some manner.
The second instance in which the use of households of differing size and
composition in the estimation of an Engel curve appears warranted is
when the similarity of expenditure behavior of the particular group of
households has been established in some way. In both instances, the
households observed may be regarded as having similar theoretical Engel
curves, and observations of their food expenditure may be regarded as

estimates of points on a single empirical Engel curve.

Methods of Obtaining Households with Similar
Engel Curves

 

 

As has been noted, if the observation of the behavior of different
households are to be used in the estimation of elasticities, some 'means
must be found to eliminate the effects of differences in size and compo-
sition so that the observations can be regarded as estimates of points on
the same Engel curve. - Or alternatively, some means of measurement

must be found so that similarities of the Engel curves of different household

27

types can be established. Households of varying sizes and composition
can be regarded as having similar Engel curves if the observations of
their income and expenditure are deflated so as to eliminate the effect
of these differences. The observations of households are thus reduced
to become what is, in effect, observations of some standardized individual.
The two different types of standardized individuals which have often been
employed in past studies are the per capita unit and the adult male
equivalent. The per capita unit is obtained by using absolute measures
of household size as deflators, while the adult male equivalent is obtained
by using relative measures of household size and composition as deflators.
The per capita unit measures of income and expenditure are obtained
simply by dividing these variables by the number of individuals in the
household. This operation reduces the observations on all the households
to a common per capita unit measure. The use of the absolute size of the
household in individual members as a deflator does not take account of
important differences in individual needs, requirements and behavior.
The use of household size as a deflator implicitly assumes that the con-
sumption of any two individuals is equal, since all individuals are weighted
equally in this procedure. The use of the per capita measure is particu-
larly unsatisfactory for food expenditures, because of the wide variation
of intake between different age and sex groups.
The adult male equivalent is the standardized individual type which
has been most often used in recent studies employing relative measures
of household size and composition as deflators. The first measure of
relative size was developed by Ernst Engel, an early student of household
expenditure budgets.1 This scale for food expenditures assigned the weight
of 1. 0 _to a child under one year and corresponding weights of l. 1 to two
year-olds, 1. 3 to three year-olds, 3. 5 to adult males, and so forth,

depending on their relative share in household food consumption.

 

1Cochrane and Bell, p. 188.

28

The some of these coefficients for a household divided into its food
expenditure reduces expenditure to a per equivalent basis. The expendi-
ture per equivalent is thus considered to be freed of the effects of dif-
ferences in size and composition. Since Engel's time, a variety of similar
measures have been developed for various types of individuals.1 Such
scales may provide coefficients for a few types of individuals or many,
and are developed on the basis of age, sex, occupation and other classifi-
cations. . Most of the more recent scales have been developed using the
adult male equivalent as the basic category. In these scales the adult
male is assigned a coefficient of l. 0, rather than the infant, as in Engel's
scale.

Relative scales for food expenditure have been developed on the
basis of estimated requirements or recommended allowances, as well
as observed behavior. The difference between scales developed on the
basis of requirements and those developed from actual expenditures is
probably slight since relative scales are ratios rather than absolute
quantitie s . 7‘

The derivation and use of equivalence scales requires the assumption
that behavior is fairly uniform within the individual types distinguished.
If the coefficient of the individual type has not taken the number and kinds
of meals eaten at home into account, these are assumed to be compara-
tively uniform within a particular type, although they may vary widely
between types. In addition to the necessity of these assumptions, other

problems arise in the use of equivalence scales.

 

1A general discussion of equivalence scales, their uses and the co-
efficients produced by important studies is given by Robert M. Woodbury,
"Economic Consumption Scales and Their Uses, " Journal of the American
Statistical Association,» XXXIX, No. 228 (December, 1944), 455-68.

 

 

zWoodbury, 464.

29

Allen has questioned the accuracy of some of the scales obtained,
noting that the appropriate scales for food expenditures appear to be
different for families of varying social position and for the first or
second child as compared with later children. 1 Allen observed that
children in clerical families seemed to have greater weights in the food
scale than those in wage-earner families, and the first or second child
seemed to have greater weight than the third or fourth. Scales derived
for one group of households may not be applicable to other groups.
Woodbury noted that scales are likely not uniform between places because
of differences in local habits and prices and that scales are also likely

7' A further problem in the use of equivalence scales

to change over time.
arises from the assumption of constant elasticities across household types
which is used in the Brown and Prais and Houthakker techniques of esti-
-mating scales. Such an assumption presupposes the solution of the very
problem to which this study is addressed.

Besides the use of per capita and equivalence scale deflations,
another method of obtaining groups of households whichmay be expected
to have similar Engel curves is available. This other method is the
separation of the observations into groups in which all of the households
have similar consumption characteristics and therefore may be expected
to have similar Engel curves. If sufficient observations are available in
each of these groups, the Engel curve line and the elasticity may then
be estimated for each one. The use of such a method permits us to avoid

the patent oversimplification of per capita measures and possible

inaccuracies of equivalence scale measures.

 

1R. G. D. Allen, "Expenditure Patterns of Families of Different
Types, " Studies in Mathematical Economics and Econometrics, ed.
0. Lange, F. McIntyre, T. O. Yntema (Chicago: University of Chicago
Press, 1942), p. 201.

zWoodbury, 459, 466-67.

 

30

The method of grouping households which have similar consumption
characteristics into types which may be assumed to have similar Engel
. curves has an important further advantage. This study has undertaken
toestimate the income elasticities for food in households of differing
size and age-sex composition. The compositional types forwhich
elasticities may be estimated because of the similarity of their Engel
curves, may perhaps also serve as the system of household types re-
quired for this study. The criteria for the selection of the final system
of household types for which elasticities are to be estimated will be dis-
cussed in the next chapter. A

This study, therefore, proceeded first to combine households into
groups which would be assumed to have similar Engel curves. 2 The
households which were combined were assumed to have similar food
consumption behavior by reason of the similarity of the consumption

behavior of‘ the individual types composing them.

The Use of Individual Types in Grouping Households
with Similar Engel Curves

 

Types of Individuals in the Household

 

The behavior of households of a particular size and composition
Can be expecteditobe uniform, if the behavior of the individual types of

which .the household type consists is reasonably uniform. 1 In the

development of individual types, age and sex categories are grouped ‘
. I

according'to the similarity of their behavior with respect to the commodity

under consideration. These groupings should be expected to differ from

m 1

7’ ' '—F

1Throughout this study "individual type" will be used to refer to
individuals of a particular age'and sex category, such as males age 15-64.
"Household type" Will be used to refer to households made up of a particu-
lar combination of individual types. For example, two person households
1 made up of aer age 15-64, and a female age 15-64, could be regarded
as a particular household type, which is made up of two distinct individual

types .

31

commodity to commodity. In distinguishing individuals on the basis of
age and sex alone, it is assumed that these characteristics are the princi-
pal determinants of food consumption behavior and that other influences
such as occupation and climate may be omitted from consideration.
Since few urban workers are employed at heavy labor and the effects of
climate are mitigated by central heating and air conditioning it seems
not unreasonable to assume that the effects of occupation and climate on
food consumption. are small.

Ideally the food consumption behavior of each member of an indi-
vidual type should be more like that of other members of that type than
it is like the behavior of any member of another type. This cannot be
expected to be the case in the real world if we distinguish types by age
and sex alone. ~ Individual consumption behavior is probably more
accurately described as lying along a continuum in which consumption
behavior patterns overlap and shade into each other, than as classifiable
into a set of discrete behavior types with significantly different consump- ,
tionicharacteristics. . Each individual could be regarded as constituting
a separate type, but such an approach is hardly useful. Economic
principles and relations if they are to be of any use must have some
degree of generality. - It is only by grouping individuals into more or
less homogeneous types that we may ascertain principles and relations
of economic behavior whichmay be said to have some generality. The
fact that the divisions between these groups must be drawn somewhat
arbitrarily does not weaken the validity of the economic relations which
may be found to exist. However, after deciding that consumption behavior
does not fall naturally into any limited number of age-sex types, and
accepting the necessity of establishing somewhat arbitrary type divisions,
we are confronted with the problem of the number of types which it is

us eful to distinguish.

32

In addition to the need to aggregate individuals into a limited number
of types in order to obtain useful generalizations about economic behavior,
the requirements of analytical simplicity and the limitations of total
sample size also make such aggregation necessary. .As the number of
individual types distinguished is increased the number of household types
which can be constructed from these individual types increases rapidly.
For example, the number of resulting two person household types can be
seen to increase rapidly as the number of individual types distinguished is
increased:1

5 individual types produce 15 household types
6 individual types produce 21 household types
7 individual types produce 28 household types
8 individual types produce 36 household types
9 individual types produce 45 household types
10 individual types produce 55 household types

In going from 5 to 7 individual types the number of different resulting
household types is almost doubled. In doubling the number of individual
types distinguished from five to ten the number of household types pro-
duced is almost quadrupled. Certain combinations of the types which are
distinguished are unlikely to occur for sociological, biological and
economic reasons. Two person households consisting of a male over 65
and an infant are unlikely to occur in the population from which we are
sampling, as are ones consisting of two infants. The problem of the
multiplication of household types with increases in the number of individual
types must be recognized, however, and the number of individual types
distinguished must be limited in order to keep the number of resulting

household types manageable.

 

1The number of household types of a given size r is the number of
different possible samples of size r which can be drawn with replacement
. . . I‘ . . .
from n 1nd1v1dual types, or n , less all but one of any duplicated comb1-
nationsi. Thus the duplicated combination (Male 15-64, Female 15-64)
and (Female 15-64,. Male 15-64) would be counted as only one household
type. -In this example r equals 2 throughout.

33

Since little information is available about actual individual food
intake behavior, we are forced also to use other criteria for the develop-
ment of individual type divisions. In addition to observed behavior,
nutritional requirements and certain economic and social considerations
will be used in the construction of a classification of individual types.

In the use of nutritional requirements to separate individual types
it must be remembered that these are measures of what should be con-
sumed rather than of actual consumption. Since few persons in this
country are barred from attaining the requirements by low income, the
recommended levels and actual intakes can. be expected to be closely
related. Individual types may be separated on the basis of widely differ-
ing requirements, which can be expected to be closely related to actual
consumption and thus to food expenditures in behalf of the individual.
Calories will be used as a general measure of intake for the purposes
of this study since they provide the best general measure of total intake.
Table 2. 1 presents the National Research Council's (N.R. C.) recom-
mended caloric allowances by age and sex.

Table 2. 1 seems to suggest that on the basis of requirements,
individuals over age 12 should be distinguished by both age and sex.

The absolute changes in requirements being greatest in the first 20 years
of life, several different child types should be distinguished, while it
should be possible to group adults into types covering a much wider age
range. . Because of the large absolute increase in requirements of males
age 16-19 over the 13-15 age group, these two types should be held
distinct if possible. . The large increases between each of the children's
recommended levels would indicate that each of these classes should

also be held distinct if possible. Pregnant and lactating women should

be a separate type. Because of the accelerated decrease in. requirements
after age 50, adults over~50 should be distinguished and the groupover

age 70 should probably also be distinguished for the same reason.

34

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35

Individual types may also be distinguished on the basis of differences
in costs in the food budget plans designed to fulfill N. R. C. recommenda-
tions. These plans give costs for several different family types and a
variety of individual types for low-cost, moderate cost and liberal levels
of expenditure. Table 2. 2 gives costs for individual types for the moderate-
cost food plan developed by the United States Department of Agriculture.

The conclusions based on the estimated cost of a week's food for
various individual types are substantially the same as the ones drawn from
the allowances on which the estimated costs are based. The slight change
in costs with age among adult types seems to indicate that wide groupings
by age is not likely to result in any serious heterogeneity of expenditure
behavior within the groups produced. The wide differences in costs
between the different children's age groups indicate that a number of child
types should be used, however.

In considering the available information about observed individual
food consumption behavior, we find it to be largely of two types, food
intake data and equivalent adult coefficient scales. Only a few studies
of individual's food nutrient intakes exist because of the problems and
expense involved in amassing sufficient data to ensure some degree of
reliability. - One study of individual intakes in farm, rural non-farm and
village families in Southeastern New York by Young and Pilcher provides
information on calorie intakes in all age and sex categories.1 The authors'
finding that the diet of the average family in the study was essentially a
reflection of the dollar value of food eaten would seem to support the
belief that the calorie intake of an individual provides some measure of
expenditures in his behalf. 2 Calorie intakes by age and sex are given in

Table 2. 3.

 

lCharlotte M. Young and Helen L. Pilcher, "Nutritional Status Sur-
vey, Groton Township, New York, " Journal of the American Dietetic
Association, XXVI, No. 10, (October 1950), 776-81.

 

 

zIhid., 780.

36

Table 2. 2 - Estimated Cost of One Week's Food by Age-Sex Categories,
April 1959a

 

 

 

 

 

 

Men Women Children

Age - Cost Age Cost Age Cost
75 years and over $8. 25 75 years and over $6.50 10-12 $8.00
55-74 8.50 55-74 6.75 7-9- 6.75
35-54 9.00 35-54 7.25 4-6 5.50
20-34 9.50 20—34 7.50 1-3 4.50
16-19 11.00 (Pregnant) 8.75 Under 1 year 3.75
13-15 9. 50 (Nursing) 10.75

16-19 8.50

13-15 8.50

 

5"U. S. Department of Agriculture, "Estimated Cost of One Week's Food, "
Family Economic Review (June, 1959), p. 31. . Estimates are based on
1958 N.R. C. recommended dietary allowances and average prices per
pound paid by middle-income nonfarm survey families. Estimates have
been rounded to nearest $0. 25.

 

37

Table 2. 3 - Calorie Intakes by Age and Sex, Groton Township Studya

 

 

 

Age Male Female
1-3 1569 1697
4-6 2028 1849
7-9 2193 2026
10-12 2557 2275
13-15 3654 1945
16-20 3375 1976
21-29 3321 2066
30-39 2999 2047
40-49 2821 1982
50-59 2730 1843
60-69 ‘2032 1982

70 years and over

2341

1614

 

a'Charlotte M. Young and Helen'L. Pilcher, "Nutritional Status Survey,
Groton Township, New York, " Journal of the American Dietetic
Association, XXVI, No. 10, (October 1950), 779.

 

38

The Groton Township Study results indicate that while male and
female calorie intakes differ throughout life the differences become
marked after age 13. The differences in intake between the age categories
for children suggest that several child types should be used. - Children's
types should be differentiated by both age and sex after age 13. The dif-
ferences between the intakes of males in the 16-20 and those in the 21-29
‘age groups is slight, indicating that these groups could be combined.
Females in these age groups could also be combined. The decline in adult
male intakes suggest that several adult male types are needed, and that
those over 59 should be a separate type. . Female intakes fall only
slightly up to age 69, but women above this age should be a separate type.

. Additional information on the intakes of women is provided by a

1 The results indicate

North Central regional study of over 2000 women.
that women over 70 should definitely be a separate type, their intakes
being far lower than those in the 60-69 age group. The next greatest
change in intake occurs between the 40-49 and 50-59 age groups. This
suggests the use of three types for adult women, a type for ages 30-49,
one from 50-69 and a third for over age 70.

The results of the North Central project and of other Federal-State
cooperative nutritional status research have’been summarized by Morgan
and Odland. z The combined results indicated that the maximumvintake
for'males occurs at age 16, after an almost linear increase from age 7

to 16. The maximum intake for females was at age 11, with a sharp

increase in intake from age 8 to 11. The intake of females was found to

 

1Iowa State College, Food Intakes of 2, 189 Women in Five North
Central States, Research Bulletin 468,. North Central Regional Publica-
tion No. 83, (Ames: Iowa Agricultural and Home Economics Experiment
Station, 1959).

.zAgnes Fay Morgan and LuraM- Odland, "The Nutriture of People, "
Food--The Yearbook of Agriculture 1959,, U. S.- Department of Agricul-
ture (Washington, U. S- Government Printing Office, 1959), pp. 201-206.

 

 

 

39

decline after age 11 with the decline becoming more marked after age 17.
The intakes of adult males were found to decline linearly with age, with
the decline becoming sharper after age 65. The intakes of adult women
.were found to decline slowly up to age 45 and decline more 'sharply there-
'after. These studies included some 8, 400 individuals throughout the

I United States and lend further support to the general conclusions reached
on the basis of the smaller studies which have been cited.

'A number of consumption scales, or adult equivalent scales, such
as were discussed previously have been derived. We will consider here
only those based on actual studies of food intakes, disregarding those
based on the N.R. C. dietary allowances, since the differences in require- _
ments between age-sex types have already been considered. » Differences
in coefficients between the types distinguished will be considered to mean
I. that these types should be maintained. - Large differences in coefficients
between age types indicate that the differentiation of additional types may
be in order. Only more recent scales will be considered in. light of the
changes in scales which have been noted by Woodbury:

The outstanding difference between the later and earlier scales
is the increased values assigned to children. This doubtless
reflects the change in food habits in accordance with the modern
tendency towards an increase in. provision of relativelyimore
expensive protective foods in the diet, especially for children.

1
For this reasonattention will be confined to only a few of the many studies
which have derived scales. These are presented in Table 2.4 and include ,
bothUnited States studies and the two recent British studies by Prais
andHouthakker and by Brown.

The United States scales indicate that while important differences

existbetween the coefficients for boys and girls from about 6 years of

age onwards, these differences become marked at about age 12 or 13.

 

lWoodbury, 459.

40

The slight changes with age in the coefficients for young children suggest
that children under 4 or 5 years could be included in one type. The scales
also suggest that children between 13 and 20 should be regarded as a class
separate from adults or younger children. The classification of those
between 13 and 20 as adults would be a more satisfactory approximation in
the case of females than for males, the scales indicate. The changes
between age 3 and 13 would make the division of this period into at least
two age groups desirable. The differences between the two British scales
lend support to Woodbury's comments on the increased weight of children
in. more recent scales. The Brown scale from 1951 data more closely
resembles prewar United States scales than does the Prais scale which

is from 1937-1938 data, suggesting that some of the same changes which
Woodbury noted in United States scales occurred in Britain between 1937
and 1951.

Certain economic and social considerations are also important in
our development of individual types. It will be useful to place type
divisions at ages where changes in economic or social status affect eating
behavior. Child types should probably be divided at age 6, for instance,
the age when many children begin to eat lunch at school rather than at
home. We will also want to establish a break between child and adult
types at the age at which the formation of independent households begins.
This is the period of increasing financial independence and the beginning of
the accumulation of a stock of consumer durables. Another important
change in eating behavior probably occurs at retirement age. . Lunch is
no longer eaten at work, energy requirements are lower and income has
declined.

The preliminary system of individual types which was decided upon
after consideration of differences in intake and differences in eating
behavior with social and employment status will be presented in the next

section.

41

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43

The Combination of Individual Types to‘ Obtain
fipusehold Types

 

 

After determining individual types which can be assumed to contain
individuals with similar consumption characteristics, we are then able
to begin combining these individual types into household types. The
households which constitute a household type contain the same number
and types of individuals. Because the behavior of the individuals in the
individual types has been assumed to be similar, it will also be assumed
that households made up of the same number and types of individuals will
display similar behavior, and have similar Engel curves.

' In order that the household types distinguished be broad enough to
contain sufficient cases for study, attention must be given both to the
number of individual types employed and the boundaries of these types.
Individual types which, in addition to distinguishing age-sex categories
with distinctive consumption characteristics, permit the construction of
"typical" household types containing a large number of observations will
be preferred. If we choose to distinguish several types of children it
will be desirable to employ broad age classes for adults in order to limit
the number of types of households consisting of parents and children.
Since adult intakes vary less with age than those of children, this analytical
necessity presents few problems.

The individual types chosen for a preliminary construction of house-
hold types were:

Infant - under 1 year

Pre-school child - l to 5 years
School age child - 6 to 11 years
Adolescent male - 12 to 14 years
Adolescent female - 12 to 14 years
Young male - 15 to 19 years
Young female - 15 to 19 years
Young adult male - 20 to 49 years
Young adult female - 20 to 49 years
Mature male - 50 to 64 years
Mature female - 50 to 64 years
Older male - 65 and over

Older female - 65 and over

44

Infants were separated from pre-school children because the average
calorie requirement for infants under one year of 830 calories is sub:-
stantially below that for older pre-school children. It also was hoped

that it would be possible to parallel the infant classification in J. A. C.
Brown's scale and other studies. The division between age 5 and 6 takes
account of changes in eating patterns with the commencement of schooling.
- It divides younger children with substantially lower observed intakes from
the school-age group with its higher intake levels. The division is also

at about the midpoint of the age 1 to 11 interval in which calorie require-
ments increase linearly. The first differentiation between the sexes is
not made until age twelve in order to reduce the number of types, although
there is evidence of differences as early as age 8 or 9. The 12 to 14 age
group distinguishes the period of highest recommended allowances for
females, except for the periods of pregnancy and nursing. - Observed
intakes for females were generally observed to reach. a maximum just
prior to this period, declining somewhat in the period itself. ‘ It was
expected that if necessary this group could be combined with the age 15

to 19 group. The 15 to 19 age group covers the period in which the

recent nutritional status studies reported by Morgan and Odland found
observed intakes of males to reach a maximum. 1 Thisis also the period
in which both the United States consumption scales reported in Table 2. 4
and male calorie requirements reach a maximum. This group was
expected to be somewhat under-represented in this study, with many of
those in this category away from home at school or in the Armed Services.
The division at age 20 was selected to separate young adults with more
stable levels of intake from the older adolescent group. This division
also allows the classifications of the greater part of those maintaining

independent households as adults. The young adult age category was

 

lMorgan and Odland, pp. 201-206.

45

extended to age 49 so that the parents of younger children would fall
into one category. The division provides a break in the linear decline
of male intakes observed in recent Federal-State cooperative nutritional
studies, and comes a few years after the age at which female intakes
were observed to begin to decline more sharply. The 50 to 64 age cate-
gory separates mature adults with established households from the
younger households and the households of the retired. This group con-
tains adults with more rapidly declining requirements and separates them
from the younger adult groups. The division at age 65 was chosen to
permit the separate study of the households of the retired and to separate
older adults with still declining energy requirements and observed lower
intakes from the mature adult group. This break is at the age at which
the Federal-State cooperative nutritional status studies and the Groton
Township Study found male intakes to begin to decline more sharply.

- Some 550 distinct size, age-sex composition types of household
were produced when the households of the urban portion of the 1955
U.S. D.A. Household Food Consumption Survey were classified using the
13 proposed individual types. - Only a very few of the household types
produced contained over 75 observations, suggesting immediately that the
combination of individual types would be necessary.

The second set of individual types developed was:

Pre-school child - birth to 5 years
School age child - 6 to 14 years
Young adult male - 15‘to 39 years
Young adult female - 15 to 39 years
Mature male - 40 to 64 years
Mature female - 40 to 64 years
Older male - 65 and over

Older female - 65 and over

For this second set of individual types the age 6 to 11 and the age
12 to 14 groups were combined, while individuals in the age 15 to 19 type

were combined with the appropriate young adult group. The new young

46

adult category produced was for ages 15 to 39 inclusive. The mature
adult group was enlarged to run from age 40 to 64. The older adult

group remained unchanged, including those 65 and over. The number of
individual types distinguished was reduced from 13 to only 8. While the
categories are more gross, two categories of children are still dis-
tinguished. Older adolescents were classified as adults, since on the
basis of observed intakes it was felt that their consumption more resembled
that of adults than that of the school age children. The enlarged category
of mature adults includes the group whose intakes have declined from
previous levels and are beginning to decline more sharply. The age break
at 40 still classifies most parents of younger children in a single age
category.

The second set of individual types was found to provide a substantial
number of household types containing a sufficient number of observations
to permit study. This second group of eight individual types is the basis
for all the household types selected for the study. It was necessary,
however, to combine individual types in a few instances in order to obtain
a sufficient number of observations for study. The selection of the house-
holds to be included in each of the household types and the household types

chosen for study will be discussed in the next chapter.

CHAPTER III

THE HOUSEHOLD TYPES

Criteria for the Selection of the Set of Household Types
for which Elasticities Are To Be Estimated

 

 

In the last chapter, it was pointed out that the income elasticity
for food of a group of households can be estimated properly only if the
households can be regarded as having similar‘Engel curves. ‘ It was
expected that the Engel curves of households of a particular size and
composition could be expected to be Similar if the behavior of the
individual types of which the households consist is reasonably uniform.
A set of individual types, containing individuals with similar food con-
sumption characteristics was constructed. These individual types were
then combined to obtain household types composed of households which
could be assumed to have similar Engel curves. The set of household
types chosen was, it must be noted, designed to produce groups which
7 could be expected to have similar Engel curves. . This set of types thus
may not fulfill certain other requirements which. arise out of the
objectives of this study. 9

. This study undertook to determine the income elasticities of demand
for food in households of varying size and age-sex. composition. A The set
of household types which is implicit in this objective is based on criteria
other'than the expectation of similar Engel curves. The household types
for which elasticities should be estimated should be chosen so that the
results will best show such differences as do exist and so that the results
will have the greatest meaning and usefulness in the consideration of

other economic problems. Such a set of types should be based on the

47

48

natural and typical household types which are found in our society.
Further, they should be such that they can be related easily to other
economic data on households and to available census information and
projections.

- Available census data and projections, however, provide few criteria
for the selection of a set of household types for which income elasticities
should be estimated. Projections are made for individual types by age,
sex, and marital status, but no attempt is made to project numbers of

l The principal projection for house-

households by size and composition.
hold numbers is by age of the male head and is similar to the one given in
Table 1.4, in Chapter I.

Current numbers of households are available in a somewhat more
detailed set of categories than are used in projections. Information from
the 1960 Census on households gives numbers by age of head, size of
family and number in certain children's age categories. 2‘ Thus, if we
wish to relate our results to the available projections, only the age of
the household head is of concern. If we desire to match the categories of
the projections, we shall want to employ the same three age categories:
under twenty-five years, twenty-five to fifty—four years, and those fifty-
five and over. If we wish to match the categories used in detailing current
numbers a more elaborate set of types would be required.

The choice of types, however, should also be related to the typical

or natural type categories of our society. This would suggest in a most

 

1It was learned in an interview with‘Paul C. Glick,. Chief of the
Social Statistics Branch, Population and Housing Division, U. S. Bureau
of the Census, that the projection of numbers of households by size and
age-sex composition is regarded as a most difficult problem and that no
official estimates of this nature are being attempted. 9

zSuch a description of current numbers is given in U. 5. Bureau of
the Census, "Household and Family Characteristics: March 1960, "
Current Population Reports, Series P-ZO, No. 106 (Washington: Bureau
of the Census, January 9, 1961), p. 15.

 

49

general way that types should be distinguished by their location in the
economic and family life cycle.1 Young married couples and couples with
young, children just starting their families and likely involved in acquiring
the set of durable goods considered necessary for housekeeping should be
distinguished from older couples with children. Both these household types
should be distinguished from older families in which the children are
grown, or have left home. And all of these should be distinguished-from
the households of the retired and the aged.

Recent consumption research provides increasing evidence of changes

in consumption behavior with changes in the economic and family life cycle. 2

 

1The concepts of the family life cycle and the economic life cycle
have not yet been developed to the point where either may be stated in
other than a rather general way. The family life cycle details the chang-
ing membership of a family group from its formation by marriage to its
dissolution by divorce or the death of the surviving spouse. Demographers
considering the family life cycle have concerned themselves particularly
with the ages of the husband and wife at such stages as first marriage,
birth of last child, marriage of last child, death of husband and death of
surviving spouse. See for example, Paul C. Glick,, American Families
("Census-Monograph Series"; New York: John Wiley and Sons, 1957),

p. 55.

The concept of the economic life cycle has been sketched only in
broad outlines to date. The economic life cycle concept when further
developed should provide information on changes in family economic
behavior with the changing family responsibilities and occupational status
of its head.

 

’ 2Among the studies which have found changes in expenditure behavior
with changes in the economic or family life cycle are:

Charles Zwick, "Demographic Variation: Its Impact on Consumer
Behavior, " Review of Economics and Statistics, XXXIX, No. 4 (November
1957), 451-56.

 

. Janet A. Fisher, "Income, Spending and Saving Patterns of Con-
sumer Units in Different Age Groups, " Studies in Income and Wealth,
Vol- XV,, Conference on Research in Income and Wealth (New York:
National Bureau of Economic Research, 1952),, pp. 75-102.

 

Harold Lydall, "The Life Cycle in Income, Saving and Asset Owner-
ship, " Econometrica,. XXIII, No. 2 (April, 1955), 131-50.

 

Vernon G- Lippitt, Determinants of Consumer Demand for House
Furnishings and Equipment ("Harvard Economic Studies, " Vol. CX;
Cambridge: Harvard University Press, 1959). , ‘

 

 

50

The evidence for the existence of such changes makes this a central con-
sideration in the choice of a system of household types. This study can
best build on this previous work and perhaps make some contribution to
knowledge in this area if life cycle stages are the basis of the household
type system employed. — It is felt that such considerations as matching
existing census projections are only of secondary concern, especially in
view of the types of projections which are available. It seems more
reasonable to proceed in hopes of developing a useful type system and
thenlmodify available projections to fit it. ~ It is expected that an experi-
enced demographer could make any required changes in the one relevant
projection, numbers of households by age of head, if it is desired to use
the results of this study in connection with projections.

, Because the existing knowledge of the effects of stage in the
economic and family life cycle is of only the most rudimentary nature, it
seems desirable to use life cycle categories in the most simple manner
possible. The four categories mentioned previously are probably as
many as we can hope to distinguish at this stage in the development of this
approach. These basic categories were: Young couples with no children
or with young children, couples with older children, older couples whose
children may or may not have left home, and couples of retirement age.

- It will be remembered that in the last chapter, in constructing the
types of households which could be expected to have similar Engel curves,
no attempt was made to aggregate households of greatly different compo-
sition, or of different sizes even though in many cases certain types
undoubtedly could have been assumed to have similar Engel curves.

The household types produced, it is felt, generally conform to the cate-
gories of the economic and family life cycle. The household types for two
or more persons fall in the four life cycle categories discussed. . These
categories are roughly younger households with and without children in

which the 'wife is under forty, those with and without children in which the

51

wife is under sixty-five, the households in which all members are fifteen

or over but under sixty-five and the households maintained by those
sixty-five and over or including such individuals. While certain of the

age categories for adult members of the household are broader than

those which would be most desirable, the age of the child household members
is more closely detailed and can be used to fix the location of the type in

the economic and family life cycle.

Because size and age-sex composition were the basis for aggregating
households into types with simnar Engel curves it will be possible to use
this same system of household types as the types for which income
elasticities are estimated. We must now turn to another important prob-
lem, that of clearly identifying the consumption unit whose behavior is

under consideration.

Identifying the Unit of Inquiry

 

Studies of consumption behavior have used a variety of names for
the micro-economic group on which they focused their attention. This
group has been labeled the "household, " the "family" and sometimes the
"economic family. " This variety of names for the unit of consumption,
each with its own somewhat different meaning, have caused investigators
to lose sight of the fact that the group whose behavior we wishto observe
is an economic group, whose boundaries must be precisely described if
empirical studies of consumption behavior are to have real economic
meaning. This unit is often closely related to groups defined on a bio-
logical, legal and sociological basis. . In our society certain groups such
as the household and the family, which are defined in non-economic terms,
are usually coterminous with the economic group in which consumption
takes place. Because the family and the household often have the same

boundaries as the consumption group they are easily mistaken as identical.

52

"Family" is a term used to describe a social-biological relation-
ship andaliving arrangements. ) Its census definition as "a group of two
or'more persons who live together and who are related by blood, marriage,
or adoption, "1 contains no economic dimension and makes the term un-
suitable for defining the boundaries of an economic group. - "Household"
as defined by the Census is similarly an unsuitable definition of the
consumption group we wish to observe. - Its census definition as "the
entire group of persons whooccupy a dwelling unit, "2 i. e. , a group of
rooms or a single room occupied as separate living quarters with
separate cooking equipment or a separate entrance, is on the basis of
living arrangements. - It does define the group which jointly consume a
set of housing facilities, but lacks full economic dimension as far as the
consumption of food and other goods is concerned.

The group which is most nearly coterminous with the consumption
unit is the "economic family" as defined in the U. S. Department of
Agriculture Household Food ConsumptionSurvey in 1955. The "economic
' family" is defined as "a person living alone or a group of persons who
lived together and drew from a common fund for their major items of
expense. Family members temporarily away from home--at school, at
work, or on vacation, were consideredrmembers of the economic family,
although not residing in the dwelling unit at the time of the interview. "3
This group, however, does not include members of the consumption unit
who live apart on a permanent basis. If the consumption behavior of a

group is to be understood, the entire number of those dependent on its

 

lGlick, p. 2.10.
zlbid.

.3U. S.. Department of Agriculture, Food Consumption of House-
holds in the United States ("Household Food Consumption Survey 1955., "
Report No. 1; Washington: U. S. Government Printing Office, 1956),
p. 193.

 

 

53

income for support should be known. In neglecting family members

living apart permanently, "economic family" likely understates the
demands on the income of the group, since members who live apart from
the group are often dependent on it (e. g. , aged parents in nursing homes).
Those living apart may also be sending money home, thus giving rise to
another complication.

Because the terms used to delimit the group in which consumption
occurs do not always precisely define economic boundaries, it becomes
desirable to adopt some new term which can be used to describe the unit
we wish to observe. For this purpose the term used by Cochrane and
Bell, "consuming unit, " seems particularly suitable. "This is a unit
Whose members pool their funds (or incomes) and where decisions with
respect to the use of those funds are made as a unit. "I

Just as we cannot understand the behavior of the consuming unit
without knowing its entire membership, in the study of the consumption
of particular commodities we must know which members of the group
consume the commodity. Not all members of the group participate in
the consumption of every commodity used within the group. The level of
cigarette consumption is more easily understood if we know the number
of adults in the group, and baby food consumption is best understood in
relation to the number of infants present. In order to further refine our
study of consumption behavior, we must know the size and composition
of the consuming unit and the size and composition of the subset which
consumes a particular commodity or group of commodities.

9 Since this thesis is concerned with expenditures for food consumed
at home, we will consider the behavior of the subset of the consuming unit
in which home food consumption occurs. This subset hereafter will be

referred to as the "eating unit. "

 

1Cochrane and Bell, p. 14.

54

The "family" is a socially defined kinship group whose members do
not from its definition necessarily have any economic relationship to each
other. We will turn from it to consider the interrelationships among the
household, the consuming unit and the eating unit, groups which do have
an economic dimension. - Since the household consists of a group of
individuals who jointly consume a set of living facilities, it may in a sense
be considered to be at least partly economically defined. The consuming
unit is defined in a purely economic dimension as the group of individuals
who meet their living expenses from a common shared income. To be
most useful in the study of consumption behavior the membership of the
eating unit should not be restricted to members of the consuming unit but
should also include all others who share in the home consumption of the
food provided by the consuming unit. Here it is assumed that guests will
share without direct repayment, while boarders will receive their share
in return for payment and that hired help receive their share inlieu of
pay. In so defining the eating unit we include all those who are making
demands upon it, rather than ascribing all the expenditures in behalf of
the entire eating unit to the members of the consuming unit alone.

The interrelationships between the household, the consuming unit
(CU) and the eating unit (EU) are illustrated in Figure 3. 1. The household
consists of all those resident in the dwelling. The EU includes all who
draw on the food supplies of the CU, and the CU includes all those who
pool their incomes and share the goods and services purchased with this
income. - Each of these three groups is made up of four sub-groups, three
of which overlap or intersect with one or both of the other groups. The
CU, for example, is made up of (1) members of the CU, who are not
resident in the household and do not eat in the household, and are thus
not included in the EU or household, (2) members of the CU who eat in
the household but are not residents, and thus are included in the EU but

not the household, (3) members of the CU who are resident in the household

55

FIGURE 3.1

GROUPS ASSOCIATED WITH HOME FOOD CONSUMPTION

Non-CU, Resident, Non-eaters

(Roomers)
CU, Resident, Non-eaters Non-CU, Resident, Eaters
(Consuming unit and household (Resident Hired Help, Boarders,
members receiving all meals at House Guests)

work or outside household I

.-~' .-

. e a.-
00-0. ll ..-
'lgol".I ".'-.n-‘n

 

 
   
    
 

CU, Non-resident,
Non- eaters
(Students away at school,

Other Non-resident °_ ‘ .;.':;.71,":;,"’,, 9,; '
Dependents) \ 1.1.1.1.”3.7751): "ml”

CU, Resident,Eaters

(Resident dependents who
eat some meals in the
household)

 

 

‘
T

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

CU, Non-resident, Eaters j Non-CU, Non-resident

(Non-resident dependents who Eaters

regularly eat some meals in the (Hel -
p Hired by Day, Meal Guests,
household) Non-resident Boarders)

“WW Eating Unit

 

Household Consuming Unit (CU)

 

 

 

 

 

56

but do not eat there, and thus are included in the household but not the EU,
and (4) members of the CU who are residents of the household and eat
there, ' and are thus included in all three groups, the CU, household and

. EU. The EU and household are each similarly composed of three sub-
groups which overlap with one or both other groups and one sub-group
which does not.

For most CU, the three groups, the CU, the EU and the household
will be coterminous. The EU will consist solely of resident members of
the CU and will include all members of the household and the CU. - In most
other cases only a few of the other sub-groups mentioned are present.
Figure 3. 1 represents all possible intersections of the three groups.

- Although the existence of the CU is a necessary condition of the existence
of sub-groups, its existence is not a sufficient condition for the existence
of the household or the EU. . An individual who by himself constitutes a
CU may have no permanent dwelling unit and may eat all his meals in
restaurants. In this case, no household or EU exists, despite the exist—
ence of a CU. The situation of many inmates of institutions and members
of the Armed Forces is of this type.

This study will be concerned chiefly with the behavior. of the con-
suming unit and its expenditures on behalf of the eating unit. _ However,
since the survey data used in this study was collected on the basis of
household groups, it will be necessary to bear in mind the differences in
the memberships of the consuming unit, the eating unit and the household
in setting out to determine the relationship between income and expendi-

ture on food.

57

Households Included Within the Household
Type Classifications

 

 

Only a portion of the households in the urban sample of the 1955
Household Food Consumption Survey were included in this study.1 The
households eliminated were those for which income information was not
available and those in which differences in the size of the consuming unit,
eating unit, and household obscured the relationship of food expenditure
to income. - In addition, households of six or more persons were eliminated
because the number of households of any particular type was insufficient
for analysis.

Many households in the urban sample contained more than one
"economic family" or group living together and drawing from a common
fund for major items of expense. The group in these households with
primary responsibility for maintaining the dwelling unit was designated

"2

as the "primary economic family. Other resident family members

outside the primary economic family were labeled as the "secondary

"3 In the households which contained more than one

economic family.
economic family and in those which included roomers, boarders and
resident hired help, income information was collected only for the primary
economic family. , No information on the income of the secondary economic
family or other residents of the household was requested.~ Income infor-
mation was thus available only for a part of the group eating regularly

within the household, while food expenditures are dependent on the size

and composition of the entire group.

 

1The objectives of the survey and the sampling techniques which
were employed are discussed in Appendix I.

2U. S. Department of Agriculture, Food Consumption of House-
holds in the United States ("Household Food Consumption Survey 1955, "
Report No. 1; Washington: U. 5. Government Printing Office, 1956),
p. 193. -

31bid.

 

 

 

58

Any relationship of the food expenditures of households contain-
ing a secondary economic family or other individuals to the income of
the primary economic family understates the total income which. in fact
governs the food expenditures of the group. . Even if the secondary
family's contributions to the food budget and boarder's payments are
included in the income of the primary family, only a part of the income
of the entire group is included in the available income figures. To avoid
the problems of understatement of income, only households which con-
sisted solely of the members of a single and thus primary economic
family were considered. All households which contained a secondary
. economic family, roomers, boarders or resident hired help were
eliminated. In the group of households retained for study the size of
the primary economic family was equal to the size of the household, all
households whibh contained more than one economic family having been

. eliminated. The households retained were those for which exact income
I , information covering every member of the household was available.

_ The Survey definition of the primary economic family is closely
related to that which was put forward for the "consuming unit. "' The
chief difference in these two groups is the omission of members who are
living apart on a permanent basis from the primary economic family.

. Since this difference is important in only a very few cases, 'the members
of the primary economic family will be considered to be a consuming
unit, in households which consist only of a primary economic family.
The income of the primary economic family will be regarded as the
income of the consuming unit for the purposes of this study.

- A few households were found in which a member of the consuming
unit ate no meals in the household. - It was decided that these households
should also be eliminated from the study, since the household composition
overstated the demands on the food supplies of the eating unit. Comparisons

of the expenditures of households of the same compositional type would be

59

clouded by the differences in the actual number and types of individuals
being fed. - If households containing non-eaters had been retained with
the non- eaters eliminated from household composition, in order that
household composition reflect only the demands on food expenditures,
the demands of other items in the family budget and thus on total income
would likely be understated. To avoid such complications these house-
holds were eliminated altogether.

. After eliminating all households in which the consuming unit dif-
fered from the household size, and those in which amember of the house-
hold ate no meals in the household during the survey week, a residual
group is obtained in which the consuming unit, the non-guest portion of
the eating unit and the household are equal in size and of identical compo-
sition. 1 This group of households is represented graphically inFigure 3.1
by the darkest shadedarea, consisting of resident members of the con-
suming unit who eat at least some meals at home. . For this group of
households we have complete information on income, and full information
.on the age and sex of each of the individuals who make regular demands
on the consuming unit. . It should be noted that households which had
entertained guests during the survey week..were not excluded from the
study for this reason. Although. it was recognized that guest meals would
increase total expenditures no attempt was made to adjust for this factor
because of the difficulties in. arriving at a basis for adjustment and the
expectation that its effects would be minor.

. Certain other households for which complete income information
was not available were also eliminated. . These households were those
whorefused to provide information on their incomes and others which
had been recently established and were not asked for the information.

. The lack of datarfor recently established households may have an important
effect on the results for certain household types, especially for the type

including young married couples. - It will be necessary to remember

60

that this group is not included in interpreting the results of the analysis.
. In addition, households which reported negative incomes, under the
income definition of the survey, were eliminated. These households
were not included because of conceptual and computational difficulties
in handling negative incomes.

, The number of households eliminated from the urban portion of the
survey for each of the reasons discussed is given in Table 3. 1. ~ A total
of 444 households were excluded from the household types constructed
for the reasons which have been discussed. In addition, 241 households
of six persons and over were not utilized in this study. . These larger
households were not studied because the number of households included
of any particular compositional type was not sufficient for analysis.

- A total of 2140 households remained and were classified according to

the system of household types which was employed. After the households
had been classified into types, types containing a sufficient number of
observations to permit analysis were selected for further study.

The exclusion of certain observations included in the survey sample
from the household types of this study raises the possibility of biases
beyond those present in the survey sample itself. This study is concerned
with the behavior of individual household types and is not concerned with
the biases of the survey sample arising from under-representation of
certain household types. 1 The biases of concern to this study are those
within household types. For the purposes of this study it is not necessary
to preserve the proportional relationship of household types found in the
population from which the survey is drawn, but only the prOper proportions
of characteristics of particular household types within the population.

The biases of the survey sample resulting from refusals to supply
income information may result in under-representation of households with

A

1The biases noted in the survey sample are discussed in Appendix I.

 

Calm NMH N mom was «~me mfimuofi

 

 

«new AM In ON MA mom GOmHum 23h
cow NM . nu mv mH cum GOmhom pick
6
9% mm. i S. 3 N3 523 3.2:.
So 3. , N 0.2 p omw 83mm 2:.
mom mm in om u: mmN GOmHoQ ocO.
pouosuumaou DD 05 mo muonfiuz . 0502; 0502; wag non—mm 362.502 3.8223 unfim flab.
momfwm. cw popgomH qu mfimdpgfipfi 95 o>3mwoz uuuomom «OZ m wcfipgosm >o>ufim cw mafifismooo
mcofimkfimmno .6325 mEvomdom waflnomom mgoaomdom , mgofiomdom mooflmnrnomno

 

mo Hofiafiz mgoho .0503 Mayo .H.
. . mcoflmnzomno popfiaoxm

 

 

363m 23 E poooaumaov moth. Eogomaom mg» 859m popgoafin mgosomsom mo mnongz ... H .m Bound“.

62

employed homemakers within any given household type. The bias of the
survey sample resulting from not asking recently established households
to supply income information will result in the under-representation of
such households in all household types. This under-representation will
be most important in the household types for smaller and younger
families.

- It is held that the results will not be biased by the other exclusions
discussed, if we remember in considering the results that we are no longer
considering all households of a particular size or of a particular size and
composition, but only a subset of them. This subset has certain specified
characteristics, which were the basis for the selection of the households
included in the subset. After the exclusions, the results for a particular
household type should be representative of all households of that size and
composition, consisting solely of members of one consuming unit, all of
whose members eat at least some meals at home. For each such house-
hold type it should be possible to estimate the relationship of food expendi-
tures to income free from disturbances arising from heterogeneity in the
number of meal eaters and family dependents after the eliminations which

have been discussed have been made.

CHAPT ER IV

THE ECONOMIC VARIABLES AND EXPRESSIONS
OF THEIR RELATIONSHIP

Having selected a method of classifying individuals with similar
consumption characteristics into individual types and having within the
limits of the data combined these types into household types of uniform
size and similar composition, we can proceed to study the relationship
between. income and expenditure on food within each household type
assuming the influence of household size and composition on expenditure

to be constant within each household type.

The Variables of Economic Theory

 

The variables derived from static consumption theory for consider-
ation in this study are income and total food expenditure. It is desired to
observe the relationship between these two variables at varying levels of
income in households of each particular type. In order to isolate this
interaction so that it can be observed independently, some means must
be ,found- of holding the other variables of the system constant. - Since the
data to be employed were obtained in a cross-sectional survey many of
the variables which must be held or assumed constant in static analysis
are fixed by the nature of the data collection method; others require study
to determine their possible effects.

Consumer prices must be assumed to have remained constant
throughout the survey period, and to have been the same to all households
in all of the areas represented by the survey. Food supplies must be

assumedto have remained at the same level throughout the survey period.

63

64

Food expenditures must be assumed to have been a function only
of the income received in the income period Specified by the survey and
uninfluenced by any recent changes or changes in the more remote past.

The effects of certain factors which have been found in empirical
studies to influence the level of expenditures, must either be removed
or be assumed to be negligible, so that the Engel curves of different
households within a given household type may be regarded as similar.
Unless their effects are removed or can be assumed to be negligible,
these so-called "empirical variables" may produce substantial unexplained
variability in the relation of expenditure to income. The influence of
these variables, education, occupation, social status, employment of the
homemaker, ethnic background, urbanization, region and others, is
discussed in the next section. All of the effects of differences in house-
hold size and composition are assumed to have been eliminated by the
system of household type classification which is employed.

_ Institutional factors, technology and population numbers are con-

sidered to be fixed by the use of the cross-sectional method.

Empirical Variables

 

Empirical studies of consumption behavior have focused on a number
of variables which have been found to be useful in explaining differences
in expenditure behavior in addition to those prescribed by utility and indif-
ference formulations of consumption theory. . In addition to income,
which is taken as the determining variable of consumption theory in cross-
sectional studies, family size and composition, stage in the economic life
cycle, occupation, social class, education, employment of the homemaker,
ethnic background, region and urbanization have been used as partial

1

explanations of differences in tastes and preferences. These empirical

 

lCochrane and Bell, pp. 196-202. See also, Irma H. Gross and
E. W. Crandall, Management for Modern Families (New York: Appleton-
Century-Crofts, 1954), pp. 94-131.

 

65

variables are highly interrelated, and only part of the effects of any one
variable are independent of the others. Income, level of education,
occupational status and social class can be seen to be quite closely
related, as are race or ethnic background, income and education.

For example, differences in negro and white expenditure behavior may
be due to differences in income, education and occupation rather than to
any racial differences.

In our consideration of the expenditure behavior of differing house-
hold types we will be able to deal with some of these variables, but will
be forced to assume that the effects of the others are negligible. Since
the data used in this thesis include only urban households, the independent
effects of urbanization can be considered to be constant. The system of
household types which will be used takes account of the size and compo-
sition of the household and should also hold constant most of the independent
effects of age of the homemaker and family stage in the economic life
cycle. The effects of occupation, social class and education are related
so closely to income that it was felt that these factors could be ignored,
since income was being treated as a variable.z Education, social class
and occupation, however, probably should be considered more carefully
I in any study of the allocation of total food expenditure between food groups.
Three other empirical variables, employment of the homemaker, region
and race, will not be controlled and may have an important effect on
expenditure behavior.

- It is generally expected that food expenditures will be higher in
households in which the homemaker is employed because of the use of
more highly processed and more costlytime-saving prepared foods.

The results of a study of the total sample from which the data for this

study was drawn does show food expenditures per person were greater in

 

ZMoss, pp- 140-141. In his study Moss found no significant dif-
ferences in food expenditures per capita with education of homemaker or
occupation of household head when income and family-size were controlled.

66

households in which the homemaker was employed.1 It does not appear
that the difference can be laid solely to this factor with any certainty,
however. - Expenditures for the week were $8; 33 per person in urban
households in which the homemaker was employed as compared to $7. 65
in the households in which the homemaker was not employed. The house-=
holds in which the homemaker was employed were smaller, had a smaller
proportion of children under 16 and a larger proportion of adults and had
higher total incomes than did the other households. All of these factors
are generally associated with higher expenditures per person. The
employment of the homemaker may have had little or no net effect on
expenditure independent of these influences, all of which are included as
variables in this study. For this reason it is felt that the omission of a
control for employment of the homemaker will have little effect on this
study.

Regional differences in food expenditures are of some importance,
however, as compared to the probable influence of employment of the
homemaker. One indication of the extent of this difference is the wide
variation in the cost of a week's food in the four Census regions of the
United States. Estimates for the cost of a week's food in July 1959 based
on the United States Department of Agriculture low-cost food plan gave
the following regional estimates for a family of four (husband, wife, boy,

age 10, girl, age 8):7‘

 

1U. S. Department of Agriculture, Food Consumption and Dietary
Levels of Households As Related to Emjloyment of Homemaker, United
States, by Region ("Household Food Consumption Survey 1955, " Report
No. 15; Washington: U. S. Government Printing Office), pp. 1-2.

 

 

 

ZEloise Cofer, "Estimated Cost of One Week's Food-~U. S. A.
Average and Four Regions, " U. S. Department of Agriculture,
Family Economics Review (September 1959). P. 11.

 

67

South $20. 80
Northeast $26. 50
North Central $25. 30
West $26. 10
U. 8. Average $24. 00

A special adaptation of the low-cost food plan which takes the larger
quantities of grain products and fats consumed in the South more fully into
account estimated the cost of a week's food in the South for a family of
four at $19. 80, instead of $20. 80.1 The lower cost of a week's food in the
South arises out of the consumption of the less expensive foods within a
given food group, 2 e. g. , a preference for pork rather than beef, and a
higher consumption of grains and fats and a lower consumption of dairy
products, meat and milk in comparison with other areas, 3 in addition to
such price differences as may exist.

The differences in actual expenditure between urban households in
the four regions is somewhat less marked, as can be seen in Table 4. 1.
When the effect of income differences between regions is removed by
considering a single income class, in this case the households of two or
more persons with incomes between $4000 and $4999, the differences
between food expenditures in the four regions are further diminished.
. Althoughtimportant differences can still be seen to exist in food expenditure
behavior between regions, in order to maintain the number of cases avail-
able for study it was necessary to proceed on the assumption that these

known differences in behavior would not seriously damage the results.

 

lCofer, "An Adaptation of the Low-Cost Food Plan for the South, "
U.- S. Department of Agriculture, Family Economics Review (September
1959). P. 17.

' 2Cofer, "Estimated Cost of One Week's Food - U. S. A. Average
and Four Regions, " p. 11.

 

3Cofer, "An Adaptation of the Low Cost Food Plan for the South, "
p. 15.

68

Table 4. 1 — Average Weekly Food Expenditures in Urban Households of
Two or More Persons, By Region, 1955.

 

 

 

 

 

1 __ :2:
All Incomes Income $4000n$4999
Expenditure Expenditure Expenditure Expenditure
Region per Household per Person per Household per Person
Southa $21.50 $6. 34 $23. 23 $6.87
Northeastb 27. 48 8. 36 28. 04 8. 07
North Centralc 28.10 8. 31 27. 34 7. 61
Westd 26. 97 8. 23 25.97 7.45
U- s. Averagee 26.15 7.83 26.67 7.63

 

aU. S. Department of Agriculture, Food Consumption of Households in the
South ("Household Food Consumption Survey 1955, " Report No. 4;
Washington: U. S. Government Printing Office, 1956), p. 17.

 

U. S. Department of Agriculture, Food Consumption of Households in the
Northeast ("Household Food Consumption Survey 1955, " Report No. 2;
Washington: U. S. Government Printing Office, 1956), p. 16.

 

 

(:U. S. Department of Agriculture, Food Consumption of Households in the
North Central Region ("Household Food Consumption Survey 1955, "
Report No. 3; Washington: U. S. Government Printing Office, 1956),

p. 17.

 

 

U- S. Department of Agriculture, Food Consumption of Households in the
West ("Household Food Consumption Survey 1955, " Report No. 5;
Washington: U. S. Government Printing Office, 1956), p. 15.

 

eU. S. Department of Agriculture, Food Consumption of Households in the
United States ("Household Food Consumption Survey 1955, " Report No. 1;
Washington: U. S. Government Printing Office, 1956), p. 17.

 

 

69

Information available on the effects of race and ethnic background
on food expenditures seems to indicate that the influence of this factor on
behavior may be declining. - Earlier information is drawn chiefly from
the Bureau of Labor Statistics 1935-1936 study of family expenditures.

In the New York City portion of the study it was found that expenditures
for food by low-income negro families were smaller than those of white
families of comparable incomes.1 The meaning of these food expenditure
figures is complicated by the employment of many negroes as domestic
servants and kitchen help in restaurants where meals were part of the
wage. Sufficient other differences existed between the negro and white
families studied to indicate real differences in consumption behavior
between the two groups, for example, negro families were found to save
more at the same level of current income than did white families.

A more recent B. L.S. study of food expenditures in Washington, D. C.
and Richmond, Virginia in 1947 and 1948 found the differences in the food
expenditures of negro and white households to be greatest at the lowest
income level.2 Less difference could be noted for households with over
$2, 000 a year income. . The negro households were, it should be noted,
larger than the white households in most cases. The consumer expendi-a
‘tures study of 12, 500 urban households conducted by the Bureau of Labor
Statistics in 1950 and early 1951 also reported average expenditures for
home food to be generally larger in white households than in negro house-
holds at a given income level, the difference being greatest at lower income

levels.3 The results of these studies would seem to indicate that as negro

 

lCochrane and Bell, pp. 199-201.

2Helen M. Humes, "Family Food Expenditures, 1947 and 1948, "
U. S. Department of Labor, Monthly Labor Review, LXVI, No. 6 (June
1949), 621-30. .

 

I 3University of Pennsylvania, Study of Consumer Expenditures, In—
comes and Savings, Vol. III: Expenditures for Food, Beverages and
Tobacco, tabulated by the Bureau of Labor Statistics for the Wharton
School of Finance and Commerce (Philadelphia: University of Pennsylvania,
1956), pp. 138-40.

 

 

 

70

households move to higher income levels differences in behavior become
less important. Since the living standard of negro households can be
expected to have further improved between the B. L.S. 1950 study and the
U.S. D.A. Household Food Consumption Survey in 1955, differences in
behavior can be expected to be somewhat smaller than noted here. - In
order to preserve the size of the sample of each household type, data for
households of both races will be used on the assumption that the net
effects of racial differences in behavior will be small.

The urban portion of the U. S. D.A. survey contained 11 percent
negro households. 1 Because of characteristic compositional differences
between negro and white households it cannot be expected that this
proportion of negro households will be present inmost of the household
types to be considered. The household types to be considered in this
study are chiefly smaller-sized, husband and wife households with some
children present. Non-white urban households average somewhat over a
half a person larger than white households, include lodgers in about
three times as many cases, average fewer male heads, have fewer
dependent children present and have many more married couples without
their own households present. 2 Because of these variations it is expected
that there will be a high proportion of negro households among households
excluded from the study because the consuming unit, eating unit, and
household were not of equal size. It should be expected, however, that a
high proportion of the small households,wil~1 be negro. . Glick has related
the high proportion of small negro households to the high proportion of

childless non-white women.3

 

1U. S., Department of Agriculture, Food Consumption of Households
in the United States, ("Household Food Consumption Survey 1955, ”
Report No. 1; Washington: U- S. Government Printing Office, 1956),
p. 190.

ZGlick, pp. 19, 24, 61, 196.
"31618., p. 24.

 

71

In studying the data to be used in this thesis it became clear that
another variable, the total number of meals eaten in the household, had
to be taken into consideration. This variable has not been generally used
in studies of household food expenditure except in some recent studies by
the U.S.D,A.1 Apparently the effects of differences in the total number
of meals eaten on expenditures independent of differences in the size and
composition of the household have been considered to be small. This,

. however, can no longer be considered to be the case, since with increas-
ing incomes in recent years, the proportion of meals eaten out by house-a
hold. members has increased producing substantial variability in the number
of meals eaten at home.

In the'households eligible for inclusion in the household types used
in this study the following results were found:

Number of Meals Eaten at Home

 

 

 

Mean Standard Deviation
One person households _ 19. 7 5. 8
Two person households 40. 4 10. 7
Three person households ' 59. 9 12. 4
Four person households 78. 6 10. 0
Five person households 100. 3 9. 9

The substantial standard deviations seemed to indicate that the vari=
ability in the number of meals eaten, even after household size was con:-
trolled, was of such a magnitude that it was certain to exert an important
influence on the level of expenditures. For this reason it was considered

most important that some method be found of dealing with the meals variable

 

1The number of meals served as a variable has been dealt with through
the use of household size in "equivalent persons" in these studies. The
number of equivalent persons in a househOld is determined by dividing total
meals served by 21, to obtain the number of full-time, 21 meals-a-week
eaters. _ The measure is thus, in effect, a measure of total meals served.
The use of this variable will be discussed more fully later in this chapter
in the section Forms of the Variables.

 

72

in this study. Some of the possible methods are discussed later in this

chapter .

. Economic Expressions of the Relationship
Between Income and Expenditure

 

 

The relationship between income and food expenditure has been
expressed by economists both in the form of income-expenditure elasticities
of demand for food and as Engel curves representing food expenditures at
increasing levels of income.

Graphic representations of food expenditure with increasing income
are referred to as Engel curves, since the curve forms obtained in studies
of consumption in Western nations have borne out Engel's law:1 "The
poorer the family, the greater the pr0portion of income that must be used
for food. "2 Most budget studies have found food expenditure to increase
less than proportionally to income, giving the Engel curve a slope which
decreases as the level of income increases.

. Economists have also utilized the concept of income elasticity to
express the relationship between the income and expenditure variables.
- Income-expenditure elasticity is defined as the ratio of the percentage
change in expenditure to the percentage change in income and is expressed

mathematically as

 

1Findings of Asian studies of food expenditure which contradict
Engel's Law and suggest the need for a more general formulation of the
law are discussed by Carle C. Zimmerman, "Ernest Engel"s Law of
Expenditures for Food, " Quarterly Journal of Economics, XLVII
(November 1932), 78-101.

 

. zErnest Engel, "Die Lebenskoster Belgischer Arbeiter-Familien
Fruher Und Jetzt-Ernittelt Aus FamilieneHauschaltrechnungen, " Institute
of International Statistics Bulletin, IX (1895), 26, as translated and cited
inMarguerite C. Burke, "A Study of Recent Relationships Between Income
and Food Expenditures, " U. S. Department of Agriculture, Agricultural
Economics Research, III, No. 3 (July, 1951), 87.

 

 

 

73

dY X

332 ° 7
where Y is expenditure and X is income.1 The Engel curve for total food
expenditure and the income elasticity of demand for food are mathematically
related since the slope of the Engel curve, 3%, is part of the mathematical
expression for income elasticity. The slope of the Engel curve may be
regarded as the marginal propensity to consume for total food, since it
is the derivative of food expenditure with respect to income.

Graphic representations of the change in the physical quantity of a
particular food purchased with changes in income have also been referred
to as "Engelgcurves. " This study is confined to the consideration of the
relationship between income and food expenditure and the expression of
this relationship in the form of Engel curves and income elasticities.

It does not deal with physical quantities of food purchased.

Regression Equation Forms

 

Studies of household budget data have produced Engel curves from
the observation of the food expenditure behavior of many households at
various levels 0f income. 7 It is assumed that while a single household's
Engel curve might be kinked and discontinuous, it can be represented by a
curve derived from a large number of observations which will be smooth
and continuous and which can be approximated by a continuous function.

There are two theoretical criteria which must be considered in the
search for an appropriate functional form to approximate the Engel
curve. The first such requirement is that the functional form chosen
take account of the satiability of wants. Theory assumes that the demand
for any particular commodity is eventually satiated as the individual

consumes increasing quantities of it. The marginal rate of substitution

4‘

1Herman Wold and Lars Jureen, Demand Analysis (New York:
John Wiley and Sons, 1953), p.- 98.

 

74

of a given good for all other types of goods is expected to increase as

the individual acquires increasing quantities of it. There is, however,
less reason to assume that demand for a broad group of commodities,

such as total food, is in fact satiable. - As income increases the possibility
arises of replacing inferior foods with those of successively higher
qualities and of adding more exotic types of food to the diet. While the
demand for a particular quality of a particular food may be satiable,

there is perhaps less intuitive necessity to assume that wants for a

1 The second criterion derived

broad group of commodities are satiable.
from theory concerns the existence of negative income and expenditure.
The functional form specified for the Engel curve may be such that it

is defined in quadrants in which either income, expenditure or both are
negative. Forms intercepting the income axis at negative values imply
positive levels of consumption at zero income. Such a formulation has

no meaning in traditional consumption theory. For this reason forms
which intercept the income axis at the origin or at positive values are
sometimes preferred, However, if we consider the functional form as
applicable only for the range of the data, this requirement assumes less
importance. Other than these considerations theory prescribes no certain
form which the Engel curve for a broad commodity group can ,be expected
to take. The choice of a functional form must therefore also be governed
by the results of previous investigations of forms which approximate the
Engel curve and by certain technical criteria.

. Prais has listed additivity, homoscedasticity and ease of numerical

estimation as technical criteria. on which functional forms being used to

 

1The probable forms of Engel Curves for groups of complementary
goods, such as different articles of clothing and substitute goods, such as
different qualities of tea, are discussed by H. S.. Houthakker "La Forme
des Courbes d'Engel, " Centre Nationale de la Recherche Scientifique
(France) Cahiers du Seminaire d' Econometrie (1953 Volume), pp. 65—66.

 

75

approximate the Engel curve should be considered. 1 If the same functional
form is being used to approximate the Engel curves for many commodities,
the additivity criterion requires that the sum of the expenditures on
individual commodities including saving, equal income at eachvincome

level. . If the equation is of the form

Y1: ai+ biX+ui (4,1)

where Yi is expenditure on the i-th commodity (saving is included as a

commodity) and X is total income,
Zai= 0 and Zbi = 1 (4. 2)

so that the sum of the eXpenditures on individual commodities is equal
to total income, i. e. ,

2Y1: X (4.3)

A

at all levels of income. This criterion indicates that when considering
all expenditures, we cannot postulate an asymptotic functional form for
every commodity if saving is included, since the use of such a form for
every expenditure category would violate the additivity criterion at upper
income levels. Since this study is considering only total food expenditures
rather than all of the components of total expenditure, the additivity
criterion seems of little importance and in view of Nicholseon's proof
that any least squares estimation will satisfy the additivity criterion, will
not be considered further. 7‘

The least squares requirements include the specification that the
variances of the disturbances from the functional form employed shall

be equal or homoscedastic. 7 If the variance of the disturbances varies

 

1S. J. Prais, ("Non-linear Estimates of the Engel Curves, "
Review of Economic Studies, XX (1952—1953), 89-90.

zNicholson, 388-89.

 

76

systematically with the exogeneous variable, income in the present case,
Valavanis has noted that the least squares method yields maximum likeliu

1 Prais has taken

hood, unbiased, consistent but inefficient estimates.
the position that the prior problem is the establishment of the form of
the Engel curve and that, if upon completion of least squares estimation
the residuals are found not to be homoscedastic, appropriate correction
procedures should be employed.2 The study will proceed on this basis.

The final technical criterion in the choice of a functional form to
approximate the Engel curve is ease of numerical estimation. This
criterion leads to a preference for forms which are suitable for least
squares estimation. Equation forms which require graphical estimation
are unsuitable for use in mass data problems. Others which require the
use of special computer programs must also be eliminated from con-
sideration because of the time delay and expense involved in writing new
programs.

The most frequently used equation forms have been simple linear

functions or linear functions in which all or some of the variables have

undergone logarithmic transformations. The simple linear form
Y=a+bX+u (4.4)

where Y is total expenditure per family or expenditure per equivalent
adult and X is household income was used by Allen and Bowley as a first
approximation of the Engel curve in their pioneering study.3 Although this

form seems to have produced good fits in the homogeneous social class

lStefan. Valavanis, Econometrics, edited from manuscript by Alfred
H. Conrad (New York: McGraw-Hill Book Co. , 1959), pp. 47-49.

 

zPrais, "Non-linear Estimates of the Engel Curves, " p. 90.

3R. G. D. Allen and A. L. Bowley, Family Expenditure ("London
School of Economics and Political Science: Studies in Statistics and
Scientific Method, " No. 2; London: Staples Press, 1935), pp. 1-58.

 

77

groups which Allen and Bowley studied, these groups covered only
narrow ranges of income. In samples covering wider ranges of income
there is less reason to believe that the simple linear form provides an
adequate approximation of the Engel curve.

Two equation forms involving logarithmic transformations of the
variables which meet the theoretical requirement that expenditure take

place only at positive values of income are:

logY a+blogX+u (4.5)
Y=a+blogX+u (4.6)—

since logarithms are defined only for positive values of the income
variable X. An additional form involving a logarithmic transformation
is:

1
logY=a-b(-)-()+u (4.7)

The semi-log form (4.6) has no upper asymptote. The use of the
logarithmic scale for the X variable has the same effect as if the

1 The curve will be convex from

abscissas were compressed near zero.
above when b is positive. When both variables are expressed in logs, as
in the double-log form (4. 5), both variables are affected as if the axes
were compressed near zero. The curves may be either convex or con-
cave from above when b is positive.

The log-inverse form (4. 7) produces a sigmoid curve, as a result
of the logarithmic transformation of the dependent variable, expenditure.
This form differs from the linear form, and the two logarithmic forms
in that it has an upper asymptote. The form is of interest because it
provides a sigmoid or S-shaped curve form by transformations of the

variables of a linear function. Other sigmoid curve forms such as the

lognormal form are difficult to employ since they require graphical

 

 

1Mordecai Ezekiel and Karl A. Fox, Methods of Correlation and
Regression Analysis (3rd edition; New York: John Wiley and Sons, '
1959). pp. 72-3.

 

78

estimation, or an iterative process of estimation using deck calculators
or special computer programs.l

Certain other forms which have been used in the estimation of elas-
ticities should also be mentioned. Parabolic forms have been found to
provide the best approximation to the Engel curve for certain individual

commodities, such as canned peaches.z Parabolic curves

X -a+by-cYZ+u (4.8)

X

-a+blogY-c(log Y)z+u (4.9)

seem suitable only for a particular quality of a good, which with increas-
ing income has the characteristics of an inferior good. Equation forms
which include a quadratic term or terms of a higher degree have been
held to be little superior to linear forms. Prais noted in this connection,
that "while a polynominal of sufficiently high degree can assume any
required shape such flexibility is only an advantage in cases where the
degree of scatter is small enough to allow the precise determination of
the curvature, " and that since household budget data lacks such regularity
it is desirable to choose a simple regression form which imposes a suit--
able degree of curvature.3 General hyperbolic forms of the type devised
by Tornquist‘ require graphical estimation, unless certain assumptions
are made about parameter values which make the equations linear in form.

A simplifiedvlinear hyperbolic form

 

lJ. Aitchison and J. A. C. Brown, The Lognormal Distribution
(University of Cambridge, Department of Applied Economics Monographs, "
No. 5; Cambridge: Cambridge University Press, 1957), pp. 31-34,
141-45. See also, Aitchison and Brown, "A Synthesis of Engel Curve
Theory, " Eview of Economic Studies, XXII (1954-1955), pp. 23-46.

 

 

2Economic Commission for Europe, Committee on Agricultural
Problems, Income Elasticity of the Demand for Food--Household Survey

.Analysis, p. 31.

3Prais, "Non-linear Estimates of the Engel Curves, " p. 90.

 

‘Prais and Houthakker, p. 86. See also, Wold and Jureen, pp.
107-108.

79

l
Y=a-b-)—(+u (4.10)

was used by Prais and Houthakker who found that while it produced only
a slightly lower correlation of income and expenditurethan most of the
other forms used, it produced a fit which was generally less satisfactory
than that for any of the other forms including the simple linear form since
it had too much curvature and flattened out at too low an income. 1
In. light of Prais' criticism and the poor results which they have produced,
the parabolic forms (4. 8), (4. 9), and the simplified linear hyperbolic
form (4. 10), do not seem to merit further attention.

. Equation forms may also be evaluated on the basis of the results
which they have produced when used in analyzing the same data. Lewis
and Douglasz in their study of 1901 BLS data on food expenditure for

particular household types used four equation forms, the simple linear

(4.4) and the double-log (4. 5) form, plus two parabolic forms.

Y

a+bx+cxi+u (rim

logY a+blogX+c(logX)2+u (4.12)

The log parabola form (4. 12) produced the highest coefficient of multiple
determination followed by the parabolic form (4. 11). The double-log

(4. 5),. and the linear form (4.4) produced coefficients of determination
which were only slightly smaller, the lowest being . 957. Although all of
the forms fitted the data well, Lewis' and Douglas' preference was for
forms (4. 11) and (4. 12), since they produced elasticities and marginal
propensities to consume which-in general, varied with changes in the

value of income.3 The similarity of the results for the four forms employed

 

lPrais and Houthakker, pp. 95-96.
2Lewis and Douglas, Appendix A - Table IV.
31bid., p. 13.

80

give little reason for preferring the more complicated parabolic forms.
The parabolic forms performed well in this study of 1901 data, in which
the variability was small. In view of Prais' criticism of the performance
of equations containing quadratic terms, the usefulness of parabolic
equation forms in handling the highly variable consumer behavior recorded
in recent surveys is questionable. Prais and Houthakker expressed a ,
preference for the use of the semi-log form (4.6) with food groups after
evaluating its results along with those of four other forms, the double-
log, (4.5), log-inverse (4.7), linear (4.4) and hyperbolic (4.10).l While
the log-inverse, double-log and semi-logiforms were found to produce
approximately equal closeness of fit, as measured by their correlation
coefficients, the semi-log form was judged superior from the standpoint
of uniformity of fit along the entire curve. The semi-log form was found
to be satisfactory for all the commodity groups in which the elasticity was
less than unity and the best form, in general, for food commodities.

The double-log form was preferred for all non—food commodities.

The selection of any equation form involves certain implicit assump-
tions about the income-expenditure elasticity for food and the marginal
propensity to consume for food. The income elasticities and marginal
propensities to consume for the four equation forms which seemed most
promising after taking the factors discussed above into account, are
given in Table 4. 2. These assumptions must be considered to determine
how well they conform to the requirements of theory and expectations
formed on the basis of previous studies of food expenditures. The simple
linear form (4.4) produces a constant marginal propensity to consume
(MPC). . It also implies that the income elasticity for all goods in the
aggregate tends to unity as income increases, since if the additivity
criterion is met the slope of the line must be equal to one. The double-

logarithmic form (4. 5) produces a MPC which is inversely related to

 

lPrais and Houthakker, pp. 93-103.

81

Table 4.2 - Income-Expenditure Elasticities and Marginal Propensities
to Consume for Certain Engel Cu‘rve Forms

-
E

II

Marginal

Propensity Income
to Consume Elasticity
dY dY . X _

 

 

Equation Equation Form 53(- = MPC c—iX z? - E

. X

(4.4)L1near Y=a+bX+u b be?
. . Y
(4. 5) Double-logarithmic log Y = a + b log X + u b - 32 b
. . . l l
(4.6) Semi-logarithmic Y = a + b log X + u b ° X logloe b ° §'log10e
(47)Lo inerse lo Y-a b -1-+ b°¥-l
' g V g _ - X u X2 Ogloe X logloe

 

82

income, a result which conforms to requirements developed from both,
-micro and macro economic theory. The double-log form gives a constant
income elasticity, a result which runs counter to the findings of studies
which have used other equation forms and have found that income elasticity
for most goods declines with income. The double log form, however, has
been favored by some for the very reason that it does provide a single
constant elasticity coefficient which describes behavior throughout the
entire income range. The semi-logarithmic form (4.6) gives an _MPC
which is inversely proportional to income and an income elasticity which
is inversely proportional to expenditure, which seems acceptable both
from the standpoint of theory and the findings of previous studies. The
log-inverse equation form (4. 7) produces an MPC which is inversely
proportional to the square of income and anincome elasticity which is
inversely proportional to income.

The importance of selecting a form which permits elasticity to
decline with increasing income was demonstrated by Prais and Houthakker
in a comparison of income elasticities for food in working-class and
middle-income households.1 The elasticities for six food groups were
estimated for each class using the double-log form and were found to be
significantly higher for working-class households. 7 The elasticities
estimated for the two class groups using the semi-log form were found to
differ only slightly, and these differences were explained by differences
in. income between the two groups. The hypothesis that both groups could
be represented on a single Engel curve was not rejected. These results
were considered to support the "law of diminishing elasticity" for food
stuffs and demonstrate the superiority of the estimates of elasticity pro-
duced by the semi-log form over the constant elasticities derived using

the double-log form.

 

11bid.. pp. 96-98.

83

Forms of the Variables

 

Past studies of income elasticities have used both income and
expenditure as well as income and expenditure per capita or per equivalent
adult as variables in their analysis. Per capita forms of the variables
were used in an attempt to eliminate the effects of differences in housem-
hold size when elasticities were being estimated for a group containing
households’of varying sizes. The equivalence scales discussed in
Chapter II also have been used to deal with differences in household size
by converting the expenditure variable to expenditure per equivalent adult.
When this is done the same scale properly cannot be used to convert
income, however. A scale for total expenditure is required.1 The use
of either per capita or per equivalent adult forms of the variables involves
the implicit assumption that expenditure per person or per adult equivalent
depends only on income per person or per adult equivalent. Both these
forms of the variables, thus in effect deny the possibility of economies
of scale in household food preparation. 2

Since this study will be estimating elasticities for household types
especially constructed to be homogeneous in size and composition, there
is no need to employ special forms of the income and expenditure to com—-
trol variations in household size and composition.

The "equivalentperson"has been used in some United States Depart—
ment of Agriculture studies to control for differences in the number of

meals eaten.3 Household size in equivalent persons is the number of

1Wold and Jureen, pp. 223-24.
ZPrais and Houthakker, pp. 88-89.

3Two such studies are FaithClark, Janet Murray, Gertrude S.
Weiss, and Evelyn Grossman, Food Consumption of Urban Families in
the United States, U. S. Department of Agriculture, Agriculture Inforw
mation Bulletin No. 132 (Washington, U. S. Government Printing Office,
1954), and the series on the 1955 Household Food Consumption Survey,
the initial report of which was U. S. Department of Agriculture, Food
Consumption of Households in the United States ("Household Food Con-
sumption Survey 1955, " Report No. 1; Washington: U. S. Government
Printing Office, 1956).

 

 

 

84

meals served in the household during a week, divided by 21, so as to

obtain the number of full-time Zl-meals-a-week eaters who could have
been fed from the household's meal production. The "equivalent person"

is thus not a "person" at all, but a measure of the level of household meal
production. This study required some method of controlling for differences
between households in the number of meals eaten, but the use of "equivalent
persons" as a separate variable did not appear to provide any advantages
over the use of total meals.

Another method of controlling for differences in meals (eaten is to
divide the expenditure variable by total meals or by equivalent persons.
This, however, would result in an income-expenditure per meal (or per 21
meals) elasticity which is of little use in most economic contexts, and
whose usefulness would be further confused by changes in the number of
meals eaten at home with changes in income. For the purposes of this
study the introduction of meals served as a separate variable is considered
clearly preferable to any of these alternative methods.

The equation and variable forms chosen for employment in this study

will be discussed in the next chapter.

CHAPTER V

ANALYSIS

The Variables and Equation Forms Employed

 

There are several measures of food consumption which are of
interest to the economist. - Information on quantities consumed and on
nutritional levels are of interest because of the information they provide
on the possibility of expanding the demand for food by improving or up»
grading diets. This study however, is concerned with household
expenditures on food, and therefore concentrates on food purchases from
the supplies moving through commercial channels rather than on total
food consumption, which also includes home produced food, food gifts,
and food received as pay. The urban portion of the 1955 U.S.D.A'.
Household Food Consumption Survey was selected in part for the reason
that urban households were observed to depend chiefly on purchased food,
while rural farm and non-farm households in many cases relied heavily
on home-produced food.l Urban households within a given income class
were expected to display little variability in food expenditure dueto dif—
ferences in the amount of home-produced food available since virtually
all were almost completely dependent upon purchased food.

Total expenditure has often been used in place of income as the
determining variable where income information was not requested or where
respondents refused to provide the information in household budget studies.
In studies of total household expenditures it was expected that the sum-of
the expenditures recorded would provide a close approximation to actual

income. Since income figures are available for the greatest part of the

 

.lU. S. Department of Agriculture, Food Consumption of Households
in the United States, pp. 17-18.

 

 

85

86

households in the U.S.D.A. 1955 Survey and no information is available
on expenditures other than food, income rather than total expenditure
will be employed as a determining variable in the analysis. The income
figures collected are for 1954 diSposable income after State and Federal
taxes. . It is agreed generally that disposable income after taxes provides
the best simple estimate of the resources available for allocation by the
household. . It should be noted however, that while this measure is satis»
factory for the households of salaried and hourly workers, it is less satis-
factory for self- employed businessmen and farmers whose business and
household accounts are less easily distinguished. A rigorous definition
of income is necessary to handle the problem of determining the income
of the self- employed, and for dealing with the occurrence of negative
incomes. - Only two negative incomes were found in the households con=
sidered for inclusion in this study. It is likely, however, that many
other incomes reported were affected by business losses and that the
relationship between these incomes and food expenditure was not the
same as that between the disposable income of salaried and hourly workers
and their expenditures. The problem of defining income for consumption
studies, although of great importance, was necessarily left unexamined.
The income data of the Survey was used without adjustment, except for
households with zero reported incomes; these were assigned incomes of
one dollar~in order to permit the use of logarithms and inverses of the
income variable.

Current consumption increasingly is considered to be dependent both ..

l Itis

on current income and on habits built on the basis of past income.
not the purpose of this study to consider the problem of the suitable
length of lags for consumer expenditure studies; it should be noted,

however, that the income figures used here were for 1954 disposable

 

1James S. Duesenberry, Income, Saving and the Theory of Con-
sumer Behavior, ("Harvard Economic Studies, " Vol. LXXXVII; Cambridge:
Harvard University Press, 1952), pp. 76-89.

 

 

87

income, a period which ended 5 to 6 months prior to the interview period.
The expenditures measured are thus lagged by a half year in relation to
the end of the income period used.

In order better to handle the effect of differences in the number of
meals eaten at home on expenditures, it was decided to introduce the
total number of meals eaten as a second independent variable. The actual
variable employed is the total number of meals eaten by members of the
consuming unit, and does not include guest meals. Although this variable
weigh-s each meal equally, and does not take account of the differences in
the intakes of household members or differences in the costs of breakfasts,
lunches and dinners, it was felt that the use of even such a crude measure
was better than neglecting the independent effect of the number of meals
eaten on expenditure. The use of total meals as a variable also avoids
the problems involved in the use of other methods of correcting for dif-
ferences in the number of meals eaten, such as were discussed in the
last chapter.

It was decided that elasticities would be estimated for the household
types using the four equation forms presented in Table 4. 2 plus a total

meals variable:

Linear:Y = a + b1X1 + bzXz + u (5.1)
Double Log: log Y = a + b1 log X1 + b; log X; + u (5. 2)-
Semi-Log: Y = a + b, log X1 + bzxz + u (5. 3)
Log-Inverse: log Y = a - b1 (£1) + bZXz + u (5.4)

where Y is total food expenditure, X1 is disposable income after Federal
and State taxes and X2 is total meals eaten by members of the household.
Since there was no clear expectation as to therform of the relationship of
total meals to expenditures, the meals variable was entered in logarithmic
form in equation (5. 2) and without transformation in the other three
equation forms. , In order to obtain the desired curve form, the inverse of

income was entered as a negative number in equation (5. 4).

88

The four equation forms will continue to be designated by the
names used in the previous chapters, despite the addition of the meals
variable to their basic form. The names are those used by Prais and
Houthakker to describe equations of the same basic types and thus have
a certain general usage. 1

The elasticities estimated from these equations with two independent
variables will, of course, be partial elasticities obtained from the partial
derivative of expenditure with respect to income. The income elasticities

thus obtained will be independent of the effects of changes in the number

of meals eaten.

The Household Types Analyzed

 

The classification of the household survey observations into house-
hold types was discussed in Chapters II and III. It was expected from the
individual type classifications employed in constructing the household types
that the households of a particular type would have similar Engel curves,
but that behavior would differ between household types. The household
types constructed to include households with similar Engel curves were
the same system of types for which it was decided to estimate elasticities.

The 2140 household observations of households of five persons or
less remaining after the necessary eliminations made up some forty-eight
different household types. Many of these household types contained too
few observations to merit analysis. It was decided arbitrarily that
because of the high variability of expenditures at a given level of income
and the known tendency of consumption survey data to cluster around the
mean income, regressions would be estimated only for household types
containing twenty-four or more observations. Twenty-six different house-

hold types of one to five persons were found to contain sufficient observations.

 

lPrais and Houthakker, p. 87.

89

Most of the household types contained forty or more observations; only
seven of the twenty-six contained fewer than forty. A total of 1829
observations were employed in the twenty-six household types for which
regressions were estimated. The omission of the other household types
from the study is thus not so wasteful of data as it may appear, since
only 320 of the usable observations were not employed for this reason.
The composition of the household types selected and the number of
observations in each is given in Table 5. 1. The number—letter designation
assigned to each household type is also given in this table, the initial
number being the household size. For the sake of brevity each household
type will be referred to by its number~letter designation in the succeeding

discussion.

Analytical Proce s s

 

Preparation of the Data

 

The portion of the data from the U.S. D.A. 1955 Household Food
Consumption Survey which was made available to the study was obtained
on punched cards. The sets of cards on which this study drew were
obtained with the Special permission of the Institute of Home Economics
of the Agricultural Research Service and the Agricultural Marketing
Service, agencies of the United States Department of Agriculture. Card
decks duplicating those used in preparation of the results of the 1955
Survey were obtained from National Analysts, Incorporated, the organi—
zation that conducted the Survey under a contract with the U.S. D.A.

Three of these decks of cards were the source of most of the data
used. . Information on each individual's age, sex, number of meals eaten
and economic family membership was obtained from the Individual Card
(02 Deck). The Economic Family Summary Card (01 Deck.) provided

information on the number in the primary and secondary economic families.

90

Table 5. 1 - Description of the Household Types Analyzed

 

 

Household Type Number of
Number De 8 c ription - Obs ervatiOns

1A Female (15-64) 105

1B . Female (65 or over) 71

2A Male (15-64), Female (15-39) 113

2B Male (15-64), Female (40-64) 266

2C Two females (15-64) 25

2D Male or Female (65 or over) Male (15-64) 23

2E Male or Female (65 or over), Female (1564) 89

2F Male (65 of over), Female (65 or over) 98

3A Male (15-64), Female (15-39), Child (under 6) 137

3B Male (15-64), Female (15-39), Child (6-14) 77

3C Male (15-64), Female (40-64), Child (6-14) 43

3D Male (15-64), Two Females (15-64), (Wife or 66
female head, 40-64)

3E Two Males (15-64), Female (15-64), (Wife or 63
female head, 40-64) _

3F Male or Female (65 or over), and Two other 74
adults (15-64)

4A Male (15-64), Female (15-39), Two children 117
(under 6)

4B Male (15-64), Female (15-39), Child (6-14) 73-
Child (under 6)

4C .Male (15-64), Female (15-39), Two children 77
(6-14)

4D Male (15-64), Female (40-64), Two children 24 -
(6-14) .

4E Male (15-64), Two Females (15-64), Child 40
(6-14)

4F Two Males (15-64), Female (15-64), Child 49
(6-14)

5A Male (15-64), Female (15-64), Three children 31
(under 6)

5B Male (IS-64),. Female (15-64), Child (6-14) 44
Two children (under 6)

5C Male (15-64), Female (15-64), Two children 40
(6-14), Child (under 6)

5D Male (15-64), Female (15-64), Three children 30
(6-14)

5E Male (15-64), Two Females (15-64), Two children 28
(under 15)

5F Two Males (15-64), Female (IS-=64), Two children 26

(under 15)

 

 

91

The; Master Card provided income, urbanization, race, age of wife, and
the money'value of food purchased per equivalent person. In addition to
this information, the number of equivalent persons in the household was
obtained from Summary Card N.

The individual cards of members of the primary economic family
were coded into the thirteen original individual type classifications used.
The number of individuals in each of these types and the total number of
meals eaten by members of the consuming unit were collected on a single .
card for each household. Since the number of household types produced
using thirteen individual types was found to be too large, individuals were
reclassified into eight types and a new set of household types was obtained.
The number of individuals in each individual type, the household compou
sition code and other information was collected on a new Economic Family
Summary Card (06 Deck). - Information on expenditures was collected to
produce the Expenditure Card (07 Deck). The information on these last
two decks was combined to produce an Analysis Card (08 Deck), which
contained complete information on all the variables, the household compou-
sition, and other control and record data. The information required from
Deck 08 for the estimation of the regressions, plus the logarithmic and
inverse values required were collected on the MISTIC Card (09 Deck).

The construction of this card completed the preparation of the punched
cards for use with the computer programs written for card input of data. _
Bythis point in the preparation of the data, all of the eliminations of
households in which the eating unit, consuming unit, and household were

not of equal size, as discussed in Chapter HI, had been made.

, Estimation of the Regressions

 

The regressions estimated for this study were computed using
Michigan. State University's digital computer, MISTIC, and programs for

, the card input of data. The regressions with logarithmic transformations

92

of all three variables (Equation 5. 2) were computed using the K75
Program, "Product Moment Correlations in Logarithmic Scale, Card
Input, " and the M13 Program, "Linear Matrix Equation Solver and Matrix
Inversion. " The other regression forms (Equations 5.1, 5. 3, and 5.4)
were estimated using the K5M Program, "Product Moment Correlations,I
Means, Standard Deviations, Variance—Card Input, " and the M13 Program
for one, 7 two and three person households. The regressions for the four
and five person households were computed using the K13 Program, a
special program written by members of the Agricultural Economic Depart-
ment's Statistical Pool, which combines the K5M and M13 Programs.

The estimates of the regression coefficients, constant terms, standard
errors of the regression coefficients, standard errors of estimate and
coefficients of multiple determination were obtained using the Holz Program,

a special regression program used within the Department.

 

The Regression Results

The Format of the Tables - The regression estimates for the four

 

regression equations are presented in Tables 5. 2 to 5. 5. The household
composition description for each equation number was given in Table 5. l.
The "a" term estimates the value of the constant term of the regres«
sion, the b1 and bz terms estimate the coefficients for the regression of
expenditure on income and total meals, respectively. The standard errors
of the regression coefficients are presented in parentheses below the
regression coefficients. The adjusted coefficient of multiple determination,
R2 is obtained frdm R2, the coefficient of multiple determination. R2 is a
biased estimate of multiple correlation for small sample sizes, to adjust

for this, R2 can be used when sample sizes are small. Its relation to R2 is

'82 =1-(1-R)z(fifiz) (5.5)

1

where k is the total number of variables. R2 indicates the percentage

 

.lEarl O. Heady and‘John L. Dillon, Agricultural Production Func=
tions (Ames: Iowa State University Press, 1961), pp. 118-19.

 

93

of the variation in the observed values of Y that is explained by the ,

regression equation. The variance of the disturbances is estimated by

 

$31" 12. the standard error of estimate squared. It is the variance in
observed Y for fixed values of the independent variables. Its form is, in
this case,
2(dy. 12)‘2
Z :
SY. 12 n-3 (5 ' 6)

a

where dy. 12 is the deviation of observed Y from estimated Y. , The esti-
mate is the sum of squares of the deviations from the regression divided
by the degrees of freedom.1 This statistic is of concern since certain -
tests of elasticities require an assumption of the equality of the variances
of the disturbances.

Regression Results for the Linear Equation Form - The results for

 

the linear equation form, equation (5. 1), vary somewhat between types

(Table 5. 2). ~ Almost half of the equations produced negative estimates

of the constant term; the regression coefficients estimated were all

positive except in one instance. The equations with negative estimates

'of the constant term were concentrated in the larger household types,

the four and five person households, in particular. The size of the esti-

mated b1 regression coefficient shows no clear pattern of change, but

does appear to become larger with increasing household size. The Sign

of the coefficient is positive as would be expected, expenditure increasing

with income. The estimate of the b2 coefficient can be interpreted as the

number of dollars spent for each additional individual meal serving.

In only one case, equation 2E-l, was the sign of this coefficient negative.
The values of the adjusted coefficient of multiple determination,

R2, ranged from . 024 to .671. t The 52 varies widely, but is generally

Y. 12
greater for equations with low values of R2, as would be expected.

 

'lGeorge W. Snedecor, Statistical Methods-~Applied to Experiments
in Agriculture and Biology (5th ed.; Ames: Iowa State College Press,
1956), p. 125.

 

 

94

Table 5. 2 - Regression. Estimates for the Linear Equation Form

Y=a+bX1+ch+u

 

Equation
._7 2

Number a b1 bz R SY.‘ 12

LA-l 1.009 .000596 ‘ .346 .269 13.26

(.000226) (.059) ’

lB-l 2.032 .000495 .200 .168 10.14
(. 000224) (. 066)

2A.1 11.447 .001245 .028 .128 49.28
(.000334) (.009)

23-1 13.909 .000908 .035 .186 ‘ 83.36
(.000181) (.005)

2c-1 ~6.022 .000290 .581 .170 38.66
(.000231) (.257)

20-1 2.371 .000742 .281 .133 42.16
(.000271) (.083)

2E-1 13.580 .001988 -.101 .104 36.60
(.001004) (.177)

25ml 4.272 .000514 .202 .152 30.61
(.000191) (.051)

3A-1 5.618 .001351 .198 .240 ‘52.31
(.000249) (.049)

3B-1 -12.203 .001428 .540 .343 73.85
(. 000570) (. 089)

3c-1 12.934 .000437 .195' .135 37.27
(.000235) (.081)

3D-1 2.096 .000821’ '.312‘ .198 61.67

( 000259) (.107) ’

3E—1 2.507 .000515‘ '.368‘ .296 87.59
(.000269) (.071)

3Fu1 -13.793 .002189' '.412 .263 78.77

(.000440) (.143)

 

Continued

Table 5.2 - Continued

 

w

 

Equation
—2 2
Number a b1 b; R SY‘. 12
4A’1 -8.981 .001962 .334 .158 77.32
(.000503) (.103) ’
43-1 -16.465 .000250 .565 .184 83.37
(.000339) (.132)
4c-1 -1.163 .000976 .328‘ .136 79.46
(.000347) (.116)
40-1 -17.446 .002814' .405 .671 111.42
(.000469) (.218)
4E-1 3.763 .000455' .326‘ .040 103.07
(.000654) (.174)
4Fu1 -9.478 .002495 .354' .326 126.54
(L000558) (.154)
5A,1 8.717 .001182 .145 .024 116.06
(.000717 (.345)
5B-1 4.597 .001514 .181 .482 77.89
(.000290) (.124)
5c-1 2.446 .001821 .207 .413 58.51
(.000348) (.109)
50-1 -13.844 .000854 .422 .103 231.27
(.000432) (.340)
5E-1 -14.324 .002261 .309 .554 48.76
(.000412) (.138)
5F>1 4.783 .001654 .188 .172 64.43
(.000617) (L161)

96

Regression Results for the Double-Log Equation Form - The results

 

for the double-log equation form (5. 2) were generally similar (Table 5. 3).
The estimates of the constant terms were negative in all but two instances,
equations (313—2), and (SA-2). The estimates of the b1 coefficients of the
regression of expenditure on income were positive in all but one instance,
equation (SA-Z). The negative sign of estimated b1 for equation (SA-2)
indicated that the-estimated income elasticity for household type 95A was
negative. The signs of the estimated bz coefficients of the regression of
expenditure on total meals were positive in all but one instance, equation
(2E-2).

The values of p? obtained ranged from .000 to .458. The 5;. 12

varied substantially, the largest value being five times the smallest.

Regression Results for the Semi-Log Equation Form - The results

 

for the semi-log equation form, equation (5. 3), were chiefly of one type
(Table 5.4). The estimates of the constant terms had negative values, or
low positive values. The values of the estimated b1 regression coefficient
were positive, except for one case, equation (SA-3), the largest values
occurring in the four and five person households. The one negative esti-
mate of b1 is of concern because it means that the estimated income
elasticity for this household type will also be negative. The estimates of
the b2 coefficients were positive in all but two cases. .

The values of R2 obtained ranged from .000 to . 543. The values
of SEX... 12. differed Widely, the largest being twenty times the minimum
value obtained.

Regression Results for the Log-Inverse Equation Form - The re«-

 

sults for the log-inverse equation form, equation (5.4), were affected
seriously by problems in handling the income variable (Table 5.5 ). The
estimates of the constant terms were all positive and generally of similar
value. However, the estimates of the b1 regression coefficients differed

greatly, ranging from positive values of over 900 to negative values of . 09.

97

Table 5. 3 - Regression Estimates for the Double-Log Equation Form

 

 

f

logY=a+b1 logX1+bzlong+u

j
‘

 

Equation
"'2 2

Number a b1 b; R SY. 12

LA~2 -.16155 .112 .565 .201 .02930
(.030) ( 133)

13-2 -.13801 .008' .687 .060 .05531
(.036) (.270)

2A,2 -.73522 .322 .508 .152 .02521
(.079) (.157)

23—2 -1.06399 .297 .776 .290 .02686
(.042) (.092)

2c-2 -1.35407 .177 .123 .209 .03193
(.104) (.600)

2D-2 -.62035 .108 .891 .146 .02722
(.049 (.228)

ZE—Z .08129 .414 -.216 .194 .02163
(.162) (.440)

2F-2 -.13912 .087 .606 .188 .02393
(.023) (.163)

3A~2 -1.02140 .298 .730 .260 .01629
(.054) (.151)

33-2 -1.34084 .217 1.100 .389 .01729
(.083) (.163)

3c;2 .03619 .174 .419' .186 .00974
(.066) (.178)

30-2 -1.08836 .282 .804 .252 .01768
(.067) (.240)

3E-2 -.51407 .208 .657 .186 .02140
' (. 072) (. 206)

3F-2 -1.49206 .435 .684 .372 .03272
(.065) (.372)

 

Continued

Table 5. 3 - Continued

 

 

Equation
' -2 2
Number a b1 b2 R SY . 12
4A-2 -1.80539 .392 .937 .217 .01975
.081) (.262)
743-2 -1.09351 .088 1.170 .154 01770
.080) (.312)
4c-2 -.77047 .243 .701 .117 °01707
.083) (.304)
4D-2 -2.31032 .410 1.189 .451 .01660
.110) (.521)
4E-2 -.27609 .099 .733 .030 .02191
.147) (.416) -
4F-2 -1.77650 .362 1.017 .373 .01303
.076) (.313)
5A-2 1.41121 .008 .019 .000 .03562
(.050) (1.339)
53-2 -1.35220 .423 .629 .458 .01405
.078) (.359)
5c-2 -1.29184 .390 .681 .452 .01111
.069 (.338)
5D-2 -2.54169 .404 1.262 .276 .03629
.121) (.952)
5E-2 -2.42144 .421 1.154 .391 .01367‘
.107) (.542)
5F-2 -1.19709 .406 ‘.597 .189 .01334
.145) (.482)

 

99

Table 5.4 - Regression Estimates for the Semi-Log Equation Form

Y=a+b1 logX1+bzXz+u

 

 

 

Equation
"'2 2

.Number a b1 b; R SY. 12

1Am3 -4.435 2.033 .362 .295 12.80
(;617) (.059)

lB-3 1.214 .363 ".223 .115 10.78
(. 508) (.068)

2A-3 -42.785 14.021 .273 .145 48.34
(3.469) (.084)

23-3 -37.865 12.200 .330 .193 82.59
(2.320) (.051)

zc-3 -26.657 6.845 .524 .245 35.14
(3.449) (. 247)

2D-3 5.560 .042 .267 .105 43.47
(.019) (.084)

2E-3 -26.377 13.452 -.109 .114 36.18
(6. 570) (.176)

2Fu3 -1.277 2.386 .186 .161 30.31
(.829) (.050)

3As3 -46.928 16.102 .208 .231 52.96
(3.071) (.049)

3B-3 -50.460 12.302 .543 .332 75.07
(5. 512) (.089)

3c-3 -19.426 9.518 ‘.190 .178 35.41
(3.976) (.078)

3D-3 -49.703 14.181 .380 .233 61.67
(3.881) (.107)

3E-3 -38.681 12.004 .367 .334 87.59
(4.452) (.069)

3F=3 -54.780 15.003 .369 .237 78.77
(3.233) (.144)

 

Continued

100

Table 5.4 - Continued

 

w

 

Equation __

Number a b1 b2 R?- s; . 12
4A-3 -73.955 20.574 .325 .166 76.56
(5.061) (.103)

743-3 -42.142 7.524 .557 .200 81.76
(5.408) (.129) '
4c-3 -58.503 16.945 .328 .148 78.30
(5.615) (.115)
40-3 .483.359 44.536 .622 .482 175.63
(11.427) (.265)
4Ek3 -28.783 9.263 .333 .049 102.06
(10.035) (.173)
4523 -129.141 33.404 .485 .319 127.90
(7.603) (.158)
5A-3 34.263 -1.554 -.004 .000 126.11
(2.985) (.354)
5B-3 -1l8.342 33.018 .272 .542 68.94
~ (5.501) (.110)
5c-3 -85.817 27.091 .195 .441 55.66
(4.892) (.106)
50-3 -97.634 24.710 .398 .189 209.06
(9.213) (.323)
5E-3 —125.447 32.603 .347 .480 56.91
(6.923) (.149)
5Fu3 -75.688 25.353 .144 .157 65.66
(9.861) (.155)

 

101

Table 5. 5 - Regression Estimates for the Log—Inverse Equation Form

L0 Yza-bl(l)+bzXz+u
g Xfi

 

 

 

Equation _
Number a b1 b; R2 5;. 12
1Am4 .67048 .325 .0126 .185 .02898
(.124) .0028)
1B-4 .52465 -.090 .0121 .068 .05484
(.121) .0049)
2A’4 .12778 443.147 .0058 .153 .02515
(108.572) .0019)

2B-4 .13952 574.539 .0067 .299 .02653
(73.528) .0009)

2C-4 .65528 122.542 .0157 .171 .03345
(101.699) .0077)

2D-4 .92078 -2.097 .0064 .075 .02948
(13.299) .0021)

ZELA: .40486 338.290 .0026 .157 .02265
(143.706) .0044)

2F¥4 .94554 .223 .0044 .115 .02608
(.095) .0015)

3Am4 .23368 352.788 .0035 .225 .01708
(67.673) .0009)

3B-4 .89124 179.807 .0092 .367 .01790
(89.954) .0014)

3C-4 .32277 293.171 .0028 .241 .00909
(92.339) .0013)

3D-4 .09526 369.227 .0063 .279 .01705
(80.749) .0018)

3E-4 .26483 348.884 .0040 .252 .01965
(104.581) .0011)

3F-4 .11844 287.021 .0044 .410 .03069
(39.716) .0028)

 

Continued

Table 5. 5 - Continued

102

 

 

 

Equation
“"2 2

Number a b1 b2 R SY. 12

4Am4 1.10505 557.863 .0054 .206 .02001
(119.250) (.0017)

743-4 .88795 86.351 .0073 .167 .01743
(105.182) (.0019)

4c-4 1.22497 435.139 .0041 .103 .01733
(176.757) (.0017)

4D-4 1.15045 793.230 .0062 .371 .01902
(255. 399) (. 0027)

(TE-4 1.19129 241.438 .0043 .028 .02196
(338.837) (.0025)

4F-4 1.03641 585.737 ".0074 .355 .01341
(122.382) (.0018)

5A-4 1.45678 -.253 -.0004 °000 .03346
(.187) (.0057)

53-4 1.25030 889.441 .0041 .444 .01441
(174.414) (.0015)

5c-4 1.38771 556.184 .0025 .420 .01175
(105.026) (.0015)

50-4 1.15884 836.330 .0052 .291 .03551
_ (241.437) (.0042)

5E-4 1.05848 616.682 .0052 .286 .01603
(202.167) (.0025)

5F-4 1.48246 965.065 .0022‘ .187 .01336
(346.440) (.0021)

 

103

The estimates of the b2 coefficients were positive in all but two equations.
The values of R-2 ranged from . 000 to .444. The lowest values of R2
generally occurred in equation numbers in which the value of the estimates
of the b1 regression coefficient were small or negative. The values for
9;. 12 differed rather substantially.

The widely differing values of the estimates of the b1 regression
coefficient are a result of retaining observations of low and zero income
households in certain of the household types. . Household types in which
such observations occurred have mean inverses of income which are sub-
stantially larger than those of the other household types, due to the unusually
large values of the inverse of income for the few low and zero income
households included. 1 The extent of the distortion can be seen in a com-
parison of the harmonic means, i. e. , the inverse of the mean of the
inverses of income, with the arithmetic mean of income for the same
household type. Household type 1A, for example, had an arithmetic mean
income of $2, 157. 46, while its harmonic mean income was only $49. 88.
The deviation in the estimated b1 coefficients appears to arise from the
least squares solution property of fitting the regression line through the
means of the independent variables. The means affected by the inclusion
of low and zero income households thus resulted in the estimation of
deviant b1 values.

Comparison of the Regression Results of the Different Equation

 

Forms - On the basis of a comparison of the adjusted coefficients of
multiple determination, the four regression equation forms did not differ
greatly in the percentage of the variation in the expenditure variable
explained. In making comparisons of R2 between equation forms, it should
be noted that in some cases one will be comparing the percentage of the

variation in expenditure explained with the percentage of the variation

 

1The zero income households had previously been assigned incomes
of one dollar. They were assigned inverses of income of . 9999999.

104

in the log of expenditure explained. Although, a method of correction of
the correlation coefficient for this difference has been worked out, the
corrections for past studies have been so small that their squared value,
as required here, would scarcely affect the value of R2, if at all. 1

The coefficient of multiple determination provides a basis for evalu-
ating the closeness of fit of the different regression equation forms.
It would also be desirable to have some evaluation of the linearity of fit
in order to determine the goodness of fitthroughout the length of the
regression line. Since it was not the purpose of this study to determine
the best equation forms for fitting Engel curves, four different forms
which have performed successfully in past studies have been utilized and
no attempt will be made here to further refine or improve upon these
forms.

In considering the four different equation forms on the basis of
closeness of fit, we are able to say that the double—log equation form
(5. 2) seems to have performed the best. This form gave the most highest
values of R2 and the fewest lowest values. The semi-log form (5. 3), was
rated next best on this basis, the log-inverse equation form (5.4) per-
formed well in a number of cases, but not so well overall as either the
double-log or semi-log forms. The blame for this poor performance
seems to be due in part to the problems which arose from the handling of
the income variable. The linear form (5. 1), generally gave low values of
R2, although its performance was not erratic like that of the log-inverse

form.

The Income Elasticity Coefficients

 

The formulas for the calculation of the income elasticity coefficients

are given below:

 

lPrais and Houthakker, pp. 95-96.

105

Linear form E = b1(X-1) (1/Y) (5. 7)
Double-log form E = b, i (5. 8)
Semi-log form E = logloe (b1)(l/Y) (5. 9)
Log-Inverse form E =

b1(1/X1)(1/log10e) (5. 10)

The values of the estimated income elasticities, evaluated at the means of
the variables, are given in Table 5.6.

It should be noted that the means employed in calculating the elas-
ticities are the arithmetic means of logarithms and reciprocals as well
as natural numbers. Anti-logs of the arithmetic means of logarithms
are geometric means, while reciprocals of the arithmetic means of
reciprocals are harmonic means. Because of the differences in their
computation these three types of means should not be expected to have

the same values .1

The Elasticities Estimated

 

The elasticities produced by the linear equation form (5. 1) ranged
from . 044 to . 543. The estimates are presented in Table 5. 6 along with
those for the other equation forms. The highest estimates of elasticity,
(4D-l), (3F-1), (4F-l) and (2E-1) seem to be best explained as due to the
high values of the b1 coefficient, along with average or high ratios of
mean income to mean expenditure. The lowest elasticities are due chiefly
to the very low values of the estimated b1 regression coefficient in the
equations for these household types. The estimated b1 coefficients in the
household types with the lowest elasticities were one-fifth to one-tenth
those of the types with the highest elasticities. . The differences in elas-
ticities between the types, thus seem to be due chiefly to differences in

the estimates of the b1 coefficients.

1A discussion of the properties of geometric and harmonic means
may be found in Frederick E. Croxton and Dudley J- Cowden, Applied
General Statistics (2d ed.; Englewood Cliffs, N. J.: Prentice-Hall,
1956), pp. 198-99, 203.

 

106

Table 5.6 - Estimated Income Elasticities

 

 

 

Household Linear Double-Log Semi-Log Log-Inverse
Type Form (5.1) Form (5. 2) Form (5.2) Form (5.4)
1A .147 .112 .101 .015
1B .105 .008 .022 -.012
2A .323 .322 .329 .261
2B . 238 . 297 . 264 . 344
2C .082 .177 .181 .119
2D .163 .108 .001 -.003
2E .413 .414 .360 .281
2F .108 .087 .071 .016
3A . 249 . 298 . 295 . 234
3B .268 .217 .213 .106
3C .093 .174 .154 .159
3D .197 .282 .241 .196
3E .105 .208 .183 .200
3F .466 .435 . 314 . 272
4A .326 .392 .342 .339
4B .044 .088 .110 .048
4C .182 .243 .247 .215
4D .543 .410 .568 .378
4E .088 .099 .128 .105
4F .440 . 362 .451 . 308
5A .183 -.008 -.024 -.019
5B . 297 .423 .432 .426
5C .307 .390 .353 .312
SD .173 .404 . 314 .437
SE 7.390 .421 .511 .376

SF . 288 . 406 . 347 . 478

 

107

The income elasticities estimated by the double-log form (5. 2)
ranged from -. 008 for equation 5A-2 to .435 for equation 3F-2. . Most of
the estimates were above . 200. '

The elasticities estimated by the semi-log from (5. 3) ranged in
value from -, 024 to . 568. The difference between the elasticities is
due chiefly to differences in the b1 coefficients, which ranged widely in
value. The highest elasticity estimate of . 568 for 4D-3 is due to the high
estimate of b1, which swamped the low value of the inverse of mean
expenditure. The lowest elasticity estimate of -. 024 for 5A-3 was a
result of the negative estimate of the regression coefficient.

The elasticities estimated by the log-inverse equation form (5.4)
ranged from -. 019 to .478 and included three negative estimates. .'The
three negative values are due, of course, to the negative values of the
estimated regression coefficients. The differences in the elasticities
estimated are due chiefly to differences in the estimated regression
coefficients which varied greatly in value, although the means of the
inverse of income also varied markedly. These variations are due to the
difficulties which arose in handling the income variable, as was discussed

previously.

Comparison of the Elasticities Estimated

 

In comparing the elasticities estimated by the four equationforms
for particular household types, several interesting differences can be
noted. The elasticity estimates produced by the double-log form (5. 2)
were generally the largest of those for a particular household type,
followed by those of the semi-log form (5. 3), the linear form (5. 1) and
the log-inverse form (5.4), in that order. The results for the-linear
form were usually either the highest or the lowest elasticity estimate for
the particular household type. It should be noted in making this com-

parison that the elasticities being compared have not been evaluated at the

108

same means of income and meals served. Each one has been evaluated
at the appropriate arithmetic, geometric or harmonic mean. , Although
the double-log form generally gave the highest estimates, its range of
values was smaller than that of any of the three other equation forms.

Inmaking comparisons between equation forms, household types
with relatively high estimated elasticities for one equation form were
found to occupy approximately the same position among the elasticities
estimated by the other equation forms. The household types with low
elasticities for one equation form were found to also have low estimated
elasticities for the other equation forms. The low and negative elasticites
obtained cannot be ascribed then to any failure of the equation forms, but
must be considered truly descriptive of the behavior of the samples under
consideration.

The elasticity estimates produced by the four equation forms thus
appear to be consistent with each other. None of the results deviated
from the general pattern of those of the other equation forms. It is felt,
however, that the results of the log-inverse form are, as a group, the
least reliable, because of the effects produced by the handling of the

income variable.

Methods of Testing for Differences Between
Elasticity Coefficients

 

C ovarianc e Analysis

 

An exact test of the significance of differences in the elasticities
estimated with double-log equation (5. 2), is available through the use of
the techniques of covariance analysis. Since the income elasticities are
the estimated b1 regression coefficients, the relevant covariance analy-
sis test is a test of the equality of the regression coefficients. The co-

variance test for the equality of regression coefficients compares the

109

variation among the regression coefficients of the different household
types with the sum of squared deviations of individual observations from

1 The ratio of these

their type regression lines, totaled over all types.
two values, each divided by its degrees of freedom, has an F distribution.
, The differences between the regression coefficients will be judged signifi-
cant if the variation among the regression coefficients is large in relation
to the variation of individual observations from the type regression lines.
Covariance analysis techniques require the assumption that the
disturbance variances are equal or that the ratio of the real variances
is known or can be assumed. 2 On applying Bartlett's test to the residual
variances it was found that equality of disturbance variances could not
be assumed.3 The disturbance variances were found to be significantly
different at the one percent level, with 27 degrees of freedom. . On the
basis of the results of the test it was decided that covariance analysis
techniques could not be employed unless weighting procedures were used.
Since the ratios of the real variances were not known, some assump-
tions about these ratios were therefore required. Since Gustafson has
found the results of F tests of regression coefficients to be sensitive to
variations in. the ratios assumed, 4 it was decided that other alternative
methods should be considered before making such assumptions. The de—
cision to consider other methods was also influenced by the desire to

have a test which could be used with the elasticities estimated by all four

 

lWilfrid; J. Dixon and Frank J- Massey, Jr. ,- Introduction to Statisti-
cal Analysis (Zd ed.; New York: McGraw-Hill Book Co. , 1957), pp. 216-19.

 

 

2Robert L. Gustafson, "Testing Equality of Coefficients in Different
Regressions, " Note of April 13, 1961 (Revised), Department of Agricultural
Economics, Michigan State UniVersity, East Lansing (Mimeographed), p. 17.

3Snedecor, pp. 285-89.

‘ 4Gustafson, "Testing Equality of Coefficients in Different Regressions, "
p. 20.

110

of the regression forms employed. Covariance analysis techniques would
have provided a test only of the elasticities estimated with the doubleulog

form.

C onfidenc e ' Inte rval s

 

The covariance analysis techniques would have provided a test of
the equality of the elasticities estimated by the double-log equation form.
The use of confidence intervals to determine the existence of significant
differences in elasticities provides a test of somewhat different type.

In dealing with a ninety-five percent confidence interval for an elasticity
we are estimating bounds which we expect will include the elasticity
coefficient of the population from which we are sampling, unless the
sample with which we are dealing is of a divergent type that occurs only
once in twenty trials.1

In using confidence intervals as a test for significant differences in
the elasticities we will want to ascertain whether any of the confidence
intervals of the elasticity estimates do not overlap. Estimates whose
confidence intervals do not overlap may be regarded as significantly
different. 7‘ For simplicity, the elasticities used in the example which
follows are those estimated by the double-log equation form (5. 2) for two
household types containing the same number of observations; The method
for the other equation forms would be similar. The upper limit of the

ninety-five percent confidence interval of E1 is less than the lower limit

 

1Snedecor, p. 76.

2A general discussion of the interpretation of confidence statements
as a family of tests is given in. E. L. Lehmann, Testing Statistical
ijpotheses (New York: John Wiley and Sons, 1959), pp. 173-76. Note
that the test of the significance of the differences of the estimated elas-
ticities assumes that the covariance of the two estimated elasticities
equals zero, which appears to be a reasonable assumption. Thus the test

may be inexact but is probably % .

 

 

111

of the ninety-five percent confidence interval of E2. Then E1 + SE1 tows
< E; - SE2 tog-,5, where SE1 and SEz are the standard errors of the
respective regression coefficients, and thus of the two elasticities. The

two elasticities are significantly different at the 2. 5 percent level since

fl > a,” (5.11)
For household types which do not contain the same number of observations,
we‘can replace the t value, t.975 (L), of the type containing the larger
number of observations with the t value used in the confidence interval of
the household type with the smaller number of observations, t. 975 (S) in
order to obtain a conservative test. Remembering that the value of I

tabled t increases as the number of degrees of freedom declines, we

note that the inequality becomes

5:: J: :22 > t.975 (S) (5.12)
The difference between the two elasticities can be seen to be significant
at the 2.5 percent level in this case also.

The use of confidence intervals has the advantage that they may be
used with all four of the regression equation forms which have been
employed in this study. ~ As has been noted, covariance analysis can be
used only in testing for differences in the elasticities estimated by the
double-log form (5. 2) and its use for this purpose requires assumptions
of doubtful validity or others which may seriously influence the outcome
of the test. Under these circumstances, the use of confidence intervals

as a test for significant differences between the elasticity coefficients

5 eemed clearly preferable.

112

The Significance of the Differences Between the
Elasticities of Different Household Types

 

 

After deciding upon the use of confidence intervals as the method
for testing for differences between the estimated income elasticities of
the different household types, the required confidence intervals were
calculated.

. Confidence intervals were estimated for the linear (5. l), double-=-
log (5. 2) and semi-log (5. 3) equation forms. . Because of the doubtful
reliability of the regression results for the log-inverse equation form
(5.4), confidence intervals were not estimated for the elasticities estimated
by this equation form. Even if significant differences were found to exist
in the elasticities estimated by the log-inverse equation form, these dif-
ferences could not be laid to differences in behavior between household
types with any degree of certainty, because of the important differences
between the regression results for different household types due solely to
the handling of the income variable.

The confidence intervals of the household type elasticities for each
of the three equation forms are presented in Tables 5.7, 5. 8, and 5. 9.

. Ninety-five percent confidence intervals were employed in order to have
confidence intervals of such width that household types having elasticity
confidence intervals which did not overlap could be regarded as having
significantly different elasticities with a high degree of certainty. The
ninety-five percent confidence intervals can be expected to contain the
income elasticity for the population of that household type, unless the
sample chosen is an abnormal one such as would be expected only five
times in a hundred.

The confidence intervals for the elasticities estimated by the linear

equation form (5. l) are presented) in Table 5. 7.1 It will be noted that the

1The method employed to estimate the confidence intervals for
elasticities estimated by the linear equation form (5. l) is presented in
R- L. Gustafson, "Inferences about 'Elasticities' in Linear Relations, "

113

confidence intervals are not symmetric about the estimated elasticity,
because of the skewed distribution of the elasticity estimate.1 The
confidence intervals for the elasticities estimated by the double-log form
(5. 2) are presented in Table 5. 8. The confidence intervals for the
double-log form are symmetric about the elasticity estimate. The con-
fidence intervals for the elasticities estimated by the semi-log equation
form (5. 3) are given in Table 5. 9. These confidence intervals are also
not symmetric about the estimated elasticity.

For each of the three equation forms the confidence intervals esti»
mated do not overlap for a number of different household types, indicat-
ing that their income elasticities may be regarded as significantly different.
The number of household types with elasticities significantly different
from the elasticity of a particular household type are given in Table 5. 10. _
The number of household types whose confidence intervals lie completely
above that of any particular household type are given, along with the
number of household types whose confidence intervals lie entirely below
that of the particular household type. The numbers are thus the numbers
of household types whose elasticities are significantly greater or signifi-
cantly smaller than those of the indicated type. There are household types
whose elasticity is both significantly greater and significantly smaller

than that of some other type only for the semi-log equation form (5. 3).

 

Note of March 27, 1961. Department of Agricultural Economics,
Michigan State University, East Lansing (Mimeographed). This method
was adapted to estimate the confidence intervals of the elasticities esti-
mated by the semi-log equation form (5. 3). The confidence intervals for
the elasticities estimated by the double-log equation form (5. 2) were -
estimated by the procedures employed to estimate confidence intervals of
regression coefficients, as discussed in Dixon and Massey, Introduction
to Statistical Analysis, pp. 193-194.

 

 

1R. L. Gustafson, "Inferences About "Elasticities' in Linear
Relations, " Note of March 27, 1961. Department of Agricultural
Economics, Michigan State University, East Lansing (Mimeographed),
p. 4.

114

Table 5. 7 - Ninety-Five Percent Confidence Intervals for the Elasticities
Estimated by Linear Equations

 

Equation Estimated - Lower Upper
Number ‘ Income Elasticity ‘ Limit Limit
lA-l -147 .028 . 254
1B-1 .105 .011 .199
2A-1 .323 .012 .635
2B-1 .238 . 146 .333
2C-1 .082 -.053 .220
2D-1 .163 .045 .283
2E-1 .413 -.020 .870
2F-1 .108 .028 . 188
3A-1 .249 .016 .483
3B-1 .268 .053 .483
3C-1 .093 .014 . 170
3D-1 . 197 .072 . 324
3E-1 .105 -.006 °215
3F-1 .466 . 278 .665
4A-1 . 326 . 161 .494
4B-1 .044 -.074 .162
4C-1 .182 .053 .315
4D-1 . 543 . 349 . 756
4E-1 .088 —. 169 . 345
4F-1 .440 . 241 .650
5A-1 .183 .046 .418
5B-1 .297 .180 .416
5C-1 . 307 . 186 .432
5D-1 .173 -.007 . 360
5E-1 . 390 . 242 . 544
SF-l .288 .064 .516

 

115

Table 5. 8 - Ninety-Five Percent Confidence Intervals for the Elasticities
Estimated by Double-Log Equations

 

 

Equation Estimated , Lower Upper
Number Income Elasticity Limit Limit
lA-Z .112 .058 .165
lB-Z .008 -.065 .080
2A-2 . 323 .167 .478
2B-2 .297 .215 .380
3C-2 . 177 «.038 . 393
2D-2 .108 .011 . 206
2E-2 .414 .075 .752
2F-2 .087 .041 .134
3A-2 . 298 .191 .405
3B--2 .217 .050 .384
3C-2 . 174 .041 .307
3D-2 .282 . 147 .417
3E-2 .208 .065 .352
3F-2 .435 . 304 . 565
4A-2 .392 .231 .553
4B-2 .088 -.071 . 247
4C-2 . 243 .077 .409
4D-2 .410 .180 .641
4E-2 .099 -. 199 . 397
4F-2 .362 .209 .514
5A-2 -.008 -.111 .094
5B—2 .423 . 265 . 580
5C-2 .390 .250 .530
5D-2 .404 .155 .653
5E-2 .421 .201 .641
5F-2 .406 .107 .705

 

116

Table 5. 9 - Ninety-Five Percent Confidence Intervals for Elasticities
Estimated by Semi-Log Equations

 

 

Equation . Estimated Lower Upper
Number Income Elasticity Limit Limit
1A-3 .101 . 038 .164
1B-3 .022 -.036 .082
2A-3 . 329 .167 .495
2B-3 . 264 .164 . 364
2C-3 . 181 —.007 . 377
2D-3 .001 0 . 002
2E-3 . 360 -.006 . 744
2F-3 .071 .027 .117
3A-3 . 295 . 182 .410
3B-3 .213 .022 .406
3C-3 . 154 .025 . 285
3D-3 .241 .108 .376
3E-3 .183 .046 .322
3F-3 .314 .179 .455
4A-3 .342 .176 .510
4B-3 .110 -.048 . 268
4C-3 .247 .084 .412
4D-3 .568 .247 .921
4E-3 .128 -. 153 .413
4F-3 .451 . 244 .668
5A-3 -.024 -.117 .069
5B-3 .432 . 286 . 582
5C-3 . 353 . 224 .484
5D-3 .314 .073 .571
5E-3 .511 .287 .747

5F-3 .347 .068 .634

 

 

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118

A number of household types had elasticities which were not significantly
different from those of any other household type, however, most house-
hold types had elasticities which were either significantly smaller or
significantly greater than those of some other household type. The
pattern of Table 5. 10 suggests that for all three equationforms, the
elasticities of the smaller households, especially the one and twolperson
households, were generally significantly smaller than those of other types,
while the elasticities of the larger household types were generally signifi-

cantly greater than those of other types.

CHAPTER VI

CONCLUSIONS

The Economic Significance of the Results

 

The significance of the results has, up to this point, been considered
chiefly in a statistical sense. ‘ It is, however, the economic significance of
the differences between the elasticities of the household types that is of
central concern. . Regardless of their statistical significance, the results
are of little concern unless they indicate differences in expenditure
behavior which cannot be ignored safely nor validly assumed away.

It is felt that the differences in the income-expenditure elasticities
for food which have been demonstrated are of such a magnitude that their
effects should be borne in mind in future studies. > In order to illustrate
the economic significance of the results, alternatifve projections of 1966
average weekly food expenditure will be presented for each household type.

- Our model will be based on two principal assumptions, and will be
used to estimate 1966 average weekly food expenditure for the 26 house-
hold types of this study under each of two alternative assumptions about
the'relevant income-expenditure elasticities for food. The two primary
assumptions of this naive‘model are that: (1) each household type shares
equally in increases in personal disposable income, and that (2) the dis-_
tribution of household types remains unchanged. _ The two alternative
assumptions about the relevant income elasticities are (A) the income-
expenditure elasticity for food is the same for all household types, and

(B) the income-expenditure elasticity for food differs between household

types.

'119

120

Disposable personal income will be assumed to increase by 62. 5
percent in the 1954-65 period. Since the elasticities of the household
types derived from the 1955 Survey are based on 1954 income, 1965 dise-
posable personal income will be assumed to govern1966 food expenditure.
This estimate of the increase in personal disposable income was obtained
from the projection of 1965 disposable personal income (in 1958 dollars)
of the "judgment model" of the Colm report. 1 The projected personal
disposable income was deflated through the use of the implicit personal
consumption expenditure deflator2 to 1954 dollars and compared with
1954 personal disposable income.3

The income elasticity under assumption (A) that the income
elasticity is the same for all household types, will be assumed to be . 29.
This is the estimate of incomeuexpenditure elasticity for food at home
and away for the urban United States developed from the data of the 1955
U.S.D.A. Survey, and is the available estimate which is most closely
comparable to those produced by this study.‘ The elasticities of this study
differ from this overall estimate of elasticity in that they are based on
expenditures for home consumption only and were estimated by an equation

form including total meals served as a variable. The elasticities of

 

1National Planning Association, Long-RanfiProjections for
Economic Growth: the American Economy in 1970 (Washington: National
Planning Association, 1959), pp. 30-31.

 

 

. 2U. S. Department of Commerce, "National Income and Product
Accounts of the United States in 1958, " Survey of Current Business,
XXXIX, (July, 1959), 40.

 

3U. S. Department of Commerce, U. 5.. Income and Output,"
A Suiplement to the Survey of Current Business (Washington: U. S.
Government Printing Office, 1958), pp. 144-45. -

 

 

4Marguerite C. Burk, "Some Analyses of Income-Food Relation-
ships, " Journal of the American Statistical Association, LIII, No. 284
(December, 1958), 915. The elasticity was estimated with the double-
log equation form (4. 2).

 

121

assumption (B) will be those estimated by the doublemlog equation form
(5. 2) for each of the household types.1

The results of the projection of average weekly food expenditures
with the naive model under the two alternative assumptions about income
elasticities are presented in Table 6. 1. It will be noted that although
there is substantial difference in the projected averages of weekly expend—is»
ture, there is little difference between the weighted overall averages of
expenditure under the two alternative assumptions. The overall weighted
average expenditure under the assumption of the same elasticity for all
household types is $24. 83. Under the assumption of differing elasticities,
the overall weighted average expenditure is $24. 65. This might seem to
indicate that the economic significance of differing elasticities between
household types is slight.

It will be remembered, however, that two rather restrictive assumpw
tions about changes in income distribution and in the distribution of house»
hold types were employed in the naive model. It was assumed that all
household types would share equally in the increases in income and that
the distribution of household types would remain unchanged. There is
little reason to believe that these conditions will actually be the case, or
that they are typical of past changes. The current projections of house-
hold numbers for 1965 by age of head presented in Table 1.4 provide little
basis for an assumption that the distribution of household types would

remain unchanged. . The evidence of changes in the distribution in recent

 

1We are thus employing cross-sectional elasticities rather than
time-series elasticities for both projections of average weekly expenditure.
- Although time-series elasticities would ordinarily be employed for such
projections, we will use the cross-sectional elasticities here as conserva—
tive estimates of the applicable time-series elasticities. Time-series
estimates of elasticities have beenlarger than the cross-sectional esti-
mates for similar groups in recent studies as pointed out by Marguerite
Burk, "Some Analyses of Income-Food Relationships, " pp. 919-21.

 

 

 

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124

years, whichis presented in Table 6. 2 raises further question as to the
validity of such an assumption. The table shows that the proportion of
households with children declined from 1940 until sometime after 1953,

as did the number of households with three or more children. Both propor—
tions then began to increase about 1953. In the period after 1953 the
proportion of households with three or more children increased rapidly

and by 1960 the proportion was substantially above that in 1940.

Under the naive model the two alternative assumptions about
elasticities produce estimates of average weekly expenditure which differ
fairly markedly for some household types, but differ little in the overall
weighted average. The differences between the estimates under assump-
tion (A) and (B) are given in Table 6. 1. If either primary assumption
(1) or (2) or both are relaxed to permit changes in the income distribution,
the distribution of household types or both, these differences become of
greater importance.

If we relax assumption (2) in light of the evidence of changes in the
distribution of household types which has been presented, we can see that
the naive‘model under assumption (A) will tend to underestimate overall
average weekly food expenditure as compared to a model in which the
proportion of larger household types, with their higher income elasticities,
is assumed to increase. ~ If we also relax assumption (1), and assume
that the larger household types receive a disproportionate share of the
increases in income, the tendency of the naive model under assumption
(A) to underestimate overall average weekly expenditure as compared
to our new model becomes even more marked.

In the absence of the necessary projections of income distribution
and numbers by household type the above somewhat intuitive demonstration
seems the best method available for showing the possible economic signifi-
cance of the differences in elasticities between household types found in

this study. . The above demonstration indicates that the economic

125

Table 6. 2 - Distribution of Husband-Wife Households by Number of Related

Children Under 18, Selected Years 1940-60.

 

Number of

 

 

 

 

Related Percent of Total Husband-Wife Households

Children b d

Under 18 194.0a 1947 1950a 1953C 1956 19608
None 40.9 42.3 42.2 41.2 39.6 38.7
One 24.1 23.5 23.3 22.0 20.0 19.3
Two 16.9 17.9 18.4 18.9 20.5 19.6
Three 8.6 16. 3f 8.8 10.1 10.8 12.1
Four or more 9.5 ---- 7.3 7.8 9.1 10.3
Total percent100.0 100.0 100.0 100.0 100.0 100.0
Husband-Wife

h°useh°lds as 76 78 78 76 76 75

a percent of

total hou s eholds

 

aU. S. Bureau of the Census, "Marital Status and Household Characteristics:
March 1950, " Current Population Reports, Series P-20, No. 33 (Washington:

Bureau of the Census, February 12, 1951), p.

b

 

15.

U. S. Bureau of the Census, "Households by Type, Composition and Hous-
March 1947, " Current Population Reports, Series

ing Characteristics:
P- 20,. No. 16 (Washington:

 

Bureau of the Census, May 5, 1948), p. 12.

c:U. S. Bureau of the Census, "Household and Family Characteristics:
April 1953, " Current Population Reports, Series P-20, No. 53 (Washington:

Bureau of the Census, Aprvi'l“11:7”1'954), p.

d

 

11.

U. S. Bureau of the Census, "Household and Family Characteristics:

March 1956, " Current POpulation Reports, Series P-20,. No. 75
Bureau of the Census, June 9, 1957), p.

(Washington:

11.

6U. S. Bureau of the Census, "Household and Family Characteristics:

March 1960, " Current Population Reports, Series P-20, No. 106
Bureau of the Census, January 9, 1961), p.

(Washington:

 

Three or more children.

18.

126

significance of the differences in elasticities between household types
increases as changes in the distribution of household types become more
marked, and as increases in income become more disproportionate
between household types. In a period of rapidly rising personal dispos-
able incomes, such as we are now experiencing, in which the distribution
of household types is also changing substantially, the results of this study
are of greater significance than they would be in a period in which income
and population were changing only slowly. In the absence of the required
projections it is difficult to evaluate the full economic significance of the
differences in elasticities which have been found in this study. It is felt.
however, that the results can be seen, from the somewhat intuitive
demonstration given, to be of real economic significance. The full
determination of this significance requires substantial further study, and
cannot be attempted here.

Another aspect of the economic significance of the results is their
implications for the estimation of consumption equivalence scales.
The techniques used by Brown and Prais and Houthakker to estimate scales
require the assumption of a single income elasticity for all household
types, as was indicated in Chapter 1. While such an assumption may
have been warranted for the British data employed in these two studies,
the results of this study indicate that such an assumption would not be
warranted for the data of the urban portion of the 1955 U.S. D.A. Household
Food Consumption Survey. If the assumption of a single income elasticity
for all household types was warranted for the 1955 data, the problem of
estimating equivalence scales would be eased substantially. The techniques
used to estimate scales in the two British studies do not appear to be
suitable for use with recent United States data except in so far as we are
willing to accept and take account of the errors introduced by the assump-
tion of a single income elasticity for all household types. It may well

be, however, that even though they do require this contrary to fact

127

assumption, the techniques of Brown and of Prais and Houthakker may
still provide the best equivalence scale estimates which can be obtained

at the present time.

Justification for Acceptance of the Hypothesis

 

The evidence produced relevant to a general hypothesis never
establishes its truth or falsity, but is intended rather to provide justifi-
cation for its acceptance or rejection. This study has brought forward
evidence relevant to the acceptance and rejection of the hypothesis that
significant differences exist between the elasticities of households of
differing size and composition. Evidence about the significance of these
differences in both a statistical and in an economic sense has been pre-
sented.

The evidence provided by the confidence intervals of the elasticities
appears to warrant fully the acceptance of the hypothesis in its statistical
sense. Statistically significant differences were shown to exist between
the elasticities of different household types, as estimated by three dif-
ferent equation forms. Differences were found to exist in a number of
instances within each of the groups of household type elasticities estimated
by a particular equation form. . The elasticities estimated for eighteen
household types by the linear equation form (5. 1) were found to be signifi-
cantly different from those of one or more other household types.

Nineteen household types were found to have elasticities which were sig-
nificantly different from those of one or more other household types for

the elasticities estimated by the double-log equation form (5. 2). Twenty-
three of the twenty-six household types were found to have elasticities
which were significantly different from those of at least one other household
type for the elasticities estimated by the semi-log equation form (5. 3).

In cases where most of the household types differed significantly only from

one other household type, it would be easy to explain away these differences

128

as due solely to a single unrepresentative sample. However, for each

of the equation forms there were several household types whose elasticie
ties differed significantly from those of a number of other household types,
far too many to make the appearance of unrepresentative samples seem a
likely explanation of the differences.

As usual, the evidence of the economic significance of the results
is somewhat less clear-cut. The illustrative projections presented did
indicate, however, that the naive model usually used in projections of
food expenditures and implicit in historical per capita consumption series
is least reliable in periods like the present when incomes and population
composition are changing rapidly. It is held, therefore, that the results
do have an economic significance under present conditions, which they
would not have in periods of relatively stable incomes and relatively
stable population composition.

The acceptance of the hypothesis is further supported by the similarity
of the results of this study to the general pattern which was noted in
previous studies. The one general pattern noted in the previous studies
discussed in Chapter I was the tendency for income elasticities to
increase with household size. This tendency was also noted in the
results of this study. The conformance of the results to the pattern
noted in previous studies is further evidence of their validity and thus

lends additional support to our decision to accept the hypothesis.

Further Studies Needed

 

The needed research most immediately suggested by this study is
an evaluation of the full economic significance of the results which have
been presented. Until detailed projections of numbers by households
type and income by household type are available or can be estimated

roughly, it will be impossible to determine the exact significance of the

129

differences which have been found to exist between the elasticities of

the different household types. ~ It is felt that the results of this study

raise serious questions about the validity of using certain projection
techniques employed in the past under present conditions. Full evaluation
of the current usefulness of these techniques requires a fuller exploration
of the economic significance of the results of this study.

The results of this study suggest a partial explanation of the changes
which have been noted in historical per capita food consumption series.
These changes in consumption over the years have been laid chiefly to _
"changes in tastes. " The results of this study indicate that these changes,
in consumption may be due, at least in part, to changes in the distribution
of household types and in the age-sex composition of the population.
Changes in the kinds of individuals making up the population may be as
important in explaining changes in per capita food consumption as actual
changes in the preferences of these different kinds of individuals. The
effects of changes in population composition on per capita consumption
are probably less dramatic for all food in the aggregate than they are
for many individual food categories. The income elasticity for milk
seems likely to differ greatly between household types with children and
those without, for example. While the results of this study provide some
evidence that changes over time in per capita food consumption can be
explainedin part by changes in the distribution of household types and in
population composition, its evidence cannot be considered conclusive.
Further studies are needed to evaluate fully the influence of changes in
population characteristics on per capita consumption of all food in the
aggregate, and on per capita consumption of particular foods.

The difficulties experienced in handling the income variable in the
course of this study indicate that a better definition of income is needed
for survey work on household budgets. A definition is required which

will clearly separate the business and household accounts of the

130

self—employed and will not permit the reporting of zero or negative
incomes along with a positive level of expenditure.

The variables included in this study generally explained less than
half of the variation in food expenditure for a particular household type.
Recent changes in tastes and consumption behavior may have made new
variables, not employed in previous studies, relevant. Theoretical and
empirical work is needed to identify these variables. It may be the case,
however, that with increasing discretionary income the forces acting on
consumption have become too complex to be described by the functional
forms which have been employed in the past. Other methods of describ-
ing of the relationship between expenditure and income plus other
determining variables should be investigated; elasticities and single-
equation models may be becoming altogether inadequate to describe the
increasing complexity of the forces influencing household consumption
behavior.

. In addition to the effects of household composition on expenditure
behavior, certain other effects of the economic and family life cycle
clearly appear to merit further study. One such study which seems
indicated in this area is the effects of changes in the stock of consumer
durables and other assets on household expenditure behavior. - It may
well be that the major inadequacy of the income variable as usually
formulated lies in the vastly different asset structure with which any

given income may be associated over the family and economic life cycle.

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138

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APPENDIX I

THE 1955 HOUSEHOLD FOOD CONSUMPTION
SURVEY SAMPLE‘I

The data which is utilized in this study was drawn from the urban
portion of the United States Department of Agriculture's 1955 Household
Food Consumption Survey. The purpose of the U. S. D.A. study was to
collect current information on patterns of food consumption, expenditures,
dietary levels and household food practices. The study includes data
from 6, 060 households in which at least one member of the household
ate 10 or more meals from household food supplies in the preceding week.
Of the 6, 060 households from which complete interview schedules were
taken, 4, 556 were in the basic national sample. The basic national
sample was supplemented by interviews of 1, 504 farm-operator house-=-
holds, which were selected in the same manner as the basic national
sample, but were drawn from rural areas only. The interviews were
collected in the months of April, May and June, 1955.

Only households in which one member ate 10 or more meals in the
preceding week were considered eligible. The 4 percent of the population
whichlives in non-housekeeping units, such as rooming houses, institu-
tions and prisons, is thus omitted from the study. Of the 5, 927 dwelling
units selected for the basic sample, 5, 625 were found to be occupied
and 5, 207 were found to have served 10 or more meals to at least one
person in the previous week. . Complete schedules were collected for

4, 605 of these eligible households in the basic sample, the other' 732

 

r

1This appendix summarizes the description of the survey and the
sampling procedures employed given in U. S. Department of Agriculture,
Food Consumption of Households in the United States ("Household Food
Consumption Survey 1955, " Report No. 1; Washington: U. S. Government
Printing Office, 1956),, pp. 1-3, 186-195.

 

139

140

eligible households had no one at home or refused to supply the desired
information. Only 91 percent of the urban households selected for the
basic sample were found to be eligible, of these 3, 276 eligible households
2, 832 households actually participated in the survey by supplying the
information requested.

The survey employed the "recall-list" method and used specially
trained interviewers to help respondents recall the quantities of food used
during the week and the amounts paid for purchased items. The information
collected was on food consumed or used up, rather than on purchases.

In addition to this information on the quantities used at home for all food
items in the previous week, information was collected on the number of
meals eaten at home and away by each individual in the household (and
expenditures on food eaten away from home.

The basic sample was a national, self-weighting, area, probability
sample. It was drawn by first separating metropolitan areas with a
population of over 50, 000 from the non-metropolitan areas. The 168
metropolitan areas were divided into five size classes on the basis of
their population in the 1950 Census. Each of the 8 metropolitan areas
in the over 2 million population size Class was regarded as a
separate stratum. The other metropolitan areas were grouped into 3 to
8 geographic areas within each of the remaining four size classes. Each
of these groups of metropolitan areas had a population of approximately
2 million and were made up, with few exceptions, of varying combi-
nations of states within the four Census regions, Northeast, North Central,
South and West. This grouping produced 32 metropolitan area strata,

8 of which consisted of a single major'metropolitan area, with the re-
maining 24 strata each consisting of a group smaller metropolitan areas
of the same approximate size, all located within the same region.

In each of the 8 major metropolitan area strata, cities were classie-

fied by size. One city was selected from each size stratum, for a total

141

of 23 cities. A total of 24 cities was selected from the other 20 metro-
politan area strata. The 45 cities selected were chosen with a probability
proportional to their 1950 population.

The 605 cities with populations between 10, 000 and 50, 000 outside
the standard metropolitan areas were grouped within Census regions
into 15 strata, averaging about 85 thousand people per strata. One city
was selected from each of these 15 strata with probability proportional
to its 1950 population. These 15 strata for cities outside standard metro-
politan areas and the 45 strata for cities within standard metropolitan
areas provided a total of 60 cities for the national sample.

In the 32 standard metropolitan areas, the 81 counties (excluding
cities of over 10, 000) were grouped into 33 strata. The remaining 2, 697
counties outside the standard metropolitan areas were grouped into 82
strata of contiguous economic areas, each having about 650, 000 persons.
One county was selected from each of these 115 county strata. A total of
60 cities and 115 counties were thus selected for the sample.

Within the cities, sample segments were selected by numbering all
the segments set up within the city and drawing every n-th one with prob-
ability proportional to the number of dwelling units in the segment.
Sample segments were selected randomly in each county from a listing of
Census enumeration districts which excluded places of 10, 000 or more
population. ~ One smaller segment was selected with equal probability
from each of these enumeration districts. A total of 2, 000 segments were
selected from the 60 cities and 115 counties in the sample, of these 1, 527
were allocated to the basic sample.

The dwelling units to be visited within each segment were selected
from lists made up in a specified geographic order. A random number
was used to select the first sample dwelling unit to be interviewed, it and
every n-th succeeding unit were then designated for interview. The number

"n" was determined by dividing the expected number of dwelling units in

142

the segments by the expected number of units to be visited. Each segment
was expected to yield 3 interviews. No substitutes were provided for
households which were not eligible to participate, or which were absent

or refused to participate. In urban areas, interviewers were required

to make as many as four return visits if necessary, in order to make
original contact.

The "urban" households whose behavior is considered in this thesis
are those in the U.S. D.A. survey which were located in communities of
2, 500 or more population, or in fringe areas around cities of 50, 000 or
more. This includes all the households in the sample in the 60 cities of
10, 000 or more, all those in the 33 county strata made up of areas lying
within the standard metropolitan areas but outside cities of 10, 000 or
more population, and all the households within the remaining 82 county
strata which were located in cities of 2, 500 to 10, 000 population.

The survey sample may be appraised by comparing it with Census
data. The distribution of households by number of persons, the proportion
of non-white households and the proportion owning television sets were
found to be much alike. In the urban sample, the chief discrepancy in
comparison to Census data was the over representation of persons under
15 years of age at the expense of those between 15 and 29 years. In all
other respects the nonfarm households were considered to be well repre-
sented.

About 13 percent of the eligible urban households failed to participate
in the survey by supplying the requested information. The resulting non—
response bias was considered to be small on the basis of comparisons of
the answers to certain questions obtained from those classified as non-
respondents with those obtained from participating households, and the
comparatively small proportion of non-respondents. The proportion of
non-participants to participants was smaller than average in the South and

larger in the North Central region. The nonuparticipating households had

143

fewer husband-wife households and fewer household members. The
members of the non-participating households included fewer children and
more adults over 50. A higher proportion of the housewives in the non»
participating households were employed.

- Income was not reported by about 9 percent of the households which
participated in the survey. Some of these households were not asked for
their income in the previous year, 1954, since they were only recently
established. Others refused to provide the information on income, but
answered all other questions. The resulting bias was not investigated;
it was expected that the group of households not asked showed the charactere
istics of recent establishment and that those who refused to provide the
information were, like the eligible non-participants, not. different enough

or numberous enough to distort the total results.

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