The name is absent

TABLE 1. Partial Regression Coefficients and
Standard Errors for Different Beef Expenditure
Categories, Griffin Consumer Panel, 1975-1977

Note: Numbers in parentheses are estimated standard er-
rors.

* Significant at the 0.10 significance level.

** Significant at the 0.05 significance level.

^a Variable identifications are: H = household size; H₁ = 1;
H₂ = 3; D_i = 1, if H > H₂, and = 0, otherwise, Y = household
income; Yi = 1,285; Y₂ = 10,000; Y₃ = 25,000; Si = 1, if Y ⅛
Y₂, and - 0, otherwise; S₂ = 1, if Y ⅛ Y₃, and = 0, otherwise.

ferent from quadratic or linear splines for each
beef expenditure category. The results indicate
that none of the cubic segments is statistically
significant at the 0.10 significance level. Except
for ground beef, the results also suggest that the
quadratic segments for income are not signifi-
cantly different from the linear segments. Thus,
the additive quadratic splines in both income and
household size were selected as the statistically
appropriate model for ground beef expenditure.
For the other beef expenditures categories (i.e.,
fresh beef, beef roasts, and beef steaks), the
statistically appropriate model incorporates a
quadratic spline in household size and a linear
spline in household income.⁷

The coefficient of multiple determination, R²,
indicates that the spline function fits the data rea-
sonably well (Table 1). The F-Statistic of each
regression suggests that variations in household
expenditure for beef accounted for by level of
income and household size were significant at the
0.001 significance level. Partial R²s calculated for
income and household size for each expenditure
equation were all highly significant; however, the

TABLE 2. Coefficients of Partial Determina-
tion, Partial R², for Different Beef Expenditure
Categories by Household Income and Size, Grif-
fin ConsumerPanel, 1975-1977

Note: Numbers in parentheses are calculated F-values. All
the partial R²s are significant at the 0.05 significance level.

relative contributions of household income and
size in explaining household beef expenditures
vary among different equations (Table 2).⁸ The
results show that household size is of major im-
portance in determining the levels of household
beef expenditures, with the exception of beef
steaks. This observation is consistent with Rog-
ers and Green’s findings based on the 1972-73
BLS expenditure survey. Comparing the 1972-73
and 1960-61 BLS survey data, Rogers and Green
observe that income has become less important
in explaining the level of expenditures for food
consumed at home.

Perhaps the most revealing results were the
contrasts in expenditure patterns for the different
types of beef purchased. The flexibility of the
spline functions facilitates the examination of the
structural differences for different income and
household size groups. For a given income level,
expenditures for beef generally increase as the
size of the household increases, suggesting the
prevalence of economies of scale. Since all the
quadratic terms in the interval relating to house-
holds with more than three persons have the
negative sign, economies of scale in beef expen-
ditures as household size increases above three is
indicated.⁹ These changes are statistically sig-
nificant for fresh beef and ground beef. More-
over, the number of households with 3 persons or
less is approximately equal to the number with 4
persons or more in the sample. However, larger
households (i.e., H>3), on average, consist of
3.6 adults and teenagers, and 1.6 younger chil-
dren (under 10 years of age). In contrast, house-
holds with 3 or less persons, on average, consist
of 2 adults and teenagers, and 0.2 younger chil-
dren. Thus, the fact that younger children eat
less than teenagers and adults may also contrib-
ute to the decreasing rate of increase in beef ex-
penditures as household size increases (Huang
and Raunikar). Also, this may be attributed in
part to the flexibility of serving ground beef and
beef roasts in family meals as compared with
serving beef steaks.

⁷AIthough the polynomial pieces in income were found to be of linear form, the improvement in goodness of fit of the present formulation was found to be statistically
significant over the form in which income is treated as an additive linear variable.

^sInstead of examining the significance of individual segments of income and household size, partial R²s that compare residual sum of squares associated with spline
functions in income and household size, respectively, are appropriate measures for determining the relative contributions of income and household size in explaining
household beef expenditure variations.

⁹Prevaous research suggests that the impact of an additional member on household food expenditures decreases with an increase in household size ( Buse and Salathe; Prais
and Houthakker; Price). This effect is generally referred to as economies of scale in household food expenditure. Economies of scale in food expenditure may arise in the
purchasing, storage, and preparation of foods, and the effect is approximated by the square of the number of persons in the household. Thus, the negative quadratic terms of
household size greater than three suggest that for larger households, beef expenditures increased at a decreasing rate with the addition of household members.

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