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7.19. The demand for chicken in the United States, 1960–1982. To study the per capita consumption of chicken in the United States, you are given the data in Table 7.9,
where Y = per capita consumption of chickens, lb X2 = real disposable income per capita, $ X3 = real retail price of chicken per lb, ¢
X4 = real retail price of pork per lb, ¢
X5 = real retail price of beef per lb, ¢
X6 = composite real price of chicken substitutes per lb, ¢, which is a weighted average of the real retail prices per lb of pork and beef, the weights being the relative consumptions of beef and
pork in total beef and pork consumption
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TABLE7.8 |
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Defense |
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U.S. military |
Aerospace |
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budget |
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sales/ |
industry |
Conflicts |
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Year |
outlays, Y |
GNP, X2 |
assistance, X3 |
sales, X4 |
100,000+, X5 |
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1962 |
51.1 |
560.3 |
0.6 |
16.0 |
0 |
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1963 |
52.3 |
590.5 |
0.9 |
16.4 |
0 |
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1964 |
53.6 |
632.4 |
1.1 |
16.7 |
0 |
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1965 |
49.6 |
684.9 |
1.4 |
17.0 |
1 |
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1966 |
56.8 |
749.9 |
1.6 |
20.2 |
1 |
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1967 |
70.1 |
793.9 |
1.0 |
23.4 |
1 |
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1968 |
80.5 |
865.0 |
0.8 |
25.6 |
1 |
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1969 |
81.2 |
931.4 |
1.5 |
24.6 |
1 |
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1970 |
80.3 |
992.7 |
1.0 |
24.8 |
1 |
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1971 |
77.7 |
1,077.6 |
1.5 |
21.7 |
1 |
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1972 |
78.3 |
1,185.9 |
2.95 |
21.5 |
1 |
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1973 |
74.5 |
1,326.4 |
4.8 |
24.3 |
0 |
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1974 |
77.8 |
1,434.2 |
10.3 |
26.8 |
0 |
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1975 |
85.6 |
1,549.2 |
16.0 |
29.5 |
0 |
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1976 |
89.4 |
1,718.0 |
14.7 |
30.4 |
0 |
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1977 |
97.5 |
1,918.3 |
8.3 |
33.3 |
0 |
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1978 |
105.2 |
2,163.9 |
11.0 |
38.0 |
0 |
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1979 |
117.7 |
2,417.8 |
13.0 |
46.2 |
0 |
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1980 |
135.9 |
2,633.1 |
15.3 |
57.6 |
0 |
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1981 |
162.1 |
2,937.7 |
18.0 |
68.9 |
0 |
Source: The data were collected by Albert Lucchino from various government publications.
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Source: Data on Y are from Citibase and on X2 through X6 are from the U.S. Department of Agriculture. I am indebted to Robert J. Fisher for collecting the data and for the statistical analysis.
Note: The real prices were obtained by dividing the nominal prices by the Consumer Price Index for food.
Now consider the following demand functions:
ln Yt = α1 + α2 ln X2t + α3 ln X3t + ut (1)
ln Yt = γ1 + γ2 ln X2t + γ3 ln X3t + γ4 ln X4t + ut (2)
ln Yt = λ1 + λ2 ln X2t + λ3 ln X3t + λ4 ln X5t + ut (3) ln Yt = θ1 + θ2 ln X2t + θ3 ln X3t + θ4 ln X4t + θ5 ln X5t + ut (4) ln Yt = β1 + β2 ln X2t + β3 ln X3t + β4 ln X6t + ut (5)
From microeconomic theory it is known that the demand for a commod- ity generally depends on the real income of the consumer, the real price of the commodity, and the real prices of competing or complementary commodities. In view of these considerations, answer the following questions.
a. Which demand function among the ones given here would you choose, and why?
b. How would you interpret the coefficients of ln X2t and ln X3t in these models?
c. What is the difference between specifications (2) and (4)?
d. What problems do you foresee if you adopt specification (4)? (Hint: Prices of both pork and beef are included along with the price of chicken.)
e. Since specification (5) includes the composite price of beef and pork, would you prefer the demand function (5) to the function (4)? Why?
f. Are pork and/or beef competing or substitute products to chicken? How do you know?
g. Assume function (5) is the “correct” demand function. Estimate the parameters of this model, obtain their standard errors, and R2 , R¯ 2 , and
modified R2 . Interpret your results.
h. Now suppose you run the “incorrect” model (2). Assess the conse- quences of this mis-specification by considering the values of γ2 and γ3 in relation to β2 and β3 , respectively. (Hint: Pay attention to the dis- cussion in Section 7.7.)