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 the following table,

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

Now consider the following demand functions:

ln Y_t = α₁ + α₂ ln X_2t + α₃ ln X_3t + u_t.............................................(1)
ln Y_t = γ₁ + γ₂ ln X_2t + γ₃ ln X_3t + γ₄ ln X_4t + u_t ............................(2)
ln Y_t = λ₁ + λ₂ ln X_2t + λ₃ ln X_3t + λ₄ ln X_5t + u_t ............................(3)
ln Y_t = θ₁ + θ₂ ln X_2t + θ₃ ln X_3t + θ₄ ln X_4t + θ₅ ln X_5t + u_t .........(4)
ln Y_t = β₁ + β₂ ln X_2t + β₃ ln X_3t + β₄ ln X_6t + u_t .......................... (5)

From microeconomic theory it is known that the demand for a commodity 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 X_2t and ln X_3t in these models?
c. What is the difference between specifications (2) and (4)?
d. What problems do you foresee if you adopt specification (4)?

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 €œcorrect€ demand function. Estimate the parameters of this model, obtain their standard errors, and R², RÌ…² , and modified R². Interpret your results.
h. Now suppose you run the €œincorrect€ model (2). Assess the consequences of this mis-specification by considering the values of γ₂ and γ₃ in relation to β₂ and β₃, respectively.

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Year X2 Xз X4 X5 X6 27.8 50.7 52.0 1960 397.5 42.2 78.3 65.8 1961 29.9 29.8 413.3 38.1 79.2 66.9 79.2 79.2 67.8 1962 439.2 40.3 54.0 1963 30.8 459.7 39.5 55.3 69.6 31.2 37.3 1964 492.9 54.7 77.4 68.7 63.7 80.2 73.6 1965 33.3 528.6 38.1 1966 35.6 560.3 39.3 69.8 80.4 76.3 36.4 1967 624.6 37.8 65.9 83.9 77.2 64.5 78.1 1968 36.7 666.4 38.4 85.5 1969 38.4 717.8 40.1 70.0 93.7 84.7 1970 768.2 40.4 38.6 73.2 106.1 93.3 89.7 1971 40.3 843.3 39.8 67.8 104.8 39.7 1972 41.8 911.6 79.1 114.0 100.7 113.5 1973 40.4 931.1 52.1 95.4 124.1 1974 40.7 1,021.5 1,165.9 1,349.6 1,449.4 1,575.5 1,759.1 1,994.2 2,258.1 2,478.7 48.9 94.2 127.6 115.3 1975 40.1 58.3 123.5 142.9 136.7 42.7 57.9 1976 129.9 143.6 139.2 1977 44.1 56.5 117.6 139.2 132.0 1978 46.7 63.7 130.9 165.5 132.1 1979 50.6 61.6 129.8 203.3 154.4 50.1 219.6 1980 58.9 128.0 174.9 1981 51.7 66.4 141.0 221.6 180.8 1982 52.9 70.4 168.2 232.6 189.4