Use the data for the demand for chicken given in Exercise 7.19. Suppose you are told that the true demand function is

ln Y_t = β₁ + β₂ ln X_2t + β₃ ln X_3t + β₆ ln X_6t + u_t                                            (1)

but you think differently and estimate the following demand function:

ln Y_t = α₁ + α₂ ln X_2t + α₃ ln X_3t + v_t                                                              (2)

where Y = per capita consumption of chickens (lb)

X₂ = real disposable per capita income

X₃ = real retail price of chickens

X₆ = composite real price of chicken substitutes

a. Carry out RESET and LM tests of specification errors, assuming the demand function (1) just given is the truth.

b. Suppose β₆ in Eq. (1) turns out to be statistically insignificant. Does that mean there is no specification error if we fit Eq. (2) to the data?

c. If β₆ turns out to be insignificant, does that mean one should not introduce the price of a substitute product(s) as an argument in the demand function?