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 β̂₆ 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 β̂₆ 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?