Although log models as shown in Eq. (11.6.12) often reduce heteroscedasticity, one has to pay careful attention

Question:

Although log models as shown in Eq. (11.6.12) often reduce heteroscedasticity, one has to pay careful attention to the properties of the disturbance term of such models. For example, the model

Y_i = β₁X^β2_i u_i ……………………………………………. (1)

can be written as

ln Y_i = ln β₁ + β₂ ln X_i + ln u_i …………………………… (2)

a. If ln u_i is to have zero expectation, what must be the distribution of u_i?

b. If E(u_i) = 1, will E(ln u_i) = 0? Why or why not?

c. If E(ln u_i) is not zero, what can be done to make it zero?

Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...