Exercise 16.9. Consider the stochastic permanent income hypothesis model studied in Section 16.5. Suppose that instead of being distributed independently, w (t) follows a Markov chain. Show that (16.24) still holds. Now suppose that u

(c) takes a quadratic form and assume that the econometrician incorrectly believes that w (t) is independently distributed, so that the individual has superior information relative to the econometrician. Show that a regression of consumption growth on past income realizations will still lead to a zero coefficient (thus the excess sensitivity test will not reject). [Hint: make use of the law of iterated expectations, which states that if Ω is an information set that is finer than Ω0 and z is a random variable, then E[E[z | Ω] | Ω0 ] = E[z | Ω0 ]].