Exercise 16.8. (1) Consider the stochastic permanent income hypothesis model studied in Section 16.5 and assume that the interest rate r is no longer constant, but is equal to r (t) > 0 at time t. Derive the equivalent of (16.24) in this case. Show that excess sensitivity tests can be applied in this case as well. (2) Now suppose that r (t) is a random variable taking one of finitely many values, r1, ..., rJ , and to simplify the analysis, suppose that the realizations of the interest rate are independent over time. Derive the equivalent of (16.24) in this case. Show that excess sensitivity tests can be applied in this case as well.