3. {30 points) Consider the consumption function regression AC: 2 330 + {313er + 262'} + 5r where Ac} 2 A h1(Ct) denotes real consumption growth, A}; = A 1110c?) represents real income growth and 3'} represents the real interest rate. Let 1: denote the information set at time t, which contains current and lagged values of all variables, and assume that 3: is a martingale difference sequence so that E[:t |If_1] = 0 . The pure form of the permanent income hypothesis (PIH) has 331 : 162 : 0. The PIH with a non-constant real interest rate has ,81 22' 0 . If some part of the population are current income consumers then ,81 2: 0