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ECON4570/6560 : Problem Set 4 Due by 05:00pm on Aug 17, 2021. 1. Consider the instrumental variable regression model Yi = β0 + β1Xi + β2Wi + ui >where Xi is correlated with ui and Zi is an instrument. Suppose that E(ui|Wi) = 0; (Xi,Wi, Zi, Yi) are i.i.d. observations drawn from the same population, and large outliers are unlikely: the variables (Xi,Wi, Zi, Yi) have nonzero finite fourth moments. Which IV assumption is not satisfied when: (a) Zi is independent of (Xi,Wi, Yi) (b) Zi = Wi. (c) Wi = 1 for all i (d) Zi = Xi. 2. Suppose we have the following AR(2) process yt = 0.3yt−1 + 0.1yt−2 + εt, where εt v WN(0, 1) (a) Determine whether yt is weakly stationary? Please justify your an- swer. (b) Compute E(yt), V ar(yt) and Cov(yt, yt−k) for k = 1, 2. (c) Compute the ACF ρk for k = 1, 2. (d) Compute the PACF akk for k = 1, 2. 3. Suppose we have the following AR(1) process yt = 2 + yt−1 + εt, where εt v WN(0, 1) for all t, y0 v WN(0, 1) and is independent of εt for all t, (a) Compute E(yt), V ar(yt) and Cov(yt, yt−k) for k = 1, 2. (b) Compute the ACF ρk for k = 1, 2. (c) Compute the PACF akk for k = 1, 2. 1
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