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PS1 Solution.pdf - Tutorials in International...

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Tutorials in International MacroeconomicsPS1: Intertemporal approach to the current account1Model solution with growth shocksConsider the baseline model from the lecture which assumes quadratic consumption utilityand (1 +r)β= 1.Assume that output follows a growth process, i.e.{Δyt}is an AR(1)process with decay coefficient 0< ρ <1.1. Set up the household’s problem and derive the Euler equation.2. State the transversality condition.3. Derive the policy function for consumptionct=f(yt, yt-1, dt-1) by following the samesteps as in the lecture. Why does the policy function for consumption depend onyt-1?4. Also state the policy function for debtdtand for the current accountcat.2Guess and verifyConsider the same set-up as in Problem 1 on this Problem Set. As in the lecture, you hadobtained the policy function for consumption by using the intertemporal resource constraintof the economy. Another way of derivingfis called the “guess and verify” approach, whichworks as follows.1. Guess that the policy function is of the formct=ζ0+ζ1yt+ζ2yt-1+ζ3dt-1,for a set of unknown coefficients{ζ0, ζ1, ζ2, ζ3}.2. Insert the guess into the model equilibrium conditions (the one-period resource con-straint and the Euler equation)3. Choose coefficients{ζ0, ζ1, ζ2, ζ3}such that the model equilibrium conditions are alwayssatisfied. You should obtain the same coefficients as in the policy function of Problem1, which tells you that you have obtained the correct solution of the model.3Anticipated endowmentsConsider again the same model as in Problems 1-2 on this Problem Set, but now assume that{yt}follows the processyt=ρyt-1+εt-1,that is, an AR(1) but the shock entering from periodt-1. This specification implies thatendowment shocksytare known one period in advance!

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Term
Spring
Professor
Kunst, Robert
Tags
Macroeconomics, current account, Leonhard Euler

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