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hw-06-sol

hw-06-sol - Homework 6 Solution Graduate Macroeconomics...

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Homework 6. Solution Graduate Macroeconomics. Viktor Tsyrennikov Question 1. Your task is to solve a model in which consumption growth process resembles that in the data and compare the model’s predictions about the equity premium with the data. Model environment is as follows. Uncertainly is modeled by a stochastic shock λ t that follows a two-state first-order Markov process with a transition matrix Π. That is π ( λ t | λ 0 ) = π ( λ t | λ t - 1 ) ...π ( λ 2 | λ 1 ) π ( λ 1 | λ 0 ) . An agent’s preferences are given by U ( c ) = E [ summationdisplay t =0 β t u ( c t ) | λ 0 ] = summationdisplay t =0 summationdisplay λ t β t π ( λ t | λ 0 ) u ( c t ( λ t )) . Assume that u ( c ) = c 1 - γ / (1 - γ ). The agent faces the (sequential) budget constraint: c t ( λ t ) + summationdisplay λ t +1 Q t ( λ t +1 | λ t ) a t +1 ( λ t +1 ) lessorequalslant y t ( λ t ) + a t ( λ t ) , where income of the agent is given by y t ( λ t ) = λ t ...λ 2 λ 1 , λ t , t greaterorequalslant 1 and y 0 ( λ 0 ) = 1. Assume annual frequency. a) Construct the transition matrix and the two states to match the fol- lowing data facts: 1 M1. Expected growth rate is 0.018%. M2. Std. deviation of the growth rate is 0.035%.

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hw-06-sol - Homework 6 Solution Graduate Macroeconomics...

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