Distinguish the state and control variables and construct the Bellman equation.
economics
Description
Assignment 1
Given this environment solve the follow questions.
1. Distinguish the state and control variables and construct the Bellman equation.
2. Derive the system of equations to solve the model.
3. Solve the stationary state of K, H, Y, C, r.
4. Derive the Log-linear version of the model.
5. Discuss the method of solving the model to estimate the technological shock.
6. Assume β = 0.99, δ = 0.025, θ = 0.36. Calibrate other parameters needed to solve the model.
7. Estimate the standard errors of Yt , Ct , Ht , rt and It and show the relative standard of these variables with respect to output. Assume Hansen’s model of RBC with labour where Households sign contracts with firms to provide h0 units of labour in period t with probability αt . Since αth0 hours of work are being provided to the market, labour demanded by the firms is ht = αth0. Firms produce using the production function yt = λtk θ t h 1−θ t and pay the factors as per their marginal productivities. Technology follows the stochastic process, ln λt+1 = γ ln λt + εt+1. Given initial values for k0 and λ0, an infinitely lived household maximizes
