1.B HP filter and plot US quarterly (log) GDP. Store it in postcript or pdf. Compute the same table as in the Cooley book for those 4 variables using data up to 2003:4 or later. 1.C Calculate a linear trend and decompose log GDP in the linear trend the hp trend and the hp residual.
1.D Plot the growth rates together with the hp residual and comment the differences.
1.E Compute a VAR of those 4 variables and plot the impulse responses. Make sure that you explicitly state what are the identifying assumptions that you make.
Write a routine that linearly interpolates. Apply it by storing the value of exp (x) between 0 and 1. in intervals of .1 and assessing the value by interpolation in intervals of .05. Plot the function and what results from using approximation.
What about with Cobb-Douglas ( r =1).
Note that Labor share = w*N/Y, and that under competition w=(dY/dN).
6.A Use NIPA and the logic of the imputation of income to either labor or capital found in Cooley and Prescott (1996) to compute an updated series of the Solow residual.
6.B Estimate a univariate process for the Solow residual. Make sure that you argue forcefully for your specification.
6.C Compute a bivariate VAR with the Solow residual and output and a trivariate VAR with the Solow residual, output and hours worked.
7.B Solve for the steady state. Be lazy and use software to get the derivatives and dynare to get the steady state.
7.C Answer the question using dynare.
7.D Reassess your answer with data since 82. Get labor data from Manovskii, here and described here of labor in the CPS and reestimate your answer.
7.E Redo your answer posing TFP shocks and shocks to the relative price of investment.
8.B Pose a version of the model with the same steady state calibration than in Question 7 but now estimate processes for three independent shocks to hours worked in the utility to patience and to productivity by ML (or by Bayesian methods).
8.C Redo the estimation adding labor share and the Frisch elasticity of labor to the parameters that govern the three shocks (there are 6 of those as we assume them to be independent).
8.D Compare the answers obtained in 8.A, 8.B, and 8.C.
9.B Write a f90 or f95 code that computes a piecewise linear approximation to the decision rule of capital for the optimal capital accumulation function. Use collocation (or the Dirac measures at the grid points) to weigh the errors. Plot it.
9.C Compare it with one that results from doing the same approximation with only 7 grid points over the same range. Was it worth to go from 7 to 21 grid points?
10.B Compute the steady state of this economy. Use both an approximation to the cdf. And a huge sample.
10.C Compute and plot the Lorenz curve for earnings.
11.A Compute the interest rate and wage that constitute a stationary equilibrium of a close economy.
11.B Set risk aversion to 2, the Frisch elasticity of labor to .7, labor share to 2/3, and depreciation to .1. Then find parameters for the discount rate, the coefficient of labor in the utility and the constant that multiplies the production funtion that yield a closed economy equilibrium with a wealth to output ratio of 4, a value of output of 1 and average fraction of time working of .3.
12.A Take your favorite version of the neclassical growth model. Calculate its steady state.
12.B Now suppose that by surprise, TFP doubles. Compute the new steady state and the transition from the old to the new, assuming that it has completed in 200 periods. Compute such transition three ways and specify how long it takes to solve it each way. The first way is a system of 200 equations and unknowns, the second by guessing first period capital and hoping that the system gets the right capital in period 201, and by guessing capital in the period 200 hoping that if you moved backward you obtain the right initial capital.