Homeworks for Econ 8185 Quantitative Macro, Fall of 2010

There may be preliminary versions of future homeworks in this page. I may change them until the day I state in the course homepage that the relevant homework batch is ready.
  • First Homework batch. Due Wed September 14th. Name them sept_14_h1, sept_15_h2 and so on.
    1. Data manipulation.

      1.A Fetch and plot US quarterly GDP Investment plus durables plus net exports, non-durables plus services, and aggregate hours both from CPS and from the firm survey (see Cooley chapter 1, page 30). Store it in pdf, eps, and emf or wmf formats.

      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.

    2. Interpolation.

      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.

    3. Solving Equations of one unknown.

      (Parts of Homework 1 of Chapter 5 of Judd's book.) Solve sin 2

      x- 2x=0 using bisection between x 0 =-5 and x 1 =5 (If this interval is a bad one change it).

    4. Production Function manipulation.

      Compute labor factor shares with a CES production function

      Y=[ q K r +(1- q )N r )] 1/ r

      when K=N=1, and K=2, N=1. Are they the same?

      What about with Cobb-Douglas ( r =1).

      Note that Labor share = w*N/Y, and that under competition w=(dY/dN).

    5. Using symbolic software to obtain derivatives.

      Write in two equations in the capital-labor ratio and total labor the steady state conditions of the growth model with log utility and constant Frisch elasticity of labor (look up what this means if necessary). Use the CES production function with depreciation. Use mathematica or maple or matlab with the symbolic toolbox or even sciword if this does the job.

  • Second Homework batch. Business Cycles Questions. Due Wed September 21th.

    1. Computation of the Solow Residual.

      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.

  • Third Homework batch. Business Cycles Questions. Due Wed September 21.

    1. Use a standard growth model suitable to measure the contribution of productivity shocks as represented by the Solow residual to movements in output and hours worked between 1954-2010.

      7.A Specify some steady targets that your model should satisfy.

      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 and the estimated process for the Solow residual.

      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 alternative processes for the Solow residual (random walk with drift, AR(2)).
  • Fourth Homework batch. Business Cycles Questions II. Due Wed September 28.

    1. Using a growth model with separable utility.

      8.A Specify the steady targets that your model should satisfy. Argue your case thoroughly.

      8.B Compute you answer using dynare.

      8.C Explore alternative specifications of the calibration targets based on some alternative logic and report your answers. What matters.

      8.D Redo your answer posing TFP shocks and shocks to the relative price of investment (which you have to compute using mostly Violante and coauthor's series).
  • Fifth Homework batch. Econometrics and Global Approximation. Due Wed Oct 5.

    1. Comparison of calibration and estimation.

      9.A Pose a version of the model with the same steady state calibration than in Question 8 but now estimate processes for two independent shocks. One to hours worked in the utility function and another to the Solow residual using data of output and hours by using ML or by Bayesian methods.

      9.B So it again with three independent shocks. One to hours worked in the utility function, another to patience, and another to productivity using data of output the Solow residual and hours by using ML or by Bayesian methods.

      9.C Redo the estimation adding labor share and the Frisch elasticity of labor to the parameters that govern the three shocks.

      9.D Compare the answers obtained in 9.A, 9.B, and 9.C.

    1. Global approximation.

      10.A Take a deterministic version of the growth model without leisure. Find the steady state and construct a 21 point grid from half to two times the steady state of capital. Do it in logs.

      10.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. If you insist, use some alternative global solution method.

      10.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.D Redo homeworks 8, 9, or 10 using this other solution method.
  • Sixth Homework batch. The Aiyagari Economy I Due Wed Oct 26.

    1. The household problem

      11.A Write fortran (or C, but better f95) code for the problem that a household solves in an Aiyagari economy with leisure and a Markov shock to earnings. Use the calibration of say my paper with Ana Casta~neda and Javier Diaz-Gimenez (or another is you prefer it). Make sure that in your parameterization of the problem you choose an arbitrary value for the wage and a value for the interest rate that is small (smaller than (1/beta)-1). Use either Chebyshev or piecewise linear in the Euler equations or splines in the value functions. Use only proportional labor taxes that pay for social security transfers. Use arbitrary values for this.

      11.B Compute the steady state of this economy. Use both an approximation to the cdf. And a huge sample.

      11.C Compute and plot the Lorenz curve for earnings.

  • Seventh Homework batch. General equilibrium and Transition issues in the Aiyagari Economy Due Wed Nov 16.

    1. General equilibrium and Calibration.

      12.A Compute the interest rate and wage that constitute a stationary equilibrium of a close economy.

      12.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.C On top of the previous target, pose a 4 state Markov chain (15 parameters 3 for levels of productivity and 12 for the markov matrix), and aim at replicating various targets of the income and wealth distribution and of the process for income. Get some of the targets from here and some from whatever Section 5.2 here inspires you,

  • Eighth Homework batch. Data Sets Questions. Do one of the three. Due Nov 23.

    1. Read data sets: I. The Cross-Section data set Problem.

      Denote by i,g your own age plus 12 and your gender. Now take the CPS or the CEX and find out the average number of hours worked by people of type g, i plus/minus 2. Sort this group into quartiles by education, and report the average time worked and the average wage for those that work, the average time worked per person, the fraction that work, the fraction married, the number of children among those married and the number of children per parent. This for the years 1980 and the latest available. Report an additional feature of this group that you may find interesting.

      As an added bonus go back to 1970 through 1979.

    2. Read data sets: II. The Panel-Data data sets question.

      Create a table describing the time series properties using PSID data with information on household heads- their gender, marital status, number of other people in the household, hours worked by each member of the household and their wage rates. Use this data to think about a way to summarize hours worked and the labor force engagement per household over time. Also track the stability of households over time i.e. changes in marital status and number of household members. Do you notice any interesting features?

    3. Read data sets: III. A new data Sets. The IPUM or Census

      Recent news reported that most Americans now do not live in traditional families. Using the most recent wave of Census data (find out what this is) the proportions of people in age-sex group living in each type of household. Find out what the census uses as partitions for types of households. Report an additional feature that you may find interesting.

  • Ninth Homework batch. Transition in a Growth Economy Due Wed Nov 23.

    1. General equilibrium, Calibration and Transition.

      16.A Take your favorite version of the neclassical growth model. Calculate its steady state.

      16.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.