Econ 8501 Wages and Employment Spring 2008

José-Víctor Ríos-Rull:,

Last modified: Wednesday, 9 April 2008 at 20:08 UTC.

  • Department of Economics, University of Minnesota, 1130 Heller Hall, 271 19th Avenue South, Minneapolis, MN 55455
  • Tue and Th 12:20 pm to 14:15. In BlegH 115. Off Hours: Before and after class and by appointment., email:, Phone-(612) 625-0941 Fax: (612) 624-0209 Fed Phone (612) 204-5528

  • Homeworks 16-19 are ready. see below. This is it.

    What are we doing? A class by class ex-post diary.

    1. May 6

      We will look at housing and demographics.
    2. May 1

      We talked about the value of a life and how to look use MPI to solve large problems. We also talked about homeworks. YOu can look and MPI things in here and especially here using Makoto's page.
    3. April 29

      We went over a model of defaulting and discussed the case where there are two types of agents which are private information.
    4. April 24.

      We covered a bond economy. Also, we discussed how to model defaulting.
    5. April 22

      We continued the discussion of how to compute the models introduced in the last class. Also, we covered the algorithm to solve the Aiyagari model with aggregate shock and with/without leisure.
    6. April 17

      We covered a theorem about the existence and uniqueness of the stationary equilibrium. Then, we discussed how to solve the stationary distribution of Aiyagari economy. The model with aggregate shock and leisure was introduced.
    7. April 15.

      We continued the discussion of the mixed marriages from the last class. Then, we began to review the Aiyagari model.
    8. April 10.

      We discussed why black men married to white female twice more than black female married to white men. Then, we discussed how to model it.
    9. April 8.

      Kevin Wiseman discussed Thebyshev polynomials and how increasing the order does not require recalculating its lower index coefficients. He also discussed Smolyak polynomials and how they can be used to extend the number of states. I discussed the role of multiple choice variables and some problems associated to nonconvexities. We continued with the discussion of the model that accounts for the increase of single women.
    10. April 3.

      We continued with the discussion of "What Accounts for the Increase in the Number of Single Households?"
    11. April 1.

      We discussed the problem of discrete versus continuous choices and we started looking at What Accounts for the Increase in the Number of Single Households? .
    12. March 27.

      We discussed the estimation of Economies of Scale and of altruism from purchases of life insurance and on how identification operates. We also discussed how the Euler equation changes when there is a change in the decision maker. This is the GEE.
    13. March 25.

      Andy reported his answers to HW 7 and his experience with AMPL. For more details look at Andy's link to AMPL. We finished with families as shocks and saw various issues that appear in this context (bargaining versus Pareto weights, sources of risk, divorce laws and so on).
    14. March 13.

      We went over families as shocks.
    15. March 11.

      We discussed how to model a household throughout its lifetime. What is a family, how to think of changes in family status, what types of shocks are faced by individuals, and things like that. We also discussed the link between micro and macroeconomics.
    16. March 6.

      We went over the model of Bethencourt and Rios-Rull (08) on cross-sectional distribution of fertility, female hours worked and intertemporal patterns of college attendence. We discussed its question and its computational issues.
    17. March 4.

      We gave a general talk about approximation and numerical methods. We gave a unified view of what is it to approximate a function and what are the things that we have to specify in order to do so. We talked in detail about splines. This was a dense clase.
    18. Feb 28.

      We did various things. We talked about calibration and also about certainty equivalence. We then started with posing an economy with shocks and incomplete markets where there are a large number of agents with different and changing types but with a stationary distribution. These we referred to as the Aiyagari-Bewley-Huggett-Imrohorogly environments.
    19. Feb 26.

      We (Tolga actually) finally went over the model of centralized bargaining of Stole and Zwiebel. We also discussed the role of nonconvexities in shaping wage differentials through specialization. We started talking about market incompleteness environments.
    20. Feb 21.

      We (Kevin) talked about the differences in hours worked between Europe and France amd the role of taxes and transfers. We then discussed OLG models with learning by doing and learning by not doing.
    21. Feb 19.

      We spent some time with the centrailized bargaining problem. We will come back to it. We also overviewed the mechanics of log-linearization. We then went to discuss an OLG model with agents that died. I discussed the definition of steady state and the three ways of solving the individual decision problem.
    22. -8. Feb 12.

      We had a double session. We went in some detail over the homeworks 5 and 6. While we reviewed the notion of linear approximations that Dynare gently does for us, we did not finish reviewing the theory. We talked about capital-skill complementarity in production and how this technology helps us understand the behavior of relative wages given quantities based only on observables. We started with with overlapping generation models and theories of age-wage profiles. We looked at a growth model with exponential death.
    23. Feb 7.

      We discussed lotteries in some detail. We tried to go over homework 5 but really did not. We discussed issues like the 35 hour week and various others regarding the role of adustment costs to labor versus externalities in commuting to have hours and bodies adjusting in the model in the same proportions as the data.

    24. Feb 5.

      We went over exercises 3 and 4 and I asked for how to have a balanced growth path with a CES production function. We also discussed some properties of maximization algorithms, from details about the mid point one to the virtues of Nelder and Mead versus Newton Rampson for estimation purposes. I verified that there were no issues about homeworks 5 and 6 that we will go over in the next two classes. We talked about an alternative to Homework 7, perhaps Homework 8 (but I forgot which one). We then discussed a representative agent economy with lotteries. We started with a case where the only two options where to work or not work. We then moved to a case where the choice of hours worked is continuous but the existence of commuting costs justifies lotteries. We left for the future the discussion of centralized bargaining.

    25. Jan 31.

      We finished the discussion of the economy of Charon and Langot with frictions. We also talked about the meaning of VARs.

    26. Jan 29.

      We started looking at Charon and Langot version of Andolfatto and Merts RBC model with frictions. We looked at the beginning of HW1. We will explore various extensions and variants of this economy.
    27. Jan 24.

      We talked about allocations between two agents, contract curves, planning problems and bargaining, Nash bargaining. We then went to set up labor hoarding and its equilibrium implementation with a household consisting of many individuals.

    28. Jan 22.

      We talked about the class, and what it is about. We defined recursive equilibrium for a representative agent stochastic growth model with leisure. The basics with no thrills.

  • Ninth Homework batch. Due May 21.
      1. Read data sets: II. The Panel-Data data sets. Use these notes to learn how.

      2. Use now either the NLSY or the PSID. Get again your own group of people the {i,g}. See how many of them were married in the initial period and 10 years later and build a transition matrix with the number of children in the household. Again separate them by education groups. Four this time. Report an additional feature of this group that you may find interesting.

      3. More On Statationary Distributions: The races model.

      4. Imagine a population with a measure .85 of white females. .85 of white males, and .15 of both black females and black males. Life expectancy of females is 60, of white males 55 and of black males 45. Compute the steady states of a population that does not grow and where the marriage rates of white females is .02, and of black females .015 and the average age of marriage for white men is 12. Is the system exactly identified? Overidentified, underidentified? In any of the latter two cases change the assumptions and calculate the steady states.

      5. MPI.

      6. Make any of the codes of Makoto's page work on some computer. Adapt your answer to homework 13-b to an MPI machine with 25 nodes.

  • Eighth Homework batch. Due April 7.
      1. Read data sets: I. The Cross-Section data set Problem. Use these notes to learn how.

      2. 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.

  • Seventh Homework batch. Due March 27.
      1. The Household Problem of Bethencourt and Rios-Rull (later we will get to the estimation part)
      2. Take one of models (either the baseline or one of the extensions) in these slides and write two pieces of code to solve the decision problem of the household. One piece of code inputs the objective function (with the budget constraint and the technology of educational attainment substituted in) and outputs three first order conditions (one for children, one for time allocation and one for investment) symbolically. You can use at least either mathematica or maple (within matlab or by itself). The other piece of code, best treated as a subroutine and written in fortran inputs a vector of parameters of preferences technology earnings and the like as described in the slides above and outputs an allocation that solves the first order conditions. You can use the Nelder and Mead algorithm to solve the such system of equations.

    1. Sixth Homework batch. Problems 11 and 12 due March 20. Problems 13 and 14 due April 10.
      1. Decision rules of the Aiyagari Economy Solve for the decision rule of the problem in Aiyagari (94) (without leisure) or in Castaneda, Diaz-Gimenez, and Rios-Rull (2003) JPE paper (with leisure). Make sure that you allow the shock to affect pref also and not only income. Use any global continuous method of your choice (preferably Schumaker or Hermitian splines on values or some polynomial on decisions say piecewise linear or Tchebyshev). The range of asset holdings should go from zero to 25 times the highest income endowment. The intervals or pieces should increase with wealth. Indicate the details of the logic of your approximation.

      2. Stationary Distribution I of the Aiyagari Economy Solve for the stationary distribution that you found. Describe some of its inequality properties using efficient communication methods.

      3. Stationary Distribution II of the Aiyagari Economy Obtain the stationary distribution of the economy using two methods.
        1. An approximation to the measure that uses its cdf with some function approximation. Make sure that you use many points and check the quality of the approximation.
        2. Use a large sample of individuals, say 50000 and simulate it until the first 4 moments and some key points of the Lorenz curve of the approximation
        3. Calculate the autocorrelation of consumption.

      4. GMM Estimation/ Calibration of the Aiyagari Economy Estimate the Aiyagari economy. This is choose its parameters to generate some properties of the joint distribution of earnings and wealth. Do so by using GMM. Explain.

  • Fifth Homework batch. Due March 6th.
    1. A life cycle steady state with human capital accumulation. Solve for the steady state of one of the two economies described in this paper. There is a learning by doing economy and a learning by not doing economy. Make any shortcuts that you wish provided that the ghist of the issue is still there.
      1. Plot the implied wages and time allocation.

  • Fourth Homework batch. Due Feb 26st.
    1. A life cycle steady state. Solve for the steady state of an economy where agents live up to 90 years (assume they are born at 16) and have the wage profile and survival probibilities of American persons. Each period there is an inflow of new borns of measure 1. In other respects, the economy is a standard growth model. Let the agents have standard per period preferences over consumption Let the labor share of output be .67 and the depreciation rate .07. Ensure that the discount rate is such that the wealth to output ratio ends up being 4. Make sure that your calculations are accurate up to .0001. Solve the problem of the agents by the three methods that we discussed in class and comment their advantages and disadvantages. Discuss how to solve for equilibrium (that factor prices come from the capital labor ratio that comes from households decisions) and for calibration (that wealth to output ratio is 4) simultaneously so that you solve for a system of two equations and two unknowns.
      1. Do it now with leisure in the utility function.
      2. Do it now with population growing at 1.25%.
      3. Plot age profiles for consumption and hours worked.

  • Third Homework batch. Due Feb 21st.
    1. An exponential population steady state. Solve for the steady state of an economy where agents have a probability of dying of .01 every period. Each period there is an inflow of new borns. In other respects, the economy is a standard growth model. Let the agents have standard per period preferences over consumption and leisure like the ones used in previous papers. Let the labor share of output be .67 and the depreciation rate .07. Ensure that the discount rate is such that the wealth to output ratio ends up being 4. Make sure that you plot the age distribution of consumption wealth and leisure. If you think that you have to truncate the age distribution when making your calculations, make sure that you explain your criteria. Make sure that your calculations are accurate up to .0001. Do the calculations both for the case of constant populations and for the case of a 1.25 per cent population growth rate.

  • Second Homework batch. A third of it due Thursday Feb 7th the rest, due Feb 12th.
    1. Solving the baseline real business cycle model and measuring the contribution of productivity shocks to output and employment fluctuations. Use whatever you want to solve it. I recommend Euler equation approximations implemented with Dynare and Matlab. But feel free. This is perhaps not the best homework for f90. Pose now the standard stochastic business cycle model with two inputs of production capital, and labor.
      F(z,K,N) = exp(zt )   Kt q   Nt1 - q  
      The shock z follows the univariate process that you estimated in homework 9.

      Per period Preferences are log ct + a (1-nt).

      This means that there are a total of four parameters to pick (b ,a , q , d).
      1. Pick values for those parameters so that the steady state of the economy of a quarterly version of this model matches some statistics that you your self specify.
      2. Define recursive competitive equilibria.
      3. Compute a loglinear approximation to the decision rules and plot them.
      4. Generate 500 samples of length 200 each and compute the standard business cycles statistics as found in the Cooley volume.
      5. Discuss the findings.
      6. Discuss optimality (and compute the optimal allocation if needed).
      7. Give an answer to the main question here. What is the contribution of the shock to movements in output and in labor.

    2. Solving the Charon and Langots model with leisure and aggregate measure the contribution of productivity shocks to output and employment fluctuations. leisure.

    3. Do the same for some other variant of Charon and Langots world.

  • First Homework batch. 1 and 2 Due Tuesday January 29th. 3 and 4 due Thursday January 31st. Name them jan_29_h1, jan_29_h2 and so on.
    1. Data manipulation.

      1.A Fetch and plot US quarterly GDP Employment, Total hours worked, Hours per worker, Hours per adult of working age and Hourse per person not in jail over 18 years of age 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 and the series in 1.A. 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 GDP, Total Hours and Labor Productivity 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 p 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).

    Course Description

    This course should be thought of as a Labor course with a close link to Macro that should be of interest to people with interest in both areas. Its main purpose is to learn the map from models to data i.e. to answer quantitative questions that we are interested in (in the process of doing so, some interesting theoretical questions arise). We will develop tools by stating general questions, and then discussing how to approach its answer.

    The tools that we will be developing beyond those already covered in the first year can be grouped into:

    • Theoretical tools. Not all the necessary tools have been acquired in the first year. We will look at models of individual decision making, obviously, but mostly in the context of equilibrium models. We will look at representative agent models, models with a continuum of agents represented with measures, overlapping generations models, as well as models where agents form households. We will look at models where equilibria are optima and where they are not. We will look at stationary and non--stationary equilibria. We will look at models without perfect commitment and without perfect information.
    • Empirical tools. A necessary condition to be able to do applied theory is to be able to characterize some properties of the world. This involves the capability of accessing some data and of understanding the way it is organized as well as the principles that guide the construction of the main sources. This requires some knowledge of NIPA and of the way data are organized,
    • Computational Tools. Students should be able to construct and characterize the properties of the equlibrium allocations of artificial model economies.
    • Calibration. We will spend a lot of time thinking of how a model is related to the data. This is I think the more important part of the learning process. We will discuss this in much detail.

    This is a Ph.D. course not a Masters course. As such students are not expected to learn what other people have discovered, but the tools that are needed in order to discover things by themselves. Because of this reason the active work of the students is crucial to achieve the objective of mastering the tools that are described above. This is a course to learn to do things, and, therefore, it requires to do some things.

    Every class except the first one we will devote the first twenty minutes or so to students presentations of homeworks. I expect professional competence in this regard.

    Course Requirements

    Students will place the solution to the homeworks and to other requirements in electronic form in some place to be described

    There are various types of requirements that are a necessary part of the course, all of which have to be fulfilled.
    • Regular Homeworks.There are two types of homeworks. The ones that are set up in this page and that are due each Tuesday and are set usually well in advance, and those that I ask in class (that I may try to post in this page soon thereafter but are anyway due whenever I say in class). Homeworks have due dates that are enforced by the date of the file. As of now there are homeworks due next Tuesday.
    • Class Presentations Every student will make at least two class presentations with at least one being of a subset of a homework. The first presentation should take no more than 15 minutes and it will be absolutely professional. Every second wasted, every statement not planned, every bad thing will be highlighted. The second presentation (that will depend on class size and interests) maybe on a paper or on another homework.
    • Referee Report. I will assign a paper to each of you as we go along to write a referee report and perhaps also to present the paper in no more than 20 minutes. The refere report should be no longer than five pages and should contain a clear and concise exposition of the main points of the article as well as a critical evaluation of the article's contributions.
    • Wikipedia Article. This is something that should be done by the end of the course. The moment you post it email me and place a copy in your directory. Think of a topic of the course no matter how silly.

    This course believes drastically in Learning by Doing. To learn the material that we cover requires that students do all the homeworks in a timely manner. Given the way to collect the homeworks, timeliness is automatically recorded. I will look at what is done weekly.

    Class schedules.

    There are regular lectures on every foreseeable Tuesday and Thursday.

    What about knowledge of Computers?

    This is not a course in computer languages so students are responsible to learn to write computer programs. Students are also responsible for learning their way around McNeil computational facilities. I do not expect anybody to have a computer at home or anything like that. It is better to work in McNeill's computer room because you can talk to each other.

    There are three general classes of computer languages.

    • Fortran 90. This is the best and more powerfull computer language. Among economists nobody prefers C. It is a little bit hard at the beginning (you have to declare variables and the like) but all students tell it is well worth to learn it as soon as possible. A very good introduction to fortran can be found HERE.
    • Matlab, Gauss, Scilab and Octave. These are very popular packages in economics. They are relatively easy to learn and code writing is easy. They generate a lot slower code than F90 (about 100 times) but they are probably a good choice to solve some problems. They may have an interface with f90 but I have never seen it working. Matlab is growing at the expense of gauss.
    • Mathematica and Maple. These are packages capable of doing symbolic manipulation of equations. Occasionally they can also be used to do numeric calculations. It does not hurt to know them.

    Students should be able to write code in F90 in addition to matlab or gauss and to stata. Most students tell me in later years that I should have enforced harder the learning of F90, but I am willing to consider exceptions. If somebody has a serious reason not to use F90, please come and talk to me. At least one homework should be answered in f90.

    Look at Tips for Doing Computational Work in Economics by Tony Smith for insights.

    Grading Rules.

    To satisfactorily complete the course, students have to do all the requirements well.

    For those that do not register but take the course, I recommend that they do the homeworks. We learn to solve problems by facing them. Learning jointly with others greatly speeds the process. The deadline for the Empirical Requirement is the last day of class.