Econ 8108 Macroeconomics First Year Session IV Spring 2013

José-Víctor Ríos-Rull: vr0j@umn.edu,


  • Department of Economics University of Minnesota Phone-(612) 625-0941 4-101 Hanson Hall (off 4-179) Fed Phone (612) 204-5528 1925 Fourth Street South Fax: (612) 624-0209 Minneapolis, MN 55455

    Homepage http://www.econ.umn.edu/~vr0j/index.html

    http://www.caerp.com

    Department of Economics, University of Minnesota,

  • Tue and Thursday 14:30-15:45 Hanson Hall 4-170. Off Hours: Before and after class and by appointment. http://www.econ.umn.edu/~vr0j/ec8501-13/, email: vr0j@umn.edu, Fax: (612) 624-0209 Fed Phone (612) 204-5528

  • TA, Zhifeng Cai, caixx162@umn.edu, Office: 3-131 Hanson Hall Office hour: Friday 0900-1100 or by walk in Link to which notes will be posted: Recitations: Tuesdays 1600-1715 at HMH 1-170 4:00-5:15pm.

  • The final is on Thursday the 9th during class.


  • What are we doing? Brief description of previous classes and next one.

  • Course Description

  • Homeworks and Grades

  • Textbooks

  • Preliminary List of Material to Cover

  • References

  • Problem Sets Problems and solutions with due dates. Do not wait for the posting to answer them.

  • My version of the class notes as of now. Normally, these taken in class and posted by by Zhifeng are more timely.

  • What we are doing each day.
    1. March 26.

      I described the course. I discussed some context of what are the main facts over which macro has to be organized around. I discussed what is the meaning of an equilibrium (a mapping from environment to allocations). We then talked about why the social planner problem may be a problem whose solution is interesting. It is because it is the unique equilibrium of the economy once we use the welfare (and other) theorems. We construct an Arrow Debreu Equilibrium for the workhorse of macro, the growth model, using the welfare theorems. We then see how to build a sequence of markets equilibrium out of an Arrow-Debreu equilibrium (and viceversa). We argue that we can then solve for Social Planner problem sometimes, but that we do so using recursive methods (dynamic programming). Why not then always recursive methods? This is to define equilibria recursively. We then defined Recursive Competitive Equilibrium. We started with that of arbitrary expectations and moved on to a rational expectations equilibria.
    2. March 26 Recitation time.

      I posed a stochastic version of the recursive competitive equilibrium using state contingent capital to be delivered BEFORE production next period which, using the no-arbitrage condition that puts constraints on the sum of the state contingent prices. I asked how to construct a Seq of Mark equilibrium from an Arrow Debreu and viceversa, and how to transform the prices from one space to another. We did various examples of recursive equilibrium (leisure). I then described how to construct a sequence of markets from a RCE and talked about the problems for the reverse. I started describing equilibrium of economies where the welfare theorems are of no use. First, a government financing a public good with capital income taxes. We started discussing the problem of debt.
    3. March 28

      We continued with RCE and in particular with the problem of the government with debt and how to deal with the no Ponzi scheme condition in recursive environments. In doing this we talked about what constraints do current debt and wealth pose on policy. We look at other environments where the welfare theorems do not work. We looked at a "keeping up with the Jones" environment and at a "catching up with the Jones" environment. We started discussing how to pose the equilibrium of an economy where firms own the land and the capital and households own the firms.
    4. April 2

      We finished the problem of the firm with land. We started with agents differing in wealth in a model wihout leisure, and move to having them differ in wealth and efficient units of labor. We then looked at an economy with two countries and what does this mean.
    5. April 2 Recitation time

      We looked at the Lucas tree economy where the only important thing is to find prices. We went into many details of how to characterize the RCE and what are its FOCs. We obtained formulas for the price of the tree that satisfy a certain functional equation. We started with the Lucas tree with demand contributing to productivity.
    6. April 4

      We continued with the problem with the Lucas tree and demand contributing to productivity. We obtained the Euler equation of the household (with some mistakes that we will fix the following class).
    7. April 9

      We discussed the endogenous productivity with product search in a version of the Lucas tree model with competitive search. We arrived at the equilibrium of this economy. We saw the optimality of this equilibrium.
    8. April 16

      I discussed random search in the endogenous productivity Lucas tree model. We started discussing measure theory.
    9. April 18

      We finished discussing measure theory and we started Industry equilibria.
    10. April 23

      We finished Industry equilibria and started the Aiyagari economy.
    11. April 25

      We had the midterm.
    12. April 30

      We talked about the incomplete markets economies. First, without markets, then the Huggett economy and then the Aiyagari economy. We described existence of a unique stationary equilibria and existence of a steady state that required the finding of a zero of a market clearing equation. We talked about assessing policy changes in the farmers' economy.
    13. May 2

      We talked about assessing changes and computing transitions in the economies with measures of agents. First, those without markets, and then those with markets. We started growth theory. We went over the AK model, the model with externalities in capital, and the humand capital, two sector, growth model. We discussed what it takes to grow. We started posing the Romer endogeneous growth model with R&D.
    14. May 7

      We solved the Romer endogeneous growth model with R&D. We finish the class discussing a bit of search theory, whether a worker should take a job or not. We also talked about some other issues in unemployment and job search. This finished the course.
    15. May 9

      We will have the final.

    Course Description.

    This course complements 8105-8107. In my view, the ultimate goal of this course is to learn to use a variety of models that can be used to give quantitative answers to economic questions. The models can generate artificial data of both allocations and prices that can be meaningfully related to actual data. In this course most (if not all) of the material will be studied from the strict point of view of the theory, so we will not look at data in any serious manner nor at solving the models with the computer. The emphasis is on economic rigor, i.e. the target is to learn tools that will be useful later. The course, then, is not a survey of topics in macroeconomics. When some specific topic is addressed the objective is not to give a review of known results but rather to give an example of how an issue is addressed and of how tools are used.

    There will be recitations once a week. These will be used either to introduce some mathematical apparatus that we need, to solve homeworks, or to explore issues related to those presented in class. The material covered in recitations constitutes part of the required curriculum.


    Homeworks and Grades

    In the context of the course, I will assign some homeworks: usually I will ask you to prove something during a lecture, sometimes they will be posted in the homepage. These problems are not required but will give you an idea of what is expected for the exams, and especially for the prelim. The grades will be based 30% on a midterm, 60% on a final that will take place the last day of class and 10% on class participation. Zhifeng will give you feedback regarding the homeworks. He may post them on the web as well as post answers to it at a later day. Or he may not. We will see about it.


    Textbooks and papers

    No special textbooks. There are notes from previous years and Zhifeng may post class notes of this year's class. It never hurts to have the usual suspects, but I do not dwell on them. Besides those used and recommended by my colleagues, there is a good little book (out of print actually) that is useful, Harris, [1987]. The papers that I cite (in a very incomplete form below) are not to be read in general, although some students may find them useful. First year is to learn tools, not to read papers.


    Preliminary List of Material to Cover

    This list is of material that I want to go over. The first few items you have seen in a very similar way, so I will go very fast over it, but I find it very useful to go over them again.

    1  Introduction

    1.1  Equilibrium. What is its meaning.

    Competitive equilibrium in the growth model. Taking advantage of the welfare theorems.
    Stokey and Lucas, [1989], Chapters 15 and 16; Harris, [1987], Chapters 3 and 4; Cooley and Prescott, [1995].
    A stochastic version of the growth model. What are complete markets? What are one period ahead Arrow-securities? How to define Competitive equilibrium in stochastic growth model.

    1.1.1  Arrow Debreu

    1.1.2  Sequence of Markets

    1.1.3  Recursive Competitive Equilibrium

    2  Recursive Competitive Equilibrium

    2.1  The Basic Setup

    The logic of recursivity. Its principles. How it works when all is easy.

    2.2  A Model with Public Goods

    The first reason that makes life difficult. Non-optimality.

    2.2.1  Financed with Lump Sum Taxation

    2.2.2  Financed with Capital Income Taxation

    2.2.3  Adding Government Debt

    2.3  A Model with Heterogeneous Agents

    The second reason that makes life difficult. Multiple agents. Negishi works but so what?

    2.4  A Model with Uncertainty

    Expanding the model to have shocks.

    2.4.1  Markov Chains

    2.4.2  AD and SM Household Problem

    2.4.3  Recursive Formulation

    2.4.4  Lucas Trees and Asset Pricing

    2.5  A Model with Firms making Investment Decisions

    Separating decision makers.

    2.6  A Model of International Economics

    In multicountry settings people are not country. So what are they?

    3  Measure Theory

    Just counting properly. Any reference is fine.

    4  Industry Equilibrium

    A first notion of production. The sometimes useful of firms as technologies.

    4.1  A static description

    Many firms producing the same.

    4.2  A Simple Dynamic Environment

    They are long lived and still mechanical.

    4.3  Introducing Exit Decision

    Now there is some pruning by choice.

    4.4  Stationary Equilibrium

    What happens in the aggregate. An important theoretical object.

    4.5  Adjustment Costs

    Making firm less silly.

    4.6  What is a firm?

    Let' not fetichize things.

    4.6.1  An entrepreneur

    4.6.2  With some limited liability

    4.6.3  A partnership

    4.6.4  A coalition

    4.6.5  Limits to securitization of corporations

    4.6.6  What about the modern publicly traded corporation

    5  The Aiyagari Economy

    A model with many households using measures to describe them.

    5.1   The household problem

    Bounds when households are impatient.

    5.2   The steady state conditions

    An important notion.

    5.3   Aggregate Shocks

    All things are moving.

    6  Monopolistic Competition

    A detour to get market power.

    7  A Growth Model

    A detour to get economies growing.

    7.1  Exogenous growth

    7.2  Endogenous Growth

    7.2.1  A-K models

    7.2.2  Externalities

    Romer, [1986]

    7.2.3  Two sector growth models

    Lucas, [1988]

    7.2.4  R and D models with monopolistic Competition

    Romer, [1990]

    8  Life Cycle Models

    People do live and die.

    8.1  The Classic trouble making OLG Model

    8.2  A Recursive Formulation for important issues

    9  Search Models

    You can't always get what you want.
    Rogerson, Shimer, and Wright, [2005]

    9.1  The Search Problem

    Should I stay or should I go?

    9.2  A Continuous Time Formulation

    9.3  Generating Transitions

    9.4  Equilibrium

    10  Time Consistent Policy

    Government's commitment is an oxymoron. Then what?

    10.1  A primer. Going against my future self.

    10.2  Sequences of governments.

    References

    COOLEY, T. F., AND E. C. PRESCOTT (1995): "Economic Growth and Business Cycles," in Frontiers of Business Cycle Research, ed. by T. F. Cooley, chap. 1. Princeton University Press, Princeton.
    HARRIS, M. (1987): Dynamic Economic Analysis. Oxford University Press.
    LUCAS, R. E. (1988): "On the Mechanics of Economic Development," 22, 3-42.
    ROGERSON, R., R. SHIMER, AND R. WRIGHT (2005): "Search-Theoretic Models of the Labor Market: A Survey," Journal of Economic Literature, 43, 959-988.
    ROMER, P. M. (1986): "Increasing Return and Long-run Growth," 94, 1002-36.
      (1990): "Endogenous Technological Change," 98, S71-S102.
    STOKEY, N. L., AND E. C. LUCAS, R. E. WITH PRESCOTT (1989): Recursive Methods in Economic Dynamics. Harvard University Press.



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    On 22 Mar 2013, 8:59.