Econ 8108 Macroeconomics First Year Session IV Spring 2011

José-Víctor Ríos-Rull:,

  • 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


    Department of Economics, University of Minnesota,

  • Tue and 14:30-15:45 Hanson Hall 4-170. Off Hours: Before and after class and by appointment., email:, Fax: (612) 624-0209 Fed Phone (612) 204-5528

  • TA, Bernabe Lopez-Martin,, Office 3-109 Hanson Hall Office hours: Thursdays 16.00-19.00 hs. Recitations: T 4:00-5:15pm, BlegH 220. He has a page for this course.

  • There was a final Th May 5. This finished the course.

  • 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. These problems can also be found in his page.

  • Class Notes Taken in class by Bernabe. These notes can also be found in his page.

  • What we are doing each day.
    1. March 22.

      I described the course. We discussed what is the meaning of an equilibrium (a mapping from environment to allocations). We then discussed why the social planner problem may be a problem whose solution is interesting. It is because it is the equilibrium of the economy once we use the welfare (and other) theorems. We constrect an Arrow Debreu Equilibrium for the workhorse of macro, the growth model, using the welfare theorems. We then saw how to build a sequence of markets equilibrium out of an Arrow-Debreu equilibrium (and viceversa). We started the definion of Recursive equilibrium for arbitrary expectations.
    2. March 24.

      We will continued with the definition of Recursive equilibrium. We started with that of arbitrary expectations and move on to a rational expectations equilibria. I showed how to construct a Seq of Mark equilibrium from a recursive equilibrium and I hinted what are the troubles for going in the opposite direction. We then talked about a variety of environments where the welfare theorems do not apply. We started with one where there is an externality in consumption. We moved on to consider environments where a government taxes and produces a publich good. First with a period by period budget constraint with either lump sum taxes, labor or capital income taxes. Finally we considered a government that issues debt and we viewed the equilibrium conditions including the no Ponzi scheme on the part of the government.
    3. March 29

      We looked at economies with two types of agents. They differed in labor earnings and/or wealth and could also differ on other things. We also looked at two countries and carefully assessed how to model the equality of rates of return.
    4. March 31

      We looked at economies with aggregate shocks. We went from the secial planner problem to RCE (via the A-D Eq, the sequence of markets equilibrium). We put special emphasis in ensuring that we had complete markets (we discussed the first welfare theorem in this respect).
    5. April 5

      We looked to a growth model where the firm faces a dynamic problem by redefining labor in the growth model as land. We then looked at the Lucas tree. We argued its logic, we showed how to pose the problem recursively and we got a formula for the prices of the tree and for the prices of one and two period options.
    6. April 7

      We reviewed briefly the Lucas tree. We then talked about the OLG model. We reviewed how to define equilibrium in sequence of markets and the nature of the trouble that leads to the existence of money. Then I discussed why the notion of monetary equilibria maybe iffy, and I proposed an alternative allocation (which is an organizational equilibrium). Finally, and more importantly, I addressed how to write a RCE with life cycle households on top of a growth model, the modern use of OLG models.
    7. April 12

      We discussed measure theory.
    8. April 14

    9. April 19 Class 1

      We went over Industry Equilibria.
    10. April 19 Class 2

      We went over various models of Growth. The AK model, the externality in K, and the ability to accummulate human capital via goods not time.
    11. April 26

      We went go over the Romer (1990) growth model. It has an R&D sector as well as monopolistic competition and an externality in learning.
    12. April 28

      We started search, (you can use these notes for help). We posed the basic model of what job to take in both discrete and continuous time. We also talked about unemployment, and search effort.
    13. May 3

      We talked about on the job search, and posed the matching function and wage setting via Nash bargaining. Then we discussed the ingredients of a stationary equilibria with endogenous vacancy creation by posing free entry of firms.
    14. May 3

      We went over competitive search in some detail.
    15. May 5

      We had the test.

    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. Bernabe 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 Bernabe 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  Monopolistic Competition

    A detour to get market power.

    6  A Growth Model

    A detour to get economies growing.

    6.1  Exogenous growth

    6.2  Endogenous Growth

    6.2.1  A-K models

    6.2.2  Externalities

    Romer, [1986]

    6.2.3  Two sector growth models

    Lucas, [1988]

    6.2.4  R and D models with monopolistic Competition

    Romer, [1990]

    7  Life Cycle Models

    People do live and die.

    7.1  The Classic trouble making OLG Model

    7.2  A Recursive Formulation for important issues

    8  Search Models

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

    8.1  The Search Problem

    Should I stay or should I go?

    8.2  A Continuous Time Formulation

    8.3  Generating Transitions

    8.4  Equilibrium

    9  Time Consistent Policy

    Government's commitment is an oxymoron. Then what?

    9.1  A primer. Going against my future self.

    9.2  Sequences of governments.


    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.

    File translated from TEX by TTH, version 3.85.
    On 22 Mar 2010, 15:59.