Econ 8108 Macroeconomics First Year Session IV Spring 2015

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 Thursday 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, Eslami, Keyvan The recitation is on Mondays, 5:30-6:45pm (HMH 1-108), and office hours are right after that, 7:00-9:00pm on Mondays (HMH 3-125). 612.626.9248.

  • The 8108 final is Wednesday, May 13 at 8 AM in Hanson 4-170.

  • 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.

  • Class notes taken in class and posted by Keyvan

  • What we are doing each day.
    1. March 24.

      I described the course and discussed some context of what are the main facts over which macro has to be organized around:
      1. output per capita has grown at a roughly constant rate
      2. the capital-output ratio (where capital is measured using the perpetual inventory method based on past consumption foregone) has remained roughly constant
      3. the capital-labor ratio has grown at a roughly constant rate equal to the growth rate of output
      4. the wage rate has grown at a roughly constant rate equal to the growth rate of output
      5. the real interest rate has been stationary and, during long periods, roughly constant
      6. labor income as a share of output has remained roughly constant
      7. hours worked per capita have been roughly constant.

      I discussed what restrictions do these facts pose on the models that we use.

      I also discussed what is the meaning of an equilibrium (a mapping from environment to allocations) and 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 talked of how an Arrow Debreu Equilibrium for the growth model, supports the social planners solution using the welfare theorems. I referred to how to build a sequence of markets equilibrium out of an Arrow-Debreu equilibrium (and viceversa) and argued 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.
    2. March 26.

      We defined Recursive Competitive Equilibrium. We started with that of arbitrary expectations and moved on to a rational expectations equilibria. I went over equilibria with valued leisure emphasizing always what are the state variables. We started talking about a government that finances a public good.
    3. March 31

      I defined a Markovian stochastic process with finite support. I defined recursive compet. eq. for a stochastic economy emphasizing market completenes, and state contingent markets to deliver capital. I continued to describe equilibrium of economies where the welfare theorems are of no use. A government financing a public good with with capital income taxes and debt and how to deal with the no Ponzi scheme condition in recursive environments.
    4. April 2

      We continued looking at environments where the welfare theorems do not work. We looked at economies with agents differing in wealth in a model without leisure, and discussed how to write the model if agents differ in wealth and in efficient units of labor. Then we looked at an economy with two countries and what does this mean. We looked at the necessary state variables in a deterministic economy, and somebody point out that total capital and the share of wealth was sufficient. I asked as a homework to include aggregate shocks and to compare complete and incomplete markets (for Arrow securities). In this case we need to keep track of 3 state variables.
    5. April 7

      We finished standard RCE by looking at habit formation and externalities (keeping-up, catching-up) and by discussing the economy when there is a stock market and the firms own land and install capital. I talked about the Lucas tree posing special emphasis in how to price securities and in how to get pricing formulae.
    6. April 9

      We discussed the Lucas tree with demand contributing to productivity with competitive search. We arrived at the equilibrium of this economy by constructing the two functional equations that determine price and market tightness.
    7. April 14

      We saw the optimality of Competitive search equilibrium. I talked about Nash bargaining and what equilibrium condition it implies. This rapped up the first part of the course. We started measure theory.
    8. April 16

      We started industry equilibria. We defined equilibria with exit decisions.
    9. April 21

      We finished industry equilibria looking at adjustment costs. We started looking at incomplete markets by looking at the farmer's problem. We saw how the problem (when agents are impatient enough) generates a unique stationary distribution of wealth and income.
    10. April 23

    11. April 29

      We looked at how this isolated economy can be made a part of an incomplete market economy with multiple agents embodied in a growth model.
    12. April 30

      We started looking at growth. I went summarily over the AK model, the externality model, and the human capital model. I posed the Romer three sector growth model.
    13. May 5

      We finished the Romer three sector growth model. We talked about how to think of OLG models recursively as a tool to incorporate age in macroeconomics.
    14. May 7

      We finished the OLG model, we talked about entrepreneurial choice in a version of the Aiyagari model. We then talked about aggregate uncertainty in the Aiyagari model. I said a few things about monetary economics. I finished the course talking about the program and the profession.

    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. Keyvan 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 Keyvan 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. A fantastic book is being written now by Per Krusell. We will ocassionally use bits of it. 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.


    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 2013, 8:59.