Econ 8108 Macroeconomics First Year Session IV Spring 2012

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, Rishabh Kirpalani,, Office 3-109 Hanson Hall Office hours: Thursdays 16.00-19.00 hs. Recitations: T 4:00-5:15pm, BlegH 220 (please doublecheck). He has a page for this course.

  • The final is during the micro recitation on Th May 3rd.

  • 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 Rishabh. These notes can also be found in his page.

  • What we are doing each day.
    1. March 20.

      I described the course. We 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 saw 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. I posed the sequence of markets equilibrium using state contingent capital to be delivered BEFORE production next period which, using the no-arbitrage condition, puts constraints on the sum of the state contingent prices.
    2. March 22.

      I show how to construct a Seq of Mark equilibrium from an Arrow Debreu and viceversa, and how it is important to transform the prices. We then defined Recursive Competitive Equilibrium. We started with that of arbitrary expectations and moved on to a rational expectations equilibria.
    3. March 27

      We reviewed RCE. We did it with a version with leisure and no shocks. 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 went into many details of how to characterize the RCE and what are its FOCs.
    4. March 27

      We then talked about a variety of environments where the welfare theorems do not apply: the existence of public goods, of consumption externalities (concurrent and lagged). We then move on to consider environments where a government taxes and produces the public good. First, with a period by period budget constraint with either lump sum taxes, labor, or total income, or consumption 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.
    5. April 3

      We discussed the use of RCE not when the welfare theoremes fail, but when there are differnt agents. We started with agents differing in wealth in a model wihout leisure, and moved to having them differ in wealth and efficient units of labor. We then started looking at two countries and what does this mean.
    6. April 5

      We finished the discussion of two countries. We started looking at the Lucas tree model. We defined equilibrium and we also started to derive a formula for share prices (that you should finish). We also talked about how to pose the sale of state contingent shares and of state contingent fruit.
    7. April 10

      We discussed finance. What is the price of statate contingent goods and from there we used arbitrage, to get formulae for interest rates and to price shares, options, repos, the works. We then discussed the RCE when firms own land an install capital and households own firms via a stock market. Up to here is what goes to the midterm. We started measure theory.
    8. April 12

      We had the midterm.
    9. April 17

      We continued the discussion of measure theory, including measurable functions, transition functions and updating operators. We started talking about the size distribution of firms by posing the problem of a firm and deriving an aggregate labor supply function given a measure of firms.
    10. April 19

      We discussed industry equilibrium in the Hopenhayn model. For this we defined stationary equilibrium, with exogenous death, then with endogenous death. We talked about how measures describe well the size and type of firms.
    11. April 24

      We finished discussing Industry EQ theory. We looked at how to compute statistics using measures (ratios, Ginis, and the like). We also discussed adjustment costs and how the problem of the firm changes because of this. We started discussing growth. We went over the AK model and the model with an externality in capital.

      I asked a few homeworks meaning things that you should be able to do. They include the definition of Industry eq with adjustment costs, with emphasis on how to construct the transition process for firms; the ability of computing industry statistics using the equilibrium tools; the calculation of the equilibrium and the solution to the social planner in an economy with an externality in production so that output is linear in capital.
    12. April 26

      I went briefly over the human capital growth model. Then I went over the and especially I will review the Romer growth model with an externality and an R&D sector. This involves Monopolistic competition.
    13. May 1

      I went over search. Looking at environments where a worker takes a job or not with a few tweaks. I defined matching functions.
    14. May 3

      I discussed bargaining in abstract and in the context of the search and matching labor model. I went briefly over the conditions to get a stationary equilibrium. I also discussed competitive search.

    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.