Macroeconomics 704 First Year Spring 2018

José-Víctor Ríos-Rull:,

  • Department of Economics University of Pennsylvania. 507 McNeil


  • Mon and Wed 10:30-12:00 McNeil 309. Off Hours: Mondays 3:30 to 4:30 and before and after class and by appointment., email:,

  • TA, Jinfeng Luo The recitation is on Tuesday, Room 309 in McNeil Building from 1:30 to 3:00 pm. His office hours are Tuesdays 3-5 pm in office 388.

  • Class Notes taken by Jinfeng

  • The final grades from Jinfeng are now ready here or above.

  • What we are doing each day.
    1. April 25 . Last day of class.

      We look at aggregate shocks, and endogenous determination of the distribution of wages. We look into preferences with a taste for variety. We then discuss the meaning of the stock of varieties. We link it to models of new keynesian type and trade type where firms have market power.
      • April 17.

        Jinfeng proves some properties of the problem of the farmer (boundedness essentially). He reviews the meaning of a probability measure on the state of a household.
    2. April 23 .

      We finish the farmer's problem and aggregate it up into a modern economy first with credit markets then with production. We add vacations with skill loss and entrepreneurship decisions.
    3. April 18 .

      We review how to solve a transition and the notion of linear approximation. We talk about how to approximate business cycles with only the transition of an MIT shock. We start the farmer's problem.
      • April 17.

        Jinfeng discusses Industry Equilibria with endogenous state variables and reviews non stationary industry equilibria.
    4. April 16 .

      We talk about non-stationary industry equilibria. We talk about how to solve a transition. We also talk about how to approximate via linearization.
    5. April 11 .

      We finish Industry Equilibria; we talk about computing statistics.
      • April 10 28 .

        Jinfeng will discuss the midterm.
    6. April 9 .

      We have the midterm.
    7. April 4 .

      We start measure theory and Industry Equilibria.
      • April 3 .

        Jinfeng will go in detail over the equilibrium conditions of the Lucas Tree with endogenous productivity and competitive search.
    8. April 2 .

      We will finish the Lucas Tree with endogenous productivity and derive the equilibrium conditions.
      • March 28 .

        Jinfeng will discuss additional problems.
    9. March 27 .

      We continue with the Lucas Tree, pricing assets and starting endogenous productivity.
    10. March 26 .

      We look at a two country economy. We start the Lucas tree.
      • March 21 .

        Cancellation due to snow.
      • March 20 .

        Jinfeng discussed the economy with land and answered many questions.
    11. March 19 .

      We look at externalities and more than one type of agent.
    12. March 14 .

      We finish the economy with debt.
    13. March 13 .

      We add uncertainty and talk about what complete markets mean and how to deal with them in Rec Comp Eq. We discuss the role of Arrow securities. We pose a government that spends. We continue to describe equilibrium of economies where the welfare theorems are of no use: a government financing a public good with lump sum, labor and capital income taxes, and then with debt.
    14. March 12.

      I describe 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 discussed some of the limitations of this point of view.

      I also discuss 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 talk of how an Arrow Debreu Equilibrium for the growth model, supports the social planners solution using the second welfare theorem. I refer to how to build a sequence of markets equilibrium out of an Arrow-Debreu equilibrium (and viceversa) and 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 define Rational Expectations Recursive Competitive Equilibrium

  • 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 Jinfeng. Beware of some typos or other mistakes that are inevitable in these types of notes.

  • Course Description.

    This course complements the rest of 702-704. 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 be take place during the prelim and 10% on class participation. Jinfeng 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 Jinfeng 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
    2. Review: Neoclassical Growth Model
      1. The Neoclassical Growth Model Without Uncertainty
      2. A Comment on the Welfare Theorems
    3. Recursive Competitive Equilibrium
      1. Economy with Government Expenditures
      2. Lump Sum Tax
      3. Labor Income Tax
      4. Capital Income Tax
      5. Taxes and Debt
      6. An Economy with Capital and Land
      7. Adding Heterogeneity (Wealth, Skills, Countries)
      8. Shocks, Markov Processes, Complete and Incomplete Markets
    4. Asset Pricing: Lucas Tree Model
      1. The Lucas Tree with Random Endowments
      2. Asset Pricing
      3. Taste Shocks
    5. Endogenous Productivity in a Product Search Model
      1. Competitive Search
      2. Business Cycles in this Model
    6. Measure Theory
    7. Industry Equilibrium
      1. Preliminaries
      2. A Simple Dynamic Environment
      3. Introducing Exit Decisions
      4. Stationary Equilibrium
      5. Adjustment Costs
    8. Incomplete Market Models
      1. A Farmer’s Problem
      2. Huggett’s Economy
      3. Aiyagari’s Economy
      4. Policy
      5. Aggregate Shocks
    9. Wage Distribution
    10. Monopolistic Competition
    11. Endogenous Growth and R&D
    The notes are the evolution of class notes by many students over the years, both from Penn and Minnesota including Makoto Nakajima (2002), Vivian Zhanwei Yue (2002-3), Ahu Gemici (2003-4), Kagan (Omer Parmaksiz) (2004-5), Thanasis Geromichalos (2005-6), Se Kyu Choi (2006-7), Serdar Ozkan (2007), Ali Shourideh (2008), Manuel Macera (2009), Tayyar Buyukbasaran (2010), Bernabe Lopez-Martin (2011), Rishabh Kirpalani (2012), Zhifeng Cai (2013), Alexandra (Sasha) Solovyeva (2014), Keyvan Eslami (2015), Sumedh Ambokar (2016), and Omer Faruk Koru (2017).


    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.
    ROMER, P. M.   (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.