429, McNeil Bdg,
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Econ 702, Spring 2006 

Professor José-Víctor Ríos-Rull

Last modified: Fri Apr 14 11:21:51 Eastern Standard Time 2006
This page contains relevant for the course. It grows with the semester. Students should check it often.
Department of Economics
University of Pennsylvania
3718 Locust Walk
Philadelphia, PA 19104 USA
Classes are T. and Th. 1:30-2:50 in 410 McNeil.
Special Classes (rescheduled) may be M 3:30-5:00 or Fr 10:30-12:00 in the Econ Conf Room.
Off Hours: Wed 2:30 to 3:30 and by appt.
T.As.: Thanasis, (Geromichalos) and Se Kyu Choi .
Off Hrs: Thanasis Th 12:00-1:30 and Se Kyu M 3-4:30 both in MCNeil 469.
Contingent times and places for teaching are Mon 10:30 to 12 in McNeil 285 and/or Fr 10:30 to 12 in STIT B26 (Stiteler Hall).

  • What are we doing? Brief description of previous classes and next one.
  • Course Description
  • Requirements and Grades
  • Prerequisites
  • 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 by Thanasis and Se Kyu. Also last years by Kagan and Thanasis and the previous years (Ahu and Vivian, and Makoto).
  • Exams. There will be one or two midterms. The final coincides with the 2006 May Macro Qualifying Examination.

  • What we are doing each day.
    1. We will look at a recursive formulation of the two sided lack of commitment problem. We will also discuss extensions of the basic models to accommodate such issues as demographics and others.
    2. We briefly reviewed some properties of the one sided lack of commitment and discussed how it could be implemented as a contract offered by firms. We looked at the two sided loke of commitment problem and discussed the nature of the planning problem and of the solution.
    3. We discussed the problem of one sided lack of commitment. We characterized the solution.
    4. We finished studying the problem faced by the charitable planner when she cannot observe the effort placed by the unemployed agent. We saw how an additional incentive compatibility constraint shows up and how the optimal solution displays decreasing levels of promised utility and, consequently, consumption. We discuss a bit how actual policied get determined.
    5. We posed and solved the problem of the unemployed agent and discussed how is it that a planner would consider helping him.
    6. We finished the R&D Romer model. We also discussed why is it that the main questions in economics about poverty are more related to development and a theory of TFP than to growth per se. To this end I asked a few numerical questions. These notes by Per Krusell on growth might help for the growth part. We started the next part of the curse where information and enforcement problems appear and where the allocations try to get around those problems.
    7. We continued the growth part of the course. We looked at the two Romer models: We completed the study of the economy with an externality and we started the R&D model.
    8. We went over growth. In particular, we saw how to transform a growing economy (either because of exogenous population or productivity growth) into a non growing one so that we can solve it. We also covered endogenous growth models. First AK economies and discussed how is it that there are no transitional dynamics. We then went to cover the Lucas human capital model and how the specifics of human capital accumulation matters for the possibility of long run growth.
    9. We finished this part of the course talking a little about transition and welfare comparisons. We saw how a wefare comparison requires the transition and it is assessed wrt to the distribution in the initial condition (although this was not clear to everybody. We started talking about growth with an ececonomy with exogenous population growth.
    10. We looked at the solution of the problem of the farmer. We discussed its properties and the nature of the meaning of a stationary distribution. We discussed its porperties in the context of an unemployment problem. We also define equilibrium for the case when this problem is embodied in a growth model.
    11. We discussed that the growth model does not have a good theory of wealth inequality. We then moved on to the savings problem with incomplete markets and storage technology and characterized the solution. We then described an economy with many such farmers and used measures and its transitions to characterize outcomes. We stated the theorem that there exists a unique stationary distribution provided the transition has certain nice properties. We then moved on to the economy with loans and discussed the solvency constraint.
    12. We discussed the calculation of statistics using measures. We looked at the problem of individual savers. We discussed the problem of boundedness.
    13. We looked at industry equilibria with adjusment (hiring) costs to employment.
    14. We continued studying economies with measures of agents defining industry equilibria with endogenous entry and exit of firms. In order to do this we defined the updating operators that take a meausre and a transition and yield another measure that we interpreted as the distribution of firms a period later.
    15. I started economies with measures of agents. We looked at the key concepts in measure theory that we will use and we defined industry equilibria.
    16. The midterm happened
    17. We finished talking about Lucas trees and we priced all types of assets (options shares and the like under complete markets).
    18. We continued talking about stochastic environments. In particular, we discussed how to implement complete markets in both a sequence of markets and a recursive structure. We started describing the Lucas tree model.
    19. We posed 4 homeworks that define the big questions in macro so we can get an idea of their relative importance. The homeworks were about measuring the welfare costs of various things. The questions where
      1. Differences in growth rates.
      2. Business cycles.
      3. Differences in levels of output (with the additional problem of how to compare a country that lags in levels but will catch up eventually).
      4. Differences in within country income.
    20. We finished the discussion of recursive equilibrium with two countries and perfect capital mobility. We looked at the growh model when firms own land and choose the stock of capital and households own firms which they buy and sell. Finally, we looked at an economy with a consumption tax, debt and a government that spends some exogenous amounts of the good.

    21. We  reviewed again RCE by posing a couple of simple economies: leisure, a government, debt, multiple agents and multiple countries.  This latter one proved to be tricky as we had to keep track of how much capital there is in each country and how much wealth is held by citizens of each country.

    22. We defined Recursive Competitive Equilibrium (RCE) by adding to the problem of the household the condition that it has to be representative. We also added a rational expectitations/perfect foresight condition that links the perceived law of motion of the economy and the actual law of motion of the economy. We discuss some issues of existence, uniqueness and computability (the Debreu, Mantel, Mas-Colell and Sonneschein 1974 theorem and the 1986 Boldrin and Montruccio result).

    23. We posed the problem of a consumer in the SME in a recursive manner, trying to mimic the logic that uses Bellman equations to solve social planner problems. In doing so we argued that the set of state variables should include both individual assets and aggregate capital.

    24. We defined sequence of markets equilibria (SME) by having markets for current goods and for loans open every period and by adding budget constraints for each period. We showed how to prove that a ADE allocation can be supported as a SME and viceversa. Then we defined another notion of sequence of markets equilibrium a lot simpler that has the same features and that saves a lot in notation.

    25. We talked about how to construct the price that sustains the PO allocation as an ADE. For this we got around the problem of transfers (because there is only one consumer), the problem of quasiequilibrium (due to the existence of a cheaper point) and the dot product representation (because a truncated sequence is almost as valuable as a non truncated one). We then used the properties of the maximization problem of the social planner as well as of the consumer and produders to establish a complete characterization of the price system in terms of marginal conditions in preferences and technologies.

    26. We talked about how to establish existence and uniqueness of a unique Pareto optimum (that solves a social planner's problem). We also talked about the 1st welfare theorem and the second welfare theorem. We provided the logic under which we will operate, that is, pose a model that macroeconomists like, look for its Pareto Optimal allocations, and use the Welfare Theorems to support them as Walrasian equilibria. We finished by reporting the rudiments of the standard growth model and showing how it maps into the tools of General Equilibrium.

    27. We went over the homepage contents. We also talked about the course and the concept of equilibrium as the tool to pick outocomes (allocations and prices). We defined the commodity space, and the consumption and production possibility sets. We then defined Arrow Debreu Equilibrium.

    Course Description.

    This course complements 704 in its objectives. The order of the numbers is irrelevant. Essentially, 702 and 704 run parallel.

    The ultimate goal of this course is to learn to use a variety of models that can be used to give quantitative answers to a number of economic questions. These models can be used to produce time series that can be meaningfully related to data. However in this course all the material will be studied from the strict point of view of the theory, so we will not look at data nor at solving the models with the computer. This is done in second year (mostly in 714). The emphasis will be on economic rigor, i.e. the target is to learn tools that will be useful later in a variety of contexts. The course, then, is not a survey of topics in macroeconomics. When some specific topic is addressed as, say, optimal fiscal policy, the objective is less that of giving 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. The TAs will discuss with you the time and location of the recitations.

    Requirements and Grades.

    I will ask some homeworks. Sometimes I will ask you to prove something during a lecture, sometimes they will be posted here . These problems ARE required within specific due dates. While they are required and have to be submitted to the TA's they will not be all individually graded. Some random subset will do but they will not be returned. Answer keys will be posted after they are due and this is the mechanism through which you can assess your progress. The homeworks may count for up to 15% of the grade. They play the key role of giving feedback to the students and of assuring that students are going along with the course rather than waiting till the exams.

    In addition, the grades will be based on one or two midterms and a final (that will take place simulataneously with the 2006 June QUALIFYING EXAMINATION. The midterms counts for one third of the non-homework grade and the final will count for the rest. If there are two midterms the first one will be weighted considerably less. The TA's are responsible for giving you feedback regarding the homeworks.


    We start the course in the third week of the semester so that students learn the fundamentals of dynamic programming and how it can be applied to a problem like the social planner problem of the Cass-Koopman's growth model. This will be done in 704. By the time 702 starts, I assume that students know how to solve infinite dimensional maximization problems, interpret Bellman equations, know the conditions necessary to iterate on value functions, and know what is obtained as limits of such iterations.

    Some understanding of stochastic processes will be very helpful, including the notions of random variable, Markov processes, and history-dependence. We will use some amount of measure theory. Overall the math requisites would not be very hard since we do not have to go very deep into these concepts. Students are advised to master these concepts, but not doing so should not prevent going through 702.


    We will use some bits and pieces of various textbooks. They include [Harris, 1987], [Stokey and Lucas, 1989], [Cooley, 1995], [Ljungqvist and Sargent, 2004]. I recommend every student interested in Macro to have the last three, and every student to have [Stokey and Lucas, 1989]. [Harris, 1987] is out of print but it can be found. 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.

    Preliminary List of Material to Cover.

    1. Equilibrium. What is its meaning.
    2. Competitive equilibrium in the growth model. Taking advantage of the welfare theorems.
      1. Arrow Debreu.
      2. Sequence of Markets.
      3. Recursive Competitive Equilibrium.
      [ Stokey and Lucas, 1989], Chapters 15 and 16; [Harris, 1987], Chapters 3 and 4; [Cooley and Prescott, 1995].
    3. A stochastic version of the growth model. What are complete markets? What are one period ahead Arrow-securities?
      1. Competitive equilibrium in stochastic growth model
      2. Models with endogenous labor choice.
    4. Non-optimal Economies. Sequence of Markets and Recursive Equilibrium.
      1. An economy with public expenditures, income taxes and a period by period balanced budget constraint.
      2. An economy with public expenditures, income taxes and a present value balanced budget constraint.
    5. Finance and asset pricing.  What is Lucas tree model and how to price an arbitary asset. []
    6. Multiple Agents Complete Markets Economies.
      1. An economy with two types of agents differing in skills and/or wealth.
      2. A two country economy.
    7. Growth:
      1. Exogenous growth
      2. Transforming the economy
      3. The AK model: one and two sectors.
      4. Externalities.
      5. Research and development (Romer 86).
      6. Non balanced growth paths.
    8. Economies without Complete Markets and with Large Numbers of Self-Insuring Agents. Introduce measure theory, transition function and statistics describing economy inequality and mobility.
      1. A simple model without insurance markets but with individual shocks, and no aggregate uncertainty. Two examples are farmer economy with storage technolagy but no trade and economy with non-state contingent loan.
      2. A General Lack of Insurance Model with Production.
      3. A General Lack of Insurance Model with Aggregate Uncertainty and aggregate endogenous state variables.
        1. The mess.
        2. The Krusell-Smith solution.
        3. The Moody Government solution. [Diaz-Gimenez et al., 1992].
      4. Transition and Policy Analysis.
      [Huggett, 1993]; [\.Imrohoroglu, 1989]; [Diaz-Gimenez et al., 1992]; Diaz-90; [Ríos-Rull, 1995].
    9. Industry Equilibria.
      1. Exogenous entry and exit. A measure of firms.
      2. Endogenous entry and exit.
    10. How to use models to look at data: Generating statistics from models.
    11. Economies with contractual problems. Lack of observabiliy and lack of commitment.
      1. Economy with One-side Lack of commitment.
      2. Economy with Two-side Lack of commitment.
      3. Economy with Lack of Observbility. [Ljungqvist and Sargent, 2004] [Attanasio and Ríos-Rull, 2000]
      4. The Abreu-Pierce and Stachetti aproach.
      5. Constrained arrangements, and the Marcet-Marimon approach. [Attanasio and Ríos-Rull, 2000] [Kehoe and Perri, 1997].
      6. Optimal Contracting. [] and [Quadrini, 2001].
      7. Limited information. [Atkeson and Lucas, 1992].
      8. Endogenous default. [ Chatterjee et al., 2004].
    12. Recursive Preferences. Epstein-Zin recursive utility. [].
      [Ljungqvist and Sargent, 2004]
    13. Models with demographic detail.
      1. Overlapping Generations with many periods.
      2. Overlapping Generations with variable demographics.
      3. A hybrid. The exponential population, exponential aging, model.
    14. Fertility in the utility.
    15. Multiplicity of Equilibria.


    [Atkeson and Lucas, 1992]
    Atkeson, A. and Lucas, R. E. (1992). On efficient distribution with private information. Review of Economic Studies, 59:427-453.
    [Attanasio and Ríos-Rull, 2000]
    Attanasio, O. and Ríos-Rull, J.-V. (2000). On the optimal provision of aggregate insurance in the presence of enforceability problems in the provision of private insurance. Mimeo, University College, London.
    [Chatterjee et al., 2004]
    Chatterjee, S., Corbae, D., Nakajima, M., and Ríos-Rull, J.-V. (2004). A quantitative theory of unsecured consumer credit with risk of default. Unpublished Manuscript, CAERP.
    [Cooley, 1995]
    Cooley, T. F. (1995). Frontiers of Business Cycle Research. Princeton, N. J.: Princeton University Press.
    [Cooley and Prescott, 1995]
    Cooley, T. F. and Prescott, E. C. (1995). Economic growth and business cycles. In Cooley, T. F., editor, Frontiers of Business Cycle Research, chapter 1. Princeton University Press, Princeton.
    [Díaz-Giménez, 1990]
    Díaz-Giménez, J. (1990). Business cycle fluctuations and the cost of insurance in computable general equilibrium heterogeneous agent economies. Working Paper, Universidad Carlos III de Madrid.
    [Diaz-Gimenez et al., 1992]
    Diaz-Gimenez, J., Prescott, E. C., Fitzgerald, T., and Alvarez, F. (1992). Banking in computable general equilibrium economies. Journal of Economic Dynamics and Control, 16:533-559.
    [Harris, 1987]
    Harris, M. (1987). Dynamic Economic Analysis. Oxford University Press.
    [Huggett, 1993]
    Huggett, M. (1993). The risk free rate in heterogeneous-agents, incomplete insurance economies. Journal of Economic Dynamics and Control, 17(5/6):953-970.
    [\.Imrohoroglu, 1989]
    \.Imrohoroglu, A. (1989). The cost of business cycles with indivisibilities and liquidity constraints. Journal of Political Economy, 97(6):1364-83.
    [Kehoe and Perri, 1997]
    Kehoe, P. and Perri, F. (1997). International business cycles with endogenous incomplete marjets. Working Paper, Federal Reserve bank of Minnepolis.
    [Ljungqvist and Sargent, 2004]
    Ljungqvist, L. and Sargent, T. (2004). Recursive Macroeconomic Theory, 2nd Edition. MIT Press.
    [Quadrini, 2001]
    Quadrini, V. (2001). Investment and default in renegotiation-proof contracts with moral hazard.
    [Ríos-Rull, 1995]
    Ríos-Rull, J.-V. (1995). Models with heterogenous agents. In Cooley, T. F., editor, Frontiers of Business Cycle Research, chapter 4. Princeton University Press, Princeton.
    [Stokey and Lucas, 1989]
    Stokey, N. L. and Lucas, R. E. with Prescott, E. C. (1989). Recursive Methods in Economic Dynamics. Harvard University Press.

    File translated from T E X by T T H, version 3.54.
    On 11 Jan 2006, 13:28.