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 Kagan. Also last year's (Ahu and Vivian) and the year before (Makoto).

Exams. There was a midterm. The final coincides with the 2005 June Macro Qualifying Examination.

28. We finished talking about extensions to the basic model. We briefly described how to pose Overlapping Generations Models recursively. This finished the course.

27. We posed and solved a problem with one sided lack of commitment. We talked about why upon hitting the constraint the new allocation is independent of the previously promised utility. We also talked about two sided lack of commitment. We started talking about some extensions of the basic growth model that have proved popular in monetary economics.

26. We talked about how to deal with the private information problem and how to solve a planner's problem that incorporates the private information friction as a constraint. We characterized properties of the solution (the decreasing amount of unemployment insurance).

25. We talked about a model of unemployment with search intensity. We then described how a benevolent planner guarantees a certain utility level with minimum cost. We described how private information on the part of the agent's effort poses a moral hazard problem.

24. We finished talking about how to compare models with data. We started with a model with private information by looking at a model of unemployment with search intensity. We also started describing how would a planner guarantee a certain level of utility ao agents.

23. We finished the Romer R&D model, although a chunk of it was left as a homework. We discuss how to do welfare comparisons. We also talked about how to construct predictions of the model.

22. We continued with the Romer R&D model.

21. We discussed the behavior of the skilled wage premia since 1960. More importantly, in doing so we discussed the difference between using the model to make a statement and using the model to measure something.

20. We discussed the Romer model with externalities in capital and how it leads to a balanced growth path. We also discussed the differences between the market and the planner's allocation. We started the Romer model with development of new varieties.

19. We talked about endogenous growth. We started with the AK model. We moved on to the Lucas human capital model with schools as a way to accumulate, and we compared this with studying.

18. We talked about growth. First the growth and development facts, and then how to transform the economy when there is population growth and when there is labor augmenting technological change. The transformed economy's steady state is a balanced growth path of the original economy. These notes by Per Krusell on growth might help for Today's and for next week's material.

17. We talked about the economy with many agents and uninsurable shocks. First we gave the interpretation of savings as storage which allows us to characterize the allocations both in a steady state and outside the steady state. We then posed the model as a lending economy and in the context of a growth model which poses some difficulties when characterizing non steady state behavior. Still we define both in sequence space and recursively what non steady state equilbria are for these economies.

16. We looked at a distribution of firms in an industry equilibria where now it is endogenous in the sense that firms are choosing whether to leave the industry or to continue operating. Then we discussed how to use this model to put policies that limit the size of firms or to put policies that protect employment by making it expensive to fire workers. We used this example to distinguish once again between the properties of a stationary distribution and those generated by the policy in the periods subsequent to its implementation.

15. We talked about transition probabilities and some of its properties. We started developing a multiple agents model with idiosyncratic, uninsurable shocks: the pig farmers' model. We then talked about a distribution of firms. First we looked at exogenous entry and exit.

14. We continued with the second part of the course. We finished with the necessary notions of measure theory.

13. First midterm.

12. We talked about a variety of issues raised throughout the first part of the course. We started the second part of the course by looking at the basic notions of measure theory.

11. We continued with the Lucas tree economy, obtaining formulae to compute share prices in addition to state contingent prices. We also priced some other assets such as options.

10. We finished the land economy with dynamic firms establishing the definition of equilibrium. We started the Lucas tree economy constructing the equilibrium allocation, and finding the necessary Arrow Debreu prices that sustain the allocation. We then defined and priced some assets (stocks, bonds) and went over the recursive equilibrium.

9. We finished the debt economy and started an economy with two social classes where the A agents are poorer, have lower wages and care about average consumption of those of their own type. We started an economy where firms own the land.

8. We define equilibria for a variety of growth economies with taxing governments. We started with a government that taxes lump sum and then throws away the stuff. We then moved to a proportional income tax. Then we went to a government with a constant expenditure requirement and we finally moved to a government that can issue debt. We have not finihed the latter.

7. We went again over Recursive Competitive Equilibrium. We saw an Economy with labor-leisure choice and an economy with an externality in leisure. We discussed the set of variables that are needed and the set of functions that describe the equilibrium of the economy. We talked about steady states.

6. We defined Recursive Competitive Equilibria for the growth model with and without rational expectations. For this we constructed the problem of the individual agent with state variables a and K.

5. We described in detail how to model the stochastic growth economy. We described the welfare theorems there and repeated the analysis that we did about arguing existence.

4. We proved equivalence of SME and AD equilibrium (we have to check that the SME prices are a cont linear functional, i.e. bounded). We started defining a stochastic version of the growth model.

3. We reviewed the definitions of the production possibility set Y and of the consumption possibility set X. We then defined valuation equilibrium and applied the second welfare theorem. We discussed the meaning of quasiequilibrium with transfers, and of the conditions necessary to have the implied price have a linear product representation. We then used the first order conditions from the planners problem and from the agents problem to establish properties of the price vector. We started describing what a sequence of market equilibrium is.

2. We looked at the neclassical growth model in its simplest form (the Cass (yes David Cass) and Koopmans model) and described how to solve for its Pareto optimal allocation. We looked at the necessary Euler equation that partially characterizes an interior optimum. We the defined a topological vector space and production and consumption possibility sets that implement the growth model and that we will use to be the define Arrow-Debreu (valuation) equilibrium next day.

1. 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 talked about Arrow Debreu Equilibrium and the theorems that it provides. We stated the existence of a unique Pareto optimum (that solves a social planner's problem), 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 growht model.

This course complements 704 in its objectives. The order of the numbers is irrelevant. Essentially, 702 and 704 run parallel except the first and last two weeks which are part of 704 while the last two weeks are part of 702.

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.

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 individually graded and returned. Answer keys will be posted after they are due. The homeworks may count for up to 15% of the grade. We may look at them selectively after the exams. 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 2005 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, 2000]. 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.

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, 2000] [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, 2000]
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.

References

[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, 2000]

Ljungqvist, L. and Sargent, T. (2000). Recursive Macroeconomic Theory. 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.