Macroeconomic Theory 702

429, McNeil Bdg,
Tfn: 215-8987767
Fax: 215 5732057, or 215 573-4217
http://www.ssc.upenn.edu/~vr0j/cc70207/
vr0j@econ.upenn.edu

Econ 702, Spring 2007

Professor José-Víctor Ríos-Rull

Last modified: Mon Apr 23 14:00:27 Eastern Daylight Time 2007

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 and after class.

T.As.: Se Kyu Choi and Serdar Ozkan.
Off Hrs: Se Kyu Off Hrs: Se Kyu Mondays, 10-12 (Mcneil 438) and Serdar Tue and Th 3:30 to 4:30 in MCNeil 419.
Contingent time and place for teaching is Mon 5:00 to 6:30 in McNeil 169.

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 Serdar and Se Kyu. Also last years by Thanasis and Sekyu the previous years (Kagan, Ahu, Vivian, and Makoto). Exams. There will be one or two midterms. The final coincides with the 2007 May Macro Qualifying Examination.

What we are doing each day.

We ended the course with a discussion of how people both choose to have children (as in the Alvarez model) and how do they choose partners. We discussed a variety of issues that these models can address: the fall in the marriage prevalence, the implications of uneven numbers of each sex and the nature of interracial marriage. This ended the course.

We discussed models of mulitperson households going over topics of what is marriage, how do preferences change, how are assets split, who makes the decisions in case of disagreement and so on. We also talked about having health being a state variable and how to model the investments (either in terms of goods or effort) in health. This took us to the issue of the value of life.

We build the growth model on top of an OLG structure and discussed its recursive representation. We started discussing some demographics beginning with early death and of how to handle the assets of the dead.

We discussed the determination of wages in the life cycle. We posed and characterized the properties of various theories (hormones, learning by doing, learning by not doing) and of what are the implications for the allocation of consumption and of time over the life cycle with constant interest rates. We talked about non separability of utility and about borrowing constraints. We also talked briefly about how to model the education decision (whether by the agents or its parents) and talked about possible theories of educational attainment and what do they imply.

We looked at the OLG model in its simplest form. We discussed how different equilibrium concepts fare and how is it that money can have value. We then turned to discuss the role of the welfare theoremes in this environment and of how to characterize the set of monetary equilibria. We also pointed to the issue of what is so special about the first old.

We discussed the problem of one sided lack of commitment, and how would an insurance company effectively provide as much insurance as possible. We characterized the solution.

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 posed and solved the problem of an unemployed agent that optimally chooses search effort to find jobs and discussed how is it that a planner would consider helping him.

We finished the Romer model with product development and the growth part of the course.

We looked at the model with externalities and started the Romer model with product development.

We looked at exogenous productivity growth, its balanced growth path and how to transform the economy so that it looks like a non growing economy that is easy to work with. Then we looked at the AK model, discussed its lack of transitional dynamics. We finished with a discussion of how models with human capital may look like the standard growth model (if there are limits to its accumulation with goods) or like the AK model (if it can be accummulated without decreasing returns).

We finished talking about the Aiyagari economy and associated transition and welfare issues. We also discussed how it works with leisure and whether the calculation of a stead state is a one or two equation/s (and unknown/s) system. We started talking about growh. First, with population growth.

We continued with the Huggett economy. We defined equilibria, talked abouot existence and discussed how to compute some statistics about the economy. We briefly mentioned how difficult is to talk about non steady states in this economy. We started the Aiyagari economy.

We started the problem of the household with linear saving technology and talked about why there are bounds on the amount of assets that it holds as long as beta / q < 1. We also constructed .

We finished industry equilibria looking at economies where there are adjustment costs to both labor and capital. We then talked about how to model the problem of a single agent facing stochastic endowment and a linear storage technology.

Midterm.

We continued to look at industry equilibria, now with endogenous entry and exit. We looked at other important theoretical concepts such as a transition function and the updating operator.

We started to look at economies with measures of agents. We looked at the concepts in measure theory that we use (what is a measure, a sigma algebra a measurable function) and we defined industry equilibria.

We finished the Lucas tree and pose homeworks that define the big questions in macro so we can get an idea of their relative importance. The homeworks are about measuring the welfare costs of various things:

Amount of risk aversion needed to account for the equity premium.
Differences in growth rates.
Business cycles.
Differences in levels of output (with the additional problem of how to compare a country that lags in levels but will catch up eventually).
Differences in within country income.

We talked about stochastic environments in Recursive Equilibria and how to post both securities that pay in terms of the consumption good and those that pay in terms of capital. We talked about the Lucas tree model and learned to price assets (options). I asked the homework of the equity primium and how to obtain it.

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. We also looked at an economy with a consumption tax, debt and a government that spends some exogenous amounts of the good. This finishes our discussion of Rec Comp Eq in determinisitic economies.

We reviewed again RCE by posing first an economy where agents differ in wealth. We used it to discuss the need to keep track of the wealth distribution in the state vector. We then turned to look at a two country world with perfect capital markets and discussed how capital differs from wealth. 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. We also talked about the fact that there are many ways to write down the recursive problem but that one needs to be consistent.

We reviewed the notion of Recursive Competitive and discussed existence and uniqueness both when it is optimal and when it is not. We then extended to environments with leisure and with a public sector with and without government expenditures affecting utility and with and without lump sum taxation. We started discussing the ingredients of a multiple agent type RCE.

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. We wend on to define recursive equilibrium with arbitrary expectations and with perfect foresight or rational expectations.

We went over valuation equilibrium and sequence of markets equilibrium in stochastic environments.

We talked about how to get the valuation equilibrium with a dot product representation. Then we completely characterized the prize sequence in terms of the properties of the allocation that solved the social planner problem. We then defined a SME, by having markets for current goods and for loans open every period and by adding budget constraints for each period and talked about how to proof equivalence between the two equilibrium concepts (which I asked as a homework). Finally, we started to talk about stochastic environments.

We defined a utility function over the consumption possibility set and we defined the production possibility. We defined valuation equilibrium. We then stated the welfare theorems and uniqueness of the Pareto Optima. We talked about sufficient conditions for a Quasiequilibrium with Transfers to be a valuation equilibrium. We then stated the Prescott and Lucas 71 result for having the price functional have an inner product representation. We then moved on to map the growth model into the structure of a valuation equilibrium to be able to use the welfare theorems.

We went over the homepage contents. We also talked about the differences between equilibrium and Pareto Optima and what role does the latter play in Macro. We argued that an equilibrium concept is aa the tool to pick outocomes (allocations). We defined the commodity space, and the consumption possibility set.

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 2007 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.

Prerequisites.

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.

Textbooks.

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.

Equilibrium. What is its meaning.
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].
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.
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.
Finance and asset pricing. What is Lucas tree model and how to price an arbitary asset. []
Multiple Agents Complete Markets Economies.
1. An economy with two types of agents differing in skills and/or wealth.
2. A two country economy.
Industry Equilibria
1. Exogenous Entry and Exit
2. Endogenous Entry and Exit
3. Endogenous Entry and Exit with Endogenous State Variables
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.
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].
Industry Equilibria.
1. Exogenous entry and exit. A measure of firms.
2. Endogenous entry and exit.
How to use models to look at data: Generating statistics from models.
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].
Recursive Preferences. Epstein-Zin recursive utility. [].

[Ljungqvist and Sargent, 2004]
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.
Fertility in the utility.
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, 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_EX by T_TH, version 3.54.
On 11 Jan 2007, 13:28.