Class Webpage for Macroeconomics II (Graduate)

Spring 2006

References: K=Krueger, LS=Ljungqvist and Sargent, SL=Stokey and Lucas with Prescott

FINAL DATE: Wednesday May 10th, 9am

What are we doing, class by class?

25. We extended the previous discussion to a infinitely repeated version of the static tax game, and talked a bit about some results by Abreu, Pearce and Stachetti that allow one to characterize the set of values of subgame perfect equilibria

24. We talked about optimal government policy, and defined Ramsey problems and Nash equilibria in a one period model. We discussed time consistency, and speculated about what would happen in an infinitely repeated version of the static economy (LS Ch 22) Alejandro’s solutions to HW 5

23. We finished talking about linearization Homework 7

(here are some useful materials for the homework: (i) Gauss HP filter code, (ii) my code for the non-stochastic version of the model that I put up in class, (iii) short notes on filtering and computing percentage standard deviations – see Cooley (1995) for a discussion of the HP filter)

22. We talked about linearization as a local solution method with an application to the stochastic growth model (notes)

21. We talked about Euler equation iteration as a numerical solution method for the income-fluctuations problem (notes) Homework 6

20. We discussed extensions to the Huggett (1993) economy by Aiyagari (1994) and Aiyagari and McGrattan (1998) to add capital and debt.

19. We described an economy with a continuum of agents, each subject to uninsurable income risk. We discussed Huggett’s (1993) results on the existence of a stationary equilibrium. (Huggett 1993, JEDC, my notes)

18. We characterized decision rules in the stochastic income-fluctuations problem. We explored how to eliminate a state variable with iid shocks, and conditions under which an upper bound on asset holdings does / does not exist. (slides, K Ch 10) Homework 5 Partial solutions for HW4

17. We reviewed, briefly, some theorems that allow one to characterize value function and decision rules in non-stochastic dynamic models. We reconsidered the non-stochastic income fluctuations problem (class 14) and made a few remarks about the natural borrowing constraint, and the permanent income hypothesis (slides, SL Ch 4, K Ch 10)

16. We discussed the equilibrium interest rate, and the welfare cost of market incompleteness in the HSV framework (HSV welfare paper) Homework 4

15. As an introduction to environments with heterogeneous agents and idiosyncratic risk we considered a framework in which allocations and cross-sectional moments have closed-form solutions (slides for HSV framework)

14. We discussed the performance on the midterm. We then moved to introduce income fluctuation problems in environments with (idiosyncratic) labor income risk. Notes (LS Ch 16 and start of Ch 17)

13. Midterm Exam: Questions and Suggested Answers

12. We described a recursive decentralization of the stochastic growth model in which firms make investment decisions and households trade equities. (Danthine and Donaldson 1994). Partial solutions for HW 3.

11. We talked briefly about a Recursive Competitive Equilibrium in the growth model, and then talked about Calibration (Cooley Chapter 1)

10. We defined a Sequence of Markets equilibrium for the stochastic growth model, including Arrow securities, and discussed how to price various assets. Homework 3 (LS Ch 12)

9. We compared the solution to the planner’s problem in the neoclassical growth model, to the Arrow-Debreu competitive equilibrium, and argued the allocations are the same. My code for HW2 (a) and (b) (LS, Ch 12)

8. We introduced notation to deal with Uncertainty. We revisited the example economy from Class 1, and then described the Stochastic Neoclassical Growth Model (the workhorse for the Real Business Cycle literature) (K, Ch 6)

7. We stated the Contraction Mapping Theorem, and proved the sufficiency of Blackwell’s Conditions (K, Ch 4, SL Ch 3). Alejandro’s solutions for HW 1

6. We discussed an Euler Equation approach to approximating the solution to finite horizon and infinite horizon optimization problems, and the role of the Transversality Condition in the latter. We defined a competitive equilibrium for the growth model, and discussed the Welfare Theorems for this economy. (K, end of Ch 3)

5. We talked about how to solve a special case of the growth model using a Guess and Verify approach, and about a more generally applicable numerical approach that involved Value Function Iteration on a Discrete State Space. Homework 2 (K, middle of Chapter 3)

4. We moved to the Neoclassical Growth Model. (K, first part of Chapter 3). We described the basic model ingredients, and the planner’s problem for this economy. We talked about how the Principle of Optimality allows us to switch from a sequential to a recursive formulation of the planner’s problem (K, first part of Ch 5, and SL, first part of Ch 4 for more on the POO)

3. We defined a Sequential Markets Equilibrium, and showed the equivalence between the Arrow Debreu and Sequential definitions. We also defined a Recursive Competitive Equilibrium Homework 1 (LS Chapter 7 for more on RCE)

2. We defined a competitive Arrow Debreu Equilibrium in our example, proved the First Welfare Theorem, and discussed Negishi’s method for solving for equilibria. (K, Chapter 2)

1. We outlined the class, and defined the Household’s Problem in a simple example economy (Prof. Krueger’s (K) notes, Chapter 2)