Dynamic Programming and Business Cycles
(January-February, 2014)


prof.: Sekyu Choi (sekyu.choi@uab.cat)

we meet Tuesdays and Thursdays, 10:00 - 12:30, Lecture Room C.
Office hours: by email appointment

T.A.: Alberto Sánchez Martín (alberto.sanchez@uab.cat)


Syllabus
In this course we complement what you have learned in the first part of Macroeconomics 1 (First semester of the 1st year). My focus will be on dynamic programming and business cycles, both in theory and practice. The course will consist of mainly three parts: (i) Math preliminaries and Dynamic programming, (ii) applications of dynamic programming to several macro problems and (iii) aggregate innovations and business cycle analysis (in the neoclassical growth model and newer models with market frictions).


Evaluations
One final exam and individual problem sets. You are encouraged to work in groups, but problem set should be handed in individually.

Problem Sets

[ONE]
[TWO]
[THREE]
[FOUR]
[FIVE]
[SIX]

Class Log:
Feb 13th.: We discussed calibration and results from the search and matching model and talked about the "Shimer puzzle". We discussed several alternatives to "fix" the standard model. We finished the course talking about new directions in business cycle theory andits applications.

Feb 11th: We continued the analysis of the general equilibrium model with search and matching frictions, a la Merz (1995) and Andolfatto (1996). We discussed the problem of the household, the firm and the wage setting protocol.

Feb 6th.: We discussed the problems that RBC models face in terms of replicating volatility of aggregate hours. We then discussed 'lotteries' (indivisible labor) and home production as ways of enhancing the implied volatility of hours in the model. We then introduced briefly a search and matching model of the labor market in general equilibrium.

Feb 4th.: We learned the standard Real Business Cycle model and talked about how to specify preferences and technology. Then we discussed its calibration and performance.

Jan 30th.: We reviewed the standard neoclassical growth model with savings and leisure choice. We added a notion of total factor productivity shocks to this model and started thinking of ways of putting more structure on preferences and technology in order to make it operational.

Jan 28th.:  Using the set of prices learned on the previous class, we started doing some Asset pricing: risk free bonds, the stock market (price of the whole tree) and derivates such as options and futures.

Jan 23rd.: We continued the discussion of uncertainty and itroduced markov chains. Then we analyzed the recursive version of the stochastic endowment economy, with state contingent ("pure") bonds. After this, we studied the Lucas Tree (Lucas 1978) model and defined prices for different types of assets.

Jan 21st.: We introduced the notation for dealing with uncertainty: shocks, histories and probabilities. Then we analyzed a simple version of a stochastic endowment economy in an Arrow-Debreu setting (time 0 trading).

Jan 16th.: We applied what we have learned on dynamic programming and recursive models to a simple model with two 'classes'. We then studied the McCall job-search model, as a way to introduce notions of uncertainity into our models.

Jan 14th.: We discussed characterization of optimal policies in the recursive setting of the growth model (optimal savings and leisure). We also talked about how to use the machinery of dynamic programming and the recursive setting to analyze different types of models: models with externalities and models with government.

Jan 9th.: We discussed a descentralized version of the neoclassical growth model and defined a Recursive Competitive Equilibrium. We also discussed the role of individual/aggregate state variables and aggregate consistency in the model.

Jan. 7th.: We talked about the organization of the course and some logistics. We discussed the standard neoclassical growth model and how to write it in recursive form. Then we thought of how to prove that the recursive form has a solution and how this relates to the solution of the original growth model. Then, we analyzed the Contraction Mapping Theorem.

References
Krueger, Dirk "Macroeconomic Theory" (available on line)
Guner, Nezih "Advanced Macroeconomic Theory" (available on line)
Ljungqvist, Lars and Sargent, Thomas J. "Recursive Macroeconomic Theory"
Stokey, Nancy and Lucas, Robert E. with Edward C. Prescott "Recursive Methods in Economic Dynamics"
Cooley, Thomas F. (editor) "Frontiers of Business Cycle Research"

CLASS NOTES BY JOSÉ-VÍCTOR RÍOS-RULL