Dynamic Programming and Business Cycles
prof.: Sekyu Choi (firstname.lastname@example.org)
we meet Tuesdays and Thursdays, 10:00 - 12:30, Lecture Room C.
Office hours: by email appointment
T.A.: Alberto Sánchez Martín (email@example.com)Syllabus
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
final exam and individual problem sets. You are encouraged to work in
groups, but problem set should be handed in individually.Problem Sets
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.
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
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
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.
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.
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.
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.
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
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.
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
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