Please plan to come and talk to me individually to tell me which homework are you the proudest of. Any time that I am around is good.

The Aiyagari calibration homework is ready.

• What are we doing? Brief description of previous classes and next one.
• Homeworks.
• Course description.
• Requirements. List of homeworks and other requirements and due dates. Will be updated as we go along.
• Computers? and Textbooks? and Grading rules.
• A preliminary version of the Syllabus. It is very likely that it will change. I will update it.
• Other relevant links. Here you may find an occasional paper, homepage or subroutine of interest.

What are we doing? A class by class diary.

1. Sept 5.

   We talked about the class, and what it is about, going over all the details. We started with a discussion of what is the meaning of an approximation to a function and the criterias (family of approximating functions, criteria of distance, and method to find it) that are used to describe a particular approximation approach. We then went in detail over the first set of homeworks and its purpose. We finished with a discussion of the Solow residual. This included the components of GDP on the income side (and I forgot the difference between GDP and GNP, this is the payments to foreign factors net of payments to national factors from abroad that is also ambiguous). You should read the Cooley-Prescott chapter on the Cooley book or the - appendices here or here for details of the construction of the Solow residual needed to compute it.

2. Sept 19

   We discussed how to use a model to answer quantitative questions about the economy. In particular, we talked about how calibration and estimation operate, and what are their differences and similarities. We put special emphasis in saying that what matters is not the statistical techniques as much as the sources of identification. I refer to the first 5 sections of this paper, but in particular, Section 3. Gero and Arun presented some of the homeworkds (Thanks to both). Arun will continue with the discussion of the ordering assumptions in the VAR next class. We then discussed the next batch of homeworks (and I want volunteers to present some of them in the next class, October 3). Such discussion involved a minimal description of log linearization using dynare as well as comments on the use of software to take derivatives and on how to implement the notions of calibration discussed at the beginning of hte class. While doing this, we talked about how to calibrate a model economy so that its steady state looks like the U.S. in the dimensions that we want. We may start the discussion of global approximation methods using piecewise linear functions with exact solution in the grid points.

3. Oct 3

   Arun finished discussing why some assumptions are made when estimating VARs (Thanks Arun). Zhifeng presentd the gist of homework 8 and some of the subtle issues that arise (Thanks Zhifeng). I discussed how to do global approximations and what do they mean. In particular, I went over the endogenous grid method. This paper is a great reference to a particularly efficient way to obtain a global approximation.

4. Oct 10

   George presented the endogenous grid method. I then discussed how to adapt the problem to the Aiyagari economy given its specificities.

5. Oct 17

   Gero and Zhifeng presented the problem of solving for the Aiyagari decision rules using endogenous grid methods. Thanks to both. I then discussed how to store the distribution of types in the Aiyagari economy using both a large sample of agents and approximating the cumulative distribution function. I then talked a bit about Markov perfect equilibria in a growth model with a public good.

6. Oct 24

   David Wiczer did the following (and I am sure that he did a fantastic job). These are his notes for using data sets The notes come from a long tradition.
   • He discussed the mechanics of the CPS.
     The organization of the survey with rotating groups and why "outgoing rotation groups" are special The supplements, e.g. Displaced Workers and March How hours are tricky between "actual" and "usual" How employment status definitions are nuanced and changes by year

   • He talked about using the cross-sectional data to create synthetic panels. He also talked about Autor, Katz and Kearney (2006) and Juhn, Murphy and Pierce (1993). He went over about chaining the CPS to get month-over-month data such as employment status transitions.

   • CPS data can be found in three locations
     • Went to the NBER website and looked at their chaining programs.
     • Went to IPUMS for their integrated data, mostly e March Files.
     • Went to CEPR data where they have a collection of the "outgoing rotations groups".

   • Then he talked about the CEX and SCF.
     The SCF website was used to look at some figures from the 2009 SCF follow-up of the 2007 wave.

   • He talked about using of panel data. He described cohort,time and age effects and how fixed effects are good.
     • He discussed the mechanics of the PSID: The individual and family files "line number" identifiers Occupational codes are relatively error-free.
     • He went to the PSID website and talked about the short-comings of the search feature
     • He introduced the NLSY79 and NLSY97. He talked about the ASVAB scores and other unique features.
     • The NLSY79 website was used to download some data.
     • I talked about the SIPP, that it's monthly but only for 4 years and described where to get it,

7. Oct 31

   Gero and Zhifeng presented the computation of the stationary distribution of the Aiyagari economy using the two methods (approximation to the cdf and a large sample). Thanks to both. I then discussed how to solve for the steady state of the Aiyagari economy which involves finding the equilibrium capital output ratio. From there we discussed some policies and how to compute a steady state that also involves a period by period balanced budget constraint. In this context I showed how steady state comparisons, while informative about the long run properties of the economies, do not tell us anything about welfare. For this we need a transition. I then asked you to pose a strategy to solve for such a transition starting with the economy that has no taxes to another that poses every period a 20\% labor income tax that is redistributed lump sum, and then to talk about welfare. I then discussed the Krusell-Smith method to solve for equilibria of economies with distributions as state variables when predetermined variables are sufficient statistics for current prices. I finished by developing the Generalized Euler Equation of the Markov perfect equilibrium of an economy with hyperbolic discounting and how it poses difficulties to calculate the steady state.

8. Nov 7

   Joao talked about the Fella paper on solving problems with continuous and discrete variables. We discussed the intricacies of this problem which are many. I then discussed solving the hard Krusell Smith problem, when predetermined variables are not sufficient statistics of prices (we will also see an intermediate case with two predetermined state variables).

9. Nov 21

   Joao, Richard, and Radek did various nice presentations about the homeworks and the Fella paper. Thanks to all. We are still struggling with the details of the very difficult, but fascinating, Fella paper. Another thing that we still have to clarify is how to approximate aggregate capital in the decision rule of agents when using the JPE Krusell Smith approximating method. I started talking briefly about parallel computing, especially MPI. This was enough about it

10. Nov 28

    Radek finished the Krusell-Smith I approximation. Zhifeng discussed the Krusell Smith II approximation when predetermined aggregates are not sufficient statistics to prices. Thanks to both. I discussed how to solve n equations with m< n+1 unknowns. By minimizing (or finding a zero of) a function of various variables. I discussed various forms of doing so speaking badly of Newton-Rapson and Nelder and Mead.

11. Dec 5

    Kai will deal with how to solve hyperbolic discounting type problems where the derivatives of equilibrium functions are in the Euler equations. Rocio will talk to us about how to use both values and derivatives to construct approximations to the value function using this paper for the three country example . I may talk about how to solve for problems when the value functions are not even continuous (marriage). This finishes the class.