The course is over, but I will check on the homeworks.

Alessandra Fogli has organized a session on how to analyze geographical data (things happen somewhere and we may want to know how it propagates). Anyone interested is welcome to attend. The session (GIS workshop) will be in 90 Blegen Hall from 8 a.m. until noon on Thursday of next week (12/16). More info in Geographic Information System's Page.

• What are we doing? Brief description of previous classes and next one.
• Homeworks. First homework batch ready. Due September 15.
• 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 ex-post diary.

1. Sept 8.

   We talked about the class, and what it is about. We went over all the details. We started with a discussion of the first homework and of what is the meaning of an approximation to a function and the criterias (family of approximating functions, criteria od distance, and method to find it) that are used to describe an approximation approach.

2. Sept 15

   John Seliski discussed the problems with real data that has been chain indexed (it is no longer additive) and the use of Tornquist aggregators to transform then into additive series. We discussed the construction of the series for the Solow residual. This requires the imputation of all series in NIPA on the factor side to either capital or labor and the addition of some components that are not in GDP but will be in our measure of output (services from Government capital and from consumer durables). Look at Cooley and Prescott's chapter in the Cooley volume or the appendices here or here for details.

3. Sept 22

   We discussed how to use the stochastic properties of the time series and the basic growth model to answer the question about the role of productivity shocks in shaping output fluctuations. In particular, 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.

4. Sept 29

   David Wiczer lectured on how to read data sets both cross section and panel. These are his notes for using data sets The notes come from a long tradition. The stuff David teaches is the crucial input for homework batch 4. This is perhaps the most useful class of all.

5. Oct 6

   We discussed how to use data generated by the model for comparisons with the U.S. data. We talked about how, when and what to filter and compare. We also looked at the alternative way of operationally answering the question that we are addressing with formal econometrics. Finally, we started the discussion of global approximation methods with emphasis on the piecewise approximation and exact solution in the grid points.

6. Oct 13

   David used these slides to describe Chebyshev approximations. Thanks David. He also outlined Indirect indifference and also talked about how to approximate a continuous AR(1) with a Markov chain.

7. Oct 20

   Andrea presented stuff on global methods. There we learned a few tricks of how to think of functions to approximate. Thanks Andrea. We also discussed some of the problems involved in estimation the variance decomposition to the three shocks (two to preferences and one to technology). Hopefully, we will sort it out next wednesday in the global presentation. I then talked a bit about splines and their properties; about the global approximation when there are both leisure and Markovian shocks; and about the problem with storing, saving and updating measures. The corresponding homework is a version of Aiyagari's economy with leisure. In it we do not care yet about either calibration or equilibrium. Just obtaining a stationary distribution of households giving that the parameters of the problem and constant prices and interest rates.

8. Oct 27

   We talked more about how to solve the decision rules with labor in the Aiyagari economy. We then discussed how it is the equilibrium of a small open economy or how to solve for that of a closed economy. We also discuss how to calibrate the economy at least for some moments. This is the core of the homework batch 7 that was slightly changed. Finally, we also talked about how to do once and for all unexpected changes in the environment such as the doubling of productivity. This has a small homework (batch 8).

9. Nov 3

   Marcelo talked about obtaining the piecewise approximation by iterating not on the decision rule but on its inverse. He discussed how easy it is to solve for today's assets and also how to construct the inverse checking that the bounds are fine. Among the questions asked, there is one about transition in the Aiyagari world that I still need to answer. I then talked about the Krusell Smith with no leisure and the extent that there is limited rationality.

10. Nov 15

    There were two presentations. Sebastian presented the details of the implementation of the simple Krusell-Smith environment. He also discussed some of its properties and the accuracy of the approximation. Zhen then gave as a very nice discussion of how the endogenous grid method with search and the use of consumption functions even with endogenous labor can be very useful. I learned a lot from the two presentations. I then turned to discuss how to solve equilibria with uncertainty when we do not know which moments are sufficient statistics for prices. These include economies like that in Krusell-Smith but where there is labor choice, or the possibility of savings in stocks and in bonds, or even where there are housing prices. The key here is to do a two step procedure. In it, we have a value function for tomorrow, over which we use forecasted prices. However, to solve it for today we use current prices which require the solution to a market clearing equation every time we iterate on the solution.

11. Nov 17

    We looked at a problem with discrete choice. The problem of bankruptcy. We did many things while talking about it. Discussing the problem of non concavity. The issue of the default set. The interplay between continuous and discrete variables. The iterative process to solve the model. All this is a condensed review of the 2007 Econometrica paper joint with Chatterjee, Corbae, and Nakajima.

12. Nov 24

    We talked about families. First, we look at various demographic details (early death, what about their assets), then about how to model preferences when there are two people (Pareto weights, bargaining, limited commitment a la Marcet/Marimon), then how to think about marital status as shocks. Throughout this class all problems can be solved with standard methods that use the FOC of the problem.

13. Dec 1

    We talked about the last homeworks and we discussed a couple. The one about tax policy in the Aiyagari world, and one about the second order approximation and its possible impact in the computation of welfare. We then discused a variety of issues that apper in family economics and in discrete choice models. We went over a few techniques to solve those models. Some involve discrete choices and discrete states. Others involve continues choices and discrete states. Some other times we use shocks to smooth the solutions. Finally I talked about issues that arise when two parties have to agree. I talked about seduction games and the issue that both parties of the transaction need to agree.

14. Dec 8

    This was the last day of class. I did derive the GEE of a the recursive problem that yields the time consistent Markovian optimal provision of public expenditures with income taxes and a period by period balanced budget constraint. Two functional equations are involved, that of the government FOC (the GEE) that involves not only functions but also the derivatives of those functions and the FOC of the household. We talked about how to use global methods to solve it, or to use successive derivatives (assuming the policy functions are polynomials of increasing order).

Course Description

• Theoretical tools. Not all the necessary tools have been acquired in the first year. We will look at representative agent models, models with a continuum of agents represented with measures, overlapping generations models, as well as models where agents form households. We will look at models where equilibria are optima and where they are not. We will look at stationary and non--stationary equilibria. We will look at models without perfect commitment and without perfect information.

• Empirical tools. A necessary condition to be able to do applied theory is to be able to characterize some properties of the world. This involves the capability of accessing data sets and of understanding the way they are organized as well as the principles that guide the construction of the main sources. This requires some knowledge of NIPA and of some software to read data (eviews, stata, gretl, R).

• Computational Tools. Students should be able to construct and characterize the properties of the equlibrium allocations of artificial model economies. This is the main element of the course and where you will spend most of the time.

• Calibration. We will spend a good deal of time thinking of how a model is related to the data. This is I think the more important part of the learning process.

Course Requirements

Class schedules.

What about knowledge of Computers?

This is not a course in computer languages so students are responsible to learn to write computer programs. Students are also responsible for learning their way around McNeil computational facilities. I do not expect anybody to have a computer at home or anything like that. It is better to work in McNeill's computer room because you can talk to each other.

• Fortran 90. This is the best and more powerfull computer language. Among economists very few prefer C. It is a little bit hard at the beginning (you have to declare variables and the like) but students have told me it is well worth to learn as soon as possible. A very good introduction to fortran can be found here.

• MPI and open MP. This is the mother of all serious calculations. It is a form of using f90 to parallelize code and take advantage of various hardwares.

• Matlab, Gauss, Scilab, Octave and R. These are very popular packages in economics. They are relatively easy to learn and code writing is easy. They generate a lot slower code than F90 (about 100 times) but they are probably a good choice to solve some problems. They may have an interface with f90 but I have never seen it working. Matlab is by now used in 90% of the cases. R and Octave are free. Dynare works with Matlab and Octave and it is dumb simple.

• Stata, Eviews, R, Gretl, and Maple, SAS. These are packages best suited for reading data. State is the most popular and expensive. (I have used fortran for this which is insane, others have used Gauss). Still it is worth to learn stata.

• Mathematica and Maple. These are packages capable of doing symbolic manipulation of equations. Occasionally they can also be used to do numeric calculations. It does not hurt to know them. They may work together with matlab and sciword.

• Excel, open office Calc. A dirty thing to do fast data manipulation. Perfect for grades. And to get output of models. Calc is free and slow.

• A program to write plots. Sciword does it as matlab and excel and gauss. Some dinosaurs like me use gnuplot.

Grading Rules

What about textbooks?