Quantitative MacroEconomics (MACRO III).

12. Dec 2.

We talked about modeling households. We first thought of marital status as an exogenous state. We then discussed how to index agents, how decisions are made, what is the meaning of equivalence scales and what are the issues for which this matters. We embodied the discussion in terms of asking about changes in labor force participation of women.

The then talked about fertility, its properties, and why it is important. We then look at how to model the marriage decision in a simple environment. We saw how it takes the agreement of both parties for the marriage to occur. We ended by a discussion of how to make effort a choice variable in order to convexify a problem. Of particular interest is (like in this model) the case where the state space is discrete and we are interested in estimating/calibrating it.

With this we ended the course.

11. Nov 25.

Dirk Krueger told us about Smolyak interpolation, a method that allows to use a large number of endogenous state variables. His paper is here, while his slides are here.

Makoto Nakajima talked about the implementation of parallel computation in the Penn-Macro clusters using MPI. His page on the topic is here.

10. Nov 18.

Jay Hong will review the reading of data sets both cross section and panel. See his notes. A list with the location of data sets can be found here. In the common directory of there is a stata sample program and some codebook and data information.

Associated with this topic there are two new homeworks one with cross section and one with panel data. See below.

9. Nov 11.

Nicola described briefly the issues involved in computing a simple transition to a higher level of TFP.

We then moved to the discussion of how to obtain a generalized Euler equation in a model with optimal (endogeneous) determination of public policy without commitment. Looking only at Markov equilibria.

8. Nov 4.

Lester And Philip commented the RBC homework. We discussed how to assess the model's properties in particular how to shed light on output volatility using labor volatility and its correlation with output.

We started talking about optimal policy without commitment. I almost derived the GEE of the government for a simple economy with income taxes, a public good and a period by period balanced budget ammendament.

7. Oct 28.

We discussed the Heathcote, Violante, Storesletten paper that was presented in Wharton. In doing so we went over some issues of modelling choice, question fine tunning, measurement and equilibrium computation.

We discussed the new homework on transition, which is very easy.

We also discussed the second new homework on calculating a steady state for the Aiyagari economy stationary distribution which is longer and for which there are various parts with different due dates.

We discussed the Schumaker splines. Click here to see code for the Schumacker Splines

We did not finished as we needed to add an additional condition to determine the location of the interios gridpoint.

6. Oct 21.

   We talked about the homeworks and in particular about the next one.

   We finished the discussion of Heathcote's question about the increase of consumption induced by a tax cat, and we briefly talked how to model an asymmetric (different for rich and for poor people) cost of inflation an in Erosa-Ventura-02

5. Oct 7.

   We talked about a true economic problem. What is the impact on the economy of a tax cut. See Heathcote-03. We started by looking at how to pose an exogenous policy and by discussing how to implemented the budget constraint of the government in a representative agent model. We then discussed why there is an impact of the tax cuts, why is a Ricardian proposition violated. We talked briefly about the homeworks.

4. Sept 30.

   We talked about quadratic (local) approximations to the objective function with the constraint substituted out and why they are nice to solve formazimization functions: The Bellman operator maps quadratic functions to quadratic functions.

   We then talked about linear approximations to a function and in particular we constructed a linear approximation to the Euler equations, dynamic and static. We also talked about how to end up with a linear system that we will have to end up solving (which we will do soon).

   We discussed the notions of global approximations and briefly talked about piecewise linear functions (the tent functions) and about splines.

3. Sept 23.

   We talked about more properties to use when iterating on the discretized value function (interpolation, coarseness of the grid, policy iteration, changing accuracy). We wrote some examples of subroutines and showed how to implement the ideas of concavity and monotinicity.

   We talked about the notion of empirical questions. We discussed in the context of the question about the contribution of technology shocks to output fluctuations what constitutes an answer. We introduced the notion of calibration and defined a few calibration targets.

2. Sept 16.

   We worked in three fronts after a brief discussion of the first homework.
   • We discussed how to constract a measure of labor to obtain the Solow residual.
   • We talked about the value function and how to start thinking of approximating it. We discussed the size of the involved matrices and the fact that they are too big. We distinguish between functions and matrices to evaluate things. We described which properties (monotonicity and concavity can be used to speed up dramatically iterations of the value function.
   • We also talked about sparse matrices and I described the next homework that involves the use of an uneven spare matrix to compute a stationary distribution.

1. Sept 9.

   We talked about the class, and what is it about. We discussed the role of models as measurement tools. We discussed the first problems.

   We then started the discussion of the first question, the role of technology shocks in shaping business cycles. We talked about how to get the Solow residual (why technology is Cobb-Douglas) by constructing a measure of labor share. This requires the redefinition of GDP to treat Durables and Public investemnt as investment.

Homeworks and due dates.

This course believes drastically in Learning by Doing. To learn the material that we cover requires that students do all the homeworks in a timely manner. Given the way to collect the homeworks, timeliness is automatically recorded. I will look at what is done weekly.

Some homeworks will be asked for the following Tuesday. Others require more time and will be asked with more time. The order of the homeworks is when I pose them not when they are due. The name of the homeworks should have the information of when it is due.

1. Data manipulation. Homework 1 is due Tuesday September 16th. Name it H1_sept_16.

1.A Fetch and plot US quarterly GDP, Investment plus durables, non-durables plus services, and aggregate hours both from CPS and from the firm survey (see Cooley chapter 1, page 30). Store it in pdf, eps, and emf or wmf.

1.B HP filter and plot US quarterly GDP. Store it in postcript or pdf. Compute the same table as in the Cooley book for those 4 variables using data up to 2000:4 or later.

1.C Do the same as in the previous item but with growth rates. Comment the differences.

1.D Compute a VAR of those 4 variables and plot the impulse responses. Make sure that you explicitly state what are the identifying assumptions that you make.

2. Interpolation. Homework 2 is due Tuesday September 16th. Name it H2_sept_16.
   Write a routine that linearly interpolates. Apply it by storing the value of sin(x) between -p and p in intervals of .1 and assessing the value by interpolation in intervals of .05. Plot the function and what results from using approximation.

3. Solving Equations of one unknown. Homework 3 is due Tuesday September 16th. Name it H3_sept_16.

   (Parts pf Homework 1 of Chapter 5 of Judd's book.) Solve sin 2px- 2x=0 using bisection between x₀=-2 and x₁=2 (If this interval is a bad one change it).

4. Production Function Interpolation. Homework 4 is due Tuesday September 16th. Name it H4_sept_16.

   Compute labor factor shares with a CES production function

   Y=[qK^r +(1-q)N^r)]^1/r

   when K=N=1, and K=2, N=1. Are they the same?

   What about with Cobb-Douglas (r=1).

   Note that Labor share = w*N/Y, and that under competition w=(dY/dN).

5. Stationary Distribution Homework 5 is due Tuesday September 23th. Name it H5_sept_23.

   (Part is from Exercise 3.5 of Judd's). Use sparse matrix method to model the ergodic distribution of wealth where an individual’s wealth fluctuates because if i.i.d. wage shocks and expenditures. Assume that there are N possible wealth states and that is the transition matrix where ij = Prob {Tomorrow’s wealth is a_j | current wealth is a_i}.

   Assume there are N = 1,001 wealth states. Assume that in each state there is a small probability, 0.01, of losing all wealth and that wealth stays constant or goes up or down by 10 states. Specifically,

   • if i < 10, then p_i0 = 0.34, and p_i,i = p_i,i+10 =0.33.
   • if 10 < i < 991, then p_i,i-10 = 0.5, and p_i,i+10 = 0.5.
   • if i > 990 10, then p_i,i-10 = p_i,i =0.33, and p_i,1000 =0.33.
   In this case each row of has three or four nonzero elements. Obviously if the rows of the matrix so defined do not add up to one (and they do not) you should divide by the sum of all elements of the row to ensure that the matrix is indeed a Markov matrix.
   • a. Compute the ergodic distribution of wealth.
   • b. Compute the mean, variance, and skewness of the ergodic distribution.
   • c. Plot the Lorenz Curve
   • d. Compute the Gini Index

   Assume now that the state of an agent is both wealth that takes 10000 values and a shock s that takes 3 variables. Assume any transition for the shock that satisfies the American Dream/ America Nightmare condition. Postulate an arbitrary decision rule that is

   • Monotonic in assets.
   • Monotonic in the shock.
   • If wealth is 0, and the shock is 1, then wealth tomorrow is 0.
   • If wealth is 0, and the shock is 2 or 3, then wealth tomorrow is positive.
   • If wealth is 10000, and the shock is 1, then wealth tomorrow is 9000.
   • If wealth is 10000, and the shock is 2, then wealth tomorrow is 9800.
   • If wealth is 10000, and the shock is 3, then wealth tomorrow is 9999.
   • If wealth is 9999, and the shock is 3, then wealth tomorrow is 9999.
   In this case each row of has three or four nonzero elements.
   • e. Compute the ergodic distribution of wealth.
   • f. If the scale of wealth is equally distributed compute mean and variance

6. Value function iteration Homework 6 is due Tuesday October 7th. Name it H6_Oct_7.

   You have to write computer code to do the following. For the most basic stochastic growth model with parameters a=.3, b=.99, d=.02, q=.64, s=2., , and for a stochastic version of it with a two state Markov shock that multiplies the production function. The two values of the Markov shock are 1.015 and 1/1.015.

   1. Compute the steady state of the deterministic economy so that output is one (this may require to add a TFP parameter to normalize output to 1.).

   Write code to solve the problem of the agent when you discretize around the state state in intervals of .01% from the deterministic steady state between .85 and 1/.85 of the steady state. The accuracy to use is 10-5 of the value function. You should write different versions of this code that differ in what are the tricks that you use to solve it. For each of these versions you are supposed to record the time needed to achieve the desired precision with each of the algorithms described as well as the number of iterations that is needed. The initial value of the value function to start iterating is zero.

   The set that you have to do is

   2. Brute force successive iterations of the Bellman equation.
   3. Successive iterations of the Bellman equation taking into account only monotonicity of the decision rule.
   4. Successive iterations of the Bellman equation taking into account only concavity of the value function.
   5. Successive iterations of the Bellman equation taking into account both concavity of the value function and monotonicity of the decision rule.
   6. Use Policy iterations (waiting until converged) to solve the problem.
   7. Use policy iterations with 5, 10, 20 and 50 steps in between policy reassessments.
   8. Use interpolation. Solve the problem solving for the optimal policy at intervals first of 10\% of the state, then 1\% then .1\% and then .01\%. Use to solve the intermediate problems the method that has performed best among the previous ones.
   9. Pick one the previous methods and compare the time and number of iterations it takes to find the solution starting from a value function equal to zero versus a more inteligent choice of the value function.
   10. Do any of the previous with a labor choice that is continuous. The coefficient of leisure is .34.

7. Various small items Homework 7 is due Tuesday September 30th. Name it H7_Sept_30.
   1. Kaldor. State Nicholas Kaldor's growth facts.
   2. Growth and Preferences. Argue that only a Cobb-Douglas utility function is capable of generating the same time allocation even when the wage and the wealth have doubled.
   3. IES. Derive the intertemporal elasticity of substitution for the following utility funtion
      

      u(ct,lt)=  (ctalt1-a)1-s-1 1-s .

   4. Differentiability of the T operator. Show that under some conditions (specify which) on v^m, v^m+1 is differentiable, where
      

      vm+1( z,k) = max 0 �£ k�¢ �£ f(z,k)  u[f(z,k)-k�¢]+b       �å z�¢      G z,z�¢  vm(z�¢,k�¢).

8. Linear Approximation to an Euler Equation Homework 8 is due Tuesday October 14th. Name it H8_Oct_14.
   1. With Leisure. Write a linear approximation to the the dynamic first order condition of the economy in problem 6.h. It should have as arguments 3 capitals, 2 shocks and 2 leisures (all in deviations to the steady state.
   2. Getting rid of Leisure. Use a linear approximations to the static first order conditions to get rid of leisure today and tomorrow and end up with 2 shocks and three capitals.

   (Use either a routine to numerical derivatives or a program that yields symbolic derivates to obtaind the coefficients of linear approximations.)

9. Global Approximation to a function with various methods. Homework 9 is due Tuesday October 21th. Name it H9_Oct_21.

   Take the simple function   y = e^x on the interval [1,3].

   1. Compute a piecewise linear approximation with 20 equally space pieces.
   2. Compute a Chebyshev approximation with 10 pieces.
   3. Compute a standard spline with 10 pieces.
   4. Compute a Schumaker spline with 10 pieces.
   5. Report the approximation errors using a Galerkin and a colocation criteria.

10. Local approximation to the neoclassical growth model. Homework 10 is due Tuesday October 28th. Name it H10_Oct_28.

    I recommend that you use matlab (or octave with Uhlig's toolbox).

    Take the simple RBC model of Hansen (1985) with non-convexities (and lotteries) in labor.

    1. Calibrate its steady state to have a labor force participation of 70%. Report the parameters.

    Posing the process for the shock from Cooley Prescott (1996).

    2. Solve the model by log-linearization.
    3. Simulate 500 samples of length 200, filter them and compare their statistics with those of the latest 50 years.
    4. Do the same thing with a steady state labor force participation of .5.
    5. Do the same with a process for the shocks that equates the standard deviation of hp-filtered output volatility between the model and the date.
    6. Do the same without the nonconvexity in labor and with steady state hours calibrated to .25. In this case pose a log consumption + A log Leisure utility function.
    7. Discuss your findings.

11. Simple Transition. Homework 11 is due Tuesday November 4th. Name it H11_Nov_4.

    Take the model of the previous problem with continuous leisure (10.f) and calculate the necessary TFP (a multiplicative constant to the production functions) so that in steady state output is set to be 1. Then report the implied value of capital. Assume that TFP surprisingly doubles, compute the transition to the new steady state assuming that the transition is completed after 400 quarters. Plot the implied paths for the main macro aggregates and the interest rate. How long does it take for capital to increase 70% of the total implied increase.

12. The Aiyagari Economy An economy has a continuous of agents with idiosyncratic shocks to earnings. Earnings follow a 4x4 Markov chain (take the numbers from the transition on wages of Castaneda, Diaz-Gimenez and Rios-Rull 2003). Use a discount rate of .97 and a coefficient of risk aversion of 2.
    1. Pose and solve the problem of the household given a capital labor ratio that yields an interest rate of 2%. Plot the solution for each shock and wealth. Approximate the decision rule by a suitable function that induces small errors in the Euler equation. Make sure that you explain what you are doing. Make sure that you write the code as subroutines that you can use without change for answering the rest of this problem.
    Homework 12-a is due Tuesday November 11th. Name it H12a_Nov_11.
    2. Calculate the steady state (ergodic) distribution implied by that decision rule both by approximating the distribution function and by generating a large sample of agents, say 100,000. Comment on the relative difficulty and accuracy of these two approaches.
    Homework 12-b is due Tuesday November 18th. Name it H12b_Nov_18.
    3. Solve for the steady state. This implies finding the market clearing capital labor ratio.
    Homework 12-c is due Tuesday November 18th. Name it H12c_Nov_18.

13. The Cross-Section Data Problem Homework 13 is due Thanks Giving day November 27th. Name it H13_Nov_27.

Define a subset of individuals and a year and compute the value of a labor market variable for such subset of individuals using the CPS. Compute an expenditure variable for that subset of individuals using the CEX and a wealth variable using the SCF for the closest year. Use all three data sets to compute the type of family in which they live and report them all in a coherent and simple fashion. Do not do the same thing as the other students in the class.
14. The Panel Data Problem Homework 14 is due Thanks Giving day November 27th. Name it H14_Nov_27.

1. Using the PSID characterize the transition between all relevant years of a variable for a certain group of people. Say, take those females that were 22 to 27 in 1970 and report the evolution of their marital status including children 3 or under, 4 to 6 and 7 to 17.

2. Use the NLSY and the HRS and compute the evolution of some health variable (such as smoking habits) over time. Make sure that you include the individual persistence of this variable.




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Course Description

This course should be thought of as the third course of the Macro sequence, it follows naturally after 702 and 704. Its purpose is to learn the map models to data i.e. to answer questions that we are interested in. Most of these questions are quantitative in nature and so the type of answers that we will try to give will also be quantitative. We will develop these tools by stating general questions, and then discussing how to approach its answer.

The tools that we will be developing beyond those already covered can be grouped into:

• 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 some data and of understanding the way it is organized as well as the principles that guide the construction of the main sources. This requires some knowledge of NIPA and of the way data are organized,
• Computational Tools. Students should be able to construct and characterize the properties of the equlibrium allocations of artificial model economies.
• Calibration We will spend a lot of time thinking of how a model is related to the data. This is I think the more important part of the learning process. We will discuss this in much detail.

This is a Ph.D. course not a Masters course. As such students are not expected to learn what other people have discovered, but the tools that are needed in order to discover things by themselves. Because of this reason the active work of the students is crucial to achieve the objective of mastering the tools that are described above. This is a course to learn to do things, and, therefore, it requires to do some things.

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Class schedules.

There are regular lectures on every foreseeable Tuesday.

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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.

There are three general classes of computer languages.

• Fortran 90. This is the best and more powerfull computer language. Among economists nobody prefers C. It is a little bit hard at the beginning (you have to declare variables and the like) but all students tell it is well worth to learn it as soon as possible. A very good introduction to fortran can be found HERE.
• Matlab, Gauss and Octave. 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 growing at the expense of gauss.
• 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.

In the past I have not pushed people hard to learn F90 in addition to matlab or gauss. Talking with students that took the course previously and that are in the process of writing their dissertation they recommend that students should learn languages of all types. I recommend that homeworks should be asnwered in more than one language. I also strongly recommend that you learn F90. At least one homework should be answered in f90.

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What about textbooks?

In addition to the standard macro books (Stokey-Lucas-Prescott-89, Harris-87, Ljungqvist-Sargent-00) I find that there are a few books of interest.

• Cooley-Prescott-95. It is now dated but it contains some important lines of attack on business cycles. The computational techniques are a little bit obsolete, but the questions less so.
• Judd-98 is a general computational textbook with special attention to economists. While it is short on some details that we care about (complicated equilibrium considerations, multidimensional value functions, multidimensional interpolation) it is a very useful book for many topics.
• Marimon-Scott-98 has a bunch of chapters that deal with specific problems. I find the continuous time chapter nice as well as some scattered other chapters.
• Miranda-Fackler-02 is quite a nice book. Like others it is too irrelevant in some places and too easy in others. It is designed for matlab which is a pity, but it has a nice implementation (via a downloadable toolbox) of function global approximations.

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Grading Rules and Empirical Requirement.

To satisfactorily complete the course, students will answer all the homeworks satisfactorily. To pass the empirical requirement, students have to write a project that will just require a description (not completion) of an independent paper. For those that do not register but take the course, I recommend that they do the homeworks. We learn to solve problems by facing them. Learning jointly with others greatly speeds the process. The deadline for the Empirical Requirement is the last day of class.




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Syllabus in terms of Economics.

An initial listing of the material that I will cover follows. We will not follow this order in classes necessarily. This is a conceptual order not a lectures order. In lectures we will move in and out of the theory, the computation, the empirical definitions and the calibration.

Things might (and will) be added and deleted, partly reflecting the audiences' tastes.

1. Introduction. What is a Model?
   • A measurement tool: How big is bla bla ?
   • A device to assess the implications of changes: What happens if bla bla bla?

2. First Question. How big is the contribution of productivity shocks to aggregate fluctuations: the most basic structure.
   • Review of the theory. The optimal growth model. Using dynamic programming to solve for the optimal allocation. The second welfare theorem. A Recursive version of the second welfare theorem.
   • Computation of the model. This will involve the review of more than one method to solve a functional equation.
     • Solving for the Value function.
       • Linear quadratic. Uhlig-95, Hansen-Prescott-95.
       • Discretization of the state space. Brute force iteration. Other ways: Trick-Zin-93.
       • Splines. Trick-Zin-97.
       • Piecewise linearization.
       • Other.

     • Solving for the Euler Equations.
       • Piecewise linearization. Wherever.
       • Other. McGrattan-97 in Marimon-Scott-98.

   • Calibration of the model. This is the most important part of the chapter. So far calibration has been a tainted word with too many meanings. We will introduce a very disciplined approach to restrict the model quantitatively. Cooley-Prescott-96.

3. Another question. What are the implications of increasing wage inequality? (Heathcote-Storesletten-Violante-03, Krueger-Perri-01)
   • How to measure wage dispersion? Temporary versus permanent changes.
   • Transition, deterministic evolution over time. Convergence to a new steady state.

4. Extensions to the basic question. Does feature bla bla matter? We will review a few of them to learn about other classes of economies, which means both a new set of calibration and computational issues.
   • The use of lotteries to convexify and to have heterogeneity within the representative agent structure (Indivisible labor. Hansen-85, Kydland and Prescott-91, Osuna-Rios-Rull-01.)
   • Monetary Distrubances. Cooley-Hansen-88, Chang-95, Altig-Carlstrom-91, Freeman-Kydland-98.
   • S,s investment policies. Veracierto-97 and other investment multiplant environments.

5. OLG Models. We will look at the basic Auerbach-Kotlikoff-87 model in the context of, say, a steady state social security question, or a general taxation question, Fullerton-Rogers-93.
   • Demographics. Wage profiles.
   • Demographics. Marital Status. Cubeddu-Rios-Rull-95, Cubeddu-Rios-Rull-03.
   • Demographics. Children. Hong-Rios-Rull-04

6. Economies with measures of agents. Steady states and transition.
   • The size of precautionary savings. Aiyagari-94.
   • Wealth and income inequality. Castañeda-Díaz-Giménez-Ríos-Rull-03, DeNardi-03.
   • Tax redistribution. Castañeda-Díaz-Giménez-Ríos-Rull-03, Conesa-Krueger-03.

7. Economies with measures of agents. Aggregate Fluctuations.
   • Business cycles. Krusell-Smith-97, Krusell-Smith-98, Rios-Rull in Marimon-Scott-97, Castañeda-Díaz-Giménez-Ríos-Rull-98.

8. Non-concave problems. Technical difficulties.
   • Entrpreneurship, creation and destruction of firms. Quadrini-97, Cooley-Quadrini-98a, Basaluzzo-04, Terajima-04.
   • Durable goods and housing. Diaz-Luengo-02, Fdez-Villaverde-Krueger-01, Rady-Ortalo-Magne-03, Nakajima-04.
   • Marriage choice. Burdett-Coles-01, Regalia-Rios-Rull-01, Rios-Rull-Seitz-04, Rios-Rull-Wong-04. Aiyagari-Greenwood-Guner-97, Knowles-98, Regalia-Rios-Rull-98.
   • Bankruptcy. Agents have the option to file for bankrutpcy or not. Chatterjee-Corbae-Nakajima-Rios-Rull-03,
   • Bankruptcy and private information. Chatterjee-Corbae-Rios-Rull-04.

9. Positive theory of Policy models.
   • The problem under commitment. Chari-Christiano-Kehoe-95.
   • Markov equilibria without commitment, the GEE. Klein-Krusell-Rios-Rull-03.
   • Non-Markov Equilibria without Commitment. Fdez-Villaverde-Tsivinsky-03. Phelan-Stachetii-01.
   • Debt without commitment, non concavities galore. Krusell-Martin-Rios-Rull-03.
   • Incentive problems. Kocherlakota-Tsivinsky-?-02. Others.




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Syllabus in terms of Computational Tools.

• Basic Numerical Problems
• One-dimensional Interpolation
• Multi-dimensional Interpolation
• Solution of one Equation.
• Solution of Equation systems.
• Numerical Derivatives.
• Integration.
• Functional Equations.
• Local linear approximations
• Local non-linear approximations
• Discretizations
• Other more sophisticated methods (collocation, etc etc more later).
• Storage of measures.
• The approximation of measures (distribution functions)
• Sampling.
• Forecasting of prices via moments.
• Linear regressions.
• Other.
• Data manipulation (EVIEWS, STATA, SAS, GAUSS, F90, MATLAB)
• Understanding data sets
• Reading data sets
• Processing the information..

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Sites and material of interest to people in this class.

• Splines Module and Driver for Schumacker splines with and without derivative information written by Makoto Nakajima from the algorithm described in Judd's book. These routines are particularly well written in terms of containing sufficient comments to be used by others or by the writer after some time of having written them. Take them as models of styly.

• Fortran GAMS repository. This is an excellent source of code (mostly publicly available) for standard fortran routines.
• Tom Sargent's page. It has a very usefull book in Macro with Ljunqvist. Perhaps look at the Asset pricing and money chapters. It has also Matlab codes.
• Fortran Implementation of Tauchen's method to map gaussian (normal) processes into Markov Chains in "Finite State Markov-Chain Approximations to Univariate and Vector Autoregressions," Economic Letters. If you prefer code in Gauss you have to dig from here
• Various routines of interest. They include some explicitly pointed to below and others (such as a couple of routines in fortran 77 to implement the linear approximation to the return function). quadap.f .
• Jay Hong's update of Dan Silverman's update of Claudia Olivetti's Instructions to read data sets with comments on what those data sets are good for. Fall 2002 version.
• Dan SIlverman's basic commands for stata Olivetti's Instructions to read data sets with comments on what those data sets are good for. 2002 version.
• Claudia Olivetti's Instructions to read data sets in PDF. 1999 version.
• Claudia Olivetti's dictionary file referred to in the instructions.
• Claudia Olivetti's extract from the codebook referred to in the instructions.
• Claudia Olivetti's programs in ascii 1999 version.
• Guide to available mathematical software This is a government sponsored site that has a very nice decision tree that allows you to get sets of f77 subroutines that solve a large class of specific problems. I use it specially for its non linear equation solvers. It looks to me a lot better and more useful than IMSL.
• Minneapolis Fed Research Dept. It has the wrong address in Zimmerman's page.
• Christian's Zimmerman RBC Page
All (and more) that you need to get in the RBC business. Links to papers, people and, more usefully, CODE and DATA from various sources.
• rbc.src This is a file with three procedures (the gauss name for subroutines). Two of them "quad" and "quadp" perform the linear quadratic approximation (with minor differences on something that I do not remember), the other, "reduce" does the reduction operation. This can also be found in the previous link by going to codes and then go Gary Hansen's.
• Paul Klein's lecture notes on linearizing Euler equations.
• Paul Klein's using the generalized Schur form to solve a multivariate model is no longer on line. It is a Sept 2000, JEDC paper. It is harder to read than before.
• Harald Uhlig's toolkit for the undetermined coefficient method. This page is great and it includes a fantastic set of matlab programs that do all the jobs of linearization.
• Trick and Zin on discretization of space dynamic programming.
• Trick and Zin on splines.
• My papers are here.
• A very good introduction to fortran.

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Readings

• 2. For the second day read Chapter 2 and 3.3, 3.4, 3.5 of Judd's book.
• 4. For the fourth and fifth days read these notes by Jonathan Heathcote on linearizing systems and or these notes by Fabrizio Perri or even these notes by Harald Uhlig.
José-Víctor Ríos-Rull <vr0j@econ.upenn.edu>