Quantitative Macroeconomics Econ 5725 Ra¨ ul Santaeul`alia-Llopis, Department of Economics, WUSTL, Contact:
Office Hours: Seigle 339 T.1300-1400 Lecture location and times: Seigle 304 T.1730-2030
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Course Description
This course follows the first year PhD macro sequence: 501 and 502. Our goal in this course is to learn tools that help us to relate models to data. We aim at learning how to answer quantitative questions and we will learn to do so by doing. This will require intensive computational work by students. We will learn numerical methods (algorithms) to solve for the equilibrium allocations of representative agent models, overlapping generations models and heterogeneous agents economies taking good care of distributions and aggregate consistency in stationary and non-stationary environments such as business cycles or development processes. Course website: http://loraulet.googlepages.com/econ572-spring2009 You should check this website regularly. There I will post announcements, homeworks, additional references and a class diary that keeps track of what we are doing.
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Grades and Requirements
This course is demanding and I expect you to be engaged continuosly. The grade will be some weighted average of homeworks and presentations. In this course we are learning methods, and we learn them by using them. You should expect one homework per foreseeable Tuesday and all homeworks are mandatory. One of you (not necessary at random) will present his/her homework solutions at the beginning of each class for 10-15 minutes. You are definitely encouraged to work in groups but you will submit your homeworks individually: you will place the solution to the homeworks (and to possibly other requirements) in electronic form in /XXX/QMSpring09 in subdirectories that each student should have under his/her own name. You will have access to /XXX/QMSpring09 and your own subdirectory, for example, /XXX/QMSpring09/NeilArmstrong. You should place the solutions with your name and the homeworks name, that is /XXX/QMSpring09/NeilArmstrong/HWK-1/Readme.pdf In order to gain access to your subfolder at /XXX/QMSpring09 on the server YYY, email and become members of the /XXX/QMSpring09 group. 1
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Computer Skills
It helps if you have had previous programming experience but it is not a pre-requisite. However, it is going to be a requisite, in order to solve the homeworks in this class, to learn how to program. To learn so, you are on your own. That is, I am not going to teach you how to declare variables, generate random numbers, call intrinsic functions, link external subroutines, etc., but I am assuming that you are gaining —for those who do not have it yet— expertise on language programming by yourselves as we go along. In other words, this is not a computer science course; instead, what we learn in this class are tools and algorithms that, making use of some programming language, help us to solve modern macroeconomic models. The programming language you use is at your discretion. If you are planning to do serious computational work in your research, I encourage you to learn Fortran (good alternatives are C or C++). This requires an initial fixed cost but I think it pays off. When it comes to numerical work, the scientific community speaks Fortran and most large-scale scientific computer programs are written in Fortran. One good reason to do so is that Fortran is faster than other available alternatives, and you will care a lot about the speed when you increase the scale of your work — the second half of this course with heterogeneous agents will approach that boundary. Two good sources to learn how to program in Fortran are Chapman (1998) and . Matlab is more user-friendly than Fortran and very popular in economics. It is particularly useful if you are used to think in vector-matrix operations. This application should be fine for the first half of our course given the large amount of toolkits available to solve business cycle modelizations via (log- and) linearizations around steady states (see Uhlig, Dynare, etc.) which I will ask you to use. Some alternatives are Gauss, Scilab and Octave. To do serious data work when you are ’fishing for facts’, Stata is a good application that allows you to upload and manipulate many large data sets at once. SAS or Eviews may work fine as well. You will have to contact our IT team to learn how to access all these (or other) packages in Wash.U. Finally, by the end of the semester, if time permits, we will learn the basics of parallel programming through message passing interface.
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Textbooks
A relevant set of important and excellent references —in addition to standard macroeconomic textbooks such Stokey and Lucas (1989) and Sargent and Ljungqvist (2004)— that a graduate student that plans to use computational methods in his/her research should have is: 1. Cooley (1995) 2. Marimon and Scott (1998) 3. Judd (1998)
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4. Press, Teukolski, Vetterling, and Flannery (1992) (you can find this available and free online). 5. Heer and Maussner (2005) The last two references provide code online. Though we will not strictly follow these references, you sill see obvious intersections between what we cover in class and the material presented in those books – I will try to refer you to the relevant, with respect to this course, parts of them. The set of reference papers below regarding the course outline are yet to be tuned and will grow with the semester.
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Course Outline (to be tuned) 1. Discrete Time Stochastic Dynamic Programming (a) Finite Horizon and the Theorem of the Maximum (b) Infinite Horizon and the Contraction Mapping Theorem References: Stokey and Lucas (1989), Bertsekas (1995) Sargent and Ljungqvist (2004), Heer and Maussner (2005). 2. How can we look at data? A Quick Review Aggregate data and micro data (cross-section and panel data). NIPA, CPS(-MORG), SCF, CEX, PSID, MDICP, etc. References: Krusell, Ohanian, Rios-Rull and Violante (2000), Budria, Diaz-Gimenez, Quadrini, and Rios-Rull (2002), Castro and Cohen (2007), Heathcote, Storesletten and Violante (2007), Krueger and Fernandez-Villaverde (2006). 3. Numerical Methods (a) Local and global approximation of functions (one- and multi-dimensional) • Local methods: Taylor (and Pad´e) • Spectral methods: Polynomial Interpolation – Linear, Monomial, Chebyshev and other Orthogonal Basis • Finite element methods: Piecewise Polynomial Splines – Linear, Quadratic, Cubic and Shape-Preserving Schumaker Spline Interpolation – B-Splines • Weighted residuals methods: Least Squares, Collocation, Garlekin (b) Numerical Differentiation (c) Numerical Integration • Newton-Coates quadrature • Gaussian quadrature 3
• Monte-Carlo Methods (d) Root Finding (solving systems of equations): bisection, secant method, Newton’s method, fixed-point iteration, Gauss-Jacobi, Gauss-Seidel, Brent’s method. (e) Numerical Optimization References: Marimon and Scott (1998), Judd (1998), Heer and Maussner (2005). 4. Representative Agent Models Neoclassical growth model with stand-in households, the workhorse of modern macroeconomics; real business cycle (RBC) models; and, additional cases with a large state space. (a) Value Function Methods • • • • •
Value function iteration (VFI): Discretization Linear quadratic methods, Linearization and Log-linearization Value function approximations: interpolation, splines Finite element methods and Collocation Weighted residuals methods
(b) Euler Equation Methods • • • • • •
Policy function iteration (PFI) Linearization Value function approximations: interpolation, splines Perturbation Finite element methods and Collocation Weighted residuals methods
References: Tauchen (1986), Marimon and Scott (1998), Judd (1998), Klein (2000), Heer and Maussner (2005), Trick and Zin (2005), Aruoba, Fernandez-Villaverde and Rubio-Ramirez (2006). 5. Heterogeneous Agents with Complete Markets (a) Heterogeneity as a Representative Agent (b) The Negishi Method References: Chatterjee (1994), Maliar and Maliar (2001) 6. Heterogeneous Agents with Incomplete Markets (a) Solution Methods to Bewley-Aiyagari Economies (b) Transitional Dynamics References: Imrohoroglu (1989), Huggett (1993), Aiyagari (1994), Hopenhayn and Prescott (1992), R´ıos-Rull (1995), Casta˜ neda, D´ıaz-Gim´enez and R´ıos-Rull (2003), Storesletten (2000), Floden (2008).
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7. Heterogeneous Agents with Incomplete Markets and Aggregate Risk (a) Solution Methods to Krusell-Smith Economies References: Krusell and Smith (1996), Casta˜ neda, D´ıaz-Gim´enez and R´ıos-Rull (1998), Krusell and Smith (1998), Storesletten, Telmer and Yaron (2004a). 8. Overlapping Generations with Incomplete Markets (a) Solution Methods to Bewley-Aiyagari-Hugget Economies The case of Hybrid OLGs (b) Transitional Dynamics (c) Aggregate Risk References: Huggett (1996), R´ıos-Rull (1996), Conesa and Krueger (2002), R´ıos-Rull and Cubeddu (2003), Hong and R´ıos-Rull (2004), Storesletten, Telmer and Yaron (2004b), 9. Calibration: The Quantitative Restriction of Models References: Castaneda, Daz-Gimenez and Ros-Rull (2003), Hong and R´ıos-Rull (2004), Corbae, Chatterjee, Nakajima and Rios-Rull (2007), Schorfheide, Rios-Rull, Fuentes-Albero, Kryshko and Santaeulalia-Llopis (2008).
References Aiyagari, S. R. (1994): “Uninsured Idiosyncratic Risk, and Aggregate Saving,” Quarterly Journal of Economics, 109, 659–684. Budria, S., J. Diaz-Gimenez, V. Quadrini, and J. Rios-Rull (2002): “Updated facts on the U.S. distributions of earnings, income, and wealth,” Federal Reserve Bank of Minneapolis Quarterly Review, pp. 2–35. Chatterjee, S. (1994): “Transitional Dynamics and the Distribution of Wealth in a Neoclassical Growth Model,” Journal of Public Economics, 54(1), 97–119. Conesa, J. C., and D. Krueger (2002): “Optimal Progressivity of the Income Tax Code,” Mimeo, CRES, Universidad de Barcelona. Cooley, T. F. (1995): Frontiers of Business Cycle Research. Princeton, N. J.: Princeton University Press. Heer, B., and A. Maussner (2005): Dynamic General Equilibrium Modelling. Springer. Hong, J. H., and J.-V. R´ıos-Rull (2004): “Life Insurance and Household Consumption,” CAERP, http://www.ssc.upenn.edu/ vr0j/caerp/WPapers/vicjaycaerp.pdf. Hopenhayn, H., and E. C. Prescott (1992): “Stochastic Monotonicity and Stationary Distributions for Dynamic Economies,” Econometrica, 60, 1387–1406. 5
Huggett, M. (1993): “The Risk Free Rate in Heterogeneous-Agents, Incomplete Insurance Economies,” Journal of Economic Dynamics and Control, 17(5/6), 953–970. (1996): “Wealth Distribution in Life-Cycle Economies,” Journal of Monetary Economics, 38(3), 469–494. Imrohoroglu, A. (1989): “The Costs of Business Cycles with Indivisibilities and Liquidity,” Journal Political Economics, 97, 136483. Judd, K. L. (1998): Numerical Methods in Economics. MIT Press. Krusell, P., and A. Smith (1996): “Income and Wealth Heterogeneity in the Macroeconomy,” Unpublished Manuscript. (1998): “Income and Wealth Heterogeneity in the Macroeconomy,” Journal of Political Economy, 106, 867–896. Marimon, R., and A. Scott (eds.) (1998): Computational Methods for the Study of Dynamic Economics. Oxford University Press. Press, W. H., S. A. Teukolski, W. T. Vetterling, and B. P. . Flannery (1992): Numerical Recipes in Fortran 77 The Art of Scientific Computing. Cambridge University Press. R´ıos-Rull, J.-V. (1995): “Models with Heterogenous Agents,” in Frontiers of Business Cycle Research, ed. by T. F. Cooley, chap. 4. Princeton University Press, Princeton. Sargent, T., and L. Ljungqvist (2004): Recursive Macroeconomic Theory. MIT Press. Stokey, N. L., and E. C. Lucas, R. E. with Prescott (1989): Recursive Methods in Economic Dynamics. Harvard University Press. Storesletten, K. (2000): “Sustaining Fiscal Policy Through Immigration,” .
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