Quantitative Macroeconomics [F2019]
"The era of closed-form solutions for their own sake should be over. Newer generations get similar intuitions from computer-generated examples than from functional expressions," Jose-Victor Rios-Rull (JME, 2008).
Quantitative Macroeconomics (Unit I) follows the first year PhD macro sequence. The goal of this course is to equip you with a wide set of tools to (i) solve macroeconomic models with heterogenous agents (aka Aiyagari-Bewley-Hugget-Imrohoroglu, ABHI) economies and (ii) relate these models to data to answer quantitative questions. You will learn to do so by doing. That is, this course will require intensive computational work by students.
The ABHI economies are the industry standard in macro. These economies can take the form of infinite horizon, lifecycle environments and overlapping generations (or some hybrid of these). Importantly, the presence of heterogeneity requires taking good care of distributions and aggregate consistency. We will discuss carefully how to do this in both stationary and nonstationary environments.
This course is demanding and I expect you to be engaged continuously from day one. The grade will be some weighted average of regular homework sets and a final project.
We meet Mondays and Wednesdays 15:00-16:30 in the UAB Seminar room.
- Mon Sep 16: We went over a set of the macro questions that we will cover over the course and discussed the rules of the game.
- Wed Sep 18: We covered aspects of national accounts and the construction of macroeconomic (big) ratios such as factor shares, X-to-output ratios and the rates of return. We reviewed the Kaldor facts and where they stand. We conducted growth and development accounting exercises.
References: Karabarbounis and Neimann , Koh et. al , Aum et. al [2018.], Barro 
- Mon Sep 23: Methods I: We posed a simple static multicountry problem with a union market and free mobility of capital (but not labor) where countries differ in their labor income taxes. We introduced the projection methods algorithm. Slides: [Projection Methods: An Algorithm]. We then discussed numerical differentiation (check also integration). Slides: [Numerical Differentiation and Integration] . We then started our discussion on function approximation. We covered local methods (with pros and cons) and started our dicussion on global methods. We focused on spectral. [Function Approximation]
References: For the next three lectures there are many numerical methods textbooks out there. Check Sargent's quantitative economics lectures online and the references therein. The chapter by Fernandez-Villaverde et al.  in the Handbook of Macroeconommics is very useful. For the particular case of the endogenous grid check Carroll .
- Wed Sep 25: Methods II: We went back to spectral methods going over Chebyshev approximations with least squares. We continued our discussion on function approximation with finite element methods. We focused on linear splines and cubic splines. We then described B-splines for linear (tent functions) and quadratic basis functions. We then moved to solve systems of nonlinear equations. In addition to standard quasi-newton methods, we paid particular attention to Gauss-Jacobi and Gauss-Seidel algorithms. Slides: [Nonlinear Systems]. We discussed how to use these techniques to compute a transition in the RA-NGM. Finally, we went over free derivative methods, in particular, the Nelder-Mead algorithm. Slides: [Numerical Optimization]. ].
- Wed Oct 2 [8.15am]: Methods III: We will go over the definition of tax progressivity. Slides: [A Progressive Tax Function]. We will introduce within-country household heterogeneity in productivity and income tax progressivity in our multi-country model. We will lay down the VFI algorithm. Slides: [Value Function Methods: Discrete and Continuous Methods]].
- Wed Oct 2 [3.00pm]: Methods IV: We will move to ABHI economies and work with the endogenous grid method. Slides: [Aiyagari-Bewley-Hugget-Imrohoroglu Economies]. We will briefly look at how to handle larger problems with Smolyak polynomials. Slides: [Tensors and the Curse of Dimensionality]
References: A very useful resource is Dirk Krueger's lecture notes.
- Mon Oct 14: We discussed how to conduct welfare analysis and policy evaluation. Slides: [Welfare Analysis and Policy Evaluation].
- Wed Oct 16: Optimal tax progressivity. Slides: [OLG and Optimal Taxation]
References: Conesa, Kitao and Krueger  and Krueger and Ludwig 
- Wed Oct 21: Resource (mis)allocation and aggregate productivity. Slides: [Resource Allocation and Aggregate Productivity]
References: Restuccia and Rogerson , Hsieh and Klenow  and Chen, Restuccia and Santaeulalia-Llopis 
- Wed Oct 23: Aggregate Effects of HIV/AIDS and disease.
- [Optional] Friday TBD: Women career choice, fertility and IVF technology.
- [Optional] Friday TBD: Insurance vs. Incentives. + Default models.
References: Check the chapter on "Insurance and Incentives" in Sargent's book. Also the chapter by Quadrini and Rios-Rull  in the Handbook of Inequality.
Friday Sep 27 [TA session] On the CES approximation with capital and labor
Friday Oct 4 [TA session] Solving (1) a neoclassical transition in a RA-NGM and (2) a multi-country model with heterogeneous agents and income tax progressivity.
Friday Oct 11 [TA session] VFI
Friday Oct 18 [TA session] Resource allocation and aggregate productivity: Mismeasurement by random sampling?
Friday Oct 18 [TA session] Solving a 2-age OLG consumption model with heterogenous agents and income tax progressivity
Friday Oct 25 [TA session] A primer on CPU and GPU paralell computing
Students should expect one homework per foreseeable week of class. To post your HWK solutions you must open a GitHub account and send me (and Albert) a link with your course folder. You must also create a subfolder per HWK. In each subfolder (i.e., HWK), you must upload a readme file that organizes the subfolder, all the code necessary to generate your solutions, and a pdf [or any other form of easy-to-read output] where you discuss your results:
- [Homework 1] [Due 8.30am, Mon Sep 23] The secular behavior of the labor share of income and the rate of return.
- [Homework 2] [Due 8.30am, Mon Sep 30] Numerical differentiation and function approximation, univariate and multivariate cases. Example: A CES production function.
- [Homework 3] [Due 8.30am, Thu Oct 10] Two models: (1) A Neoclassical transitions (or miracle) and (2) a multi-country model where heterogenous agents face idiosyncratic productivity shocks and labor income tax progressivity.
- [Homework 4] [Due 8.30am, Wed Oct 16] Value function iteration with discrete and continuous methods.
- [Homework 5] [Due 8.30am, Mon Oct 28] Resource misallocation and aggregate productivity. Mismeasurement by random sampling?
- [Homework 6] [Due TBD] Finding optimal tax progressivity in a 2-age OLG consumption model with heterogenous permanent productivities, stochastic income and progressive income taxation.