*"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 follows the first year PhD macro sequence: Econ 501 and 502. The goal of this course is to equip you with a wide set of tools to (i) solve macroeconomic models with heterogenous agents 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.

First, we will discuss numerical methods to solve for the equilibrium allocations of representative agent models. Second, we will study how to solve heterogeneous agents economies in infinite horizon, lifecycle environments, and with overlapping generations. In macroeconomic models, 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 such as business cycles or development processes of structural transformation.

This course is demanding and I expect you to be engaged continuously. The grade will be some weighted average of regular homeworks, and an original research project to be presented in class.

We meet Tuesdays 17:30-20:30 in Seigle Hall 348.

**Tue Feb 2:**We went over the syllabus [.pdf] and discussed the rules of the game. Then we started with some macro quantitative tools to measure big ratios and their behavior in the long run and the short run. We discuss different detrending procedures and the definition of trend and cycle. We discussed the basic business cycle statistics and associated labor market puzzles with respect to the neoclassical growth theory with TFP shocks. Slides: [Macro Data and Tools]**Fri Feb 5:**We carefully defined labor share. This required taking care of ambiguous income. We also discussed alternative meaures such as the corporate LS, the BLS labor shares (headlines vs. MPF Division), and the naive labor share. Then we used the paper with Don and Yu on IPP (i.e., intellectual property products) capital to show that IPP capital accounts for the entire decline of the US labor share, which is otherwise secularly constant for traditional capital (i.e., structures and equipment). 'Ideas' capital wrecks the notion of balanced growth, the labor share declines.**Tue Feb 9:**We discussed the construction of the price of investment in national accounts, and its implications for the growth (TFP measures) and for the business cycle. We discussed the short- and long-run identifications behind the Structural VAR systems. Our working examples were Gali 1999 and Fisher 2006. We then discussed the alternative views of Chari, Kehoe and McGrattan versus Christiano, Eichenbaum and Evans about the usefulness of SVARs to guide theory (and policy).**Fri Feb 12:**We initiated our discussion of micro data and tools. We went over the CPS, the SCF, and CEX data. We discussed the notion of skill-biased technical change. We also explored the behavior of consumption, income and wealth in the cross-section and over time. We discussed the relevance of household structure controls, and the notion of partial insurance from the evolution of cross-sectional behavior. Slides: [Micro Data and Tools]. Michael presented the 'Ideas and Growth' 2009 paper by Lucas.**Tue Feb 16:**We went over the permanent-transitory decomposition of labor income risks. We discussed how to use moments of the variance-covariance residual matrix to pin down the parameters in the PT income process. Tasks: Lijun (talked about the new SCF waves), Michael (discussed life insurance patterns in the US), Juan (went over marital sorting from Greenwood, Guner and Santos), and Hoi Pan and Alex dealt with two of the Luca's "Ideas and Growth" followups including the "Global Difussion of Ideas".**Tue Mar 22:**Quick review of computational methods. Take this as your launching pad to computation. After this you are on your own.
Slides: [Function Approximation] **Sat Mar 26:**We covered in detail value function iteration with the stochastic neoclassical model. We applied VFI using several methods to approximate for the value function, from discrete methods to continuous methods such as B-splines. We then went over some tricks that we know to speed up the turtle VFI. Slides: [Value Function Iteration]**Tue Apr 5:**We went in detail over the (log-)linearization of the stochastic neoclassical model. We characterized the solution, stationarized the economy, found the steady state, linearly approximated the economy around the steady stae, and finally discussed the matrix representation and decomposition of the linear system that we want to solve. We discussed the eigenvalue decomposition and the method of undetermined coefficients. We also discussed alternative sources of fluctuations (investment shocks) and propagation mechanisms (capital utilization). We also introduced habit persistence and the extensive margin a la Cho and Cooley (1994). Slides: [Linearized Euler Equation Methods]**Tue Apr 26:**Guest lecture by Yu Zheng (EUI)**Fri Apr 29:**David and Alex will go over the set of HWK.**Tue May 3:****Fri May 6:**

Slides: [Numerical Integration and Differentiation]

Slides: [Solving Nonlinear Systems]

Slides: [Numerical Optimization]

Students should expect one homework per foreseeable Tuesday:

- [Homework 1] The secular behavior of the labor share and business cycle analysis.
- [Homework 2] Redo HWK1 with vintage data released in 1998, and in 2012.
- [Homework 3] Permanent-Transitory decomposition of the income process.
- [Homework 4] Computing a transition in the neoclassical growth model.
- [Homework 5] VFI
- [Homework 6] Solve a business cycle model.