5. Projection methods

Readings:

(1) Miftakhova, A., Schmedders, K. and Schumacher, M. (2020), Computing Economic Equilibria Using Projection Methods, Annual Review of Economics 2020, 317-353.

• This is a recent and extremely good survey about projection methods. It gives the intuition, the state of the art, the limitations of this method as well the expected developments in this area.

(2) Maliar, L., & Maliar, S. (2014). Numerical methods for large-scale dynamic economic models. In Handbook of computational economics (Vol. 3, pp. 325-477). Elsevier.

• Another excellent survey with an emphasis on large-scale models. "This chapter provides an introduction to perturbation, projection, value function iteration, Smolyak, endogenous grid and envelope condition methods, parallel computation, supercomputers, GPUs and many other methods and shows how to use these methods to solve dynamic stochastic economic models with hundreds of state variables".

(3) Judd, K., (1998), Numerical Methods in Economics, MIT Press.

• This is the "bible" of numerical computation applied to economic problems, and, definitely, one of the most influential textbooks over the last 40 years in the field of economics.

(4) Schmedders, K., & Judd, K. L. (Eds.). (2014). Handbook of Computational Economics. Elsevier.

• This textbook represents the state of the art in numerical computation (applied to many issues in economics) at around 2014.

(5) Miranda, M.J., and Fackler, P.L. (2002), Applied Computational Economics and Finance. MIT Press..

• This is another good textbook on numerical computation and covers almost any topic we may be interested in in this field. Matlab scripts are available for the entire book.

(6) Caraiani, P. (2018), Introduction to Quantitative Macroeconomics Using Julia: From Basic to State-of-the-Art Computational Techniques, Academic Press.

• This is an excellent textbook because it covers most techniques required to solve a DSGEM (including projection methods) and provides the Julia scripts that can be used to take the models to the computer. Unfortunately, the code available is for Julia 0.6, and it does not run without amendments in Julia 1.5 (the current version).

(7) Judd, K., Maliar, L., Maliar, S., and I. Tsener, (2017), How to Solve Dynamic Stochastic Models Computing Expectations just Once, Quantitative Economics, 8, 851-893.

• This paper presents a very useful computational technique—precomputation of integrals—that makes it possible to construct conditional expectation functions in dynamic stochastic models in the initial stage of a solution procedure . "Precomputation of integrals saves programming efforts, reduces computational burden, and increases the accuracy of solutions. It is of special value in computationally intense applications ".