The working paper is out now. Read it here.
The solution method we propose uses Chebyshev Parameterized Expectations à la Christiano and Fisher (2000) at the individual level as outlined in Binder, Pesaran, and Saimei (2000). The advantage is that the method is fast and accurate. The curse of dimensionality problem can be overcome by sparse-grid methods, such as Smolyak grids and polynomials, as proposed by Malin, Krueger, and Kubler (2007), or complete polynomials, as explained in Judd (1998). Therefore, the method is promising in handling multiple state variables at the individual level.
The numerical integration methods are standard and readily applicable. Gauss-Hermite or Gauss-Chebyshev integration gives highly accurate results. Markov-chain methods like Tauchen (1986) and Kopecky and Suen (2010) are also easily applicable. Multiple shocks can be handled by monomials or by pooling and discretizing. Tauchen's method can be used for non-Gaussian, fat-tailed shocks, if need be.
The distributions are calculated via Eric Young's histogram method (Young, 2010). The aggregate shocks are handled by the method proposed by Boppart, Krusell, Mitman (2018), i.e., by assuming linearity at the aggregate level and using transitions of model variables to an MIT shock .
I am able to solve the steady state and transitions of OLG models with many periods and with ex-ante and ex-post heterogeneity with this method.
Don't hesitate to contact me if you have questions about this method.
Binder, M., Pesaran, M.H., Samiei, S.H., 2000. Solution of Nonlinear Rational Expectations Models with Applications to Finite-Horizon Life-Cycle Models of Consumption. Computational Economics 15, 25–57.
Boppart, T., Krusell, P., Mitman, K. 2018. Exploiting MIT Shocks in Heterogeneous-Agent Economies: the Impulse Response as a Numerical Derivative, Journal of Economic Dynamics and Control, Elsevier, vol. 89(C), pages 68-92.
Christiano, L.J., Fisher, J.D., 2000. Algorithms for Solving Dynamic Models with Occasionally Binding Constraints. Journal of Economic Dynamics and Control 24, 1179–1232.
Judd, K.L., 1998. Numerical Methods in Economics. volume 1 of MIT Press Books. The MIT Press.
Kopecky, K., Suen, R., 2010. Finite State Markov-chain Approximations to Highly Persistent Processes. Review of Economic Dynamics 13, 701–714.
Malin, B., Krueger, D., Kubler, F., 2007. Computing Stochastic Dynamic Economic Models with a Large Number of State Variables: A Description and Application of a Smolyak-Collocation Method. NBER Working Papers 13517. National Bureau of Economic Research, Inc.
Tauchen, G., 1986. Finite State Markov-Chain Approximations to Univariate and Vector Autoregressions. Economics Letters 20, 177–181.
Young, E.R., 2010. Solving the Incomplete Markets Model with Aggregate Uncertainty using the Krusell-Smith Algorithm and Non-Stochastic Simulations. Journal of Economic Dynamics and Control 34, 36–41.