Applying the Explicit Aggregation Algorithm to Heterogeneous Macro Models

This paper applies the explicit aggregation (Xpa) algorithm developed by den Haan and Rendahl (J Econ Dyn Control 34:69-78, 2010) to the heterogeneous-firm models of Khan and Thomas (J Monet Econ 50:331-360, 2003; Econometrica 76:395-436, 2008) and the heterogeneous-household models of Krueger et al. (in: Taylor, Uhlig (eds) Handbook of macroeconomics, vol 2. Elsevier, Amsterdam, pp 843-921, 2016). We find the Xpa algorithm is an order of magnitude faster for solving these models than the standard Krusell-Smith (KS) algorithm because it does not need to simulate the distribution of individual capital and productivity when updating the aggregate forecasting rules. However, the simulation results in the Xpa and KS algorithms in terms of both the micro- and macro-level moments are almost identical, even in levels, because of bias correction. The Xpa algorithm also exhibits accuracy comparable with the KS algorithm.