Introduction Solving economic models involves (i) finding the optimal response of individuals given the state of the economy (the policy functions); (ii) given the policy functions, simulating the model. While usually one must show great ingenuity and creativity for the former, the latter is often seen as trivial and not even mentioned. However, in this notebook I describe a simulation procedure that deserves to be advertised. Namely, I describe Young’s method (2010) to simulate a large number (infinity) of individuals. The code can be downloaded here.
Introduction The Bewley-Huggett-Aiyagari-Imohoroğlu economies are the workhorse of modern macroeconomics. In these economies, markets are “incomplete”. Agents cannot fully insure against risk and decide to self-insure by holding a safe asset to smooth their consumption (see Ljungqvist and Sargent (2018) for a textbook treatment of this topic).
In this post, I consider the model of Aiyagari (1994). While the original model abstracts from aggregate fluctuations, Economists have since developed several techniques to simulate out-of-steady-state dynamics for this class of models.
In a previous post I presented the BKM algorithm , which can used to approximate solutions of macroeconomic models with aggregate uncertainty and heterogeneous agents. This class of models has been been of great interest for Economists for quite a long time. For instance, Aiyagari (1994) already hinted that taking into consideration heterogeneity along the business cycle is both theoretically important and challenging:
This class of models may also be useful in resolving various asset return puzzles. Mehra and Prescott [1985, p. 145] suggested that these puzzles cannot be “accounted for by models that abstract from transactions costs. This is a very hard problem computationally since the distribution of assets across households can no longer be taken to be constant. Instead, the cross-section distribution is part of the state vector that evolves stochastically over time in response to aggregate shocks. This is an issue that remains to be explored