Solving Heterogeneous-Agent Models by Projection and Perturbation

By Michael Reiter. 2009

256 citations recorded by the source corpus.

The paper proposes a numerical solution method for general equilibrium models with a continuum of heterogeneous agents, which combines elements of projection and of perturbation methods. The basic idea is to solve first for the stationary solution of the model, without aggregate shocks but with fully specified idiosyncratic shocks. Afterwards one computes a first-order perturbation of the solution in the aggregate shocks. This approach allows to include a high-dimensional representation of the cross-sectional distribution in the state vector. The method is applied to a model of household saving with uninsurable income risk and liquidity constraints. The model includes not only productivity shocks, but also shocks to redistributive taxation, which cause substantial short-run variation in the cross-sectional distribution of wealth. If those shocks are operative, it is shown that a solution method based on very few statistics of the distribution is not suitable, while the proposed method can solve the model with high accuracy, at least for the case of small aggregate shocks. Techniques are discussed to reduce the dimension of the state space such that higher order perturbations are feasible. Matlab programs to solve the model can be downloaded.

View Paper: https://www.semanticscholar.org/paper/f7937382724cd8abd30ffedc8ac0c859223fd86b

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Citations in the corpus

Assessing the accuracy of the aggregate law of motion in models with heterogeneous agents (2010, unknown): “…to estimate the coe¢ cients of an approximating1 3Papers that do use more stringent tests to check the accuracy of the aggregate law of motion are, in addition to Krusell and Smith (1996, 1998), den Haan (1997), Reiter (2002), Algan, Allais, and den Haan (2008), Reiter (2009), and Silos (2007).”
Unemployment (fears) and Deflationary Spirals (2015, unknown): “For example, the technique developed in Reiter (2009) to solve models with heterogeneous agents relies on a perturbation solution for changes in the aggregate shock, which implies that the solution is imposed to be stable—for shocks of any size—as long as the Blanchard–Kahn conditions are…”
Comparison of Solutions to the Incomplete Markets Model with Aggregate Uncertainty (2008, methodology): “Those are the backward induction procedure , referred to as BInduc throughout this paper , developed in Reiter ( 2009b ) , the parameterized distribution procedure , referred to as Param , of Algan et al .”
When Inequality Matters for Macro and Macro Matters for Inequality (2018, unknown): “Our method builds on the ideas of Dotsey, King and Wolman (1999), Campbell (1998), Veracierto (2002), and Reiter (2009), and is related to Preston and Roca (2007).”
Transmission of Monetary Policy with Heterogeneity in Household Portfolios (2018, background): “I solve for aggregate dynamics by first-order perturbation around the stationary equilibrium without aggregate shocks as in Reiter (2009).”
The Power of Forward Guidance Revisited (2016, unknown): “Solving for aggregate dynamics Here we follow Reiter (2009). Our non-stochastic simulation algorithm tracks the distribution of wealth using a histogram.”
Precautionary Savings, Illiquid Assets, and the Aggregate Consequences of Shocks to Household Income Risk (2019, background): “Our baseline approach builds on and extends Reiter (2009) and solves for aggregate dynamics by first-order perturbation around the stationary equilibrium without aggregate shocks.”