Macroeconomic Dynamics

I. Dynamic General Equilibrium 1. Introduction. I will describe the aim and scope of this course and explain the prerequisite materials. I briefly review dynamic programming, dynamical systems, Markov processes, and stationary distribution. 2. Dynamic general equilibrium model. The model is explained using the stochastic optimal growth model and competitive equilibrium. Welfare theorems, risk sharing, and the role of finance are explained, following Ljungqvist and Sargent (2018). 3. Heterogeneous-agent model. A basic model of heterogeneous agents in dynamic general equilibrium is introduced using a firm heterogeneity model by Hopenhayn (1992). Its applications are explained by using a trade model by Melitz (2003). 4. Income and wealth disparity. The incomplete-markets model of Aiyagari (1994) is explained, and its implications on consumption and saving are detailed using Krusell and Smith (1998). II. Power Laws 5. Power laws of household income and wealth. Tail distributions of household income and wealth follow Pareto distributions, i.e., power-law distributions. Using a modified Aiyagari model (Nirei and Aoki 2016), the intuition and significance of the power-law tails are explained. 6. Power laws of firm size. The skewed distribution of firm size is explained by using the innovation models of Klette and Kortum (2004), Lentz and Mortensen (2008), Luttmer (2007, 2011), and Aoki and Nirei (2017). 7. Power law distributions. I review several mechanisms that generate power laws. Examples include random growth models, generalized central limit theorems, extreme value theorems, and critical phenomena. 8. Granular firms. As an application of the generalized central limit theorem, the granular hypothesis of aggregate fluctuations by Gabaix (2011) is introduced. Relations to Hulten’s theorem are explained, and implications beyond Hulten’s theorem are drawn by referring to Baqaee and Farhi (2019) and Carvalho et al. (2021). III. Synchronization. 9. Interactions and aggregate fluctuations. Firm-level interactions can be a source of aggregate-level fluctuations. This point is explained using Acemoglu et al. (2012), who highlight the heterogeneity of the input-output network. 10. Introduction to continuous-time process and optimization. Heterogeneous-agent, continuous-time modeling is reviewed using Achdou et al. (2021). 11. Power-law synchronization in (S,s) models. A tractable (S,s) model of menu-cost pricing is presented. I explain analytics of stochastic synchronization generated in this environment and that the synchronization exhibits power-law fluctuations, drawing on Nirei and Scheinkman (2024 forthcoming). 12. Self-organized criticality. The power-law synchronizations emerge in a class of models known as self-organized criticality. Models of firms’ investment and of investor herding are presented to show how the self-organized criticality may occur in economic equilibria.

Lectures

Term paper and/or presentation

It is a prerequisite for this course that students have solid understandings of introductory macroeconomics, microeconomics, and calculus.