We develop an envelope condition method (ECM) for dynamic programming problems -- a tractable alternative to expensive conventional value function iteration. ECM has two novel features: First, to reduce the cost, ECM replaces expensive backward iteration on Bellman equation with relatively cheap...

We study a class of infinite-horizon nonlinear dynamic economic models in which preferences, technology and laws of motion for exogenous variables can change over time either deterministically or stochastically, according to a Markov process with time-varying transition probabilities, or both....

We study a class of infinite-horizon nonlinear dynamic economic models in which preferences, technology and laws of motion for exogenous variables can change over time either deterministically or stochastically, according to a Markov process with time-varying transition probabilities, or both....

We introduce a deep learning classification (DLC) method for analyzing equilibrium in discrete-continuos choice dynamic models. As an illustration, we apply the DLC method to solve a version of Krusell and Smith's (1998) heterogeneous-agent model with incomplete markets, borrowing constraint and...

Heterogeneous-agent neoclassical model (HANC) studied by Krusell and Smith (1998) has savings through capital. This model has a remarkable feature of approximate aggregation: the mean of wealth distribution can be accurately predicted with the mean of past wealth distribution. However, if...