# Research

### Spooky Boundaries at a Distance: Exploring Transversality and Stability with Deep Learning

In the long run, we are all dead. Nonetheless, even when investigating short-run dynamics, models require boundary conditions on long-run, forward-looking behavior. In this paper, we show how deep learning approximations can automatically fulfill these conditions.

### Differentiable State-Space Models and Hamiltonian Monte Carlo Estimation

We propose a methodology to take dynamic stochastic general equilibrium (DSGE) models to the data based on the combination of differentiable state-space models and the Hamiltonian Monte Carlo (HMC) sampler.

### Doubling Down on Debt: Limited Liability as a Financial Friction

We investigate how a combination of limited liability and preexisting debt distort firms’ investment and equity payout decisions.

### Exploiting Symmetry in High-Dimensional Dynamic Programming

We provide a new method for solving high-dimensional dynamic programming problems, and recursive competitive equilibria with a large (but finite) number of heterogenous agents.

### Eigenvalues and Eigenvectors of Tau Matrices with Applications to Markov Processes and Economics

We study the properties of eigenvalues and eigenvectors of the generator $T_{n,\epsilon,\phi}$ of the $\tau_{\epsilon,\phi}$ algebra.

### Reconciling Models of Diffusion and Innovation: A Theory of the Productivity Distribution and Technology Frontier

We study how innovation and technology diffusion interact to endogenously determine the shape of the productivity distribution and generate aggregate growth.

### Equilibrium Technology Diffusion, Trade, and Growth

We study how opening to trade affects economic growth in a model where heterogeneous firms can adopt new technologies already in use by other firms in their home country.

### Quantitative Economics with Julia

This online textbook presents a set of lectures on quantitative economic modeling. The language instruction is Julia.

### Introduction to Economic Modeling and Data Science

This online textbook presents a series of lectures on programming, data science, and economics.

### Technology Adoption and the Big Pull

Why doesn’t migration, joint ventures and foreign direct investment rapidly diffuse technology by investing in or moving to cheaper locations?