gboehl/econpizza

Solve nonlinear heterogeneous agent models

econpizza

Solve nonlinear heterogeneous agent models using automatic differentiation

Econpizza is a framework to solve and simulate fully nonlinear perfect foresight models, with or without heterogeneous agents. The package implements the solution method proposed in HANK on Speed: Robust Nonlinear Solutions using Automatic Differentiation (Gregor Boehl, 2023, SSRN No. 4433585). It allows to specify and solve nonlinear macroeconomic models quickly in a simple, high-level fashion and provides generic and robust routines for steady state search.

The package can solve nonlinear models with heterogeneous agents, such as HANK models with one or two assets and portfolio choice. Steady state and nonlinear impulse responses (including, e.g., the ELB) can typically be found within a few seconds. The method extends the Sequence-Space Jacobian method (Auclert et al., 2022, ECMA) to fully nonlinear heterogeneous agent models models by iteratively using Jacobian-vector producs to approximate the solution to the linear system of equations associated with each Newton iteration. This not only allows to study the dynamics of aggregate variables, but also the complete nonlinear transition dynamics of the cross-sectional distribution of assets and disaggregated objects.

To solve models with representative agents a shooting methods similar to Laffargue (1990), Boucekkine (1995) and Juillard (1996) is implemented. It is faster and more reliable than the extended path method in dynare due to the use of automatic differentiation for the efficient jacobian decompositions during each Newton-step. Nonlinear perfect-foresight transition dynamics can - even for large-scale nonlinear models with several occassionally binding constraints - be computed in less than a second.

The package builds heavily on automatic differentiation via JAX. There is a presentation on how this works behind the szenes.

Documentation

▶ User guide ▶ Quickstart tutorial

Installing the repository version from PyPi is as simple as typing

pip install econpizza

in your terminal or Anaconda Prompt.

Citation

@article{boehl2023goodpizza,
    title       = {HANK on Speed: Robust Nonlinear Solutions using Automatic Differentiation},
    author      = {Boehl, Gregor},
    journal     = {Available at SSRN 4433585},
    year        = {2023}
}

econpizza's Issues

Simulating MPC

I am working on simulating MPC for India using Econpizza. I tried using the get_distributions() function to get the disaggregated variables after applying a shock to wages(e_w) through find_path(). However, I am unsure how to recover MPCs after applying the shock. Please let me know if there is any other way of simulating MPCs using Econpizza. Any help would be greatly appreciated.

Marginal Costs in the NKPC in the One-Asset HANK Example

Hey, I was wondering whether in the example of the one-asset HANK model the marginal costs in the Phillips Curve should be specified as $\frac{w_t}{z}$ rather than only $w_t$? If so, then we would have $mc_t = \frac{w_t}{z}$ and in steady state: $mc_{ss} = \frac{\theta - 1}{\theta}$ and $w_{ss} = mc_{ss}*z$, correct? Changing this had for me only a small effect anyway, but perhaps for some nevertheless important (whenever $z \ne 1$).

Forcasting

Hi Gregor,
Sorry for the new interruption. I was wondering if there is an example to do some forcasting on real data on the econpizza package.
Thank you very much in advance!

enhancement: support for jaxopt as a more robust stst solver

I'm trying to solve a rather complex model (~100 equations), the problem is that the Newton solver is not robust enough if the initial values are a bit off, it wouldn't converge, is there any chance to implement more robust solvers or add support to utilize optimization routines from jaxopt to solve the model?

Parameter on persistence of shock in `dsge.yml`

Hey, this parameter here in the dsge.yml is the persistence of the risk premium shock, right?