ikc

This repository replicates the figures and tables in "The Intertemporal Keynesian Cross" (Auclert, Rognlie, and Straub JPE 2024). [Published version]

The code requires the Sequence Space Jacobian (SSJ) toolkit version 1.0, in addition to standard numerical Python packages (numpy, scipy, matplotlib, numba, pandas) and Jupyter notebooks. We have tested it using Python 3.10+. The SSJ toolkit can be installed using pip install sequence-jacobian; please see the toolkit site for additional instructions.

If you run into any difficulties with the code, please feel free to post on the repository's issue tracker.

Organization

Most of the results of the paper are obtained in three main Jupyter notebooks, each of which is associated with some sections in the main text, and produces figures and tables for those sections, in addition to closely related appendix figures and tables:

• main_sec34.ipynb (sections 3 and 4) calibrates our household models and compares their iMPCs to those in the data
• main_sec5.ipynb (section 5) studies the effects of fiscal policy subject to the IKC
• main_sec67.ipynb (sections 6 and 7) sets up our quantitative environment and studies the iMPCs out of capital gains and effects of fiscal policy in that environment

Most of the code runs quickly, but the calibration of the two-account model in main_sec34.ipynb can take a few minutes. To make this run more quickly, you can comment out the line that solves for the calibration and uncomment a line where we hardcode it.

There are also three notebooks that correspond to more specialized parts of the appendix:

• appendix_solution_methods.ipynb considers five approaches to solving the IKC and produces Figure A.1
• appendix_shiw.ipynb processes survey data to produce the lower bound in Figure 1, as well as Figure C.1
• appendix_determinacy.ipynb tests determinacy of the models in the IKC environment via the winding number test (see our companion note)

There are supporting modules in three folders:

• models/ specifies our various models of the household consumption function and iMPCs $\mathbf{M}$ (RA, TA, BU, TABU, ZL, HA-one, HA-two, HA-hi-liq)
• plotting/ has three modules, one for each of the three main notebooks, that take the calculations from those notebooks and produce figures and tables
• base/ contains all other supporting modules

Further details are provided in README.md inside models/ and base/. Finally, data/ includes the raw input data we take in, figures/ is the output directory for figures, and intermediates/ stores the two intermediate outputs produced by our code (solved_params.json giving the calibrated household parameters produced by main_sec34.ipynb, and impc_lb_italy.txt giving the iMPC lower bound produced by appendix_shiw.ipynb).

Below we have a more complete outline of the contents of each of the main notebooks.

Detailed outline of main notebooks

Part I: IKC environment, calibration and iMPCs - sections 3 and 4 (main_sec34.ipynb )

• Figure 1 - iMPCs in the Norwegian and Italian data
  • Norwegian iMPCs: read from data/FIG2_c1R_inc_weight.csv (obtained from Fagereng, Holm, Natvik)
  • Italian iMPCs: read from impc_lb_italy.txt, computed in appendix_shiw notebook (source data in data/shiw2016.csv)
• Figure 2 - iMPCs in the Norwegian data and several models
• Figure 3 - iMPCs in eight standard models
• Figure 4 - log iMPCs out of unexpected and expected income shocks
• Figure D.1 - asset Jacobians (companion to Figure 3)
• Figure D.2 - policies and distributions in HA-one
• Figure D.3 - policies and distributions in HA-two
• Table 2 - calibrating models of the intertemporal consumption function
• Table D.1 - distributional statistics for all heterogeneous-agent models

Part II: fiscal policy in the IKC environment - section 5 (main_sec5.ipynb)

• Figure 5 - multipliers according to the IKC
• Figure 6 - effect of adding cognitive discounting to, and of truncating the tails of M
• Table 4, part I - multipliers in the IKC environment
• Figure A.2 - PE to GE: fiscal policy, monetary policy, and deleveraging
• Figure E.1 - lump-sum taxation
• Figure E.2 - multipliers across all eight models in the IKC environment
• Figure E.5 - effect of discounting applied separately to M and MT (companion to Figure 6)

The notebook also verifies numerically propositions 4, 5, 6, 7 and 11

Part III: quantitative environment (sections 6 and 7) (main_sec67.ipynb)

• Figure 7 - iMPCs out of capital gains vs income
• Figure 8 - government spending shock in quantitative two-account model
• Figure 9 - multipliers in the quantitative models
• Figure 10 - decomposing the consumption responses in the two-account and TABU model
• Figure 11 - role of monetary policy: contrasting active Taylor rule, ZLB, and constant real rate
• Table 3 - calibration of the quantitative environment
• Table 4, part II - multipliers in the quantitative environment
• Figure F.1 - robustness to holding equity only in the illiquid account
• Figures G.1-G.4 - sensitivity of impulse responses to parameters

The notebook also uses the winding number test to solve for the Taylor rule thresholds required for determinacy in the quantitative environment

Note:

The code to produce Figures E.3 and E.4 (nonlinearities and state dependence) is currently missing since running it requires us to update the public SSJ repo first. Stay tuned for an update.