Replication Files for "Household Income Inequality and Optimal Trend Inflation”

1. Software and System Requirements
The replication code was tested and executed successfully under the following environment:
    • Operating System: Windows 11 
    • Core Software: MATLAB (Version R2024a) 
    • Required Toolboxes: Optimization Toolbox, Statistics and Machine Learning Toolbox
    • Required Macroeconomic Toolkits:
        ◦ Dynare (Version 4.5.7) 
        ◦ OBC Toolkit by Tom Holden 
    • Hardware: Desktop with 13th Gen Intel(R) Core(TM) i9-13900KF (24 cores) and 128GB RAM.

2. Directory Structure and File Descriptions

    ① The "Data" folder contains MATLAB and CSV files required for plotting the inequality data.

    a. Labor Income Data.csv: This is the raw data downloaded from Realtime Inequality.

    b. intro_figure.m: This script uses the above CSV file to plot Figure 1.

    • It takes less than a minute to run this file.   

    ② The "Baseline" folder contains the MATLAB and Dynare files used to simulate the baseline no-debt model and compute the optimal inflation target.
	
    a. simul_baseline.m: This script simulates the time series of the baseline THANK model for each inflation target, each level of cyclical inequality, each level of long-run inequality, and each level of income risk.

    • This script calls THANK_zlb.mod, which is a Dynare model file specifying parameters and equations of the baseline model without debt.  

    • It takes approximately 20.5 hours to run the simulation.

    • The simulation results are saved in THANK_basesimul.mat.

b. draw_fig_baseline.m: This script loads THANK_basesimul.mat, which contains the simulation results used to compute welfare and the optimal inflation target, and generates Figures 2, 3, 4, 5, 6, 7, and 8.

    • Run this file if you want to avoid lengthy simulations and quickly replicate the results.

    • After running this file, the variables opt_inflation_rate_TANK_all_interp, opt_inflation_rate_TANK_s_interp, and opt_inflation_rate_TANK_h_interp will contain the values reported in Table 3.

    c. simul_baseline_trans.m: This script simulates the time series of the baseline THANK model for each inflation target, each level of cyclical inequality, and each degree of transfer cyclicality. 

- This script calls THANK_zlb.mod, which is a Dynare model file specifying parameters and equations of the baseline model without debt.  

    • It takes approximately 19 hours to run the simulation.

    • The simulation results are saved in THANK_endotransfer.mat.

    d. draw_fig_baseline_trans.m: This script loads THANK_endotransfer.mat, which contains the simulation results used to compute welfare and the optimal inflation target, and generates Figures 16 and 17.

    • Run this file if you want to avoid lengthy simulations and quickly replicate the results.

    e. simul_baseline_gov.m: This script simulates the time series of the baseline THANK model for each inflation target, for each level of cyclical inequality, and for each degree of government spending cyclicality. 

    • This script calls THANK_zlb.mod, which is a Dynare model file specifying parameters and equations of the baseline model without debt.  

    • It takes approximately 39 hours to run the simulation.

    • The simulation results are saved in THANK_endogovspending_alpha=lambda.mat and THANK_endogovspending_alpha=0.mat.

    f. draw_fig_baseline_gov.m: This script loads THANK_endogovspending_alpha=lambda.mat and THANK_endogovspending_alpha=0.mat, which contain the simulation results used to compute welfare and the optimal inflation target, and generates Figures 11, 12, and 13.

    • Run this file if you want to avoid lengthy simulations and quickly replicate the results.


    ③ The "Debt" folder contains MATLAB and Dynare files for simulating the model with private and government debt and for computing the optimal inflation target.  

    a. simul_privatedebt.m: This script simulates the time series of the THANK model with private debt for each debt limit and each inflation target.

    • This script calls THANK_privatedebt_zlb.mod and THANK_privatedebt_de_zlb.mod, which are Dynare model files specifying parameters and equations of the private debt model with and without direct effects of risk-premium shocks.

- It takes approximately 5 hours to run the simulation.

    • The simulation results are saved in THANK_privatedebt_simul2_1.mat and THANK_privatedebt_simul2_2.mat.

    b. draw_figfinal_privatedebt.m: This script loads THANK_privatedebt_simul2_1.mat and THANK_privatedebt_simul2_2.mat, which contain the simulation results used to compute welfare and the optimal inflation target, and generates Figures 9 and 10.

    • Run this file if you want to avoid lengthy simulations and quickly replicate the results.

    c. simul_govdebt_cycG.m: This script simulates the time series of the THANK model with government debt for each inflation target, for each degree of government spending cyclicality, for each level of tax progressivity, and for each level of government debt.

    • This script calls THANK_govdebt_zlb.mod, which is a Dynare model file specifying parameters and equations of the model with government debt.

    • It takes approximately 37 hours to run the simulation. 

    • The simulation results are saved in THANK_govdebt_simul1.mat and THANK_govdebt_simul1_3.mat.

    d. draw_figfinal_ govdebt_cycG.m: This script loads THANK_govdebt_simul1.mat and THANK_govdebt_simul1_3.mat, which contain the simulation results used to compute welfare and the optimal inflation target, and generates Figures 14 and 15.

    • Run this file if you want to avoid lengthy simulations and quickly replicate the results.