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Companion Code for "The Empirical Implications for the Interest-Rate Lower Bound"

by Chris Gust, Ed Herbst, David Lopez-Salido, and Matt Smith

The paper can be found here: https://www.aeaweb.org/articles?id=10.1257/aer.20121437&&from=f

contact: Ed Herbst [ed.herbst@gmail.com]

up to date version of this code: http://github.com/eph/empirical-implications-of-zlb

Software Requirements

This code was written for Linux. It may be possible to run it on OSX or Windows.

To run this code, you need:

  1. Intel Fortran (with MKL libraries)
  2. MVAPICH2 (i.e., a message passing interface.) Infiniband is highly recommended.
  3. Python (+ associated packages, for figures, tables, and estimation of the linear model. In particular, the DSGE package is required. Install this using anaconda: conda install dsge -c eherbst.)
  4. Matlab (for plotting + analying impulse responses and simulated moments)

Additional Fortran Libraries

  1. SparseAMA (https://github.com/es335mathwiz/sparseAMA) Sparse matrix version of the Anderson Moore Algorithm.

  2. json-fortran (https://github.com/jacobwilliams/json-fortran) A Fortran 2008 JSON API.

  3. FLAP (https://github.com/szaghi/FLAP) Fortran command line arguments parser.

  4. fortress (https://github.com/eph/fortress) Fortran utilities for Bayesian estimation of time series models. Only needed to estimate the linearized model.

Installation + Running

  1. Install the Additional Fortran Libraries

  2. Edit the makefile to reflect these libraries locations (and possibly LD_LIBRARY_PATH)

  3. To install individual programs, at the prompt (from this directory) type: make PROGRAM where the possible programs are described below:

    Program Name Description
    driver_irfs Computes the impulse reponse functions in Figures 2 and 3.
    driver_simdata Simulates data from the model.
    driver_selectmoments Simulates data from the model, and computes ZLB statistics for histogram in Figure 6.
    driver_prwmh Runs the particle-filter-based MCMC algorithm.
    driver_smoother Runs the particle filter and smoother for a given set of parameter values.
    driver_equitypremium Given a set of smoothed estimates, computes the equity premium.
    driver_altsim Given a set of smoothed estimates, run a counterfactual.
  4. Each program takes command line arguments. To see descriptions of the arguments type.

    ./PROGRAM --help
    

    For example:

    eherbst@thnkpd:$ ./driver_prwmh --help
    usage: driver_prwmh  [--p0 value] [--covariance value] [--prior-file value] [--scaling value] [--nsim value] [--npart value] [--zlb value] [--output-file value] [--seed value] [--help] [--version]
    
    Program for estimating model via particle MCMC
    
    Optional switches:
        --p0 value, -p0 value
         default value input/mean.txt
         starting value
        --covariance value, -H value
         default value input/cholM.txt
         Cholesky of covariance for proposal innvoations
        --scaling value, -c value
         default value 0.15
         scaling of innovation
        --nsim value, -n value
         default value 50000
         Length of MCMC chain
        --npart value
         default value 1500000
         Number of Particles for PF
        --zlb value
         default value .true.
         Impose ZLB
        --output-file value
         default value output.json
         Output file
        --seed value
         default value 1848
         Seed for RNG
        --help, -h
         Print this help message
        --version, -v
         Print version
    

    Finally, remember when actually running the program to invoke it using MPI (except driver_smoother)

    mpirun -n NPROCS ./PROGRAM --some arguments 
    

Figures + Table Generation

Figures

  1. Comparison of the posterior

    • Estimate the linear model: driver_linear
    • Estimate the nonlinear model: driver_prwmh
    • Run python/fig_linear_vs_nonlinear.py
  2. Response to an Exogenous Increase in the Risk Premium

    • Driver to run: driver_irfs
    • Figure script: matlab -r "run('matlab/plot_nonlinear_irf.m')"
  3. Response to a Fall in Investment Efficiency

    • Driver to run: driver_irfs -s 2
    • Figure script: matlab -r "run('matlab/plot_nonlinear_irf.m')"
  4. Smoothed Estimates of Model Objects

    • Driver to run: driver_prwmh
    • Get 1000 draws from the posterior: python python/sample_posterior.py
    • For each of 1000 draws run: driver_smoother -p0 results/thinned_posterior/NNNNpara.txt --output-file outputNNNN.json
    • Make plot python python/fig_observable_fit.py
  5. Model objects for different values of Measurement Error

    • Estimate the model with a different value for the measurement errors (i.e, change the last values of the parameter vector).
    • Then follow the steps in [4]. (You may want to change the directories to not overwrite earlier estimations.)
  6. Distribution of the Probability and Duration of Being at the ZLB

    • After estimating the model and thinning the posterior, run ./driver_zlbstats
    • Matlab script: matlab -r "run('matlab/generate_zlb_freq_duration.m')"
  7. The Path of the Estimated Shocks and Equitiy Premium During the Great Recession

    • Get the smoothed objects (See [4])
    • Estimate the equity premium for each set of smoothed estimates using driver_equitypremium
    • Run the python script python/fig_shocks_combo.py
  8. The Path of the Estimated Technology Shocks

    • Get the smoothed objects (See [4] and [5])
    • Run the python script python/fig_output_inf_tech.py
  9. The Contribution of the Estimated Shocks to the Great Recession

    • Get the smoothed objects (see [4]).
    • For each of set of smoothed estimates, run the 3 alt sims using driver_altsim
    • Run the python script python/fig_great_recession.py
  10. The Contribution of the Zero Lower Bound to the Great Recession

    • Get the smoothed objects (see [4])
    • For each of set of smoothed estimates, run the nozlb_2008 altsim using driver_altsim
    • Run the python script python/fig_effect_of_zlb_levels.py
  11. The Effect of the Lower Bound on Aggregate Spending

    • Get the smoothed objects (see [4])
    • For each of set of smoothed estimates, run the nozlb_2008 altsim using driver_altsim
    • Run the python script python/fig_effect_of_zlb.py

Tables

  1. Posterior Distribution of the Parameters For N=0,1,2,3

    mpirun -n NPROC ./driver_prwmh --p0 STARTING_VALUE.txt --seed ASEED --output-file results/mcmc/outputN.json
    

    Then

    python python/tab_posterior.py
    
  2. Standard Deviations of Aggregate Variables at Business Cycle Frequencies Run the posterior estimation, then thin the posterior with:

    python python/thin_posterior.py
    

    Then run the matlab script:

    matlab -r "run('matlab/generate_momentstable.m')"
    

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