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 [[email protected]]

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')"