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README.md

README.md

Lewis and Vazquez-Grande (2018) r* Estimation

This code uses Bayesian methods to estimate the natural rate of interest (r*) using data through 2018-Q3. This specification was introduced in Lewis and Vazquez-Grande (2018), which is included in the paper folder for reference, along with an appendix which outlines the state space structure of the model and some other estimation details.

Executing the code

Cloning the repository and running the MATLAB script estimateModel.m will produce estimates of the unobserved series for the natural rate of interest ( r* ), the longer-run natural rate of interest ( r*LR ), potential output ( yP ), the growth rate of potential output ( g ) and the non-growth component of the natural rate ( z ). Relevant percentiles from the posterior estimates of these objects will be in the structure outVals when the estimation completes, and two files will be generated in the data\output folder containing the filtered and smoothed estimates from outVals. The folder contains two files which should be replicable by running the code as-is, though you will need to specify a directory for the larger .mat files (see below). As is stated in the comments of the code itself, users should remove the first 6 lines of estimateModel.m if they do not want to use the random number generator seed used for replication purposes.

Updating the data

The data are provided through 2018-Q3 and will not be updated further. However, the code draws its underlying data from the file lvg.data.mat. Users can update the data in the spreadsheet data\input\lvg.data.xls as desired and run dataXLS2MAT.m to create a new version of lvg.data.mat which they can use to generate new model output.

.mat file output

The estimateModel.m script will generate two .mat files which will both be sizeable. The location of these files needs to be specified using the code in lines 14 to 22 of estimateModel.m or else these output files will not be saved. The first will be called AltModel_YYYYMMDD_HHMMSS.mat (if the baseAlt variable is left set to 1) where the date and time in the filename are specified by the time the script is executed. This file will have a structure in it called res, which will contain the data and the posterior draws of the model's parameters. The second file will have the same name, with _outVals added to the end. That file will contain the data and parameter draws, but also all of the draws of the unobserved variables implied by the filter, as well as time series paths of those unobserved objects based on percentiles specified in the code.

.csv file output

After the code is run, two files generated in the data\output folder will contain percentiles of the unobserved objects of interest: the natural rate ( r* ), the longer-run version ( r*LR ), potential output ( yP ), the growth rate of potential output ( g ) and the non-growth component of the natural rate ( z ). One file contains the one-sided "filtered" estimates, and the other contains the two-sided "smoothed" estimates. The files lvgEstimatesFiltered.replicate.csv and lvgEstimatesSmoothed.replicate.csv contain the values that should result from running the code as originally released.

Description of outVals output

The structure outVals has the following components, several of which are duplicates from the input data. Note that below there are T periods, M draws from the posterior, K parameters, Ny observable series, Nu exogenous series, NS elements in the state vector, and PP is the number of percentiles shown in the posterior paths which aggregate up in the information from the posterior draws (these are originally the 2.5, 5, 16, 50, 84, 95, and 97.5 percentiles).

Field Name Description
.y Observed Data in the model (Ny by T)
.u Exogenous Data in the model (Nu by T)
.dates The corresponding dates for the observed and exogenous data (T by 1)
.vintage The date when the data was pulled
.varNames The names of the parameters in text
.varNamesLatex The names of the parameters in LaTeX
.theta The draws of the parameters from the joint posterior (M by K)
.LL The log-likelihood value based on each draw from the joint posterior (1 by M)
.LLt The period log-likelihood based on each draw from the joint posterior (T by M)
.BSDraw The backward-sampled (smoothed) draws of the state variable vectors (NS by T by M)
.FFDraw The forward-filtered (filtered) draws of the state variable vectors (NS by T by M)
.yPBSDraws The backward-sampled (smoothed) draws of potential output (T by M)
.yPFFDraws The forward-filtered (filtered) draws of potential output (T by M)
.zBSDraws The backward-sampled (smoothed) draws of the non-growth component of r* (T by M)
.zFFDraws The forward-filtered (filtered) draws of the non-growth component of r* (T by M)
.gBSDraws The backward-sampled (smoothed) draws of potential output growth (T by M)
.gFFDraws The forward-filtered (filtered) draws of potential output growth (T by M)
.rSBSDraws The backward-sampled (smoothed) draws of r* (T by M)
.rSFFDraws The forward-filtered (filtered) draws of r* (T by M)
.rSLRBSDraws The backward-sampled (smoothed) draws of longer-run r* (T by M)
.rSLRFFDraws The forward-filtered (filtered) draws of longer-run r* (T by M)
.rSBSpath The backward-sampled (smoothed) path of r* (T by PP)
.rSFFpath The forward-filtered (filtered) path of r* (T by PP)
.rSLRBSpath The backward-sampled (smoothed) path of longer-run r* (T by PP)
.rSLRFFpath The forward-filtered (filtered) path of longer-run r* (T by PP)
.yPBSpath The backward-sampled (smoothed) path of potential output (T by PP)
.yPFFpath The forward-filtered (filtered) path of potential output (T by PP)
.zBSpath The backward-sampled (smoothed) path of the non-growth component of r* (T by PP)
.zFFpath The forward-filtered (filtered) path of the non-growth component of r* (T by PP)
.gBSpath The backward-sampled (smoothed) path of the growth rate of potential output (T by PP)
.gFFpath The forward-filtered (filtered) path of the growth rate of potential output (T by PP)
.BF The Bayes Factor in favor of the model with transitory shocks, as discussed in the LVG (2018) paper
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