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.
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.
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.
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.
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.
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 |