tvp-qr

Description

These codes come without technical support of any kind. The code is free to use, provided that the paper is cited properly.

Codes based on M. Pfarrhofer (2022): "Modeling tail risks of inflation using unobserved component quantile regressions" Journal of Economic Dynamics and Control 143 104493, using time-varying parameter quantile regressions (TVP-QR) with dynamic shrinkage priors and a time-varying scale parameter.

The file data_raw.rda contains the quarterly inflation series for the United States (US, 1947–2021), the United Kingdom (UK, 1960–2021) and the euro area (EA, 1990–2021).

Source files

• !example is the main file which loads the data, estimates unobserved component quantile regressions on a grid of quantiles and plots the estimated quantiles over time (requires user input)
• !qrdhs contains the MCMC sampler tvpqr() for a single quantile and the wrapper tvpqr.grid() which estimates a grid of quantiles in parallel (is sourced automatically from !example)
• aux, ffbs.cpp and jpr_qr.cpp contain helper functions, including forward filtering backward sampling for the time-varying parameters and the JPR (Jacquier, Polson & Rossi) sampler for the time-varying scale parameter (are sourced automatically from !qrdhs)
• dsp_aux implements the dynamic horseshoe prior, adapted from the dsp R-package by D. R. Kowal (see Kowal, Matteson & Ruppert, 2019, "Dynamic shrinkage processes", JRSS-B 81(4) 781–804)

All files are sourced by relative path, so the working directory must be the repository root.

Estimation options in !example

• sl.cn selects the country, choose from US, UK or EA
• grid.p sets the grid of quantiles
• prior refers to the prior on the time-varying parameters, choose from:
  • dhs dynamic horseshoe
  • shs horseshoe prior on the state innovations (time-specific local scales)
  • iG inverse gamma prior on constant state innovation variances
• MCMC settings (nburn, nsave, thinfac) are set in the file, and the number of cores via cpu in tvpqr.grid()

Both specifications are estimated, with a time-invariant (UCQR-TIS, sv=FALSE) and a time-varying scale parameter (UCQR-TVS, sv=TRUE). The posterior means of the quantiles are plotted over time for both models.

Requirements

R packages Rcpp, RcppArmadillo (with a working C++ compiler), Matrix, MASS, spam, pgdraw, stochvol, GIGrvg, invgamma, LaplacesDemon, doParallel and foreach for estimation; lubridate, reshape2, dplyr, tidyr, ggplot2, cowplot and lemon for the output.

License

GPL-2, since the repository includes code adapted from the GPL-2 licensed dsp package.