pvarife

Panel VAR Models with Interactive Fixed Effects

An R implementation of the estimator proposed by Tuğan (2021, Econometrics Journal) for panel vector autoregression (VAR) models with interactive fixed effects. The package jointly estimates VAR coefficients, latent common factors, and unit-specific factor loadings via an iterative algorithm that alternates between principal component estimation of the factors and least squares estimation of the VAR coefficients, following the approach of Bai (2009). Asymptotic inference is based on Theorem 2.3 of the paper.

Installation

# From CRAN (once accepted):
install.packages("pvarife")

# Development version from GitHub:
# install.packages("remotes")
# remotes::install_github("Rickchen0910/pvarife")
install.packages("pvarife", repos = c('https://rickchen0910.r-universe.dev', 'https://cloud.r-project.org'))

Quick Start

library(pvarife)

# 1. Simulate a balanced panel (I=50 units, T=30 periods, K=2 variables)
sim <- sim_pvarife(n_units = 50, n_time = 30, n_vars = 2,
                   n_lags = 1, n_factors = 1, seed = 42)

# 2. Estimate
fit <- pvarife(sim$y, n_lags = 1, n_factors = 1)
print(fit)

# 3. Impulse response functions (short-run / Cholesky identification)
irf <- compute_irf(fit, n_periods = 21, shock = 1)
plot(irf)

# 4. 95% confidence bands (parametric simulation from asymptotic distribution)
bands <- irf_bands(fit, n_periods = 21, shock = 1, n_draw = 500, seed = 1)
plot(bands, normalise_by_h1 = TRUE)

# 5. Asymptotic bias and variance (Theorem 2.3)
avar <- asymptotic_var(fit)
summary(fit)

Model

The model is

$$y_{i,t} = \sum_{\ell=1}^{L} \Theta_\ell, y_{i,t-\ell} + F_t \lambda_i + e_{i,t}$$

where $y_{i,t}$ is a $K \times 1$ vector for unit $i$ at time $t$, $F_t$ is an $r \times 1$ vector of unobservable common factors, $\lambda_i$ is a unit-specific loading vector, and $e_{i,t}$ is idiosyncratic noise. The data array follows the convention y[i, t, k] (unit × time × variable). Unbalanced panels (NA entries) are supported.

Key Functions

Function	Description
`pvarife()`	Main estimator — returns a `pvarife_result` object
`asymptotic_var()`	Theorem 2.3 bias and variance-covariance matrix
`compute_irf()`	Impulse response functions (short-run or long-run identification)
`irf_bands()`	Parametric 95% confidence bands from joint asymptotic distribution
`bootstrap_irf_bands()`	Classical residual bootstrap confidence bands
`sim_pvarife()`	Simulate data from the DGP of Tugan (2021, S10)
`extract_factors()`	Extract factors and loadings at an arbitrary coefficient vector

Identification Schemes

# Short-run (recursive / Cholesky) — default
irf_sr <- compute_irf(fit, n_periods = 21, identification = "short_run")

# Long-run (Blanchard-Quah)
irf_lr <- compute_irf(fit, n_periods = 21, identification = "long_run",
                      diff_vars = 1L)

Monte Carlo Replication

Scripts to replicate Table S.2 (bias/RMSE/coverage) and Figures S.1-S.2 (average IRFs) from the online appendix are in scripts/. They are designed for an SGE high-performance computing cluster and use the MonteCarlo package.

# On HPC (SGE scheduler):
bash scripts/meta_mc.sh     # Table S.2
bash scripts/meta_irf.sh    # Figure S.1 (short-run)

Citation

If you use this package, please cite the original paper:

Tugan, M. (2021). Panel VAR models with interactive fixed effects. Econometrics Journal, 24, 225-246. https://doi.org/10.1093/ectj/utaa021

@article{tugan2021,
  author  = {Tu\u{g}an, Mustafa},
  title   = {Panel {VAR} models with interactive fixed effects},
  journal = {Econometrics Journal},
  year    = {2021},
  volume  = {24},
  pages   = {225--246},
  doi     = {10.1093/ectj/utaa021}
}

Author

Binzhi Chen — University of Essex (Binzhi.Chen9@gmail.com)