Cross-Sectionally Augmented Panel Quantile ARDL

Implements the Cross-Sectionally Augmented Panel Quantile Autoregressive Distributed Lag (CS-PQARDL) model and the Quantile Common Correlated Effects Mean Group (QCCEMG) estimator for panel data with cross-sectional dependence. The package handles unobserved common factors through cross-sectional averages following Pesaran (2006) and Chudik and Pesaran (2015) . Quantile regression for dynamic panels follows Harding, Lamarche, and Pesaran (2020) . The ARDL approach to cointegration testing is based on Pesaran, Shin, and Smith (2001) .

xtcspqardl: Cross-Sectionally Augmented Panel Quantile ARDL

Overview

The xtcspqardl package implements the Cross-Sectionally Augmented Panel Quantile ARDL (CS-PQARDL) model and the Quantile Common Correlated Effects Mean Group (QCCEMG/QCCEPMG) estimator for panel data with cross-sectional dependence.

Key Features

• QCCEMG: Quantile CCE Mean Group estimator (Harding, Lamarche & Pesaran, 2018)
• QCCEPMG: Quantile CCE Pooled Mean Group estimator
• CS-PQARDL: Cross-sectionally augmented Panel Quantile ARDL
• Handles cross-sectional dependence through CCE augmentation (Pesaran, 2006)
• Lagged CSA following Chudik & Pesaran (2015)
• Long-run coefficients with delta-method standard errors
• Speed of adjustment and half-life calculations

Installation

From CRAN (when available)

install.packages("xtcspqardl")

From GitHub

# install.packages("devtools")
devtools::install_github("muhammedalkhalaf/xtcspqardl")

Usage

QCCEMG Estimation

library(xtcspqardl)

# Generate panel data
set.seed(123)
N <- 20  # panels
T <- 50  # time periods

data <- data.frame(
  id = rep(1:N, each = T),
  time = rep(1:T, N),
  x = rnorm(N * T)
)

# Add dynamics
for (i in 1:N) {
  idx <- ((i-1)*T + 2):(i*T)
  data$y[idx] <- 0.5 * data$y[idx-1] + 0.3 * data$x[idx] + rnorm(T-1, sd=0.5)
}

# Estimate QCCEMG
fit <- xtcspqardl(
  formula = y ~ x,
  data = data,
  id = "id",
  time = "time",
  tau = c(0.25, 0.50, 0.75),
  estimator = "qccemg"
)

# View results
summary(fit)

CS-PQARDL Estimation

# With long-run variables
fit_ardl <- xtcspqardl(
  formula = y ~ dx | x,  # dx is short-run, x is long-run
  data = data,
  id = "id",
  time = "time",
  tau = c(0.25, 0.50, 0.75),
  estimator = "cspqardl",
  p = 1,
  q = 1
)

summary(fit_ardl)

Methodology

Cross-Sectional Averages (CSA)

The CCE approach augments individual regressions with cross-sectional averages:

$$\bar{z}t = \frac{1}{N} \sum{i=1}^{N} z_{it}$$

where $z$ includes both the dependent and independent variables.

QCCEMG Model

$$y_{it} = \lambda_i(\tau) y_{i,t-1} + \beta_i(\tau)' x_{it} + \delta_i(\tau)' \bar{z}t + u{it}(\tau)$$

Long-Run Coefficients

Long-run effects are computed as:

$$\theta(\tau) = \frac{\beta(\tau)}{1 - \lambda(\tau)}$$

CSA Lag Order

Following Chudik & Pesaran (2015), the default lag order for CSA is:

$$p_T = \lfloor T^{1/3} \rfloor$$

References

• Chudik, A. and Pesaran, M.H. (2015). Common Correlated Effects Estimation of Heterogeneous Dynamic Panel Data Models with Weakly Exogenous Regressors. Journal of Econometrics, 188(2), 393-420. DOI: 10.1016/j.jeconom.2015.03.007

• Harding, M., Lamarche, C., and Pesaran, M.H. (2020). Common Correlated Effects Estimation of Heterogeneous Dynamic Panel Quantile Regression Models. Journal of Applied Econometrics, 35(3), 294-314. DOI: 10.1002/jae.2753

• Pesaran, M.H. (2006). Estimation and Inference in Large Heterogeneous Panels with a Multifactor Error Structure. Econometrica, 74(4), 967-1012. DOI: 10.1111/j.1468-0262.2006.00692.x

• Pesaran, M.H., Shin, Y., and Smith, R.J. (2001). Bounds Testing Approaches to the Analysis of Level Relationships. Journal of Applied Econometrics, 16(3), 289-326. DOI: 10.1002/jae.616

Author

License

GPL (>= 3)