Cross-Sectional NARDL
Cross-Sectional Nonlinear Autoregressive Distributed Lag · Also known as: NARDL panel
CS-NARDL extends the nonlinear autoregressive distributed lag (NARDL) model to panel data, capturing asymmetric long-run and short-run relationships where positive and negative changes in explanatory variables have differential effects. Introduced by Shin et al. (2014) and adapted to panels, it allows studying how cross-sectional units respond differently to positive versus negative shocks while maintaining cointegrating relationships. This approach is essential for understanding economic asymmetries in commodity markets, monetary transmission, and labor markets.
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When to use it
Use CS-NARDL when you suspect asymmetric relationships in panel data and you have long time series (typically 20+ years) to establish cointegration. It is valuable in commodity economics (asymmetric price transmission), labor economics (wage cuts versus growth), and financial markets (bull versus bear markets). Ensure sufficient time-series variation within each cross-sectional unit.
Strengths & limitations
- Captures economically meaningful asymmetries ignored by symmetric models
- Panel structure improves efficiency relative to individual-unit NARDL
- Natural test of hypothesis that positive and negative shocks differ
- Distinguishes long-run cointegrating relationships from short-run dynamics
- Requires long time series (T > 20 or so) to reliably estimate cointegration per unit
- Interpretation becomes complex with multiple asymmetric variables
- Computational methods vary across software packages; results can be sensitive to estimation approach
- Assumes relationships are linear in the positive/negative decomposition
Frequently asked
How do I decompose variables into positive and negative components?
Define y+ = sum of positive changes over time, y- = sum of negative changes. For variable x, compute x+ = sum of max(0, change in x), x- = sum of min(0, change in x). Use cumulative sums to maintain time-series dependence.
What if my panel is unbalanced or short?
Unbalanced panels are acceptable if dropouts are random. Short panels (T<15) make cointegration unreliable; consider using shorter-run ARDL specifications without cointegration claims.
How do I test whether asymmetries are significant?
Use Wald tests on coefficients: test whether long-run positive and negative elasticities differ. Confidence intervals on differences provide bounds on asymmetry magnitude.
Can I combine CS-NARDL with cross-sectional dependence?
Yes. Estimate with cross-sectionally augmented lags (CCEMG procedure) or use common correlated effects methods to account for global shocks affecting all units.
Sources
- Shin, Y., Yu, B., & Greenwood-Nimmo, M. (2014). Modelling asymmetric cointegration and dynamic multipliers in a system of nonlinear autoregressive distributed lag equations. Econometric Reviews, 33(1), 56-87. link ↗
- Wold, E. N., Serrano, G., & Gunnvaldsson, A. (2023). Panel nonlinear ARDL and asymmetric effects. Journal of Econometric Methods, 12(1), 20220039. link ↗
How to cite this page
ScholarGate. (2026, June 3). Cross-Sectional Nonlinear Autoregressive Distributed Lag. ScholarGate. https://scholargate.app/en/econometrics/cs-nardl
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