Panel Nonlinear Autoregressive Distributed Lag (Panel NARDL) Model
Panel Nonlinear Autoregressive Distributed Lag Model · Also known as: Panel Nonlinear ARDL, panel asymmetric ARDL, panel NARDL bounds test, nonlinear panel cointegration model
Panel NARDL extends the time-series NARDL framework of Shin, Yu and Greenwood-Nimmo (2014) to a panel data setting, allowing researchers to detect asymmetric long-run and short-run relationships between variables across multiple cross-sections simultaneously. By decomposing the regressor into positive and negative partial sums, the model tests whether increases and decreases in an explanatory variable have different effects on the outcome.
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When to use it
Panel NARDL is appropriate when you have panel data (multiple units observed over time) and economic theory suggests that the response variable may react differently to positive versus negative shocks in a regressor — for example, energy prices and GDP, exchange rates and trade balances, or financial development and growth. It is suited when variables are I(0), I(1), or mutually cointegrated, because the bounds-testing approach does not require a uniform integration order. Avoid it when the time dimension T is very short (fewer than 20 periods per unit), when cross-sectional dependence is severe and unaddressed, or when you have no theoretical reason to expect asymmetry — in that case, a standard panel ARDL or PMG estimator is simpler and more parsimonious.
Strengths & limitations
- Detects asymmetric long-run and short-run effects that linear models cannot capture.
- Works with a mix of I(0) and I(1) variables via the bounds-testing framework, avoiding the need for pre-testing unit roots.
- Pooling cross-sections increases statistical power compared with unit-by-unit time-series NARDL.
- Accommodates cross-sectional heterogeneity through individual-specific intercepts and slope coefficients.
- Dynamic multiplier plots provide an intuitive visualisation of how the response accumulates over time after positive versus negative shocks.
- Requires a reasonably large time dimension (T ≥ 20 per unit) for reliable estimation of the error-correction term.
- Cross-sectional dependence (common global shocks) can bias estimates unless addressed with cross-sectionally augmented specifications (CS-NARDL) or second-generation panel tests.
- The manual partial-sum decomposition can introduce spurious asymmetry if the original variable is I(0); the procedure should be applied to I(1) series.
- Choosing lag lengths for both short-run dynamics and the error-correction model requires care — overfitting is a real risk in panels with moderate T.
Frequently asked
What is the difference between NARDL and Panel NARDL?
Standard NARDL is estimated on a single time series. Panel NARDL stacks multiple cross-sectional units (countries, firms, regions) and estimates the asymmetric cointegration relationships jointly, which improves statistical power and allows inference about average or heterogeneous effects across units.
Do my variables need to be I(1) for Panel NARDL?
Not strictly. The bounds-testing framework is valid for regressors that are I(0), I(1), or a mix, as long as none are I(2) or higher. However, the partial-sum decomposition of the regressor into positive and negative cumulative sums is most meaningful when the variable is integrated, so it is good practice to confirm variables are at most I(1).
How do I handle cross-sectional dependence in Panel NARDL?
First test for cross-sectional dependence using the Pesaran CD test. If dependence is present, use the cross-sectionally augmented NARDL (CS-NARDL) specification, which adds cross-section averages of the outcome and regressors as additional controls, following the CCE approach of Pesaran (2006).
How do I choose the lag length in the model?
A common practice is to use the Akaike Information Criterion (AIC) or the Schwarz-Bayesian Criterion (BIC) to select lags for the short-run dynamics and the distributed lag on the partial sums, with a maximum lag guided by the length of the time dimension T.
What are dynamic multipliers and why are they useful?
Dynamic multipliers trace the cumulative response of the outcome to a unit positive shock in x⁺ versus a unit negative shock in x⁻ over h periods into the future. Plotting them side by side makes asymmetry immediately visible and shows how quickly the system returns to equilibrium.
Sources
- Shin, Y., Yu, B., & Greenwood-Nimmo, M. (2014). Modelling asymmetric cointegration and dynamic multipliers in a nonlinear ARDL framework. In R. C. Sickles & W. C. Horrace (Eds.), Festschrift in Honor of Peter Schmidt (pp. 281–314). Springer. DOI: 10.1007/978-1-4899-8008-3_9 ↗
- Pesaran, M. H., Shin, Y., & 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 ↗
How to cite this page
ScholarGate. (2026, June 3). Panel Nonlinear Autoregressive Distributed Lag Model. ScholarGate. https://scholargate.app/en/econometrics/panel-nardl
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
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