Nonlinear Autoregressive Distributed Lag Model (NARDL)
Also known as: NARDL, nonlinear ARDL, asymmetric ARDL, nonlinear bounds test
The Nonlinear ARDL (NARDL) model extends the linear ARDL bounds-testing framework to allow asymmetric long-run and short-run relationships. By decomposing an explanatory variable into its positive and negative partial sums, it tests whether increases and decreases in a regressor have different effects on the dependent variable — a feature that linear cointegration methods cannot capture.
Key highlights
- Simultaneously tests for cointegration and asymmetry within a single unified model.
- Works with mixed-order integration (I(0) and I(1) regressors together), so no pre-testing of unit roots is required before the bounds test.
- Provides dynamic multiplier plots that quantify the speed and path of adjustment following positive versus negative shocks.
- Directly estimates short-run and long-run asymmetric coefficients rather than treating asymmetry as a post-hoc diagnostic.
- Estimated by OLS on the error-correction form, making it computationally straightforward in standard software (EViews, R nardl package, Stata).
Intuition
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How it works
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When to use it
Use NARDL when you have time-series data (or short panels) where regressors may be I(0), I(1), or a mixture, and where economic or theoretical reasoning suggests the response to positive shocks differs from the response to negative shocks — for instance, asymmetric price transmission, asymmetric monetary policy effects, or ratchet effects in consumption. Avoid NARDL when sample size is very small (fewer than ~60 observations), when regressors are I(2) (which invalidates the bounds test), when there is no theoretical motivation for asymmetry (a symmetric ARDL is more parsimonious), or when structural breaks dominate the series (consider threshold or Markov-switching approaches instead).
Strengths & limitations
- Simultaneously tests for cointegration and asymmetry within a single unified model.
- Works with mixed-order integration (I(0) and I(1) regressors together), so no pre-testing of unit roots is required before the bounds test.
- Provides dynamic multiplier plots that quantify the speed and path of adjustment following positive versus negative shocks.
- Directly estimates short-run and long-run asymmetric coefficients rather than treating asymmetry as a post-hoc diagnostic.
- Estimated by OLS on the error-correction form, making it computationally straightforward in standard software (EViews, R nardl package, Stata).
- Requires a moderately large sample (at least ~60 time-series observations) for reliable bound critical values and lag selection.
- Cannot accommodate I(2) regressors; pre-testing to rule out second-order integration remains necessary.
- Lag order selection (AIC/SIC criteria) can be sensitive in small samples, and different lag lengths sometimes reverse asymmetry test conclusions.
- Partial-sum decomposition assumes a single structural form of asymmetry; more complex nonlinearities (regime-switching, threshold effects) require specialist models.
Common pitfalls
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Applications
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Frequently asked
What is the difference between ARDL and NARDL?
Linear ARDL treats each regressor symmetrically, estimating a single long-run coefficient. NARDL replaces each regressor with its positive and negative partial sums and estimates separate coefficients for each direction, allowing the long-run effect of a positive shock to differ from that of a negative shock.
Do I need to test for unit roots before running NARDL?
You must confirm that no regressor is I(2); if any is I(2), the bounds F-test is invalid. You do not need to classify regressors precisely as I(0) or I(1) — the NARDL bounds test is robust to mixtures — but ruling out I(2) behaviour is essential.
What is a dynamic multiplier in NARDL?
A dynamic multiplier traces the cumulative response of the dependent variable from the current period to the new long-run equilibrium following a unit positive or negative shock. The gap between the positive and negative multiplier paths at each horizon visualises the asymmetry over time.
How do I test whether asymmetry is statistically significant?
Apply a Wald test comparing the long-run asymmetric multipliers (theta+/|rho| versus theta-/|rho|) for long-run asymmetry, and separately compare the sums of short-run lag coefficients for positive versus negative partial sums. Rejection of equality at conventional significance levels supports asymmetry.
How many observations do I need for NARDL?
A general rule of thumb is at least 60 time-series observations to achieve sufficient power in the bounds test and the asymmetry Wald test. With fewer observations, long lag lengths cannot be accommodated and critical values become unreliable.
Sources
- 1.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: Econometric Methods and Applications (pp. 281-314). Springer.
- 2.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.
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Cite this page
ScholarGate. (2026, June 3). Nonlinear NARDL. ScholarGate. https://scholargate.app/econometrics/nonlinear-nardl