Quantile ARDL
Also known as: Quantile ARDL
QARDL (Quantile Autoregressive Distributed Lag) combines quantile regression with ARDL modeling to estimate conditional relationships at different points of the distribution, revealing heterogeneous short-run and long-run effects. Introduced by Koenker and Xiao (2006) and refined by Cho et al. (2015), it captures how the effect of explanatory variables on outcomes varies across quantiles, essential for understanding tail behavior and distributional impacts rather than just mean effects.
Key highlights
- Reveals heterogeneous effects across the conditional distribution
- Identifies tail behavior and extreme-event dynamics
- Nonparametric approach requires fewer distributional assumptions
- Distinguishes short-run from long-run distributional effects
Intuition
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How it works
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When to use it
Use QARDL when distributional effects matter—e.g., whether income growth policies disproportionately help the poor, whether monetary policy transmission varies between prosperous and distressed regions, or whether supply-chain disruptions affect high-cost versus low-cost producers differently. It is particularly valuable when tail risks or extreme values drive policy relevance.
Strengths & limitations
- Reveals heterogeneous effects across the conditional distribution
- Identifies tail behavior and extreme-event dynamics
- Nonparametric approach requires fewer distributional assumptions
- Distinguishes short-run from long-run distributional effects
- Computation is intensive; standard errors can be large at extreme quantiles with small samples
- Interpretation of multiple quantile-specific relationships can be complex
- Limited cointegration theory for quantile models; long-run inference less established
- Cross-quantile dependence structure often ignored, potentially biasing standard errors
Common pitfalls
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Applications
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Frequently asked
How do I interpret cointegration at different quantiles?
If a long-run relationship exists at the median but not at extreme quantiles, this suggests conditional effects vary. Test quantile-specific cointegration via quantile-unit-root tests (e.g., Koenker and Xiao 2006).
What quantiles should I estimate?
Start with deciles (10th, 20th, ..., 90th) for a comprehensive view. For focus on tails, add extremes (5th, 95th). Balance detail against computational burden and precision loss at extreme quantiles.
How do I handle standard errors across quantiles?
Use bootstrap methods that respect the temporal and cross-quantile dependence structure. Quantile-specific standard errors assume independence across quantiles, which is often violated.
Can QARDL handle structural breaks?
Yes, but structural breaks operate through quantile-specific thresholds. Test for breaks per quantile; effects may differ (e.g., break at median in 1990 but at 75th percentile in 1995).
Sources
- 1.Koenker, R., & Xiao, Z. (2006). Quantile autoregression. Journal of the American Statistical Association, 101(475), 980-990.
- 2.Cho, J. S., Kim, H., & Shin, Y. (2015). Quantile cointegration in the autoregressive distributed-lag modeling framework. Journal of Econometrics, 188(1), 281-300.
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Cite this page
ScholarGate. (2026, June 3). QARDL. ScholarGate. https://scholargate.app/econometrics/qardl