Bayesian ARDL Bounds Test
Bayesian Autoregressive Distributed Lag Bounds Test · Also known as: Bayesian ARDL, Bayesian bounds testing approach, Bayes ARDL cointegration, Bayesian PSS bounds test
The Bayesian ARDL Bounds Test extends the classical Pesaran-Shin-Smith (2001) bounds testing approach to cointegration by embedding it within a Bayesian inferential framework. Instead of relying on frequentist F- and t-statistics with tabulated critical values, the researcher specifies prior distributions on the model parameters and derives posterior evidence of a long-run level relationship between variables that may be integrated of order zero or one.
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When to use it
Use the Bayesian ARDL bounds test when studying long-run relationships in short-to-medium time series (T < 60) where classical asymptotic bounds critical values are unreliable, or when prior economic information should formally enter the inference. It is especially valuable when the integration order of the variables is uncertain (a mix of I(0) and I(1)), because the ARDL structure accommodates both without requiring a pre-test. Avoid it when no meaningful priors can be specified and a purely frequentist answer is required for regulatory or reproducibility reasons; or when the series are I(2), as the bounds framework does not apply. It is also demanding computationally — if a quick frequentist bounds test suffices, use classical ARDL instead.
Strengths & limitations
- Handles regressors that may be I(0) or I(1) without requiring a definitive pre-test for integration order.
- Formally incorporates prior economic information, improving inference in small samples where asymptotics are poor.
- Provides full posterior distributions and credible intervals for long-run coefficients rather than point estimates with asymptotic standard errors.
- Posterior model probabilities offer a coherent alternative to the F-bounds nuisance of inconclusive critical-value regions.
- Model uncertainty over lag order can be integrated out via Bayesian model averaging, avoiding ad hoc lag selection.
- Results are sensitive to the choice of prior distributions; poorly specified priors can distort inference, especially in small samples.
- MCMC estimation is computationally intensive and requires convergence diagnostics (trace plots, Gelman-Rubin statistics).
- The framework does not apply if any variable is I(2) or higher; pre-screening for I(2) is still necessary.
- Interpretation of Bayes factors and posterior probabilities requires familiarity with Bayesian reasoning, which may limit uptake in applied work.
Frequently asked
How does the Bayesian bounds test handle variables of unknown integration order?
Like the classical ARDL bounds test, the Bayesian version is designed for regressors that may be I(0) or I(1) in any combination. The level terms in the error-correction form carry the cointegration signal regardless; the posterior probability of cointegration does not require certainty about each variable's order.
What prior should I choose if I have no strong prior information?
A weakly informative Normal prior centred at zero with a moderately large variance, or a Zellner g-prior, is commonly recommended. Avoid completely flat (improper) priors on the level-term coefficients because they can yield an improper posterior for the long-run multiplier. Sensitivity analysis over a few prior choices is good practice.
How do I assess evidence of cointegration in the Bayesian framework?
Compute the posterior probability that the level-term coefficients are jointly non-zero, or form a Bayes factor comparing a model with level terms against one without. A Bayes factor above 10 (on the Jeffreys scale) constitutes strong evidence of a long-run relationship.
Can I use Bayesian ARDL with panel data?
The standard Bayesian ARDL bounds test is designed for a single time series. Panel extensions exist (panel Bayesian ARDL) but require additional modelling of cross-sectional heterogeneity and dependence, and are a distinct method.
When should I use the classical ARDL bounds test instead?
If you have no meaningful prior information to incorporate, a sample large enough for asymptotics to work (T > 80 or so), and need results that are straightforwardly replicable by reviewers unfamiliar with Bayesian methods, the classical ARDL bounds test is simpler and equally valid.
Sources
- 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 ↗
- Koop, G. (2003). Bayesian Econometrics. Wiley-Interscience. ISBN: 978-0470845678
How to cite this page
ScholarGate. (2026, June 3). Bayesian Autoregressive Distributed Lag Bounds Test. ScholarGate. https://scholargate.app/en/econometrics/bayesian-ardl-bounds-test
Which method?
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