ARDL Bounds Testing

Definition

ARDL bounds testing is a cointegration testing approach developed by Pesaran, Shin, and Smith (2001) that does not require all variables to share the same order of integration. The procedure uses F- and t-statistics on lagged levels within an autoregressive distributed lag (ARDL) error-correction model. Two sets of critical values form upper and lower bounds: one assuming all regressors are I(0) and the other I(1). If the test statistic exceeds the upper bound, the null of no level relationship is rejected; if it falls below the lower bound, the null cannot be rejected; results between the bounds are inconclusive.

Why It Matters

In applied policy research, the integration order of series is often uncertain. Traditional cointegration tests (Engle-Granger, Johansen) require all variables to be I(1), which limits their applicability. The ARDL bounds test accommodates a mix of I(0) and I(1) regressors, making it one of the most practical and widely used cointegration approaches in empirical economics.

Example

A researcher studying the relationship between Turkish GDP, exports, and energy consumption runs an ARDL bounds test. The computed F-statistic is 6.82. The lower bound critical value at 5% is 3.79 and the upper bound is 4.85. Since 6.82 exceeds the upper bound, the null of no long-run relationship is rejected, confirming cointegration among the variables.

Related Terms

• Cointegration
• Stationarity
• Unit Root
• Spurious Regression

Software Notes

• SPSS: Not natively supported; use R integration or custom syntax.
• R: Use the ardl package for model estimation and bounds_f_test() from the dynamac package, or ecm_ardl() with ardl package.
• Stata: Install xtardl or use regress with constructed lagged levels, then compute the bounds F-test manually using Pesaran et al. (2001) critical values.