Non-linear Ardl Estimation

The method separates changes in an explanatory variable according to direction by constructing distinct partial-sum variables for positive and negative movements. These components enter the model independently, allowing the estimated relationship to assign different effects to increases and decreases. This structure makes directional asymmetry directly testable rather than treating all changes as equivalent.

Positive and negative partial sums preserve the cumulative history of changes in opposite directions. Their separate roles help reveal whether an outcome responds more strongly, weakly, or differently when a factor rises than when it falls. In applications involving prices, income, or policy variables, this distinction can expose patterns that a symmetric specification would conceal.

Dynamic coefficients describe how the outcome responds over shorter periods, while the long-run relationship captures the sustained association between the outcome and the decomposed explanatory-variable components. Comparing these effects shows whether directional differences appear immediately, persist over time, or vary between the adjustment period and the eventual relationship.

Bounds testing evaluates whether the modeled variables exhibit asymmetric cointegration, meaning that their positive and negative components participate in a stable long-run relationship with the outcome. This assessment is important because short-run movements alone do not establish persistence. Evidence of asymmetric cointegration supports interpreting the long-run coefficients as meaningful relationships rather than temporary associations.

A typical application begins by separating increases and decreases in the explanatory variable into partial-sum variables. The model then estimates dynamic coefficients for short-run responses and long-run effects, followed by bounds testing for asymmetric cointegration. Researchers can interpret the resulting directional coefficients to evaluate whether the outcome reacts unequally across changes in the selected factor.

Non-linear Ardl Estimation is useful when theory or observed behavior suggests that an outcome may react differently to upward and downward movements in a factor. It can examine prices, income, and policy variables while supporting forecasting and hypothesis testing. The results also provide evidence for policy analysis when directional responses matter for decisions.