Why are the ARDL Long Run Form and Bounds Test coefficients for variables not significant?

The ARDL (Autoregressive Distributed Lag) model is commonly used for analyzing the long-run relationships between variables. When the coefficients of variables in the ARDL model are not significant, it typically indicates several possible reasons:

Weak Explanatory Power: The variables included in the ARDL model may not sufficiently explain the variation in the dependent variable. This could happen if important explanatory variables are omitted or if there are measurement errors in the variables used.

Multicollinearity: High multicollinearity among the independent variables can lead to coefficients that are not statistically significant. Multicollinearity occurs when independent variables are highly correlated with each other, making it difficult to distinguish their individual effects on the dependent variable.

Small Sample Size: ARDL models, like many econometric models, require a sufficiently large sample size to produce reliable estimates. If the sample size is small, coefficients may not achieve statistical significance even if they are theoretically important.

Specification Errors: Incorrect functional form or misspecification of the model can lead to non-significant coefficients. For instance, if the lag structure of the model is not properly specified, it can affect the significance of coefficients.

Non-Stationarity Issues: The presence of non-stationary variables in the model can lead to spurious regression results, where coefficients are not meaningful or significant. ARDL models require careful consideration of stationarity and the appropriate use of unit root tests (such as ADF or PP tests) to ensure valid inference.

Measurement Issues: Inaccurate measurement or proxies used for variables can also lead to coefficients that are not statistically significant.

To address these issues, it's important to conduct diagnostic tests such as tests for multicollinearity, check the stationarity of variables, consider alternative specifications, and ensure the model includes all relevant variables. Additionally, increasing the sample size if possible or using alternative estimation techniques may help improve the robustness and significance of coefficients in the ARDL model.

John C Frain

Surely there is feedback between your explanatory variables and GDP. For example, an increase in GDP will impact Bank deposits, Investment, government expenditure, and possibly other explanatory variables. Then the explanatory variables are not weakly exogenous and the ARDL methodology is invalid.

I would add the following points

Your sample is small for an analysis with 5 explanatory variables and a complex dynamic structure.

Why are you using an unrestricted constant and unrestricted trend?

Are you using levels of variables? Have you tested for homoskedasticity - another requirement for ARDL? In an analysis such as this, it is usually better to use logs of variables rather than levels.

Chuck A Arize

If coefficients in the ARDL Long Run Form and Bounds Test are not significant, several factors may contribute:

Lag Length Issues: Incorrect lag length selection can lead to model misspecification.

Model Specification Problems: Omitted variables or incorrect functional forms can bias results.

Data Concerns: Small sample sizes, data quality issues (like outliers), or incorrect stationarity assumptions can affect outcomes.

Testing Procedure: Inadequate bounds test or poor capture of short-run dynamics can diminish coefficient significance.

Theoretical Alignment: Discrepancies with economic theory can invalidate expected relationships.

Multicollinearity: High collinearity among variables inflates errors and reduces coefficient significance.

Estimation Methods: Unsuitable estimation techniques may not account for model complexities.

To resolve, verify lag length appropriateness, refine model specifications, improve data quality, re-evaluate theoretical justifications, address multicollinearity, and adapt estimation methods as needed.

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