Westerlund ECM Panel Cointegration Tests
Westerlund ECM panel cointegration tests study whether variables share a stable long run relation across many units. They are useful for countries, firms, regions, banks, or products observed through time. The method focuses on error correction. If a deviation from equilibrium appears, a cointegrated system should correct part of that gap in later periods.
Why Error Correction Matters
The calculator uses unit level adjustment estimates. Each panel unit has an ECM speed coefficient, a standard error, and a time length. A negative and significant speed implies correction toward equilibrium. Very small standard errors produce stronger test evidence. Longer time spans also give more weight to average adjustment measures.
Main Test Statistics
Four statistics are reported. Gt averages unit t ratios. Ga averages scaled adjustment speeds. Pt pools adjustment speeds with inverse variance weights. Pa scales the pooled speed by average time length. Negative values usually support cointegration because they show error correction. The p values use a one sided normal approximation, so they should be treated as screening values.
Input Quality
Good input matters. Estimate the long run equation first. Then estimate an ECM for each unit with suitable lags. Use the same dependent variable and long run regressors across units. Select constants or trends according to the research design. Check missing data before using the numbers. Unbalanced panels can be used, but each unit should have enough observations.
Research Reporting
This page is designed for transparent research work. It shows every unit contribution, the pooled adjustment, and the final decision at the chosen alpha level. You can export the output to CSV for spreadsheet review. You can also print the summary to a PDF file for documentation.
Important Review
Use the tool as a learning and reporting aid. Formal empirical work may need bootstrap p values, cross sectional dependence adjustments, and software specific critical values. Always compare results with the theory, sample structure, and robustness checks. Cointegration is an econometric claim, not only a button result. Strong evidence should remain stable under sensible lag choices, alternative deterministic terms, and diagnostic review. Document assumptions beside every run. Record the source model, lag order, transformation, and sample window. This makes later replication easier. It also helps readers understand why the reported evidence supports a long run relation with clarity.