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analyze_convergence_clubs — a faithful Python port of the Phillips & Sul (2007/2009) log(t) convergence test and data-driven club clustering (the Stata psecta package). Full workflow from one variable: per-unit Hodrick-Prescott trend (lambda=400), relative transition paths, the log(t) test, recursive clustering when global convergence is rejected, and adjacent-club merging. The log(t) statistic uses the Phillips-Sul scalar long-run-variance HAC (Andrews 1991 quadratic-spectral kernel, AR(1) bandwidth). Returns a tidy long frame, three figures (within-club averages, paths by club, per-club small multiples), a classification table, and an entity -> club membership frame.
Learn: a learn_convergence_clubs sandbox (recovers a planted club structure), an explain("convergence_clubs") explainer, and a "Convergence clubs" page in the Analyze app.
Data: a new bundled productivity dataset — a balanced 108-country x 25-year Penn World Table panel of log GDP per capita and log labor productivity (load_productivity).
Fixed
analyze_beta_convergence: a constant/collinear conditional control was silently dropped by the estimator, mislabelling the unconditional fit as conditional; it is now skipped with an explicit note.
analyze_beta_convergence: NaN-blind duplicate-key de-duplication could evict a valid observation; it now keeps the first non-missing value (matching the sigma/clubs paths).