Beyond linear and quadratic specifications: wage share and economic growth in OECD countries

Purpose This study examines whether the relationship between the wage share and real GDP per capita growth is adequately described by the linear or quadratic specifications that dominate the literature, or whether it instead follows a higher-order non-linear pattern. Design/methodology/approach Using an unbalanced panel of 24 OECD countries over 2004–2023, the study estimates a sequence of fixed-effects panel models — linear, quadratic and cubic — controlling for investment, trade openness, human capital, public debt, unemployment and institutional quality. The analysis is supported by Hausman, Wooldridge and Pesaran CD diagnostic tests, Driscoll-Kraay standard errors, Variance Inflation Factor checks and a sensitivity analysis excluding major crisis years (2008, 2009, and 2020). Findings The quadratic term is statistically insignificant, but the cubic specification reveals a highly significant, robust non-linear relationship. Two turning points, at approximately 36.2 and 64.9% of the wage share, delimit three distinct growth regimes: growth-supporting at low levels, growth-dampening at intermediate levels and growth-supporting again at high levels of the wage share. Research limitations/implications The analysis is based on fixed-effects estimation and does not address potential reverse causality between growth and the wage share; future work could extend the analysis with dynamic panel (GMM) estimators. Originality/value The paper shifts the debate on functional income distribution and growth from identifying wage-led versus profit-led regimes towards testing whether the functional form conventionally imposed on this relationship is itself correctly specified, showing that higher-order non-linearities materially change the empirical and policy conclusions.