We document the consequences of ambiguity in the empirical definition of the macroeconomic labor share. Depending on its definition, the properties of short-run fluctuations, medium-run swings, and long-run stochastic trends of the labor share may vary substantially. Based on a range of historical US time series, we carry out a systematic exploration of discrepancies between the alternative labor share definitions in terms of the observed stochastic trends, shares of short-, medium- and long-run variation in total volatility of the series, degree of persistence, mean-reversion properties, and susceptibility to structural breaks. We conclude that while short-run properties of the labor shares (represented by cyclical variation below 8 years) are relatively consistent across all definitions, their medium-run swings (8-50 years) and long-run trends ( 50 years) diverge substantially. As important applications, we document the implications of our findings for growth accounting, the identification of short-run responses of the labor share to technology shocks and for estimating inflation.
labor share mean reversion persistence spectral analysis structural breaks