We estimate a structural vector autoregressive model in order to quantify four main explanations for the decline of the US labor income share: (i) rising market power of firms, (ii) falling market power of workers, (iii) higher investment-specific technology growth, and (iv) the widespread emergence of automation or robotization in production processes. Identification is achieved with theory robust sign restrictions imposed at medium-run horizons. The restrictions are derived from a stylized macroeconomic model of structural change. Across specifications we find that automation is the main driver of the long-run labor share. Firms’ rising markups can, however, account for a significant part of the accelerating labor share decline observed in the last 20 years. Our results also point to complementarity between labor and capital, thus ruling out capital deepening as a major force behind declining labor shares. If anything, investment-specific technology growth has contributed to higher labor income shares in our sample.