This paper examines the causal relationship between economic policy uncertainty (EPU) and equity market uncertainty (EMU) in the US. We use daily data on the newly developed indexes by Baker et al. (2013a) covering 1985:01:01 to 2013:06:14. Results from the linear causality tests indicate strong bidirectional causality. However, the parameters stability tests show strong evidence of short-run parameter instability, thus invalidating any conclusion from the full sample linear estimations. Therefore we turn to nonlinear tests and observe a stronger predictive power from EMU to EPU than from EPU to EMU. Using sub-sample bootstrap rolling window causality tests to fully account for the existence of structural breaks, we find evidence that EPU can help predict the movements in EMU only around 1993, 2004 and, 2006. However, we find strong evidence that EMU can help predict the movements in EPU throughout the sample period barring around 1998, 2003 and 2005.