This paper examines the causal relationship between economic policy uncertainty (EPU) and equity market uncertainty (EMU) in the US using linear and nonlinear Granger causality tests. 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. We test for parameters stability, and find strong evidence of short run parameter instability, thus invalidating any conclusion from the full sample linear estimations. Therefore we turn to nonlinear tests. Using Hiemstra and Jones (1994), Diks and Panchenko (2006), and Kyrtsou and Labys (2006) symmetric test, we observe a stronger predictive power from EMU to EPU than from EPU to EMU. Using the asymmetric version of Kyrtsou and Labys (2006) test, we find no evidence of positive predictive power from EPU to EMU. However, we find strong evidence of positive predictive power from EMU to EPU and only weak evidence of negative EPU causing EMU. Performing the causality test using the Sato et al. (2007) time-varying method, we find that the causality between EPU and EMU is not constant over time but rather time-varying. Hence, we implement a sub-sample bootstrap rolling window causality tests to fully account for the existence of structural breaks. Using the intensity plots of the p-values from this, 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. Further, the analysis of total effects based on the bootstrap sum of coefficients suggests a positive and stronger causal effect from EMU to EPU but smaller and insignificant causality from EPU to EMU. The implications of these findings for both investors and policy makers are provided.