This paper examines the following question: Is there a lead-lag or causal relationship between trading volume and price volatility, or do these important market variables move simultaneously? We conduct rigorous empirical tests using procedures similar to Granger causality tests and find strong evidence that price volatility causes trading volume but no evidence that trading volume causes price volatility. We find this unidirectional causality to hold unconditionally, and also after conditioning on past volume and volatility.