Abstract: Background and Objective: Neutrality of money hypothesis is one of the widely researched topics in economics claiming that the effect of money supply on output is positive in the short-run but disappears in the long-run. Besides this level effect, relationship between the volatilities of these two variables is also another interesting subject to investigate. This study aimed to discuss the neutrality of money hypothesis in terms of level and volatility effects of money supply. Materials and Methods: Data from the United States economy covers the period of 1959: 01-2016: 05. First, mean equation of EGARCH model is utilized to investigate for a lagged effect of the stationary variables of money supply growth on output growth in the short-run. Second, Asymmetric Dynamic Conditional Correlation Model (ADCC-EGARCH) is employed to analyze the dynamic relationship between short-run volatilities of money supply growth and output growth. Last, Detrended Cross Correlation Analysis (DCCA) is applied to explore for a long-run relationship between non-stationary variables of money supply and output. Results: The lagged effect of money supply growth on output growth is positive in the short-run according to the results of EGARCHs mean equation. According to the ADCC-EGARCH analysiss dynamic cross conditional correlation results, the volatility of money supply growth and volatility of output growth vary substantially in the short-run by time. Moreover, DCCA results indicated a positive simultaneous long-run relationship between money supply and output in levels. Conclusion: It is concluded that a non-neutrality of money in the short-run and the dynamic conditional correlations vary over time.