In 2001, the Bank of Japan (BOJ) adopted "quantitative monetary easing". Since short term interest rates became almost zero, the operating target of monetary policy was changed from interest rate to the monetary base, where monetary base is defined as the sum of "Cash" and "Reserve at the BOJ". Honda et al  showed that "Reserve at the BOJ" in (2001,2006) is effective to the economy through a transmission path in a stock market, where impulse responses in VAR model are used in monthly data of Japan. Decomposing money into transaction demand and precautionary one, and estimating precautionary one, Morita and Miyagawa  tried to show that increasing "Reserve at the BOJ" makes GDP increased through the stock market in quarterly data. In this paper, the method of estimating precautionary demand in Japan is extensively improved and applied to the case of USA. Using precautionary demand estimated in the whole interval (1980m01, 2012m02), the quantitative easing at Federal Reserve Board(FRB) is shown to be effective during the period (2006m06, 2010m02).