Abstract
This paper examines the quantity theory of the money that predicts long run relationship between money and output predicated on the assumption that the velocity turnover is stable over time. Friedman and Schwartz (1963) money supply tended to grow at a higher rate than the growth of nominal GNP.[1]
Fisher (1911) forwards the classical approach to demand for money as follows:
M*V=P*Y                                                                             1
Δ M /M + Δ V /V= Δ P /P + Δ Y /Y                                     2
Δ P/P = Δ M /M - Δ Y /Y+ Δ V /V                                       3
Where M is the money supply, P is the price level, Y is the nominal GDP and V is the velocity turnover of money. Assuming growth rate of the economy (growth rate of out put y_t) increases, while growth rate of money supply m_t and velocity  _Vt are held constant, the growth rate of price level p_t must fall.[2]   This study aims to investigate the nature of the transmission mechanism by which given changes in the monetary variables affect the gross domestic product, and inflation. We expect to provide further evidence that it is possible to achieve non inflationary growth in the US economy without a significant increase in the growth of monetary aggregates. To this end we revisit the equation of exchange for the US economy through expansion of equation 3 that produces testable hypotheses relating real growth rate of money adjusted for inflation with the real growth rate of permanent income in expression 4.
m_t – p_t = β₀ +β₁ y_t + z_{t                                                                                               4}
Assuming z_t is a mean zero stationary stochastic process, equation 4 produces cointegration relationship relating real growth rate of money with that of the output. In This scenario if β₁ >1 and the trend in velocity is stochastic, the real money balance is expected to be income elastic in expression 4. Combining 1 and 4 produces the following expression for the trend in velocity.
v_t=-β₀ +(1-β₁) y_t - z_{t                                                                                                    5}                                                                  
Data & Methodology 
The data for this paper will be taken from the International Financial Statistics (IFS) Database. All time series of observations are quarterly data from 1929 first quarter to 2005 fourth quarter, including nominal GDP, three months Treasury bill rate, the yield on 10-year Treasury notes, consumer price index for all urban consumers, monetary base, M1, M2 and M3 money stock.
Empirical Hypotheses
H1:  p_t = –β₀ -β₁ y_t + β₂ m_t - z_{t                                                                                               6}
H2: β₂=1, this hypothesis measures the homogeneity between inflation and growth rate of money. Under the alternative hypothesis of β₂ = 0, there is an absence of any correlation between inflation and growth rate of money.
H3: β₁=1, velocity is stable over time,
Assuming β₁ >1 or β₁ <1, the alternative hypothesis in conintegration relation in 6 produces increasing or decreasing trend in velocity.
References; Available upon request.