Appended Note 1-11 Relationship between M2 + CD and Real GDP
- Japanese version
- English version
<Summary>
The time series data for real money supply and real GDP (both are logarithms of seasonally adjusted values) show the upward trends respectively. Using the unit root test (e.g. ADF test), the data are identified as non-stationary series that increases its mean or variance over time. If we estimate the relationship of the two as stated above, spurious regression may occur due to the influences of bilateral trends.
However, both series are non-constant, their joint linear could be a constant series, whose mean/variance is constant and in which the auto-regression covariance depends on the length of the point. In this case, the joint linear equation shows a long-term equilibrium relationship (it means that the co-integrated relationship exists) in both series.
We investigated whether or not such a long-term relationship between the two series exists by using Johansen' s cointegration test.
<Statistics Used>
The real GDP (seasonally adjusted, quarterly data) in accordance with "National Account " , Cabinet Office is used as the real GDP. M2 + CD is used as money supply in accordance with the "Financial and Economic Statistics Monthly" , Bank of Japan, the average value during three months of average monthly data was used as quarterly data. As for the money supply being converted to real terms, we used the ratio of nominal GDP seasonally adjusted in accordance with "National Account" , Cabinet Office and the real GDP (both are quarterly data).
In addition, money transaction demand is changed not only by real transactions, whose GDP is a substitute variable, but also by asset transactions. In order to consider that fact, the money transaction demand was converted to real terms in the same method as money supply by using the real total current value of stocks in the Tokyo Stock Exchange' s first section.
<Test Result>
Long-run real money demand function
RMt = 
+ 
RYt + 
RAt + ut
(RM: Real Money Supply, RY: Real GDP, RA: Real total current value of stocks; all are logarithms)
In the above equation, we tested whether or not the cointegration vector(,,)exists so that the residual, u t = ( RMt - - RYt - RAt)can be constant.(Four quarters selected as lag according to the Akaike information criterion)(1) First quarter of 1980- fourth quarter of 1997
According to the upper table, the hypothesis that a cointegration vector does not exist is significantly rejected, while the hypothesis that a cointegration vector is less than 1 cannot be rejected. Then, the cointegration vector can be detected in the lower table.
(2) First quarter of 1980- second quarter of 2002(Full Sample)
On the other hand, if we add the series after the first quarter of 1998, the hypothesis that the cointegration vector does not exist cannot be rejected. As stated in the following table, even if the number of samples is increased, the recovery for co-integrated relationship is not identified.
<Reference Materials>
1. Kimura, T., Fujita, S., "Relationship Among Monetary crisis and Money, Real Economy and Prices " (February, 1999)
2. Sugihara, S., Mihira, T., Takahashi, T., and Takeda, M., "Spread Channel for Monetary Policy and Policy Measure" , Economic Analysis, No.162 (December 2000)
3. Hosono, K., Sugihara, S., and Mihira, T., "Effectiveness of Monetary Policy and its Limit: Japan' s Positive Analysis in 1990s" , Toyo Keizai (2001).