# Applying Econometrics to Monetary Economics

I've been given a problem in which I am told that GDP is a function of the supply of money, prices and demand,

$$Y = (M/P)^\delta$$

Taking logs, $$\log(Y) = \alpha + \beta \log(m - p) +u$$

Differencing the series with constant prices, $$\Delta \log(Y) = \alpha + \Delta \beta \log(m) +u$$

My question is, I don't know how to interpret the function, $$\Delta \beta \log(m)$$. The fact that it is change is down to the fact that we took the difference, i.e. $$\beta_t$$ - $$\beta_{t-1}$$. The function is logged because we are interested in analysing the growth rate. Surely, $$\Delta \beta \log(m)$$ is the differenced time series process of the growth rate of money supply?

In our problem set we are given a number of variables in the data set:

M0: Growth rate of total notes and coins in circulation outside of the central bank

M4: Growth rate of monetary financial institutions' net lending to private sector.

Is the growth in money supply just the sum of these two variables?

How can there be a growth in notes and coins outside of the central bank, if it is the central bank controlling the supply?

• If you take logs, don't you get $log(Y) = \delta[log(M) - log(P)]$? – user17900 Mar 31 at 9:32