Answers to Monetary Aggregates questions
A. If ωdep < 1, then DIV < M.
A simple sum puts a “moneyness” weight of 1 on every asset in that measure. A weight of 1 is fine for currency since money is used purely as a medium of exchange. Deposits serve as a medium of exchange, but since they have a positive rate of return a portion of savings is allocated to deposits. That is why the “moneyness” weight on deposits should be less than 1, and that is the problem with a simple sum measure.
B. If Div < M, then M/DIV > 1.
As the interest rate on deposits gets larger, ωdep gets smaller. That makes DIV smaller but has no direct effect on M. That means the ratio M/DIV is rises.
If we look at the early 1980s we see that Divisia grew slower than simple sum. That means M/DIV increased. We noted that US interest rates were in general high in the early 1980s period, and so the prediction we just discussed fits that period’s evidence.
C. Currency falls by $100,000 while deposits rise by $100,000, and so the net effect on M is zero.
The net effect on Divisia is negative because that measure puts a “moneyness” weight on deposits less than 1. In other words, the negative effect on currency (-100,000) dominates the positive effect on deposits (+ωdep∙100,000).
The simple sum is an accounting identity and our result simply tells us wealth can be reallocated between different assets without affecting the total amount of wealth. The Divisia result says that if you shift some of your wealth from an asset that has more use as a medium of exchange to an asset that has less use as a medium of exchange, there will less medium of exchange – or in other words money – in the economy.