The magnitude of the volatility of money demand has crucial implications for the optimal way in which a central bank should carry out monetary policy and its choice of a nominal anchor.
Conditions under which the LM curve is flat, so that increases in the money supply have no stimulatory effect (a liquidity trap), play an important role in Keynesian theory.
This need arises when income is received only occasionally (say once per month) in discrete amounts but expenditures occur continuously.
Consequently, PY is nominal income or in other words the number of transactions carried out in an economy during a period of time.
This arises due to the lack of synchronization in time between when purchases are desired and when factor payments (such as wages) are made.
Under some simplifying assumptions the demand for money resulting from the Baumol-Tobin model is given by where t is the cost of a trip to the bank, R is the nominal interest rate and P and Y are as before.
The key difference between this formulation and the one based on a simple version of Quantity Theory is that now the demand for real balances depends on both income (positively) or the desired level of transactions, and on the nominal interest rate (negatively).
As a result, most models of this type resort to simpler indirect methods which capture the spirit of the transactions motive.
[3] In the cash-in-advance model agents are restricted to carrying out a volume of transactions equal to or less than their money holdings.
If these expectations are formed, as in Keynes' view, by "animal spirits" they are likely to change erratically and cause money demand to be quite unstable.
Agents will choose a mix of these two types of assets (their portfolio) based on the risk-expected return trade-off.
For a given expected rate of return, more risk averse individuals will choose a greater share for money in their portfolio.
Friedman and Schwartz in their 1963 work A Monetary History of the United States argued that the demand for real balances was a function of income and the interest rate.
Ericsson, Hendry and Prestwich (1998) consider a model of money demand based on the various motives outlined above and test it with empirical data.
The basic model turns out to work well for the period 1878 to 1975 and there doesn't appear to be much volatility in money demand, in a result analogous to that of Friedman and Schwartz.
This is true even despite the fact that the two world wars during this time period could have led to changes in the velocity of money.
Money demand appears to be time varying which also depends on household's real balance effects.
[7] Laurence M. Ball suggests that the use of adapted aggregates, such as near monies, can produce a more stable demand function.
While traditional simple-sum monetary aggregates show unstable relationships with interest rates post-1980, Divisia monetary aggregates - which account for the varying degrees of "moneyness" of different assets - demonstrate stable money demand relationships throughout the period.
Chen and Valcarcel (2024) further confirm these findings, showing that properly weighting monetary assets based on their liquidity services and using appropriate price measures (user costs rather than Treasury bill rates) reveals consistent money demand patterns even through periods of financial innovation and zero lower bound interest rates.