Money Stock Fluctuations Recall: M1 is the narrowest measure of money. It includes only highly liquid assets that can be used to make transactions, such as currency, travelers checks or checkable deposits. The total money stock is the product of the monetary base and the money multiplier. It seems like the government can change the money stock at will, through its complete control over the monetary base and reserve requirements. Why central banks often miss their announced targets for the money stock? In the real world, we can observe the fluctuation in the measure of the money stock. Does it mean central banks are playing with the money stock?
If we assume the stability of the monetary base, changes in the money stock come from changes in the money multiplier. We assumed earlier that the money multiplier is simply the inverse of the reserve requirement. In the real data, the money multiplier also fluctuates a great deal. Moreover, these fluctuations appear to be linked with real output. How can the money multiplier fluctuate if reserve requirements rarely change? Our models must have overlooked some important sources. If we can find a source of fluctuations in the money multiplier, we may be able to explain the correlation between the nominal money stock and real output.
The Correlation between Money and Output A puzzling fact in monetary economics is an observed positive correlation between the nominal money stock and real output. If the money stock can be determined by the government, it implies that the government can stimulate real output at will. What is the pattern of this relation? Correlations between two variables do not necessarily imply causality. Consider a term innovation: the unpredicted change or surprise in a variable.
The following patterns in the data have been observed: o Innovations in real output and the total nominal money stock are positively correlated. o Innovations in the total nominal money stock occur before innovations in real output. o Innovations in the interest rate help predict innovations in money and output. o The link between both innovations takes the form of changes in the deposit-to-currency ratio and the money multiplier.
A Model of Currency and Deposits Since reserve requirements rarely change, they cannot be key determinants of the observed fluctuations in money and output. Our model is adapted to permit a fluctuation in a money multiplier without any changes in the reserve requirement. Now we are relaxing an assumption of people s asset holding. People can choose to hold fiat money (currency) and bank deposits (inside money). For simplicity, there are no reserve requirements.
A Model of Inside and Outside Money Consider an economy of two-period-lived overlapping generations. The stock of fiat money (monetary base) is constant. There are three types of people in the economy. o Workers: Have an endowment when young and nothing when old. Each worker s endowment has a different size. Cannot create capital but wish to have money for the second period consumption. Each worker wishes to hold a different amount of money. Let s i be a worker i s money balance desire in units of consumption good. All workers look alike, but they can reveal the identity at a cost of φ goods.
o Entrepreneurs: Have the same endowments and preferences as workers. Can create capital with the rate of return of x goods in the next period. Can use their endowment or the other s endowment to invest in capital. The greater x, the more investment in capital. Cannot be located by workers. o Bankers: Have no endowment and cannot create capital. Can locate entrepreneurs. Their identity is costlessly known to all.
Bankers can make a profit through arbitrage. Bankers receive deposits from workers and then lend those deposits to entrepreneurs. Entrepreneurs will accept the loan as long as x r. The rate of return on deposits will rise to x. Identification cost φ can be considered as a cost of withdrawal. The return from depositing s i is xs i - φ. The average rate of return on deposits net of transaction costs is x - φ /s i.
This average rate is negatively related to the size of the transaction cost and positively related to the size of the deposit. Currency does not have a transaction cost and has a rate of return of 1 in this case. Let s* be the point where the return on deposits equal the return on currency. People will use currency as long as s* > s i, or people use currency for small purchases. Deposits will be used for large purchases.