Cash holding coefficient

The cash holding coefficient (also called Cambridge-k) is an economic indicator that shows the proportion of income that economic agents want to keep in their cash register . It also shows the average length of time the money is in a cash register, ie the period between two income payments.

History of ideas

The cash holding coefficient appears in different models of monetary equilibrium. Depending on the interpretation of the relationships, it is seen as a dependent or independent variable. The classical view assumes that assets, interest rate and expectations do not change in contrast to the cash holding coefficient. An example of this quantitative theoretical interpretation is the Cambridge equation published by Alfred Marshall and Arthur Cecil Pigou, in which the cash holding coefficient appears as an independent variable.

John Maynard Keynes criticized the fact that in quantity theory there is a clear causal relationship between the amount of money and the price level . In his opinion, keeping money is dependent on interest. If the interest rate is high, the demand for liquid funds decreases, as a financial investment seems worthwhile. In this case, the cash holding coefficient would be rather low, so that a negative correlation with the interest rate can be seen.

Derivation

Based on the quantity equation

In the quantity equation, the nominal income PY is obtained by multiplying the money supply by the velocity of money circulation V. For the transition to the Cambridge equation, this expression is converted to the money supply. The following applies: ${\displaystyle M_{s}}$

${\displaystyle M_{s}={\frac {1}{V}}PY.}$

The sum of the cash holdings of all economic agents forms the money demand. In equilibrium, this corresponds to the money supply. From the reciprocal of the speed of money circulation , the cash holding coefficient k results:

${\displaystyle k={\frac {1}{V}}={\frac {Ms}{PY}}}$

A high speed of circulation of money means that the cash holding coefficient is low.

example

The nominal economic income PY should be 100 monetary units . Assuming that the economic agents hold each monetary unit for 1 year, then the cash holding coefficient is k = 1. This requires a money supply of 100 MU. If the economic agents keep a monetary unit in the cash register for an average of 3 months, k = 0.25 years. Inserting the sizes results in:

${\displaystyle M_{s}={\frac {1}{4}}Jahre*100GE.}$

A money supply of 25 MU is thus sufficient.

Based on the LM equation

With this consideration, the reaction of the money demand to a change in the interest rate can be seen from the cash holding coefficient. The key figure can be determined by converting the money demand function (see LM function ) to the function of the interest rate L (i) and corresponds to the ratio of the money demand Md to the nominal income PY:

${\displaystyle L(i)={\frac {M_{d}}{PY}}}$

The amount of money considered here is composed of cash and sight deposits (M1).

example

Given is a real income Y of 100 MU and a price index of 2. Let the money demand M be 50 MU. How long is a monetary unit in the till on average? Inserting the sizes leads to:

${\displaystyle k={\frac {50GE}{100GE*2}}.}$

A GE was thus on average 0.25 periods in the till. This again corresponds to 3 months.

Influencing factors

From a (neo) classical point of view, the level of the cash holding coefficient is influenced by payment habits, the banking structure, the number of production stages and the degree of monopoly of an economy. The influence of payment habits should be illustrated using an example:

USA and Germany in comparison

In the USA, the increased use of credit cards has gradually reduced the level of the cash holding coefficient. With this payment method, payment is only made when the credit card statement is debited from the current account. Up to this point, only a small amount of liquid funds are required, so that a large part can be invested with interest.

However, since such financial innovations have not caught on in Germany, the cash holding coefficient rose steadily. The preferred payment method is still the direct debit procedure, in which the amount is debited directly from the current account. This means that a higher stock of money must be kept.

The decisive factors for the level of the cash holding coefficient in the Keynesian money market model are, on the one hand, the frequency of income payments and the number of conversions of money and interest-bearing assets such as B. Securities. The more often these events occur, the smaller the cash holding coefficient.

Example of frequency of income

Transaction checkout with monthly and fortnightly payment

The graph shows the development of the transaction balance with monthly and fortnightly income payments to households. The blue line corresponds to a monthly income of 1600 MU. This means that an average cash balance of 800 MU is necessary. The cash holding coefficient is 1/12. Compared to the green line, it becomes clear that the cash holding coefficient drops to 1/24 with a rather short-term payout of the income.

Since the incomes of households and companies form a cycle (see also simple economic cycle ), the cash line of the companies would run in the opposite direction.

literature

• O. Blanchard, G. Illing: Macroeconomics. 4th edition. Person studies, Munich 2006.
• E. Fees: Macroeconomics. 3. Edition. Vahlen, Munich 2004.
• B. Felderer, S. Homburg: Macroeconomics and New Macroeconomics. 9th edition. Springer, Cologne 2005.
• G. Mussel: Introduction to Macroeconomics. 8th edition. Vahlen, Munich 2004.
• K. Rittenbruch: Macroeconomics. 11th edition. Oldenbourg, Munich 2000.
• G. Schmitt-Rink, D. Bender: Macroeconomics of closed and open economies. 2nd Edition. Springer, Berlin 1992.

Individual evidence

1. ↑ ^{a b} Blanchard; Illing (2006), p. 120.
2. ↑ Mussel (2004), p. 124.
3. ^ University of Augsburg (2003), p. 9.
4. ↑ Felderer; Homburg (2005), p. 80.
5. ↑ Fees (2004), p. 24.
6. ↑ Blanchard; Illing (2006), p. 114 f.
7. ↑ ^{a b} Rittenbruch (2000), p. 215.
8. ↑ Felderer; Homburg (2005), p. 80.
9. ↑ Rittenbruch (2000), p. 215.
10. ↑ Blanchard, Illing (2006), p. 114 ff.
11. ↑ Schmitt-Rink, Bender (1992), p. 113.
12. ↑ Mussel (2004), p. 123.