Money demand
Encyclopedia
The demand for money is the desired holding of financial assets in the form of money
: that is, cash or bank deposits. It can refer to the demand for money narrowly defined as M1
(non-interest-bearing holdings), or for money in the broader sense of M2
or M3
.
Money in the sense of M1 is dominated as a store of value
by interest-bearing assets. However, money is necessary to carry out transactions; in other words, it provides liquidity. This creates a trade-off between the liquidity advantage of holding money and the interest advantage of holding other assets. The demand for money is a result of this trade-off regarding the form in which a person's wealth should be held. In macroeconomics
motivations for holding one's wealth in the form of money can roughly be divided into the transaction motive
and the asset motive
. These can be further subdivided into more microeconomically founded motivations for holding money.
Generally, the nominal demand for money increases with the level of nominal output (price level times real output) and decreases with the nominal interest rate
. The real demand for money is defined as the nominal amount of money demanded divided by the price level. For a given money supply
the locus of income-interest rate pairs at which money demand equals money supply is known as the LM curve.
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 situation occurs when the demand for money is infinitely elastic
with respect to the interest rate.
A typical money-demand function may be written as
where
is the nominal amount of money demanded, P is the price level, R is the nominal interest rate, Y is real output, and L(.) is real money demand. An alternate name for 
is the liquidity preference
function.
. According to the equation of exchange
, where M is the stock of money, V is its velocity (how many times a unit of money turns over during a period of time), P is the price level and Y is real income. Consequently PY is nominal income or in other words the number of transactions carried out in an economy during a period of time. Rearranging the above identity and giving it a behavioral interpretation as a demand for money we have
or in terms of demand for real balances
Hence in this simple formulation demand for money is a function of prices and income, as long as its velocity is constant.
The most well-known example of an economic model that is based on such considerations is the Baumol-Tobin model
. In this model an individual receives her income periodically, for example, only once per month, but wishes to make purchases continuously. The person could carry her entire income with her at all times and use it to make purchases. However, in this case she would be giving up the (nominal) interest rate that she can get by holding her income in the bank. The optimal strategy involves holding a portion of one's income in the bank and portion as liquid money. The money portion is continuously run down as the individual makes purchases and then she makes periodic (costly) trips to the bank to replenish the holdings of money. 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).
models. As a result most models of this type resort to simpler indirect methods which capture the spirit of the transactions motive. The two most commonly used methods are the cash-in-advance
model (sometimes called the Clower
Constraint model) and the money in the utility function model (sometimes referred to as the 'MIU' or the Sidrauski model).
In the cash-in-advance model agents are restricted to carrying out a volume of transactions equal to or less than their money holdings. In the MIU model, money directly enters agents' utility functions, capturing the 'liquidity services' provided by money.
, in laying out speculative reasons for holding money, stressed the choice between money and bonds. If agents expect the future nominal interest rate (the return on bonds) to be lower than the current rate they will then reduce their holdings of money and increase their holdings of bonds. If the future interest rate does fall, then the price of bonds will increase and the agents will have realized a capital gain on the bonds they purchased. This means that the demand for money in any period will depend on both the current nominal interest rate and the expected future interest rate (in addition to the standard transaction motives which depend on income).
The fact that the current demand for money can depend on expectations of the future interest rates has implications for volatility of money demand. 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.
, who considered a situation where agents can hold their wealth in a form of a low risk/low return asset (here, money) or high risk/high return asset (bonds or equity). 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. Similarly, given a person's degree of risk aversion, a higher expected return (nominal interest rate plus expected capital gains on bonds) will cause agents to shift away from safe money and into risky assets. Like in the other motivations above, this creates a negative relationship between the nominal interest rate and the demand for money. However, what matters additionally in the Tobin model is the subjective rate of risk aversion, as well as the objective degree of risk of other assets, as, say, measured by the standard deviation of capital gains and losses resulting from holding bonds and/or equity.
and Schwartz
in their 1963 work A Monetary History of the United States argued that the demand for real balances was a stable function of income and the interest rate. For the time period they were studying this appeared to be true. However, shortly after the publication of the book, due to changes in financial markets and financial regulation money demand became more unstable. Various researchers showed that money demand became much more unstable after 1975. 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. However, when the same basic model is used on data spanning 1976 to 1993, it performs poorly. In particular, money demand appears not to be sensitive to interest rates and there appears to be much more exogenous volatility. The authors attribute the difference to technological innovations in the financial markets, financial deregulation, and the related issue of the changing menu of assets considered in the definition of money.
which says that the growth rate of money supply plus the growth rate of its velocity equals the inflation rate plus the growth rate of real output. If money demand is stable then velocity is constant and
. Additionally, in the long run real output grows at a constant rate equal to the sum of the rates of growth of population, technological know-how, and technology in place, and as such is exogenous. In this case the above equation can be solved for the inflation rate:
Here, given the long-run output growth rate, the only determinant of the inflation rate is the growth rate of the money supply. In this case inflation in the long run is a purely monetary phenomenon; a monetary policy which targets the money supply can stabilize the economy and ensure a non-variable inflation rate.
This analysis however breaks down if the demand for money is not stable — for example, if velocity in the above equation is not constant. In that case, shocks to money demand under money supply targeting will translate into changes in real and nominal interest rates and result in economic fluctuations. An alternative policy of targeting interest rates rather than the money supply can improve upon this outcome as the money supply is adjusted to shocks in money demand, keeping interest rates (and hence, economic activity) relatively constant.
The above discussion implies that the volatility of money demand matters for how monetary policy should be conducted. If most of the aggregate demand
shocks which affect the economy come from the expenditure side, the IS curve, then a policy of targeting the money supply will be stabilizing, relative to a policy of targeting interest rates. However, if most of the aggregate demand shocks come from changes in money demand, which influences the LM curve, then a policy of targeting the money supply will be destabilizing.
Money
Money is any object or record that is generally accepted as payment for goods and services and repayment of debts in a given country or socio-economic context. The main functions of money are distinguished as: a medium of exchange; a unit of account; a store of value; and, occasionally in the past,...
: that is, cash or bank deposits. It can refer to the demand for money narrowly defined as M1
Money supply
In economics, the money supply or money stock, is the total amount of money available in an economy at a specific time. There are several ways to define "money," but standard measures usually include currency in circulation and demand deposits .Money supply data are recorded and published, usually...
(non-interest-bearing holdings), or for money in the broader sense of M2
M2
-In computers and electronics:*Fast Universal Digital Computer M-2, an early Russian digital computer *Memory Stick Micro , a removable flash memory card format*Modula-2 , a computer programming language...
or M3
M3
M3, M-3 or M03 may refer to:* M3 , a measure of the money supply* Metribolone* M3, a metric screw size- Science :* Cubic meter , a unit of volume* Messier 3 , a globular cluster in the constellation Canes Venatici...
.
Money in the sense of M1 is dominated as a store of value
Store of value
A recognized form of exchange can be a form of money or currency, a commodity like gold, or financial capital. To act as a store of value, these forms must be able to be saved and retrieved at a later time, and be predictably useful when retrieved....
by interest-bearing assets. However, money is necessary to carry out transactions; in other words, it provides liquidity. This creates a trade-off between the liquidity advantage of holding money and the interest advantage of holding other assets. The demand for money is a result of this trade-off regarding the form in which a person's wealth should be held. In macroeconomics
Macroeconomics
Macroeconomics is a branch of economics dealing with the performance, structure, behavior, and decision-making of the whole economy. This includes a national, regional, or global economy...
motivations for holding one's wealth in the form of money can roughly be divided into the transaction motive
Transactions demand
Transactions demand, in economic theory, specifically Keynesian economics, is one of the determinants of demand for money , the others being speculative demand and precautionary demand. Transactions demand is illustrated as a vertical line on the money demand graph.The demand of money is arisen...
and the asset motive
Speculative demand
Speculative demand is the demand for financial assets, such as securities, money or foreign currency that is not dictated by real transactions such as trade, or financing.The need for cash to take advantage of investment opportunities that may arise....
. These can be further subdivided into more microeconomically founded motivations for holding money.
Generally, the nominal demand for money increases with the level of nominal output (price level times real output) and decreases with the nominal interest rate
Nominal interest rate
In finance and economics nominal interest rate or nominal rate of interest refers to the rate of interest before adjustment for inflation ; or, for interest rates "as stated" without adjustment for the full effect of compounding...
. The real demand for money is defined as the nominal amount of money demanded divided by the price level. For a given money supply
Money supply
In economics, the money supply or money stock, is the total amount of money available in an economy at a specific time. There are several ways to define "money," but standard measures usually include currency in circulation and demand deposits .Money supply data are recorded and published, usually...
the locus of income-interest rate pairs at which money demand equals money supply is known as the LM curve.
The magnitude of the volatility of money demand has crucial implications for the optimal way in which a central bank
Central bank
A central bank, reserve bank, or monetary authority is a public institution that usually issues the currency, regulates the money supply, and controls the interest rates in a country. Central banks often also oversee the commercial banking system of their respective countries...
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
Liquidity trap
A liquidity trap is a situation described in Keynesian economics in which injections of cash into an economy by a central bank fail to lower interest rates and hence to stimulate economic growth. A liquidity trap is caused when people hoard cash because they expect an adverse event such as...
), play an important role in Keynesian theory. This situation occurs when the demand for money is infinitely elastic
Elasticity (economics)
In economics, elasticity is the measurement of how changing one economic variable affects others. For example:* "If I lower the price of my product, how much more will I sell?"* "If I raise the price, how much less will I sell?"...
with respect to the interest rate.
A typical money-demand function may be written as
where
is the nominal amount of money demanded, P is the price level, R is the nominal interest rate, Y is real output, and L(.) is real money demand. An alternate name for is the liquidity preferenceLiquidity preference
In macroeconomic theory, Liquidity preference refers to the demand for money, considered as liquidity. The concept was first developed by John Maynard Keynes in his book The General Theory of Employment, Interest and Money to explain determination of the interest rate by the supply and demand...
function.
Transaction motive
The transactions motive for money demand results from the need for liquidity for day-to-day transactions in the near future. This need arises when income is received only occasionally (say once per month) in discrete amounts but expenditures occur continuously.Quantity Theory
The most basic "classical" transaction motive can be illustrated with reference to the Quantity Theory of MoneyQuantity theory of money
In monetary economics, the quantity theory of money is the theory that money supply has a direct, proportional relationship with the price level....
. According to the equation of exchange
, where M is the stock of money, V is its velocity (how many times a unit of money turns over during a period of time), P is the price level and Y is real income. Consequently PY is nominal income or in other words the number of transactions carried out in an economy during a period of time. Rearranging the above identity and giving it a behavioral interpretation as a demand for money we haveor in terms of demand for real balances
Hence in this simple formulation demand for money is a function of prices and income, as long as its velocity is constant.
Inventory models
The amount of money demanded for transactions however is also likely to depend on the nominal interest rate. This arises due the lack of synchronization in time between when purchases are desired and when factor payments (such as wages) are made. In other words, while workers may get paid only once a month they generally will wish to make purchases, and hence need money, over the course of the entire month.The most well-known example of an economic model that is based on such considerations is the Baumol-Tobin model
Baumol-Tobin model
The Baumol-Tobin model is an economic model of the transactions demand for money as developed independently by William Baumol and James Tobin . The theory relies on the trade off between the liquidity provided by holding money and the interest foregone by holding one’s assets in the form of...
. In this model an individual receives her income periodically, for example, only once per month, but wishes to make purchases continuously. The person could carry her entire income with her at all times and use it to make purchases. However, in this case she would be giving up the (nominal) interest rate that she can get by holding her income in the bank. The optimal strategy involves holding a portion of one's income in the bank and portion as liquid money. The money portion is continuously run down as the individual makes purchases and then she makes periodic (costly) trips to the bank to replenish the holdings of money. 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).
Microfoundations for money demand
While the Baumol-Tobin model provides a microeconomic explanation for the form of the money demand function, it is generally too stylized to be included in modern macroeconomic models, particularly dynamic stochastic general equilibriumDynamic stochastic general equilibrium
Dynamic stochastic general equilibrium modeling is a branch of applied general equilibrium theory that is influential in contemporary macroeconomics...
models. As a result most models of this type resort to simpler indirect methods which capture the spirit of the transactions motive. The two most commonly used methods are the cash-in-advance
Cash-in-advance constraint
The cash-in-advance constraint is an idea used in economic theory to capture monetary phenomena...
model (sometimes called the Clower
Robert W. Clower
Robert Wayne Clower was an American economist. He is credited with having largely created the field of stock-flow analysis in economics and with seminal works on the microfoundations of monetary theory and macroeconomics....
Constraint model) and the money in the utility function model (sometimes referred to as the 'MIU' or the Sidrauski model).
In the cash-in-advance model agents are restricted to carrying out a volume of transactions equal to or less than their money holdings. In the MIU model, money directly enters agents' utility functions, capturing the 'liquidity services' provided by money.
Asset motive
The asset motive treats money, in the broader sense of including interest-bearing bank deposits, as a particular type of a financial asset among many others. While it is still assumed that money is held in order to carry out transactions, this approach focuses on the potential return on various assets (including money) as an additional motivation.Speculative motive
John Maynard KeynesJohn Maynard Keynes
John Maynard Keynes, Baron Keynes of Tilton, CB FBA , was a British economist whose ideas have profoundly affected the theory and practice of modern macroeconomics, as well as the economic policies of governments...
, in laying out speculative reasons for holding money, stressed the choice between money and bonds. If agents expect the future nominal interest rate (the return on bonds) to be lower than the current rate they will then reduce their holdings of money and increase their holdings of bonds. If the future interest rate does fall, then the price of bonds will increase and the agents will have realized a capital gain on the bonds they purchased. This means that the demand for money in any period will depend on both the current nominal interest rate and the expected future interest rate (in addition to the standard transaction motives which depend on income).
The fact that the current demand for money can depend on expectations of the future interest rates has implications for volatility of money demand. 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.
Portfolio motive
The portfolio motive also focuses on demand for money over and above that required for carrying out transactions. The basic framework is due to James TobinJames Tobin
James Tobin was an American economist who, in his lifetime, served on the Council of Economic Advisors and the Board of Governors of the Federal Reserve System, and taught at Harvard and Yale Universities. He developed the ideas of Keynesian economics, and advocated government intervention to...
, who considered a situation where agents can hold their wealth in a form of a low risk/low return asset (here, money) or high risk/high return asset (bonds or equity). 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. Similarly, given a person's degree of risk aversion, a higher expected return (nominal interest rate plus expected capital gains on bonds) will cause agents to shift away from safe money and into risky assets. Like in the other motivations above, this creates a negative relationship between the nominal interest rate and the demand for money. However, what matters additionally in the Tobin model is the subjective rate of risk aversion, as well as the objective degree of risk of other assets, as, say, measured by the standard deviation of capital gains and losses resulting from holding bonds and/or equity.
Is money demand stable?
FriedmanMilton Friedman
Milton Friedman was an American economist, statistician, academic, and author who taught at the University of Chicago for more than three decades...
and Schwartz
Anna Schwartz
Anna Jacobson Schwartz is an economist at the National Bureau of Economic Research in New York City, and according to Paul Krugman "one of the world's greatest monetary scholars"...
in their 1963 work A Monetary History of the United States argued that the demand for real balances was a stable function of income and the interest rate. For the time period they were studying this appeared to be true. However, shortly after the publication of the book, due to changes in financial markets and financial regulation money demand became more unstable. Various researchers showed that money demand became much more unstable after 1975. 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. However, when the same basic model is used on data spanning 1976 to 1993, it performs poorly. In particular, money demand appears not to be sensitive to interest rates and there appears to be much more exogenous volatility. The authors attribute the difference to technological innovations in the financial markets, financial deregulation, and the related issue of the changing menu of assets considered in the definition of money.
Importance of money demand volatility for monetary policy
If the demand for money is stable then a monetary policy which consists of a monetary rule which targets the growth rate of some monetary aggregate (such as M1 or M2) can help to stabilize the economy or at least remove monetary policy as a source of macroeconomic volatility. Additionally, if the demand for money does not change unpredictably then money supply targeting is a reliable way of attaining a constant inflation rate. This can be most easily seen with the quantity theory of money equation given above. When that equation is converted into growth rates we havewhich says that the growth rate of money supply plus the growth rate of its velocity equals the inflation rate plus the growth rate of real output. If money demand is stable then velocity is constant and
. Additionally, in the long run real output grows at a constant rate equal to the sum of the rates of growth of population, technological know-how, and technology in place, and as such is exogenous. In this case the above equation can be solved for the inflation rate:Here, given the long-run output growth rate, the only determinant of the inflation rate is the growth rate of the money supply. In this case inflation in the long run is a purely monetary phenomenon; a monetary policy which targets the money supply can stabilize the economy and ensure a non-variable inflation rate.
This analysis however breaks down if the demand for money is not stable — for example, if velocity in the above equation is not constant. In that case, shocks to money demand under money supply targeting will translate into changes in real and nominal interest rates and result in economic fluctuations. An alternative policy of targeting interest rates rather than the money supply can improve upon this outcome as the money supply is adjusted to shocks in money demand, keeping interest rates (and hence, economic activity) relatively constant.
The above discussion implies that the volatility of money demand matters for how monetary policy should be conducted. If most of the aggregate demand
Aggregate demand
In macroeconomics, aggregate demand is the total demand for final goods and services in the economy at a given time and price level. It is the amount of goods and services in the economy that will be purchased at all possible price levels. This is the demand for the gross domestic product of a...
shocks which affect the economy come from the expenditure side, the IS curve, then a policy of targeting the money supply will be stabilizing, relative to a policy of targeting interest rates. However, if most of the aggregate demand shocks come from changes in money demand, which influences the LM curve, then a policy of targeting the money supply will be destabilizing.