Friedman vs. Keynes
When comparing the money demand frameworks of Friedman and
Keynes, several differences arise Friedman considers multiple rates of return and considers
the RELATIVE returns to be important
Friedman viewed money and goods as substitutes.
Friedman viewed permanent income as more important than
current income in determining money demand
Friedman's money demand function is much more stable than
Keynes'. This is because permanent income is very stable, and
the spread between returns will also be stable since returns
would tend to rise or fall all at once, causing the spreads to
stay the same. So in Friedman's model changes in interest
rates have little or no impact on money demand. This is not
true in Keynes' model.
If the terms affecting money demand are stable, then money
demand itself will be stable. Also, velocity will be fairly
predictable (since Md is not affected by r).
Saturday, June 21, 2008
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Thursday, June 19, 2008
Friedman’s Modern Quantity Theory of Money
Friedman’s Modern Quantity Theory of Money
Milton Friedman developed a model for money demand based on
the general theory of asset demand.
Money demand, like the demand for any other asset, should be a
function of wealth and the returns of other assets relative to money.
As an asset (store of wealth) money must compete in an
individual’s wealth portfolio with other interest bearing assets.rb = interest rate or rate of return on bonds
Md is positively related to permanent income Yp (here we are
looking at the transaction demand for money); negatively related
to expected interest rates on bonds (rb), the expected rate of
return on equity (re) and expected inflation, (pie)e.
Milton Friedman developed a model for money demand based on
the general theory of asset demand.
Money demand, like the demand for any other asset, should be a
function of wealth and the returns of other assets relative to money.
As an asset (store of wealth) money must compete in an
individual’s wealth portfolio with other interest bearing assets.rb = interest rate or rate of return on bonds
Md is positively related to permanent income Yp (here we are
looking at the transaction demand for money); negatively related
to expected interest rates on bonds (rb), the expected rate of
return on equity (re) and expected inflation, (pie)e.
Tuesday, June 10, 2008
Tobin's theory 3
A higher interest rate will cause the expected return risk relationship line to rotate up (for any level of risk, the expected return is now higher since interest rate is
higher). When this happens, the new optimum point will depend
upon the expected yield-risk preference of the individual. Hence,
when interest rate increases, it could result in an increase or a
decrease in the demand for money.
An increase in the riskiness of holding bond, on the other hand,
causes the expected return risk relationship line to rotate
downward. And the maximum portfolio risk is now Rw1. There
are again two possible new optimums and this again depends on
the individual’s expected yield-risk preference. Hence, the impact
of an increase in risk may increase or decrease the demand for
money.
An increase in W will increase the demand for money if factors
affecting the composition of portfolio (the rate of interest and
the risk of holding bonds) are constant.
Still one problem with money demand remains. There are other
low risk interest bearing assets: money market mutual funds, U.S.
Treasury Bills, and others. So why would anyone hold money as a
store of wealth?
higher). When this happens, the new optimum point will depend
upon the expected yield-risk preference of the individual. Hence,
when interest rate increases, it could result in an increase or a
decrease in the demand for money.
An increase in the riskiness of holding bond, on the other hand,
causes the expected return risk relationship line to rotate
downward. And the maximum portfolio risk is now Rw1. There
are again two possible new optimums and this again depends on
the individual’s expected yield-risk preference. Hence, the impact
of an increase in risk may increase or decrease the demand for
money.
An increase in W will increase the demand for money if factors
affecting the composition of portfolio (the rate of interest and
the risk of holding bonds) are constant.
Still one problem with money demand remains. There are other
low risk interest bearing assets: money market mutual funds, U.S.
Treasury Bills, and others. So why would anyone hold money as a
store of wealth?
Monday, June 2, 2008
How is the portfolio determined?
How is the portfolio determined?
To determine the optimal portfolio allocation, we need to look at
the preference of the individual. Utility in this case is a function of
the expected return (Ye) and the risk (Rw). Since expected return is
a good and risk is a bad, the indifference curve in this case is
upward sloping, indicating that a person will be willing to accept
more risk provided it yields a higher return.
The highest indifference curve that is tangent to the expected
return risk relationship line shows the optimal expected return and
risk (K). Dropping a vertical line down from this position to the
lower diagram then indicates the optimal amount of bond holdings
(Bo). The wealth not held as bonds is held in money.
The demand for money is what Tobin terms as “behaviour toward
risk” – the result of attempting to reduce risk below what it would
be if all wealth were held in bonds. An all bond portfolio would
increase the risk to Rw* and an expected return of Ye*. The
individual would be on a lower indifference curve. People choose
to forgo a higher expected return in exchange for a decrease in risk.
To determine the optimal portfolio allocation, we need to look at
the preference of the individual. Utility in this case is a function of
the expected return (Ye) and the risk (Rw). Since expected return is
a good and risk is a bad, the indifference curve in this case is
upward sloping, indicating that a person will be willing to accept
more risk provided it yields a higher return.
The highest indifference curve that is tangent to the expected
return risk relationship line shows the optimal expected return and
risk (K). Dropping a vertical line down from this position to the
lower diagram then indicates the optimal amount of bond holdings
(Bo). The wealth not held as bonds is held in money.
The demand for money is what Tobin terms as “behaviour toward
risk” – the result of attempting to reduce risk below what it would
be if all wealth were held in bonds. An all bond portfolio would
increase the risk to Rw* and an expected return of Ye*. The
individual would be on a lower indifference curve. People choose
to forgo a higher expected return in exchange for a decrease in risk.
Tobin's theory 2
Therefore if the individual holds all wealth (W) in money and none
in bonds, the portfolio would have zero expected returns and zero
risk (refer to the diagram). As the proportion of bonds increases,
expected portfolio returns and risk both rise. The terms on which
the individual investor can increase the expected return on the
portfolio (Ye) at the cost of increasing risk (Rw) is represented
by the line C.
By holding more bonds
a person increases his expected returns and also his risk.
Higher levels of risk is associated with higher proportions of bonds
in the portfolio.
in bonds, the portfolio would have zero expected returns and zero
risk (refer to the diagram). As the proportion of bonds increases,
expected portfolio returns and risk both rise. The terms on which
the individual investor can increase the expected return on the
portfolio (Ye) at the cost of increasing risk (Rw) is represented
by the line C.
By holding more bonds
a person increases his expected returns and also his risk.
Higher levels of risk is associated with higher proportions of bonds
in the portfolio.
Tobin’s theory
Tobin’s theory in a nutshell:
Total portfolio consists of bonds & cash (W)
W = money + bond
The expected yield on holding bonds (Ye) is the interest earning on
bonds :
Ye = B. r (1)
The total risk (Rw) that the individual takes depends on the
uncertainty concerning bond prices (i.e. the uncertainty concerning
future interest rate movements), as well as the proportion of the
portfolio placed in bonds, the risky asset
Rw = B . Rg (2)
From equation (1) and (2), we can see that an increase in B
increases both the expected yield (Ye) as well as the portfolio
risk (Rw).
Total portfolio consists of bonds & cash (W)
W = money + bond
The expected yield on holding bonds (Ye) is the interest earning on
bonds :
Ye = B. r (1)
The total risk (Rw) that the individual takes depends on the
uncertainty concerning bond prices (i.e. the uncertainty concerning
future interest rate movements), as well as the proportion of the
portfolio placed in bonds, the risky asset
Rw = B . Rg (2)
From equation (1) and (2), we can see that an increase in B
increases both the expected yield (Ye) as well as the portfolio
risk (Rw).
Tobin’s Portfolio Diversification Model
Tobin’s Portfolio Diversification Model
Tobin developed a model to explain portfolio diversification that
did not require individuals to have an idea of a ‘normal’ interest
rate.
Basic idea:
This model is based on the idea that people are risk averse and
therefore choose to diversify their assets
Assumptions:
There is no ‘normal’ interest rate in Tobin’s model;
The returns on bonds = r + G.
Capital gains on bonds (G) can be positive or negative
The individual believes that gains and losses are equally
likely so that the expected capital gain is zero. Therefore the
best expectation of the total return on bonds is just the
interest rate, r. Bonds it must be noted are risky assets as
there is a possibility of capital loss when bond prices fall.
Money, on the other hand, is a safe asset by has zero
returns.
There is therefore a trade-off between bonds and money. By
holding more bonds, a person will enjoy higher returns but there
is also the risk of holding one’s wealth in bonds. Hence, a risk
averse person is willing to give up some of this possible return for
the security of holding some money.
Theory assumption
Let’s generalize what we have discussed. Assume that the
individual makes N trips to the bank over the period. On each trip
he will withdraw Y/N dollars and he then spends the money
gradually over the period. Money holdings therefore vary from Y/N
to zero and this averages to Y/(2N).
The question that we need to answer is what is the optimal choice
of N bearing in mind that the greater N is, the less money he holds
on average and therefore the less interest he forgoes. But at the
same time the greater N is, the more trips he has to make to the
bank, which increases his inconvenience.
Let’s assume that
the cost of going to the bank is a fixed amount of $F;
and
r, represent the interest foregone or the opportunity cost
of holding money.
For any N, the average amount of money held is Y/(2N). Therefore
the forgone interest is rY/(2N). The cost of making trips to the bank
is FN. Therefore, the total cost the individual bears is :
Total cost (C) = rY/(2N) + FN
The greater is N, the smaller is the cost of interest forgone but the
greater is the cost of the trips.
The individual holds more money:
if the fixed cost of going to the bank increases;
if expenditure (Y) is higher; and
when r is lower.
So contrary to the classical economist and Keynes, in Baumol’s
model, transaction demand for money is inversely related to interest
rate.
individual makes N trips to the bank over the period. On each trip
he will withdraw Y/N dollars and he then spends the money
gradually over the period. Money holdings therefore vary from Y/N
to zero and this averages to Y/(2N).
The question that we need to answer is what is the optimal choice
of N bearing in mind that the greater N is, the less money he holds
on average and therefore the less interest he forgoes. But at the
same time the greater N is, the more trips he has to make to the
bank, which increases his inconvenience.
Let’s assume that
the cost of going to the bank is a fixed amount of $F;
and
r, represent the interest foregone or the opportunity cost
of holding money.
For any N, the average amount of money held is Y/(2N). Therefore
the forgone interest is rY/(2N). The cost of making trips to the bank
is FN. Therefore, the total cost the individual bears is :
Total cost (C) = rY/(2N) + FN
The greater is N, the smaller is the cost of interest forgone but the
greater is the cost of the trips.
The individual holds more money:
if the fixed cost of going to the bank increases;
if expenditure (Y) is higher; and
when r is lower.
So contrary to the classical economist and Keynes, in Baumol’s
model, transaction demand for money is inversely related to interest
rate.
Baumol’s Inventory Approach Theory
This theory suggests that the level of inventory holding of money
depends on two factors:
the carrying cost of holding money, i.e. the interest
foregone by holding money and not bonds; and
the cost of making a transfer between money and bond
- transaction cost.
Alternatively the individual could invest a proportion of the initial
income payment in bonds and then sell the bonds when additional
money is needed for transactions. If the individual invested
his income payment in bonds at the beginning of the month,
the time profile of his money holdings will be as follows.
Money holdings at the beginning of the month is Y/2 and money
holdings are run down to zero by the midpoint of the period at a
uniform rate. Average money holding for the first half of the
period is therefore Y/4. At the mid point of the period, bonds are
sold causing money holdings to return to Y/2. This is then
spent at a uniform rate over the remaining half of the period. The
average money holding for the second half of the period is Y/4.
Thus the average money holding for the whole period is Y/4,
which is lower than Y/2 (the case where no bonds are held). The
advantage of this option is that he forgoes less interest since he is
holding less money on the average but the disadvantage is that he
has incurred some transaction costs.
depends on two factors:
the carrying cost of holding money, i.e. the interest
foregone by holding money and not bonds; and
the cost of making a transfer between money and bond
- transaction cost.
Alternatively the individual could invest a proportion of the initial
income payment in bonds and then sell the bonds when additional
money is needed for transactions. If the individual invested
his income payment in bonds at the beginning of the month,
the time profile of his money holdings will be as follows.
Money holdings at the beginning of the month is Y/2 and money
holdings are run down to zero by the midpoint of the period at a
uniform rate. Average money holding for the first half of the
period is therefore Y/4. At the mid point of the period, bonds are
sold causing money holdings to return to Y/2. This is then
spent at a uniform rate over the remaining half of the period. The
average money holding for the second half of the period is Y/4.
Thus the average money holding for the whole period is Y/4,
which is lower than Y/2 (the case where no bonds are held). The
advantage of this option is that he forgoes less interest since he is
holding less money on the average but the disadvantage is that he
has incurred some transaction costs.
Question
Question: How much money will an individual hold to make
payment for the things he buys?
Assuming that:
an individual receives an income of Y at the beginning of
the period (t=0 e.g. start of the month);
(ii) the individual spends this income at a constant rate such that he has exactly no money left at the end of the month (t=1);
Therefore, the average inventory money held during the
period = Y/2 , which is also the amount that will be held at the
midpoint of the period t/2.
Baumol’s Inventory Approach
Baumol’s Inventory Approach (Baumol-Tobin Model of
Cash Management)
Later economists further developed the Keynesian approach
to the demand for money. The transaction demand for money
according to them is also sensitive to interest rate.
The transaction demand for money arises because of the lack of
synchronization between receipts and payments. Hence, there is
a need to keep some money at hand to pay for the things we
buy.
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