# The to illiquidity. In bad times under a money

The Poole model is a useful way to
show how to reduce macroeconomic volatility as to show this as it extends the
IS-LM model to include shocks, which can be money shocks, real shocks or a mix
of the two within an economy which all cause volatility. The equation for IS
becomes  and LM becomes  where u is the shock to IS and v is the shock
to LM.  A money supply rule is
where money supply is fixed and interest rates fluctuate. An interest rate rule
is when policymakers fix interest rates and allow money supply to move around
freely depending on money demand. The policymaker wants to minimise the
variance of GDP and so we use a loss function:  where Yf is the Natural rate of GDP.

If
an economy faces only money demand shocks then this creates macroeconomic
volatility as it’s the extent to which the financial sector prefers liquidity
to illiquidity. In bad times under a money supply rule quantities of liquid and
illiquid assets are fixed however the opportunity cost of money increases and
so the interest rate resulting in higher money demand and so we get LM+. In
good times then the opposite is true. People have confidence in illiquid assets
and so the price of money goes down decreasing the interest leading to LM-. When
there are money shocks in an economy, if policymakers use a money supply rule
then output can vary between Y- and Y+. By contrast if the policy maker chose
an interest-rate rule they would fix the interest rate at i0 so the expected
level of output is   as , and we get a
horizontal LM curve because the LM function can be extended to ‘treat money
supply as interest-elastic… a pegged interest rate, of course is a polar case
in terms of interest elasticity of supply’ (Poole, 1970). This means under an
interest-rate rule actual output will be. If there is are only money
shocks in the economy under an interest rate rule there will be no volatility
as output will always be Y0 geometrically or Yf as .  If the economy faces only money demand shocks
then it should use the interest rate rule over the money supply rule to lower macroeconomic
volatility.

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More commonly an
economy can face are real shocks, when there is randomness in private spending
affecting the IS curve, with private investment being most volatile component. One
determinant of investment is the interest rate (opportunity cost of investing
in capital stock) which gives a downward sloping investment curve. The
investment curve determines the position of the IS curve as it is government
spending given the amount of investment. In good times people are optimistic
and so invest more and there is a positive spending shock giving IS+. In bad
times there is more uncertainty so people don’t want to invest resulting in a
negative spending shock, IS-.

If policymakers applied a money
supply rule to minimise expected loses then expected output is  as . To minimise loses the
policymaker would set the money supply so  giving actual output under a money supply rule
as   During bad times GDP would be Y1 and
during good times as there is more private spending IS is higher and so GDP is
Y2. If policy makers chose to fix interest rates then we again get the horizontal
LM curve and we can see in bad times, when IS is lower output is Y3 and in good
times it is Y4. We can see from the graph that the amount Y varies when fixing
money stock (Y1-Y2) is smaller than the when fixing interest rates (Y3-Y4). If
an economy faces only private spending shocks it should adopt the money supply
rule to reduce macroeconomic volatility.

In the
real world economies are more likey to be vulnerable to both financial shocks
and real shocks at the same time. If the economy is facing bad times and
policymakers use a money supply rule it will be at the point where the two blue
lines cross.  There is pessimism in financial
markets, as people have liquidity preference so Md increases
resulting in a higher LM(+). If there is pessimism in the money market then it
is more than likely that there is also uncertainty in real terms i.e.
Consumption and Investment. Financial institutions distrust of markets will
make consumers and business wearier to invest and so we get IS-. Under a fixed
money supply in bad times output will be Y1.
Oppositely in good times under a money supply rule people have
confidence in their illiquid assets we have a lower Md and a lower
LM curve (LM-). Additionally the real market will we in boom and so there will
be more consumption and investment resulting in a higher IS curve (IS+). In
good times using a money supply rule is Y2.
Conversely the policymakers could a fixed interest rate when there are money
and real shocks. We can see that in bad times GDP would be Y3 due to
significantly lower investment (and/or consumption) and in good times GDP would
be Y4 due to more spending. In this graph real shocks (to IS curve) are larger
than the shocks to the money market, and so we can see from the graph that the
policy makers should use the money supply rule because here interest rates are
acting coherently and going up in good times which offsets it and so
macroeconomic volatility is lower Y1-Y2 than with a fixed interest rate Y3-Y4.
If on the economy was in the position where the LM shocks were greater than the
IS shocks then the opposite would be true. This is because if you were to use a
fixed money supply then the interest rates are not having the desired effect;
they decrease when the economy is in good times and so this encourages more
investment and worsen the situation. Here the policymaker should use an
interest rate rule to lower macroeconomic volatility.

This could also be shown by
comparing losses because as stated earlier the objective of the policymaker is
to minimise the variance of GDP. We know under a fixed interest rate   and under fixed money supply. The loss functions
are   and with a money supply rule . To compare the
policies we find the ratio of the losses (look at the relative losses. . If the expression ?
is greater than 1 then the loss under a money supply rule is greater and so the
policymaker will chose a fixed interest rate, however if ? is less than
one then the loss under a fixed interest rate is greater so the policy maker
will fix the money supply to reduce macroeconomic volatility. If we assume that
?=-1 then  simplifying to . The term in the square brackets is
now very similar to the denominator (Pickering, 2017) and so the interest
elasticity of money demand (?2) is less relevant. What is more
important is ?1, income elasticity of money demand, ?v
and ?u. If ?1 is greater than   then
the loss from having a fixed money supply will be smaller than the loss from
having a fixed interest rate. A money shock may not matter much if ?1 is high. LM
shift left in bad times Md increases and GDP falls which feeds back
into the Md function. In economic bad times interest rates may be
increasing for other reasons such as the IS curve. This means than Md increases,
so volatility increases and GDP falls, if ?1 is
high enough it will have a corrective effect on the initial increase that
happens in bad times and counteracts what is happening to v.

An alternative is to
use fiscal policy (taxation and government spending) to reduce volatility. If
the economy is facing positive shocks real shocks then that means people are
optimistic and so IS shifts right. However if the policymaker uses
contractionary fiscal policy and increases income tax and corporation tax then this
will shift IS left again and reduce volatility in the economy. In addition to
this if money demand is very sensitive to interest rates i.e. ?2
is very high then the LM curve becomes horizontal and so fiscal
policy is more attractive.
Combination policy is another alternative where values are set for c’1 and
c’2 in the money supply equation  however for certain values the denominators of
optimal c’1 and c’2 vanish so we use  . Again we want to minimise losses so get ,                   ) , and . This gives us the
minimum expected loss as . When  there is a pure interest rate policy and when  there is a pure money stock policy. Except
these two cases combination policy is better than both pure policies (Poole,
1970) because expected losses are lower. For combination policy to be successful
there has to be more knowledge of the parameters than the pure policies.

Overall both the money
supply rule and the interest rate rule are effective at reducing macroeconomic volatility