Monetary Policy: 4th Short Run Consideration: Zero Lower Bound And Liquidity Traps Flashcards
(12 cards)
So we showed how forward looking interest rate rules can create stable type 1 equilibriums.
However interest rules were uneffective during GFC as couldn’t go below 0. Why is there a zero lower bound for interest rates?
Since no reason to hold asset with negative nominal return, hence why interest rate cannot fall below 0
Like cash in hand holding has no nominal return so noone wants to put in bank and get negative return! (Although it can have a negative real return since inflation rises!)
Liquidity trap
When monetary policy cannot affect economic outcomes!
Like this in GFC! Despite low interest, could not influence activity! Similar in japan with no interest but no economic growth!
Krugman’s ZLB model
Household utility function
U = Σ βt at lnCt
Discount factor b
Households get utility from consumption lnCt
at: demand shift variable to model recession
We also have bonds in model; they pay interest but only exchanged for money not goods
Gov either raise funds by taxes or sell bonds)
Households start period t with holdings of money and bonds from end of period t-1.
There is a market to trade money and bonds.
What are household’s purchases subject to? Expression and what does it means
A cash-in-advance constraint
Ct <= Mt/Pt
Consumption has to be <= to real money balances i.e money that you hold.
Cannot use bonds for consumption, u need money!
After household purchase consumption and sell their endowment, they get interest it on bonds they hold
Government also implements tax/transfers.
We assume competitive markets and flexible prices
2 key equations for household optimisation: first one
Ct if it>0 vs it<0
If it>0 i.e holding cash has opportunity cost, could be invested in bonds to earn this return i! Households shouldn’t hold excess cash, thus = i.e optimise perfectly!
Ct = Mt/Pt
If it=0 i.e zero lower bound, cash has no opportunity cost! Bond is useless so households can hold excess cash, thus <=!
Ct<= Mt/Pt
2nd household optimisation equation:
Euler equation (derive in seminar class)
State final answer pg13
B) what is the steady state of this equation in the long run
C) key finding
it = atPt+1/ (βat+1Pt) -1
at is demand shift variable (to model recession)
B) in long run, money supply and demand shift a are constant, so we get constant a and price level!
i* = aP/βaP -1
Which a and P* cancel out so left with
i* = 1/β -1!
C) nominal interest rate only depends on discount factor i.e household patience!
As a result given β<1, what the long run result for i?
Steady state (long run) i* = 1/β -1
And β<1. This means i*>0
Recall when i*>0, there is an opportunity cost to holding cash, so perfectly optimise and do not hold excess! So in long run we get
Ct = Mt/Pt
Recall liquidity traps are when monetary policy can no longer impact economic outcomes.
Assume the steady state occurs in period 2, and period 1 we don’t know
What do we do to our Euler equation pg14
Everything in t+1 i.e period is steady state, so replace everythign t+1 with a * instead to show steady state
Original:
it = atPt+1/βat+1Pt -1
Replace t’s with 1 to show period 1, t+1 replace with *
i₁ = a₁P* / βa*P₁ - 1
Then we show diagramatically
Diagram of steady state in period 2! Pg 15
A) exis’
B) why is CC curve downward sloping
Y axis - i₁ (nominal interest)
X axis P₁ (price today)
B) CC curve (consumption) - downward sloping as a higher P1 (price today) for a given future price, means inflation is lower. If inflation is lower, in order to keep real interest the same, they must also lower nominal i!
Recall fisher r=i-π (π fall, i must fall to keep r same!)
Where they intersect is equilibrium
Scenario 1: Central Bank increase M money supply
Assume nominal interest rate is positive before and after change in M. What happens to diagram and result(pg15 bottom)
MM curve shifts outward further right
i>0 so hold only what they need, hence why need to adjust household choices
Increase in money supply means i falls, so lower return so increase spending thus increasedP1.
So monetary supply can influence economy! No liquidity trap
Scenario 2: Central Bank increases M
But initial nominal interest rate is 0 before the change in M.
What does diagram look like now
Increasing M does not change household choices, since i=0, they can either hold in cash or bonds (perfect subs)
Same exact equilibrium, no change.
This is the liquidity trap! No effect on economy
So what were main unconventional MP they resorted to
QE: CB purchases gov bonds to keep market interest rates down to encourage spending.
Nearly £895bn spent, need to do quantititve tightening and sell gov bonds, however this increases interest rates. So have to reduce slowly
