Unit 2: Monetary Policy Optimal Monetary Policy Unit 2: Monetary Policy May, XXXXXXXXXX / 59 How does the Fed choose an it? We’ve discussed (1) how the Fed controls it and (2) how it affects spending...

Unit 2: Monetary Policy
Optimal Monetary Policy
Unit 2: Monetary Policy May, XXXXXXXXXX / 59
How does the Fed choose an it?
We’ve discussed (1) how the Fed controls it and (2) how it affects spending and
prices. But what does the Fed actually hope to achieve?
When thinking about what interest rate policy to set, the Fed takes into account
its duel mandate:
1 ‘Full’ employment
2 Stable prices (low steady inflation)
Let’s go back to our New Keynesian model from the last unit, to see how a shock
(i.e. a recession) plays out, and what monetary policy can do about the shock,
and how the Fed weighs its two goals.
Unit 2: Monetary Policy May, XXXXXXXXXX / 59
The NK model revisited
We’ll make two adjustments to the NK presented in the previous unit:
1 3 periods instead of 2 (t ∈ (1, 2, 3))
2 Downwardly rigid wages (nominal wages can never go down)
The first change will allow to add a ‘medium run’ period.
The second change will give us unemployment (why?) and let us study the
concept of potential output.
Potential output: the level of output such that all of the economy’s resources
(in our case, all workers) are put to full use and there is no inflation.
Unit 2: Monetary Policy May, XXXXXXXXXX / 59
Households
Remember that households worked for the firm every period, earning wage Wt ,
and were able to save in a bond, bt .
On the homework, you’ll solve the household’s optimization problem in 3 periods
and show that they now have:
3 intra-temporal conditions instead of 2
2 Euler equations instead of 1
c−σt =
Pt
Pt+1
βt+1(1 + i)c
−σ
t+1
Note that the β terms now have a time subscript. This means they can change
over time.
If there are only 3 periods, how much will the household save in the last period?
Then what will they consume? c3P3 = W3
Unit 2: Monetary Policy May, XXXXXXXXXX / 59
Firms
Remember that y jt = L
j
t and that firms set their prices according to the following
equation:
Pt =
(
ϵ
1− ϵ
)
E [MCt ] =
(
ϵ
1− ϵ
)
E [Wt ]
A fraction α of the firms know the true marginal cost so E [MCt ] = Wt , while
(1− α) have to base their price off of their backward looking expectations,
E [MCt ] = Wt−1.
Question: If nominal wages (Wt) never go down, will there ever be deflation in
this model?
Finally, remember that when we derived this relationship, we used the fact that
demand for the output of each firm, y jt was a negative function of their price, p
(law of demand).
Unit 2: Monetary Policy May, XXXXXXXXXX / 59
Central Bank
Finally, remember that we had a central bank that can set the nominal interest
ate, it .
We’ll show that the Central Bank can achieve its policy goals by following a
Taylor Rule of the form (ϕy and ϕπ are both positive):
it = ī + ϕy (Yt − Ȳ ) + ϕπ(πt)
Where Ȳ is ‘potential output’ and Y − Ȳ is the ‘output gap’.
Unit 2: Monetary Policy May, XXXXXXXXXX / 59
A shock to β
Suppose their is a positive shock to β2 (intuition?). Holding all else equal, what
happens to c1?
c−σ1 =
P1
P2
β2(1 + i1)c
−σ
2
Consumers demand less stuff today at cu
ent prices. Can firms lower thei
prices? No! Wages can’t fall, so firms keep prices constant, P1 = P0 and just
produce less, Y1 = c1.
How much labor do they demand then? LD1 = Y1 = c1
Do workers want to work less? Recall that the first-period intra-temporal (labo
supply) condition is:
c−σ1 W1 = L
γ
1
No! If anything they want to work more. LS1 = (W1/c
σ
1 )
1
γ
Unit 2: Monetary Policy May, XXXXXXXXXX / 59
Potential output and the ‘output gap’
We just saw that when a β shock causes demand to fall, downwardly rigid
nominal wages means that the amount of labor demanded is less than the amount
that workers are willing to supply at that wage. Therefore we do not have full
employment.
Question: could firms employ more labor and therefore produce more without
aising prices?
Yes! How do we know this?
Right now, LS(W1)− LD(W1) > 0, so firms could easily induce more workers to
work for them without needing to raise wages (and thus prices).
Therefore are we above or below potential output? Is the output gap positive o
negative?
Below full employment = output lower than potential = negative output gap
Unit 2: Monetary Policy May, XXXXXXXXXX / 59
How should the Fed respond?
The Fed has a mandate to maintain full employment and stable prices?
Has there been any inflation or deflation? Nope!
What about less-than-full employment?
Remember our Taylor Rule: i1 = ī + ϕy (Y1 − Ȳ ) + ϕπ(π1)
So the Fed should unambiguously decrease the interest rate, i1 until c1 (which
equals Y1, which equals L
D
1 equals labor supplied at the given (stuck) nominal
wage, W1.
LS1 = (W1/c
σ
1 )
1
γ = LD1 = c1
Let call this interest rate, iL
Unit 2: Monetary Policy May, XXXXXXXXXX / 59
The economy starts to recover...
Suppose that the panic that caused β2 to jump up subsides, and β3 falls to its
‘normal’ level. Suppose further that the Fed had yet to change , i2 which was still
equal to iL.
c−σ2 =
P2
P3
β3(1 + iL)c
−σ
3
Intuitively, iL was low enough to get c1 back to potential output with the highe
β2. If iL is combined with β3 instead, do we expect c2 = Y2 will equal or exceed
potential? Exceed! Y2 > Ȳ .
How will firms get workers to produce this extra output, Y2?
W2 = (C
1−σγ
1 )
γ
Unit 2: Monetary Policy May, XXXXXXXXXX / 59
Inflation
For the α flexible price firms, PF2 =
ϵ
1−ϵW2 while the (1− α) sticky price firms
still have the lower price:PS1 =
ϵ
1−ϵW1, so:
P2 = (
ϵ
1−ϵ )(αW2 + (1− α)W1) > P1
So what should the Fed do? How are they doing on full employment? How about
price stability?
i2 = ī + ϕy (Y2 − Ȳ ) + ϕπ(π2)
They should increase i2!
Unit 2: Monetary Policy May, XXXXXXXXXX / 59
Zero Lower Bound and Forward Guidance
Unit 2: Monetary Policy May, XXXXXXXXXX / 59
Taking stock
Thus far we’ve learned:
1 How the Fed controls interest rates
2 How interest rates affect spending and inflation
3 What interest rate the Fed wants to set
Recap: a fixed Wt implies a given potential output (when labor supply=labo
demand at the given wage): (Wt/c
σ
t )
1
γ = ct . The Fed wants to achieve this level
of output.
What happens when spending falls low enough that the interest rate the Fed
would like to choose is negative?
Can interest rates be negative?
Unit 2: Monetary Policy May, XXXXXXXXXX / 59
The ILB
If your bank tried to charge you to keep your money in the bank, you’d just take
out cash!
It’s possible that you’ll tolerate a slightly negative rate, but there is definitely a
interest rate lower bound (ILB).
Suppose β jumps high enough such that:(
c−σt+1β
Pt
Pt+1
(1 + iILB)
)− 1σ
= ct < Ȳ
Can monetary policy effectively stimulate the economy?
Unit 2: Monetary Policy May, XXXXXXXXXX / 59
What can the Fed do?
Let’s look at our Euler equation once again:
c−σ1 = c
−σ
2 βH
P1
P2
(1 + iILB)
Our problem is that c1 is too low (c
−σ
1 ) is too high and i1 is at its lower limit.
Can the central bank control β? Pt? No! β is exogenous given and Pt is stuck
ecause of the downward nominal wage rigidity.
What variables are still available? P2 and c2
Unit 2: Monetary Policy May, XXXXXXXXXX / 59
Forward guidance
What if the Fed promised to keep the interest rate low in period 2 - despite β
eturning to its ‘normal’ lower level? This would mean a positive output gap and
inflation!
c−σ2 = c
−σ
3 βL
P2
P3
(1 + iILB)
When β falls to BL, c
−σ
2 must fall, meaning c2 must increase. Intuition?
If c2 rises above Ȳ , what must firms do to induce more workers to produce the
additional output? Raise wages.
So what happens to P2? P2 must increase!
Trying to affect the economy today by being clear about the path for monetary
policy in the future is called forward guidance.
Unit 2: Monetary Policy May, XXXXXXXXXX / 59
Back to the recession...
If the Fed promises to keep future interests rate low (and tolerate a bif of
inflation) they can push expectations about c2 and P2 up.
c−σ1 = (c2 ↑)
−σβH
P1
(P2 ↑)
(1 + iILB)
This can raise c1 even when iILB has hit it’s lowest level.
Why does being richer tomo
ow make you want to consume more today? Why
do higher prices tomo
ow make you want to consume today?
Summary: Forward guidance allows the Fed to get around the ILB by promising
low rates and inflation tomo
ow.
Unit 2: Monetary Policy May, XXXXXXXXXX / 59
Final thoughts and Future Research
Unit 2: Monetary Policy May, XXXXXXXXXX / 59
Monetary Transmission
Throughout this analysis, the primary way that monetary policy has stimulated
output has been by directly changing households’ incentives to save (if saving is
less rewarding, consuming now is less expensive).
But is this the primary way monetary policy affects consumption?
A growing body of research suggests that this ‘direct’ mechanism may only play a
partial role.
Unit 2: Monetary Policy May, XXXXXXXXXX / 59
Two-Agent Models
Imagine that instead of a single representative household, we two-types of
households.
A fraction f is exactly the same as the household we’ve already studied with a
typical Euler equation:
u′(cUt ) = β(1 + i)u
′(cUt+1)
However, the other (1-f) households in the economy are credit constrained
meaning they have no access to the bond market.
As a result, their budget constraint is simply given by: cCt = WtL
C
t and
cCt+1 = Wt+1L
C
t+1
Unit 2: Monetary Policy May, XXXXXXXXXX / 59
Transmission in the Two-Agent Model
Does the consumption of the credit constrained agents respond to changes i?
Why not?
What does their consumption respond to?
cCt = WtL
C
t c
C
t+1 = Wt+1L
C
t+1
So the overall transmission mechanism looks like:
i ↓→ cUt ↑→ Yt ↑→ Wt ↑→ cCt ↑ (and cUt increases a bit as well) → ...
Question: When a constrained (C) agent gets more labor income today, how
much of it will they consume? MPC = dCdW = 1 What about the unconstrained
(U) agents?
Unit 2: Monetary Policy May,