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A New Approach to Monetary Policy
John H. Cochrane1
April 2016
1Hoover Institution, Stanford University.1 / 34
Papers
1. “Do Higher Interest Rates Raise or Lower Inflation?”
2. “Monetary Policy with Interest on Reserves”
3. “The New-Keynesian Liquidity Trap”
4. “Understanding fiscal and monetary policy in the great recession:Some unpleasant fiscal arithmetic.”
5. “Determinacy and Identification with Taylor Rules”
6. “Money as Stock”
7. ...
2 / 34
Recent Experience–US
1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 20160
1
2
3
4
5
6
Fed Funds
Core CPI
10Y Govt
Reserves
Fed FundsCore CPI10 Year Treas.Reserves ($Tr.)
3 / 34
Recent Experience – Japan
1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016
-1
0
1
2
3
4
5
Discount Rate
Core CPI
10Y Govt
Japan
Discount rateCore CPI10 year rate
4 / 34
Recent Experience – Europe
5 / 34
Implications and objectiveLesson:
I i hits zero. Massive ($50B → $3,000B) QE. Inflation does little.I An interest rate peg can be stable.I → Raising rates eventually raises inflation. Short run?
Implication: Standard monetary theories fail.I Old-Keynesian / Monetarist: Peg is unstable. “Deflation spiral?”I Monetarist: MV=PY. Hyperinflation?I Excusable. Can’t tell ahead of time. But failure as deep as 1970s.I New-Keynesian: Peg is stable, but indeterminate. Standard solutions
predict huge deflation / depression and “Topsy-turvy” policy.1. Far-off expectations have larger effects. 1 bp in 2050.2. Less stickiness makes matters worse. Infinite effects for ε stickiness.3. Structural reform is bad. Hurricanes are good. Wasted G is good.
Objective:I Sensible simple, economic theory consistent with recent evidence.I What will happen if central banks raise rates?
Outline:I My answer first, NK and Old K review later.I Result: Small change to NK structure, but large change to results.
6 / 34
To monetary policy; Fisher / ISRebuild:
I Start very simple. Constant (or exogenous) r, c. No monetary orpricing frictions.
I → The (forward-looking) Fisher (IS) equation.
it = r + Etπt+1
I Stable. Peg OK. π follows i . But
1. Dynamics? Story? Lower π in the short run?2. How does Fed / ECB set i with huge excess reserves?3. Indeterminacy? (NB Indeterminacy 6= instability).
πt+1 − Etπt+1 = δt+1; Etδt+1 = 0
Add ingredients...
I NK adds Taylor-type rule it = φπt ; φ > 1. But
1. Doesn’t work at i = 0.2. Lots of theoretical problems.3. Leads to deflation/depression and topsy-turvy predictions.
I Instead...7 / 34
FTPL liteSo far,
it = r + Etπt+1; πt+1 − Etπt+1 = δt+1 =?
Next step:
I Add 1 period debt, valuation equation.
Bt−1
Pt= Et
∞∑j=0
1
Rt,t+jst+j = Et
∞∑j=0
βjst+j .
I (Notes: Part of any model. No need for exogenous surpluses. Low Ris a big part of the story for low P.)
I Take Et − Et−1
Bt−1
Pt−1(Et − Et−1)
(Pt−1
Pt
)= (Et − Et−1)
∞∑j=0
βjst+j . (1)
I Unexpected inflation is determined entirely by changing expectationsof the PV of fiscal surpluses.
I → Solves determinacy. Each equilibrium δt+1 is indexed by fiscalpolicy. If there is no fiscal policy change, δt+1 = 0.
8 / 34
Interest rate targetsTo Monetary Policy?
Bt−1
Pt= Et
∞∑j=0
βjst+j
Take Et−1,
Bt−1
Pt−1Et−1
(Pt−1
Pt
)= Et−1
∞∑j=0
βjst+j . (2)
I “Monetary policy” – nominal bond sales Bt−1, with no s change –can completely determine expected inflation. (Share split).
Qt−1 =1
1 + it−1= βEt−1
(Pt−1
Pt
). (3)
Bt−1
Pt−1
1
1 + it−1= Et−1
∞∑j=0
βj+1st+j . (4)
I “Monetary policy” (B, no s) can set a nominal interest rate target.I Story: Fed, Treasury basically fix it , not Bt in bond auction.I MP can control i with IOR, and fixed, large, balance sheet.I Interest rate targets completely control expected inflation.
9 / 34
Progress so far
Bottom line: Fisher + fiscal foundations →
it = set by Fed ≈ r + Etπt+1
πt+1 − Etπt+1 = − (Et+1 − Et)∞∑j=0
βjst+j/bt
(bt = Bt/Pt)
I Rehabilitates even fixed nominal interest rate peg / targets!
I No indeterminacy. (Sargent-Wallace, Woodford.)
I No instability. (Friedman 1968, old-Keynesian policy establishment.)
I No money needed at all, not even to implement i control.
I Compelling story for recent experience: i = 0, π declines as r rises.
But, dynamics? ...
10 / 34
Interest rate targets – impulse-response
Time-3 -2 -1 0 1 2 3
Pe
rce
nt
resp
on
se
-1
-0.5
0
0.5
1
1.5
interest rate i
inflation π
π, with fiscal shocks
Time-5 -4 -3 -2 -1 0 1 2 3
Pe
rce
nt
resp
on
se
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
interest rate i
inflation π
π, with fiscal shocks
Model it = r + Etπt+1; πt+1 − Etπt+1 = −(Et+1 − Et)∑βjst+j/bt .
Left: Shock announced at t = 0. Right: Shock announced at t = −3.
I Standard NK model produces decline with a negative fiscal shock.
I Agenda: Standard prediction of (temporarily) lower π without fiscalshock? And realistic dynamics?
I Pricing frictions? Monetary frictions? Other frictions?
I Important: minimal model, not DSGE soup.
11 / 34
i targets, pricing frictions – simplest exampleModel
ct = Etct+1 − σ(it − Etπt+1)
πt = κct
To solve,πt = Etπt+1 − σκ(it − Etπt+1)
So solution:
Etπt+1 =1
1 + σκπt +
σκ
1 + σκit
πt+1 − Etπt+1 = − (Et+1 − Et)∞∑j=0
βjst+j/bt
I IR {Etπt+j} does not depend on expected vs. unexpected iI π response is stable, hence follows i .I Note: {it} is not (necessarily) a peg. Conditional on equilibrium{it}, even if produced by Taylor rule. “If equilibrium {it} is a step,here is equilibrium {πt}, {xt}.”
12 / 34
Impulse-response, simple price stickiness model
time-4 -3 -2 -1 0 1 2 3 4 5 6 7
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
interest rate i
inflation π
ct = E
tc
t+1-(i
t-E
tπ
t+1)
πt = c
t
πt+1
-Etπ
t+1=-(E
t+1-E
t)Σβ
js
t+j/b
t
I “Neo-Fisherian:” No π decline. Pricing frictions did not fix.
13 / 34
Impulse-response, simple price stickiness model
time-4 -3 -2 -1 0 1 2 3 4 5 6 7
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
interest rate i
inflation π
ct = E
tc
t+1-(i
t-E
tπ
t+1)
πt = c
t
πt+1
-Etπ
t+1=-(E
t+1-E
t)Σβ
js
t+j/b
t
with fiscal shocks
I Mix i rise with fiscal shock. Conventional NK. Data / VAR? Future?
14 / 34
Impulse-response, simple price stickiness model
time-4 -3 -2 -1 0 1 2 3 4 5 6 7
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
interest rate i
inflation π
ct = E
tc
t+1-(i
t-E
tπ
t+1)
πt = c
t
πt+1
-Etπ
t+1=-(E
t+1-E
t)Σβ
js
t+j/b
t
with fiscal shocks
I Pre-announced interest rate rise. Why pair these shocks?I → look for “monetary policy” alone (no s).
15 / 34
A Real New-Keynesian model
xt = Etxt+1 − σ(it − Etπt+1); πt = βEtπt+1 + κxt .
Time-4 -2 0 2 4 6
Pe
rce
nt
resp
on
se
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1 interest rate i
inflation π
output gap x
iπ
x
Central banks are half right! Attempts to produce a negative response...16 / 34
Mean-Reverting rate
Time-4 -2 0 2 4 6
Pe
rce
nt
resp
on
se
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1 iπ
x
17 / 34
Money
I Add monetary frictions as well as pricing frictions
I Hope: old policy raised i by lowering M. That lowers π temporarily.
I Would explain past, but not IOR. (Monetarist past, Fisherian future)
I Model:
maxE∞∑t=0
βtu(ct ,mt), ucm 6= 0...
ct = Etct+1+ (σ − ξ)(mc
)Et
[(it+1 − imt+1
)− (it − imt )
]−σ (it − Etπt+1) .
ξ = interest elasticity of money demand.
I Expected rise in interest costs lowers consumption today relative totomorrow, like a higher real rate. → Inflation too !
I Higher level of interest cost has no effect on AD. → Standardunexpected permanent i shock has no effect!
18 / 34
Impulse-response functions with money
Time-4 -2 0 2 4 6
Perc
ent re
sponse
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
m/c=0
m/c=2
m/c=4
Inflation
iUnπ , expectedπ , expected
I Expected rate rise lowers inflation! But it needs huge m/c .19 / 34
Directions
A simple, modern, economic model, consistent with experience, thatproduces a temporary decline in inflation? (Without joint fiscal policy.)Paper: Many failed attempts.
I Add more frictions?
I Borrowing or collateral constraints, hand-to-mouth consumers,irrational expectations or other irrational behavior, habits,labor/leisure, production, capital, variable capital utilization,adjustment costs, lending channel, informational, market, payments,monetary, financial frictions?
I Lose simple, modern, or economic. Admits standard monetary policysign must have complex / noneconomic ingredients; There is nosimple, modern, economic baseline. (Goal: Simple model for sign.DSGE soup for exact match.)
I VAR evidence is not strong, “price puzzle.”
I Maybe raising interest rates without s really does just raise inflation?
20 / 34
New-Keynesian analysis of the zero bound (Werning 2012)
dxtdt
= σ (it − rt − πt)
dπtdt
= ρπt − κxt
↔
xt = Etxt+1 − σ [it − rt − Etπt+1]
πt = e−ρEtπt+1 + κxt
I rt = natural rate = −5% to t = T = 5, then rt = +5%.
I it = 0 to t = T = 5, then it = rt = 5% (Or Taylor rule)
I πT = 0.
21 / 34
The standard NK analysis of the zero bound
0 1 2 3 4 5 6 7 8 9 1050
40
30
20
10
0
10
Time
Per
cent
Standard equilibrium, varying κ
xπ
I High real rate, c must grow. C jumps down. Big depression,deflation (counterfactual).
I Less friction→worse! Limit6=limit point (π = 5%, x = 0)!I Backwards unstable → forward guidance, magical multipliers.
22 / 34
New-Keynesian model: a closer look
dxtdt
= σ (it − rt − πt)
dπtdt
= ρπt − κxt
d
dt
[xtπt
]=
[0 −σ−κ ρ
] [xtπt
]+ σ
[it − rt
0
]I Two eigenvalues, λm < 0, λp > 0; two free constants.
I No forward explosions. Set eλpt term to zero.
I One-dimensional family of solutions. Index by πT .
I All equilibria have the same interest rate path {it}!
23 / 34
All Solutions of NK model
0 1 2 3 4 5 6 7 8 9 1020
15
10
5
0
5
10
Perc
ent
Time
Inflation across equilibria
I “Indeterminacy” = multiple stable solutionsI Stable forward = unstable backward. Sensitive to small ∆EtπT .I (E0 − E−1)π0 = (E0 − E−1)
∑βtst is large for conventional solution.
24 / 34
The no-inflation-jump equilibrium
0 1 2 3 4 5 6 7 8 9 105
4
3
2
1
0
1
2
3
4
5
6
Time
Per
cent
Nojump equilibrium, varying κ
xπ
I π0 = 0 → no big πt < 0, small xt effects. πt > 0 solves r < 0, i = 0.I Nice frictionless limit!I (E0 − E−1)π0 = −(E0 − E−1)
∑βtst/b = 0. “Monetary policy.”
I “Backward stable.” Faraway promises have little current effects.25 / 34
NK model summaryI Conventional NK model & equilibrium choice predicts huge
deflation, depression.I Also paradoxical policies and magical multipliers:
1. Promises in the far future have huge effects. Weird frictionless limit.2. Less stickiness makes matters worse.3. Enormous multipliers. (Fiscal → future π → more c now. Not
C = C̄ + αY .)4. All from forward-stable = backward-explosive. (Thus, robust.)
I But there are many equilibria. “Backward stable” equilibria with
1. limited π0, x0, (E0 − E−1)∑βtst = 0 jumps,
2. expectations of events t →∞ have bounded effects at 0,
solve all these problems. But then:
I Zero bound is not a big deal. Look elsewhere for slow growth.
I Gets rid of the policy magic. Alas, if you like magic.
I Bottom line: conventional NK/DSGE structure is fine. Pick differentequilibria. Here: No big jumps at t = 0. Before: No big fiscal policycoincident with monetary policy.
I But this gives quite different answers!
26 / 34
Old-Keynesian (& Monetarist) ModelsNK Model:
xt = Etxt+1 − σ (it − Etπt+1)
πt = βEtπt+1 + κxt
OK Model:
xt = −σ(it − πt) + uxt
πt = πt−1 + κxt + uπt .
OK: myopic or backward-looking behavior:
I IS: No Etxt+1; it − πt not it − Etπt+1.
I PC: πt−1 not Etπt+1
Solution:
πt =1
1− σκπt−1 −
σκ
1− σκit +
1
1− σκ(κuxt + uπt ) .
I Unstable, determinate27 / 34
Old-Keynesian (& Monetarist) Models
-4 -2 0 2 4 6-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
1 i
π
x
iπ
x
Response of inflation to an interest rate rise, old-Keynesian model.
I Peg is unstable. Predicts deflation spiral at i = 0.I “Right” sign of i policy in short and long run.I Lost “modern” and “economic.”
28 / 34
Old-Keynesian (Monetarist) Models with Taylor rule
xt = −σ(it − πt) + uxtπt = πt−1 + κxt + uπt
it= φππt + uit .
πt =1
1 + κσ(φπ − 1)πt−1 +
1
1 + κσ(φπ − 1)(κuxt + uπt − σκuit)
I Taylor rule φπ > 1 induces stability in an otherwise unstable butalready determinate model.
I NK: Taylor rule φπ > 1 induces instability, hence local determinacy,in an otherwise stable but indeterminate model.
29 / 34
Taylor / Friedman / Conventional tightening
-5 0 5 10 15 20 25
-1.5
-1
-0.5
0
0.5
1
i
π
x
ui
iπ
x
ui
Response to a permanent tightening uit in the Taylor rule it = φππt + uit .I Fisher in long run. Opposite sign in the short run.I Clearest conventional view.I Answer? No. Failed in data. And if so, monetary policy has no
economic roots.30 / 34
Caution
it = r + Etπt+1
πt+1 − Etπt+1 = −(Et − Et−1)∞∑j=0
1
R jst+j/bt
I Does raising interest rates really raise inflation? Before you jump...1. Maybe we will find enough frictions to produce a temporary negative?2. Model has short term debt. Long debt drags out the dynamics.
(∆t ≈ duration ≈ 2 years US.)3. Beware the fiscal foundations! Will they really believe s has not
changed? Like disinflations (Sargent), which always combine fiscaland monetary.
Bt−1
Pt= Et
∞∑j=0
1
R jst+j
I Fiscal foundations warning: Debt is an earthquake fault. High value(low P) comes from low R not from big s! Higher real rates(permanent, so not central banks) could be quite inflationary.
I Be careful what you wish for!31 / 34
Extra Slides
32 / 34
Low rate promise – standard equilibriumI Interest rate stays at zero for time τ after the trap ends
0 2 4 6 830
20
10
0
10
Time
Per
cent
τ = 0.0
xπ
0 2 4 6 830
20
10
0
10
Time
Per
cent
τ = 0.5
0 2 4 6 810
0
10
20
30
Time
Per
cent
τ = 1.0
0 2 4 6 810
0
10
20
30
Time
Per
cent
τ = 2.0
I Far-away promises have huge effects. Bigger for less price stickiness.
33 / 34
Low rate promise – backwards-stable equilibrium
0 2 4 6 8
2
0
2
4
6τ = 0.0
Time
Per
cent
xπ
0 2 4 6 8
2
0
2
4
6τ = 0.5
Time
Per
cent
0 2 4 6 8
2
0
2
4
6τ = 1.0
Time
Per
cent
0 2 4 6 8
2
0
2
4
6τ = 2.0
Time
Per
cent
I Faraway promises have little current effects→frictionless.
34 / 34
Taylor rule and the standard solution
0 1 2 3 4 5 6 7 8 9 1020
15
10
5
0
5
10
Per
cent
Inflation across equilibria with a Taylor rule
I Not: “if πT > 0, Fed tightens too much, lowers inflation too fast”
I Yes: “if πT > 0 people expect the Fed to explode the economy.” Orthose equilibria are not ruled out.
35 / 34
A Taylor rule could select the glidepath too
0 1 2 3 4 5 6 7 8 9 1020
15
10
5
0
5
10
Per
cent
Inflation across equilibria with a Taylor rule
I Equilibrium selection policy to choose π∗t (glidepath) is just aspossible.
36 / 34
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