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