A Risk-centric Model of Demand Recessions and ......A Risk-centric Model of Demand Recessions and...

A Risk-centric Model of Demand Recessions andMacroprudential Policy

Ricardo Caballero Alp Simsek

MIT and NBER

Summer 2017

Caballero and Simsek (MIT and NBER) Risk-centric Model Summer 2017 1 / 31

Risk Intolerance


Extremely Low Volatility


And High Valuations


Its Deliberate...

Cieslak and Vissing-Jorgensen (2017) conduct textual analysis ofFOMC minutes and transcripts: “We find 983 mentions of the stockmarket in the 184 FOMC minutes covering the 1994-2016 period...the number of negative stock market mentions... has significantexplanatory for target changes.... of the 432 [not purely descriptive]paragraphs, 265 (61%) discuss the impact of the stock market onconsumption.... the impact of the stock market on investment isanother repeated theme in FOMC discussions...”


A Risk-centric Perspective

That is, they have tried to create nearly perfect risk-market conditionsto support valuations in a risk-intolerant world.... to support AD

This is a very risk-centric perspective, which is not quite what we doin our typical output-gap-centric macro models...

A productive capacity (and its expansion) generates output and risks,both of which need to be absorbed by economic agents

Output and risk gaps emerge, which interact with each other

This paper: A macro model of these interactions, but inverting thehierarchy (risk-centric)


More (modelling) Context

Risk (in)tolerance and asset prices

Finance - Asset pricing literatureNo particular role for aggregate demand

Asset prices and aggregate demand

Macro —New Keynesian literatureNo particular role for riskFocus on output-gap

First attempts to bridge the gap:

Brunnermeier-Sannikov’s macrofinance modeling and some of thepapers in balance sheet recessions literature (supply side)Safe asset shortages and safety traps


Framework

Macrofinance model

AD/AS:

Aggregate supply: Stochastic endogenous growth model withinvestment costs a la B/SAggregate demand: NK model —aggregate demand may become anadditional constraint (excess capacity)

Two shocks: productivity (diffusion) and ERP (Poisson)Heterogenous beliefs (about ERP shocks) and speculationPolicy: r-policy, FG, macroprudential


Environment and FOCs

Potential output growth is a state (vol) contingent B/S process:

dAkt ,sAkt ,s

= (ϕ (ιt ,s )− δ) dt + σsdZt .

With convex adjustment cost of investment (Q−theory):

ι (Qt ,s ) = ψ (Qt ,s − 1) .

In equilibrium the capital-price process within each state takes theform (but with complete markets the diffusion term drops out)

dQt ,sQt ,s

= µQt ,sdt + σQt ,sdZt .

And it (may) jump in state-transitions


Continuum of consumer/investors (log-utility):

c it ,s = ρait ,s .

The capital risk foc:

ωk ,it ,sσkt ,s =

1σkt ,s

r kt ,s − r ft ,s +∑s ′ 6=s

λis ,s ′ait ,sait ,s ′

Qt ,s ′ − Qt ,sQt ,s

.The contingent securities foc (the ωs

′,it ,s are implicitly determined)

ps′t ,s

λis ,s ′=ait ,sait ,s ′

for each s ′.


Equilibrium and Interest Rate (policy)

Equilibrium in goods markets (fixed nominal prices —NK structure)

yt ,s = Aηt ,skt ,s =

∫Ic it ,sdi + kt ,s ιt ,s .

Interest rate policy ensures ηt ,s = 1, while it can

ηt ,s ≤ 1, r ft ,s ≥ 0, with complementary slackness.

Equilibrium in asset markets∫Iait ,sdi = Qt ,skt ,s and

∫Iωk ,it ,sa

it ,sdi = Qt ,skt ,s .

Contingent securities are in zero net supply∫Iait ,sω

s ′,it ,s di = 0.


Characterization of Equilibrium (Preliminaries)

The goods market side of the economy implies:

Aηt ,s = ρQt ,s + ψ (Qt ,s − 1)

Which yields an increasing relationship between factor utilization andasset prices:

qt ,s = log(Aηt ,s + ψ

ρ+ ψ

)Combining with the interest rate policy rule, we characterize thegoods markets:

qt ,s ≤ q∗, r ft ,s ≥ 0, with complementary slackness.


Instability and Hope

Expected return on capital conditional on no transition:

r kt ,s = ρ+ ψqt ,s − δ︸︷︷︸=g (Qt,s )

+µQt ,s + σsσQt ,s .

Two destabilizing effects:Lower asset prices lower aggregate demand, offsetting the effect ofcheaper capital on dividend yieldAlso, lower asset prices reduce investment, which leads to lower returnto capital (lower growth)

Hope: The stabilizing force is due to the transition back to the lowvol state. Equilibrium in capital risk market implies:

σks =1σks

(r kt ,s +

∑s ′λs ,s ′

(Qt ,s ′ − Qt ,sQt ,s ′

)− r ft ,s

)First best: qt ,s = q∗; r kt ,s = ρ+ ψq∗ − δ = ρ+ g∗


Equilibrium with common beliefs (and 2 states)

Let S = {1, 2}, with σ1 < σ2

ωkt ,s = 1 and ωs′t ,s = 0 for each s ′, µQt ,s = σQt ,s = 0, to yield:

σs =ρ− δ + ψqs + λs

(1− Qs

Qs′

)− r fs

σs

Assumption 1. σ22 > ρ− δ + ψq∗ > σ21.

In this case, the low-volatility state 1 features, r f1 > 0, q1 = q∗ andη1 = 1, whereas the high-volatility state 2 features, r f2 = 0, q2 < q∗

and η2 < 1.


Equilibrium in high volatility state

σ2 =ρ− δ + ψq2 + λ2

(1− Q2

Q∗

)− 0

σ2

The adjustment through Q2 leads to an (ineffi cient) recession.The severity of the recession rises as λ2 drops (pessimism) since theeffect of a decline in q2 on the expected return becomes weaker


0 0.1 0.2 0.3 0.4 0.5

0.9

1

1.1

1.2

1.3

1.4

0.08 0.1 0.12 0.14 0.16 0.18

0.2

0.4

0.6

0.8

1

1.2

1.4


Equilibrium in low volatility state (rstar)

σ1 =ρ− δ + ψq∗ + λ1

(1− Q∗

Q2

)− r f1

σ1

Given Q2, this equation determines the interest rate (rstar), r f1 ....which is depressed by Q2 < Q∗ , especially when the economy ispessimistic (high λ1 and low λ2)


Belief Disagreement and Speculation

λt ,s =∑i

αit ,sλis , where α

it ,s =

ait ,skt ,sQt ,s

.

ps′t ,s = λis

ait ,sait ,s ′

= λt ,sQt ,sQt ,s ′

,

σs =1σs

(r kt ,s − r ft ,s +

∑s ′λt ,s ,s ′

(1− Qt ,s

Qt ,s ′

)),

ωk ,it ,s = 1 for each t, s, i .

ωs′,it ,s = λis ,s ′ − λt ,s .


The Economy becomes Extrapolative

dαit,sαit,s

= −∑s ′ 6=s

(λis ,s ′ − λt ,s ,s ′

)dt, if there is no state change,

αit ,s ′ = αit ,sλis,s′

λt,s,s′, if there is a state change to s ′.

λt ,s ,s ′ = λps ,s ′ + αt ,s∆λs ,s ′ .

∆λs ,s ′ ≡ λos ,s ′ − λps ,s ′ ,


Which hurts Aggregate Demand

Optimism raises AD and r f1But the speculation associated to heterogeneous beliefs makes theeconomy extrapolative and depresses AD

0 0 .2 0 .4 0 .6 0 .8 1

0 .8 5

0 .9

0 .9 5

1

1 .0 5

1 .1

1 .1 5

1 .2

1 .2 5

1 .3

1 .3 5

0 0 .2 0 .4 0 .6 0 .8 10 .0 1

0

0 .0 1

0 .0 2

0 .0 3

0 .0 4

0 .0 5

0 .0 6


An Example (Average over diffusion)

0 10 20 30 40 501

1.5

2

0 10 20 30 40 500

0.5

1

0 10 20 30 40 500.9

11.11.21.3

0 10 20 30 40 50

Year t

0.010

0.010.020.03

0.5 1 1.5 2 2.50

0.5

1

0 0.2 0.4 0.6 0.8 10

2

4

0 0.2 0.4 0.6 0.8 10

2

4

0.01 0 0.01 0.02 0.030

50


Equilibrium Value Functions

Let vs = v∗s + ws , where v∗s denotes the first-best (no interestrigidities) wealth-normalized value functionThe top panels reflect pecuniary externalities while the bottom onesreflect the AGGREGATE DEMAND externality

0 0.2 0.4 0.6 0.8 1

40

30

20

10

Value for s=1

0 0.2 0.4 0.6 0.8 114

12

10

8

6

4

2

0

0 0.2 0.4 0.6 0.8 1

40

30

20

10

Value for s=2

0 0.2 0.4 0.6 0.8 120

15

10

5

0


Macroprudential Policy During Boom

0 0.2 0.4 0.6 0.8 1

0.002

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.03 0.035 0.04 0.045 0.05

0.5

0.4

0.3

0.2

0.1

0

0.1

0.2

0.3

0.4


Macroprudential Policy During Boom (beliefs neutral)

0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

1

2

3

4

5

6

7

0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

1

2

3

4

5

6

0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

0.2

0.4

0.6

0.8

1

1.2


An Example

0 10 20 30 40 501

1.5

2

0 10 20 30 40 500

0.5

1

0 10 20 30 40 500.9

11.11.21.3

0 10 20 30 40 50

Year t

0.010

0.010.020.03

0.5 1 1.5 2 2.50

0.5

1

0 0.2 0.4 0.6 0.8 10

2

4

0 0.2 0.4 0.6 0.8 10

2

4

0.015 0.01 0.005 0 0.005 0.01 0.015 0.02 0.025 0.030

50


Other Results

Other results in paper:

Forward guidanceEndogenous volatility

Companion paper:

Incomplete markets and unconventional monetary policyStronger feedback between speculation and instability through leverage.


Final Remarks: The Global Economy

Nearly perfect risk-markets conditions needed to support aggregatedemand

Depressed rstar

Limited space for monetary policyFertile ground for speculation

Extremely vulnerable to a lasting volatility spike

Very large gap between geopolitical risks and financial marketsvolatility


Appendix: Forward Guidance

The planner commits to setting an interest rate path subject to thelower bound constraint, r ft ,s ≥ 0, as well as the remaining equilibriumconditions

We let factor utilization, ηt ,s , exceed one. However, excess utilizationis costly and induces a faster depreciation of capital (in first best theplanner never uses this margin):

dkt ,skt ,s

=(ϕ (ιt ,s )− δ − δη max

(0, ηt ,s − 1

))dt + σsdZt ,.

We focus on the model without disagreements and simplify further bysetting ψ = 0 and by restricting policy to a fixed interest rate duringthe recovery


As before, there is an increasing relationship between asset prices andfactor utilization

q1 = q (η1) ≡ log(Aη1ρ

).

Applying the risk balance condition for state s = 1, we show that thepolicy implies a lower interest rate as long as η1 ≥ 1.

r f1 = ρ− δ + λ1 (1− exp (q (η1)− q2))− δη (η1 − 1)− σ21 ≥ 0,

Likewise, using the condition for state s = 2, we obtain,

r f2 = ρ− δ + λ2 (1− exp (q2 − q (η1)))− σ22 = 0,

as long as q2 ≤ q∗. This illustrates that providing greater stimulus instate 1 also increases the asset price in state 2 by increasing theexpected capital gains.


A surprising aspect of the equilibrium is that the prices in both statesmove in tandem regardless of transition probabilities.

This is a manifestation of the “forward guidance puzzle”: the phenomenon that, in standard New Keynesian

models, interest rate announcements far in the future have large effects on current output as well as inflation

due to backward induction of expansions.

Consider an alternative policy exercise in which the (perceived)strength of the policy is decreasing in the amount of time theeconomy spends in state s = 2 before transitioning into state s = 1.Then:

0 2 4 6 8 10

0. 82

0. 84

0. 86

0. 88

0. 9

0. 92

0. 94

0. 96

0. 98

1

1. 02

0 2 4 6 8 10

0. 82

0. 84

0. 86

0. 88

0. 9

0. 92

0. 94

0. 96

0. 98

1

1. 02


Appendix: Endogenous Volatility

Given some ∆t > 0, we define the proportional change in aggregatewealth over this time interval as,

∆kt ,sQt ,s/∆tkt ,sQt ,s

≡ (kt+∆t ,sQt+∆t ,s − kt ,sQt ,s ) /∆tkt ,sQt ,s

.

Consider the homogenous belief benchmark. In this model, while theinstantaneous volatility conditional on there being no transition isexogenous (given by σs ), the unconditional volatility that alsoincorporates the jump risk in asset prices is endogenous as:

lim∆t→0

Vart ,s

(∆kt ,sQt ,s/∆tkt ,sQt ,s

)= σ2s +

∑s ′ 6=s

λs ,s ′

(Qs ′ − QsQs

)2.

(Extension) With heterogeneous beliefs and incomplete markets (nocontingent securities), agents bet using risky capital: w0 > wp , whichmakes σQ > 0


A Risk-centric Model of Demand Recessions and ......A Risk-centric Model of Demand Recessions and...

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