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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
Caballero and Simsek (MIT and NBER) Risk-centric Model Summer 2017 2 / 31
Extremely Low Volatility
Caballero and Simsek (MIT and NBER) Risk-centric Model Summer 2017 3 / 31
And High Valuations
Caballero and Simsek (MIT and NBER) Risk-centric Model Summer 2017 4 / 31
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...”
Caballero and Simsek (MIT and NBER) Risk-centric Model Summer 2017 5 / 31
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)
Caballero and Simsek (MIT and NBER) Risk-centric Model Summer 2017 6 / 31
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
Caballero and Simsek (MIT and NBER) Risk-centric Model Summer 2017 7 / 31
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
Caballero and Simsek (MIT and NBER) Risk-centric Model Summer 2017 8 / 31
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
Caballero and Simsek (MIT and NBER) Risk-centric Model Summer 2017 9 / 31
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 ′.
Caballero and Simsek (MIT and NBER) Risk-centric Model Summer 2017 10 / 31
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.
Caballero and Simsek (MIT and NBER) Risk-centric Model Summer 2017 11 / 31
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.
Caballero and Simsek (MIT and NBER) Risk-centric Model Summer 2017 12 / 31
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∗
Caballero and Simsek (MIT and NBER) Risk-centric Model Summer 2017 13 / 31
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.
Caballero and Simsek (MIT and NBER) Risk-centric Model Summer 2017 14 / 31
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
Caballero and Simsek (MIT and NBER) Risk-centric Model Summer 2017 15 / 31
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
Caballero and Simsek (MIT and NBER) Risk-centric Model Summer 2017 16 / 31
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)
Caballero and Simsek (MIT and NBER) Risk-centric Model Summer 2017 17 / 31
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 .
Caballero and Simsek (MIT and NBER) Risk-centric Model Summer 2017 18 / 31
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 ′ ,
Caballero and Simsek (MIT and NBER) Risk-centric Model Summer 2017 19 / 31
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
Caballero and Simsek (MIT and NBER) Risk-centric Model Summer 2017 20 / 31
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
Caballero and Simsek (MIT and NBER) Risk-centric Model Summer 2017 21 / 31
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
Caballero and Simsek (MIT and NBER) Risk-centric Model Summer 2017 22 / 31
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
Caballero and Simsek (MIT and NBER) Risk-centric Model Summer 2017 23 / 31
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
Caballero and Simsek (MIT and NBER) Risk-centric Model Summer 2017 24 / 31
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
Caballero and Simsek (MIT and NBER) Risk-centric Model Summer 2017 25 / 31
Other Results
Other results in paper:
Forward guidanceEndogenous volatility
Companion paper:
Incomplete markets and unconventional monetary policyStronger feedback between speculation and instability through leverage.
Caballero and Simsek (MIT and NBER) Risk-centric Model Summer 2017 26 / 31
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
Caballero and Simsek (MIT and NBER) Risk-centric Model Summer 2017 27 / 31
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
Caballero and Simsek (MIT and NBER) Risk-centric Model Summer 2017 28 / 31
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.
Caballero and Simsek (MIT and NBER) Risk-centric Model Summer 2017 29 / 31
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
Caballero and Simsek (MIT and NBER) Risk-centric Model Summer 2017 30 / 31
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
Caballero and Simsek (MIT and NBER) Risk-centric Model Summer 2017 31 / 31