Quantifying Confidence
George-Marios Angeletos
Fabrice Collard
Harris Dellas
Bank of Portugal, June 11, 2015
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Standard approach
coordination failure = multiple equilibria
aggregate demand = gaps from flex prices, NKPC
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An alternative

coordination failure 
aggregate demand
Angeletos, Collard, Dellas
= strategic uncertainty / beliefs

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An alternative

coordination failure 
aggregate demand
= strategic uncertainty / beliefs

This Paper
1. tractable formalization
2. quantitative evaluation
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Contribution
1
explore observable implications of
I
imperfect coordination
I
relaxed solution concept
2
accommodate fluctuations in “confidence”
3
decouple AD from sticky prices
4
I
bypass empirical failures of old and NK Philips curves
I
great recessions 6= great deflations
explain multiple salient features of the data
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Roadmap
Baseline Model and Methodological Contribution
Quantitative Evaluation
Extension to Medium-Scale DSGE & Estimation
Complementary Empirical Work
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Baseline Model
belief-enrichment of textbook RBC model
geography
I
islands: differentiated intermediate goods, local L and K markets
I
mainland: final good (→ consumption and investment)
I
heterogeneous beliefs across islands
sources of volatility
I
permanent shock to technology: At
I
transitory shock to HOB, or “confidence”: ξt
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Modeling Beliefs
Stage 1
Stage 2
observe xit = log At + εit
observe (At , Yt , prices)
form beliefs about (Yt , Yt+1 , ...)
update beliefs
make production choices
consume and invest
t
Angeletos, Collard, Dellas
Quantifying Confidence
t +1
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Modeling Beliefs
Stage 1
Stage 2
observe xit = log At + εit
observe (At , Yt , prices)
form beliefs about (Yt , Yt+1 , ...)
update beliefs
make production choices
consume and invest
t
t +1
heterogeneous priors:
εit
∼ N (0, σ)
εjt
∼ N (ξt , σ)
ξt → aggregate variation in HOB → “confidence” or “AD”
Angeletos, Collard, Dellas
Quantifying Confidence
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ξt as a proxy for strategic uncertainty
standard:
Yt = Ēt [Yt ] = YtRBC ≡ χ At
strategic uncertainty:
Yt 6= Ēt [Yt ] = YtRBC + “belief wedge”
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Quantifying Confidence
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ξt as a proxy for strategic uncertainty
standard:
Yt = Ēt [Yt ] = YtRBC ≡ χ At
strategic uncertainty:
Yt 6= Ēt [Yt ] = YtRBC + “belief wedge”
Angeletos and La’O (Ecma 2013)
I
impose common prior (no biases)
I
abstract from capital, add market segmentation
⇒ observational equivalence
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ξt as a belief enrichment
DSGE models vs “beauty contests”:
behavior depends on beliefs of many endogenous outcomes (prices,
wages, sales...) in many dates
ξt = disciplined, parsimonious, and tractable belief enrichment
research task: understand observable implications & quantify
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Methodological Contribution
tractability, tractability, tractability....
take the limit as σ → 0 ⇒
I
no learning, no Kalman filter
I
no cross-sectional heterogeneity, no Krusell-Smith
I
ξt is sufficient statistic for gap between higher- and first-order beliefs
⇒ small state spaces!
solution almost as in representative-agent models
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Recursive equilibrium
recursive equilibrium = PBE among fictitious local planners
key objects: G, P, V1 , V2
I
G = aggregate policy rule for capital:
Kt+1 = G(At , ξt , Kt )
I
P = local beliefs about prices (demand):
I
V1 , V2 = value functions of local planner in stages 1, 2
p̂it = P(xit , ξt , Kt )
heterogeneous priors → tractable fixed point
→ solution “almost” as in representative-agent models
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Recursive equilibrium
stage-1 problem:
V1 (k; x, ξ, K ) = max V2 (m̂; x, ξ, K ) −
n
s.t.
1
1+ν
1+ν n
m̂ = p̂ ŷ + (1 − δ)k
ŷ = xk θ n1−θ
p̂ = P(x, ξ, K )
stage-2 problem:
R
V2 (m; A, ξ, K ) = max{c,k 0 } U(c) + β V1 (k 0 ; A0 , ξ 0 , K 0 )df (A0 , ξ
s.t.
c + k0 = m
K 0 = G(A, ξ, K )
n(k, x, ξ, K ) & g(m, A, ξ, K )= policy rules for (n, k)
y(x, A, ξ, K ) = output implied by policy rules
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Recursive equilibrium
belief consistency:
P(x, ξ, K ) =
y(x + ξ, x, ξ, K )
y(x, x, ξ, K )
aggregation:
X
G(A, ξ, K ) = g y(A, A, ξ, K ) + (1 − δ)K ; A, ξ, K
bottom line: tractable fixed-point problem
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Log-linear solution
original model:
(Ct , It , Nt ; Kt+1 ) = Γk · Kt + Γa · At + Γξ · ξt
belief-augmented model:
(Ct , It , Nt ; Kt+1 ) = Γk · Kt + Γa · At + Γξ · ξt
generalization to arbitrary linear DSGE models (see Appendix) →
simulate/calibrate/estimate as in standard DSGE models
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Calibration
fix all familiar params to conventional values
Parameter
Role
Value
β
δ
ν
α
ψ
Discount Rate
Depreciation Rate
Inverse Elasticity of Labor Supply
Capital Share in Production
Inverse Elasticity of Utilization
0.990
0.015
0.500
0.300
0.300
fix persistence of belief shock to ρ = .75
choose σa and σξ so as to match of BC volatilities of Y , H, I , C
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Observable implications: IRFs to confidence shock
Output
% deviation
2
Productivity
0.5
1.5
Consumption
0.2
0.15
1
0
1.5
1
2
0.5
0.05
0
0
-0.5
0
10
Quarters
20
Hours Worked
2
4
0.1
0.5
Investment
6
0
0
0
10
Quarters
20
0
10
Quarters
20
0
10
Quarters
20
0
10
Quarters
20
co-movement patterns very different from
I
I
I
investment- or consumption-specific shocks
news or noise shocks
any shock that works through TFP (e.g., uncertainty shocks)
similar to monetary shock in NK, but w/o inflation
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Pony Race: Confidence Shocks vs NK Demand Shocks
NK with TFP plus...
Data
Our RBC
stddev(y )
stddev(h)
stddev(c)
stddev(i)
1.42
1.56
0.76
5.43
corr(c, y )
corr(i, y )
corr(h, y )
corr(c, h)
corr(i, h)
corr(c, i)
corr(y , y /h)
corr(h, y /h)
corr(y , sr )
corr(h, sr )
I shock
C shock
News
Monetary
1.42
1.52
0.76
5.66
1.24
1.18
0.86
7.03
1.15
0.97
0.95
7.04
1.29
1.02
0.84
7.24
1.37
1.44
0.77
6.20
0.85
0.94
0.88
0.84
0.82
0.74
0.77
0.92
0.85
0.34
0.99
0.47
0.42
0.82
0.80
-0.19
1.00
-0.17
0.37
0.75
0.77
-0.29
1.00
-0.33
0.43
0.84
0.86
-0.07
1.00
-0.13
0.73
0.90
0.84
0.24
0.99
0.35
0.08
-0.41
0.82
0.47
0.15
-0.37
0.85
0.47
0.37
-0.24
0.92
0.52
0.54
-0.10
0.92
0.49
0.61
0.13
0.94
0.65
0.20
-0.36
0.94
0.61
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Take-home lesson (so far)
a simple formalization of non-monetary demand shocks
superior performance within “textbook” models
key to quantitative success:
I
waves of optimism/pessimism about “demand” in the short run
I
disconnect from TFP and labor productivity
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Quantifying Confidence
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Extensions
medium-scale DSGE → robustness and structural estimation
multiple shocks → multiple competing mechanisms
I
I
I
I
I
I
permanent and transitory TFP shock
permanent and transitory investment-specific shock
news about future productivity
discount-factor shock
fiscal shock
monetary shock
also: IAC and HP → endogenous persistence, plus help NK
two versions: flexible vs sticky prices
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Observable Implications
Output
1
Consumption
0.5
0.8
0.4
0.6
0.3
0.4
0.2
0.2
0.1
0
10
Quarters
20
1
1
0.5
0
0
-1
0
10
Quarters
20
Hours Worked
1.5
2
0
0
Investment
3
-0.5
0
10
Quarters
20
Inflation Rate
0.08
Nom. Interest Rate
2
0.06
0
0.04
-2
0.02
-4
0
-6
-0.02
0
10
Quarters
Flexible Prices (RBC)
20
-8
0
10
Quarters
20
0
10
Quarters
20
Sticky Prices (NK)
similar effects in RBC vs NK, or in textbook vs medium-scale models
important: that’s NOT the case for other shocks/mechanisms
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Quantifying Confidence
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Estimated Contribution
despite multiple competing forces, estimation attributes more than
half of the observed business cycles to “confidence”
contribution to volatility (6-32 quarters)
Flexible Prices
Sticky Prices
Y
C
I
h
π
R
50.98
47.73
43.72
40.89
54.63
44.24
76.04
65.66
0.00
11.95
99.15
32.64
contribution to covariances (6-32 quarters)
Flexible
Sticky
(Y , h)
(Y , I )
(Y , C )
(h, I )
(h, C )
(I , C )
75.80
68.53
60.06
53.23
56.34
58.40
75.67
62.64
96.53
106.30
84.75
107.41
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Quantifying Confidence
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What Is Aggregate Demand?
posterior odds of competing models:
RBC <<< NK << RBC with confidence
interpretation: a potent theory of AD (even) w/o nominal rigidity
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Quantifying Confidence
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Complementary Empirical Work (Angeletos-Collard-Dellas)
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Quantifying Confidence
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Complementary Empirical Work (Angeletos-Collard-Dellas)
bypass any particular model or any structural VARs
“anatomy” of comovement
I
construct factors designed to capture volatility of certain variables
I
inspect comovement patterns across variables and/or frequencies
Angeletos, Collard, Dellas
Quantifying Confidence
23 / 29
Complementary Empirical Work (Angeletos-Collard-Dellas)
bypass any particular model or any structural VARs
“anatomy” of comovement
I
construct factors designed to capture volatility of certain variables
I
inspect comovement patterns across variables and/or frequencies
Angeletos, Collard, Dellas
Quantifying Confidence
23 / 29
Complementary Empirical Work (Angeletos-Collard-Dellas)
bypass any particular model or any structural VARs
“anatomy” of comovement
I
construct factors designed to capture volatility of certain variables
I
inspect comovement patterns across variables and/or frequencies
show that this anatomy points towards shocks/mechanisms that are
I
highly transitory
I
disconnected from both productivity and inflation
I
unlike usual suspects
Angeletos, Collard, Dellas
Quantifying Confidence
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Identifying a “Business Cycle Factor”
1
VAR/VECM on
{Y , H, I , C , PI /PC , π, R, G , ...}
with 2 unit-root components
2
“business cycle factor” = combination of VAR innovations that
maximizes band-pass volatility of Y and/or (H, I ) at 6-32 quarters
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Quantifying Confidence
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Factor: Variance Contribution
Y
Baseline, with permanent
6–32 quarters
49.62
32–80 quarters 21.49
80–∞ quarters
0.00
Angeletos, Collard, Dellas
I
h
C
components excluded
55.70 49.22 24.34
28.52 28.19
8.89
0.00
3.37
0.00
Quantifying Confidence
Y /h
Pi
π
R
15.03
6.44
0.00
5.92
4.24
0.00
17.74
14.63
2.08
31.33
31.38
5.15
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Factor: Variance Contribution
Y
Y /h
Pi
π
R
components excluded
55.70 49.22 24.34
28.52 28.19
8.89
0.00
3.37
0.00
15.03
6.44
0.00
5.92
4.24
0.00
17.74
14.63
2.08
31.33
31.38
5.15
Variant, with permanent components included
6–32 quarters
47.97 55.87 58.97 21.45
32–80 quarters 17.27 25.01 26.55
9.46
80–∞ quarters
6.67
6.67
7.26
6.66
23.23
12.89
6.67
4.96
6.22
6.62
15.87
15.86
6.68
44.39
43.44
9.52
Baseline, with permanent
6–32 quarters
49.62
32–80 quarters 21.49
80–∞ quarters
0.00
Angeletos, Collard, Dellas
I
h
C
Quantifying Confidence
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Factor: Comovement Patterns
Output
Consumption
Investment
0.5
2
0.5
0
0
0
-0.5
-2
-0.5
5
10
15
Quarters
Hours Worked
20
5
10
15
Quarters
Productivity
20
1
0
-0.5
0
0
-0.5
-0.5
-1
5
1
10
15
Quarters
Gov. Spending
10
15
Quarters
Rel. Price of Inv.
20
20
0.5
0.5
0.5
5
5
10
15
Quarters
Inflation Rate
20
0.2
0.2
0.5
0.1
0.1
0
0
0
-0.5
-0.1
-0.1
-0.2
5
10
15
Quarters
Nom. Int. Rate
20
5
10
15
Quarters
20
-0.2
-1
5
10
15
Quarters
baseline
Angeletos, Collard, Dellas
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5
10
15
Quarters
20
variant
Quantifying Confidence
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Model Counterpart?
has to be transitory
has to trigger strong comovement in (Y , H, I , C ),
without strong comovement in either (Y /H, TFP, Pi/PC ) or π
unlike any of the “usual suspects” in standard models
I
not technology
I
not news/noise
I
not financial or uncertainty shock that work through TFP
I
not I- or C-specific shocks
what can this be? “confidence”, or something else
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Quantifying Confidence
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Confidence shock (model) vs factor (data)
4
Output
15
Investment
6
Hours Worked
Consumption
2
3
10
4
5
2
1.5
2
1
1
0.5
0
0
0
-5
-2
-10
-4
0
-0.5
-1
-1
-2
-3
-1.5
-2
-4
-15
1970 1980 1990 2000
-6
1970 1980 1990 2000
1970 1980 1990 2000
1970 1980 1990 2000
this explains why structural estimation favors confidence shock
evidence in favor of our theory and/or against standard theories
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Conclusion
Methodological contribution:
I
embed tractable higher-order beliefs in a large class of macro models
I
accommodate a certain relaxation of solution concept
Applied contribution:
I
reveal observable implications of HOB
I
accommodate waves of optimism and pessimism about SR
I
accommodate “aggregate demand” without sticky prices
I
explain multiple salient features of the data
Angeletos, Collard, Dellas
Quantifying Confidence
29 / 29