[PPT] - Quantifying Confidence George-Marios Angeletos Fabrice Collard PowerPoint Presentation

SLIDE 1

Quantifying Confidence

George-Marios Angeletos Fabrice Collard Harris Dellas Bank of Portugal, June 11, 2015

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SLIDE 2

Standard approach

coordination failure = multiple equilibria aggregate demand = gaps from flex prices, NKPC

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SLIDE 3

An alternative

coordination failure aggregate demand    = strategic uncertainty / beliefs

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SLIDE 4

An alternative

coordination failure aggregate demand    = strategic uncertainty / beliefs

This Paper

1. tractable formalization
2. quantitative evaluation

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SLIDE 5

Contribution

1 explore observable implications of ◮ imperfect coordination ◮ relaxed solution concept 2 accommodate fluctuations in “confidence” 3 decouple AD from sticky prices ◮ bypass empirical failures of old and NK Philips curves ◮ great recessions = great deflations 4 explain multiple salient features of the data Angeletos, Collard, Dellas Quantifying Confidence 4 / 29

SLIDE 6

Roadmap

Baseline Model and Methodological Contribution Quantitative Evaluation Extension to Medium-Scale DSGE & Estimation Complementary Empirical Work

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SLIDE 7

Baseline Model

belief-enrichment of textbook RBC model geography

◮ islands: differentiated intermediate goods, local L and K markets ◮ mainland: final good (→ consumption and investment) ◮ heterogeneous beliefs across islands

sources of volatility

◮ permanent shock to technology: At ◮ transitory shock to HOB, or “confidence”: ξt Angeletos, Collard, Dellas Quantifying Confidence 6 / 29

SLIDE 8

Modeling Beliefs

t t + 1

Stage 1

bserve xit = log At + εit

form beliefs about (Yt, Yt+1, ...) make production choices

Stage 2

bserve (At, Yt, prices)

update beliefs consume and invest

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Modeling Beliefs

t t + 1

Stage 1

bserve xit = log At + εit

form beliefs about (Yt, Yt+1, ...) make production choices

Stage 2

bserve (At, Yt, prices)

update beliefs consume and invest

heterogeneous priors: εit ∼ N(0, σ) εjt ∼ N(ξt, σ) ξt → aggregate variation in HOB → “confidence” or “AD”

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ξt as a proxy for strategic uncertainty

standard: Yt = ¯ Et[Yt] = Y RBC

t

≡ χ At strategic uncertainty: Yt = ¯ Et[Yt] = Y RBC

t

+ “belief wedge”

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ξt as a proxy for strategic uncertainty

standard: Yt = ¯ Et[Yt] = Y RBC

t

≡ χ At strategic uncertainty: Yt = ¯ Et[Yt] = Y RBC

t

+ “belief wedge” Angeletos and La’O (Ecma 2013)

◮ impose common prior (no biases) ◮ 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 ⇒

◮ no learning, no Kalman filter ◮ no cross-sectional heterogeneity, no Krusell-Smith ◮ 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

◮ G = aggregate policy rule for capital:

Kt+1 = G(At, ξt, Kt)

◮ P = local beliefs about prices (demand):

ˆ pit = P(xit, ξt, Kt)

◮ V1, V2 = value functions of local planner in stages 1, 2

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

n

V2( ˆ m; x, ξ, K) −

1 1+ν n1+ν

s.t. ˆ m = ˆ pˆ y + (1 − δ)k ˆ y = xkθn1−θ ˆ p = P(x, ξ, K) stage-2 problem: V2(m; A, ξ, K) = max{c,k′} U(c) + β

V1(k′; A′, ξ′, K ′)df (A′, ξ

s.t. c + k′ = m K ′ = 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: G(A, ξ, K) = g

y(A, A, ξ, K) + (1 − δ)K ;

XA, ξ, K

bottom line: tractable fixed-point problem

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SLIDE 17

Log-linear solution

riginal 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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SLIDE 18

Calibration

fix all familiar params to conventional values

Parameter Role Value β Discount Rate 0.990 δ Depreciation Rate 0.015 ν Inverse Elasticity of Labor Supply 0.500 α Capital Share in Production 0.300 ψ Inverse Elasticity of Utilization 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

Quarters 10 20 % deviation 0.5 1 1.5 2 Output Quarters 10 20

0.5

0.5 Productivity Quarters 10 20 0.05 0.1 0.15 0.2 Consumption Quarters 10 20 2 4 6 Investment Quarters 10 20 0.5 1 1.5 2 Hours Worked

co-movement patterns very different from

◮ 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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SLIDE 20

Pony Race: Confidence Shocks vs NK Demand Shocks

NK with TFP plus... Data Our RBC I shock C shock News Monetary stddev(y) 1.42 1.42 1.24 1.15 1.29 1.37 stddev(h) 1.56 1.52 1.18 0.97 1.02 1.44 stddev(c) 0.76 0.76 0.86 0.95 0.84 0.77 stddev(i) 5.43 5.66 7.03 7.04 7.24 6.20 corr(c, y) 0.85 0.77 0.42 0.37 0.43 0.73 corr(i, y) 0.94 0.92 0.82 0.75 0.84 0.90 corr(h, y) 0.88 0.85 0.80 0.77 0.86 0.84 corr(c, h) 0.84 0.34

0.19
0.29
0.07

0.24 corr(i, h) 0.82 0.99 1.00 1.00 1.00 0.99 corr(c, i) 0.74 0.47

0.17
0.33
0.13

0.35 corr(y, y/h) 0.08 0.15 0.37 0.54 0.61 0.20 corr(h, y/h)

0.41
0.37
0.24
0.10

0.13

0.36

corr(y, sr) 0.82 0.85 0.92 0.92 0.94 0.94 corr(h, sr) 0.47 0.47 0.52 0.49 0.65 0.61

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SLIDE 21

Take-home lesson (so far)

a simple formalization of non-monetary demand shocks superior performance within “textbook” models key to quantitative success:

◮ waves of optimism/pessimism about “demand” in the short run ◮ disconnect from TFP and labor productivity Angeletos, Collard, Dellas Quantifying Confidence 18 / 29

SLIDE 22

Extensions

medium-scale DSGE → robustness and structural estimation multiple shocks → multiple competing mechanisms

◮ 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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SLIDE 23

Observable Implications

Quarters 10 20 0.2 0.4 0.6 0.8 1 Output Quarters 10 20 0.1 0.2 0.3 0.4 0.5 Consumption Quarters 10 20

1

1 2 3 Investment Quarters 10 20

0.5

0.5 1 1.5 Hours Worked Quarters 10 20

0.02

0.02 0.04 0.06 0.08 Inflation Rate Quarters 10 20

8
6
4
2
2Nom. Interest Rate

Flexible Prices (RBC) 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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Estimated Contribution

despite multiple competing forces, estimation attributes more than half of the observed business cycles to “confidence” contribution to volatility (6-32 quarters)

Y C I h π R Flexible Prices 50.98 43.72 54.63 76.04 0.00 99.15 Sticky Prices 47.73 40.89 44.24 65.66 11.95 32.64

contribution to covariances (6-32 quarters)

(Y , h) (Y , I) (Y , C) (h, I) (h, C) (I, C) Flexible 75.80 60.06 56.34 75.67 96.53 84.75 Sticky 68.53 53.23 58.40 62.64 106.30 107.41

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SLIDE 25

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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Complementary Empirical Work (Angeletos-Collard-Dellas)

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Complementary Empirical Work (Angeletos-Collard-Dellas)

bypass any particular model or any structural VARs “anatomy” of comovement

◮ construct factors designed to capture volatility of certain variables ◮ inspect comovement patterns across variables and/or frequencies Angeletos, Collard, Dellas Quantifying Confidence 23 / 29

SLIDE 28

Complementary Empirical Work (Angeletos-Collard-Dellas)

bypass any particular model or any structural VARs “anatomy” of comovement

◮ construct factors designed to capture volatility of certain variables ◮ inspect comovement patterns across variables and/or frequencies Angeletos, Collard, Dellas Quantifying Confidence 23 / 29

SLIDE 29

Complementary Empirical Work (Angeletos-Collard-Dellas)

bypass any particular model or any structural VARs “anatomy” of comovement

◮ construct factors designed to capture volatility of certain variables ◮ inspect comovement patterns across variables and/or frequencies

show that this anatomy points towards shocks/mechanisms that are

◮ highly transitory ◮ disconnected from both productivity and inflation ◮ unlike usual suspects Angeletos, Collard, Dellas Quantifying Confidence 23 / 29

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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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Factor: Variance Contribution

Y I h C Y /h Pi π R Baseline, with permanent components excluded 6–32 quarters 49.62 55.70 49.22 24.34 15.03 5.92 17.74 31.33 32–80 quarters 21.49 28.52 28.19 8.89 6.44 4.24 14.63 31.38 80–∞ quarters 0.00 0.00 3.37 0.00 0.00 0.00 2.08 5.15

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Factor: Variance Contribution

Y I h C Y /h Pi π R Baseline, with permanent components excluded 6–32 quarters 49.62 55.70 49.22 24.34 15.03 5.92 17.74 31.33 32–80 quarters 21.49 28.52 28.19 8.89 6.44 4.24 14.63 31.38 80–∞ quarters 0.00 0.00 3.37 0.00 0.00 0.00 2.08 5.15 Variant, with permanent components included 6–32 quarters 47.97 55.87 58.97 21.45 23.23 4.96 15.87 44.39 32–80 quarters 17.27 25.01 26.55 9.46 12.89 6.22 15.86 43.44 80–∞ quarters 6.67 6.67 7.26 6.66 6.67 6.62 6.68 9.52

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Factor: Comovement Patterns

Output Quarters 5 10 15 20

0.5

0.5 Consumption Quarters 5 10 15 20

0.5

0.5 Investment Quarters 5 10 15 20

2

2 Hours Worked Quarters 5 10 15 20

1
0.5

0.5 1 Productivity Quarters 5 10 15 20

0.5

0.5

Rel. Price of Inv.

Quarters 5 10 15 20

0.5

0.5

Gov. Spending

Quarters 5 10 15 20

1
0.5

0.5 1 Inflation Rate Quarters 5 10 15 20

0.2
0.1

0.1 0.2

Nom. Int. Rate

Quarters 5 10 15 20

0.2
0.1

0.1 0.2

baseline variant Angeletos, Collard, Dellas Quantifying Confidence 26 / 29

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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

◮ not technology ◮ not news/noise ◮ not financial or uncertainty shock that work through TFP ◮ not I- or C-specific shocks

what can this be? “confidence”, or something else

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Confidence shock (model) vs factor (data)

Output 1970 1980 1990 2000

4
3
2
1

1 2 3 4 Investment 1970 1980 1990 2000

15
10
5

5 10 15 Hours Worked 1970 1980 1990 2000

6
4
2

2 4 6 Consumption 1970 1980 1990 2000

2
1.5
1
0.5

0.5 1 1.5 2

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:

◮ embed tractable higher-order beliefs in a large class of macro models ◮ accommodate a certain relaxation of solution concept

Applied contribution:

◮ reveal observable implications of HOB ◮ accommodate waves of optimism and pessimism about SR ◮ accommodate “aggregate demand” without sticky prices ◮ explain multiple salient features of the data Angeletos, Collard, Dellas Quantifying Confidence 29 / 29