Quantifying Confidence George-Marios Angeletos Fabrice Collard Harris Dellas Bank of Portugal, June 11, 2015 Angeletos, Collard, Dellas Quantifying Confidence 1 / 29
Standard approach coordination failure = multiple equilibria aggregate demand = gaps from flex prices, NKPC Angeletos, Collard, Dellas Quantifying Confidence 2 / 29
An alternative coordination failure = strategic uncertainty / beliefs aggregate demand Angeletos, Collard, Dellas Quantifying Confidence 3 / 29
An alternative coordination failure = strategic uncertainty / beliefs aggregate demand This Paper 1. tractable formalization 2. quantitative evaluation Angeletos, Collard, Dellas Quantifying Confidence 3 / 29
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
Roadmap Baseline Model and Methodological Contribution Quantitative Evaluation Extension to Medium-Scale DSGE & Estimation Complementary Empirical Work Angeletos, Collard, Dellas Quantifying Confidence 5 / 29
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: A t ◮ transitory shock to HOB, or “confidence”: ξ t Angeletos, Collard, Dellas Quantifying Confidence 6 / 29
Modeling Beliefs Stage 1 Stage 2 t observe x it = log A t + ε it observe ( A t , Y t , prices ) t + 1 form beliefs about ( Y t , Y t +1 , ... ) update beliefs make production choices consume and invest Angeletos, Collard, Dellas Quantifying Confidence 7 / 29
Modeling Beliefs Stage 1 Stage 2 t observe x it = log A t + ε it observe ( A t , Y t , prices ) t + 1 form beliefs about ( Y t , Y t +1 , ... ) update beliefs make production choices consume and invest heterogeneous priors: ε it ∼ N (0 , σ ) ∼ N ( ξ t , σ ) ε jt ξ t → aggregate variation in HOB → “confidence” or “AD” Angeletos, Collard, Dellas Quantifying Confidence 7 / 29
ξ t as a proxy for strategic uncertainty standard: Y t = ¯ E t [ Y t ] = Y RBC ≡ χ A t t strategic uncertainty: Y t � = ¯ E t [ Y t ] = Y RBC + “belief wedge” t Angeletos, Collard, Dellas Quantifying Confidence 8 / 29
ξ t as a proxy for strategic uncertainty standard: Y t = ¯ E t [ Y t ] = Y RBC ≡ χ A t t strategic uncertainty: Y t � = ¯ E t [ Y t ] = Y RBC + “belief wedge” t Angeletos and La’O (Ecma 2013) ◮ impose common prior (no biases) ◮ abstract from capital, add market segmentation ⇒ observational equivalence Angeletos, Collard, Dellas Quantifying Confidence 8 / 29
ξ t as a belief enrichment DSGE models vs “beauty contests”: behavior depends on beliefs of many endogenous outcomes (prices, wages, sales...) in many dates ξ t = disciplined, parsimonious, and tractable belief enrichment research task: understand observable implications & quantify Angeletos, Collard, Dellas Quantifying Confidence 9 / 29
Methodological Contribution tractability, tractability, tractability.... take the limit as σ → 0 ⇒ ◮ no learning, no Kalman filter ◮ no cross-sectional heterogeneity, no Krusell-Smith ◮ ξ t is sufficient statistic for gap between higher- and first-order beliefs ⇒ small state spaces! solution almost as in representative-agent models Angeletos, Collard, Dellas Quantifying Confidence 10 / 29
Recursive equilibrium recursive equilibrium = PBE among fictitious local planners key objects: G , P , V 1 , V 2 ◮ G = aggregate policy rule for capital: K t +1 = G ( A t , ξ t , K t ) ◮ P = local beliefs about prices (demand): p it = P ( x it , ξ t , K t ) ˆ ◮ V 1 , V 2 = value functions of local planner in stages 1, 2 heterogeneous priors → tractable fixed point → solution “almost” as in representative-agent models Angeletos, Collard, Dellas Quantifying Confidence 11 / 29
Recursive equilibrium stage-1 problem: 1 1+ ν n 1+ ν m ; x , ξ, K ) − V 1 ( k ; x , ξ, K ) = max V 2 ( ˆ n y + (1 − δ ) k s . t . m = ˆ ˆ p ˆ y = xk θ n 1 − θ ˆ p = P ( x , ξ, K ) ˆ stage-2 problem: V 1 ( k ′ ; A ′ , ξ ′ , K ′ ) d f ( A ′ , ξ � V 2 ( m ; A , ξ, K ) = max { c , k ′ } U ( c ) + β c + k ′ = m s . t . 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 Angeletos, Collard, Dellas Quantifying Confidence 12 / 29
Recursive equilibrium belief consistency: P ( x , ξ, K ) = y ( x + ξ, x , ξ, K ) y ( x , x , ξ, K ) aggregation: � � X A , ξ, K G ( A , ξ, K ) = g y ( A , A , ξ, K ) + (1 − δ ) K ; bottom line: tractable fixed-point problem Angeletos, Collard, Dellas Quantifying Confidence 13 / 29
Log-linear solution original model: ( C t , I t , N t ; K t +1 ) = Γ k · K t + Γ a · A t + Γ ξ · ξ t belief-augmented model: Γ k · K t + Γ a · A t + Γ ξ · ξ t ( C t , I t , N t ; K t +1 ) = generalization to arbitrary linear DSGE models (see Appendix) → simulate/calibrate/estimate as in standard DSGE models Angeletos, Collard, Dellas Quantifying Confidence 14 / 29
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 σ a and σ ξ so as to match of BC volatilities of Y , H , I , C Angeletos, Collard, Dellas Quantifying Confidence 15 / 29
Observable implications: IRFs to confidence shock Output Productivity Consumption Investment Hours Worked 2 0.5 0.2 6 2 1.5 1.5 0.15 4 % deviation 1 1 0 0.1 2 0.5 0.5 0.05 0 0 0 -0.5 0 0 10 20 0 10 20 0 10 20 0 10 20 0 10 20 Quarters Quarters Quarters Quarters Quarters 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 Angeletos, Collard, Dellas Quantifying Confidence 16 / 29
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 Angeletos, Collard, Dellas Quantifying Confidence 17 / 29
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
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 Angeletos, Collard, Dellas Quantifying Confidence 19 / 29
Observable Implications Output Consumption Investment Hours Worked Inflation Rate 2Nom. Interest Rate 1 0.5 3 1.5 0.08 0.8 0.4 0.06 0 2 1 0.6 0.3 0.04 -2 1 0.5 0.4 0.2 0.02 -4 0 0 0.2 0.1 0 -6 0 0 -1 -0.5 -0.02 -8 0 10 20 0 10 20 0 10 20 0 10 20 0 10 20 0 10 20 Quarters Quarters Quarters Quarters Quarters Quarters 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 Angeletos, Collard, Dellas Quantifying Confidence 20 / 29
Estimated Contribution despite multiple competing forces, estimation attributes more than half of the observed business cycles to “confidence” contribution to volatility (6-32 quarters) π Y C I h 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 Angeletos, Collard, Dellas Quantifying Confidence 21 / 29
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