The Propagation of Monetary Policy Shocks in a Heterogeneous Production Economy E. Pasten 1 R. Schoenle 2 M. Weber 3 1 Banco Central de Chile and Toulouse University 2 Brandeis University 3 Chicago Booth Federal Reserve Bank of Cleveland Inflation Conference September 29, 2016
Introduction MOTIVATION Fact 1: Sectors are heterogeneous in their input-output linkages with other sectors.
Number of sectors The Propagation of Monetary Policy Shocks in a Heterogeneous Production Economy Introduction MOTIVATION Fact 2: Sectors are heterogeneous in their frequency of price changes, which is heavy-tailed. 140 120 100 80 60 40 20 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Frequency of price change
Introduction MOTIVATION Fact 3: Sectors are heterogeneous in their importance for GDP. 250 200 Number of sectors 150 100 50 0 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 Value Added Weights
Introduction Motivation (and literature review) How does the interaction of these three forms of heterogeneity affect the propagation of monetary policy shocks? Big picture: Interaction of heterogeneities with heterogeneous pricing frictions can change identity of sectoral effects on aggregate marginal cost. Companion paper: Propagation of idiosyncratic shocks.
Introduction Motivation (and literature review) Which heterogeneity matters the most for real output effects? Price stickiness >> consumption shares >> input-output linkages. Does the choice of granularity matter? N=1? N=350? Most disaggregated calibration yields 34% larger real effects Similar impact response for inflation What is the role of heavy tail in frequency of adjustment? How does monetary policy rule interact with heterogeneities?
Introduction Motivation (and literature review) Relevant papers: Monetary policy shocks and production networks: Basu (1995), Clark (1999), Huang and Liu (2002, 2004), Carvalho (2006), Nakamura and Steinsson (2010), Bouakez, Cardia, and Ruge-Murcia (2009, 2013), Carvalho and Lee (2011), Carvalho and Schwartzman (2015). Asymmetry in sector size or input-output structure: Gabaix (2011), Acemoglu et al. (2012). Many others on markups, real rigidities, trade linkages, etc.
Introduction Outline Two parts: Theoretical results Empirical analysis
Model Abridged description of the setup 1/5 Households utility: ( max E 0 β t Ct 1 σ 1 1 σ t=0 K k=1 ) L 1+ϕ kt g k 1 + ϕ s.t. BC where C t C kt [ K k=1 [ n 1/θ k ] η 1 1 η 1 η ωck C1 η kt, C 1 1 θ kjt I k ] θ θ 1 dj, and η < θ.
Model Abridged description of the setup 2/5 Firms production function: where Y kjt = L 1 δ kjt Zkjt, δ Z kjt Z kjt (r) [ K r=1 [ n 1/θ r ] η 1 η ωkr Z kjt (r) 1 1 η 1 η, ( Z kjt r, j ) ] θ 1 1 θ dj θ 1, I r and η < θ.
Model Abridged description of the setup 3/5 Demand for sector k, variety producer j : from households: from other firms: ( ) η C kt = ω Pkt ck P c Ct, Z t k j t (k) = ω k k ( Pkt P k t ) η Zk j t, C kjt = 1 n k ( Pkjt P kt ) θ Ckt. Z k j t (k, j) = 1 n k ( Pkjt P kt ) θ Zk j t (k) where price aggregators are: for households: P c t = P rt = [ K r=1 ω crp 1 η rt [ 1 nr ] 1 1 η, P k t = for other firms: ] 1 [ I r P 1 θ 1 θ rjt dj. P rt = 1 nr [ K r=1 ω k rp 1 η rt ] 1 1 η, ] 1 I r P 1 θ 1 θ rjt dj.
Model Abridged description of the setup 4/5 Sectoral heterogeneity of price stickiness: where Q t,t+s αk s Y kjt+s s=0 and sectoral prices follow [ P kjt θ ] θ 1 MC kjt+s = 0 MC kjt = 1 ( ) δ δ W 1 δ ( ) kt P k δ 1 δ 1 δ t P kt = [ (1 α k ) P 1 θ kt ] 1 + α k P 1 θ 1 θ kt 1
Model Abridged description of the setup 5/5 Equilibrium conditions: + the usual equations: Y kjt = C kjt + - sectoral labor supply, - Euler equation, K k =1 I k Y t = C t + Z t - production efficiency condition, - Taylor rule, and - standard equilibrium conditions. Z k j t (k, j) dj,
Model Mechanism: Intuition The effect of monetary policy shocks depends on the properties of marginal cost: Highlight individual feedback mechanisms Analytical expressions from simplified model
Model Mechanism: Intuition Defining aggregate price indices: CPI : p c t = sectoral input price index: p k t = K ω ck p kt, k=1 K ω kk p k t k =1 Sectoral participation in total production (note: ψ = Z/Y): ( K ) n k = (1 ψ) ω ck + ψ n k ω k k for all k. k =1 ℵ = (1 ψ) [ I ψω ] 1 Ω c
Model Mechanism: Intuition Feedback at the sectoral level: and w kt solves mc kt = (1 δ) w kt + δp k t (labor sup) w kt = ϕl kt + σc t + p c t, (sect prod. fn) y kt = l kt + δ ( w kt p k t ), (sect demand) y kt = y t η [p kt (1 ψ) p c t ψ p t ] where p t = ( K K ) k=1 k =1 n k ω k k p kt.
Model Mechanism: Intuition Overall, sectoral prices follow βe t [p kt+1 ] (1 + β) p kt + p kt 1 = κ k (mc kt p kt ) βe t [π kt+1 ] π kt = κ k x kt where κ k (1 α k ) (1 α k β) /α k and x kt = (1 + ϕη) γ 1 (δ) (p c t p kt ) + γ 2 (δ) ( p k t p c t ) + γ3 (δ) ( p t p c t ) + (σ + ϕ) γ 4 (δ) c t Compare to δ = 0 : x δ=0 kt = (1 + ϕη) (p c t p kt ) + (σ + ϕ) c t
Model: Predictions Analytical Results Simplified model: utility log in consumption, linear in leisure exogenous nominal demand, one-time permanent shock future fully discounted: p kt = mc kt Intuition carries through in full model, and calibration.
Model: Predictions Analytical Results Three propositions on effect of monetary policy: Homogeneous price stickiness Heterogeneous price stickiness but irrelevance of heterogeneity in I/O linkages Heterogeneous price stickiness and no restriction on I/O linkages Two propositions on effect of granularity
Model: Predictions Analytical Results: Monetary Policy Shock Assume that α k = α for all k, so κ k = κ for all k (homogeneous stickiness) Unrestricted consumption shares {ω ck }and I/O linkages {ω kk } Proposition Following a permanent monetary shock m at time t, heterogeneity of {ω ck } and {ω kk } is irrelevant for the response of output. The existence of I/O linkages amplifies the response of output. Proof. Follows directly from [ ( ) ] p c α t t +1 t (α) = 1 m for t t (1) 1 δ (1 α)
Model: Predictions Analytical Results: Monetary Policy Shock Assume that ω ck = ω kk (no price wedge), otherwise unrestricted. Assume that {α k } are heterogeneous, E[α k ] = α Proposition Following a permanent monetary shock, 1. The sectoral heterogeneity of price stickiness and consumption shares are irrelevant for the response of output to the monetary shock on impact. 2. p c t p c t (α) for t > t. The response of the aggregate consumption prices for t t is weakly decreasing in the dispersion of price stickiness.
Model: Predictions Analytical Results: Monetary Policy Shock No restrictions, allowing for ω ck ω kk (price wedge) Proposition 1. The response of p c t is now weaker on impact when u k K k =1 ω ck (1 α k ) ω k k > (1 α) ω ck for the sectors with the most sticky prices. 2. The response of p c t for t > t is now more persistent when for sectors with the most sticky prices either of the following conditions hold: (i) ω k 1 K K k =1 ω k k > ω ck, (ii) u k > (1 α) ω ck, (iii) COV(ω ck α τ k (1 α k ), ω k k) > 0. where first-order and second-order outdegrees are K K u k ω ck (1 α k ) ω k k, v k u k (1 α k ) ω k k. k =1 k =1
Model: Predictions Summary of Results: Monetary Policy Shock The real effects of monetary policy shocks are bigger if share of intermediate inputs is high, sticky-price sectors are important suppliers to the rest of the economy, sticky-price sectors are important suppliers to flexible-price sectors, sticky-price sectors are important suppliers to large sectors, sticky-price sectors have large covariance of connectedness with function of customer size and price stickiness.
Model: Predictions Analytical Results: Effect of Aggregation What is the effect of sectoral aggregation? Granularity matters for the real effects of monetary policy Convexification of price stickiness Size heterogeneity and I/O linkages can amplify effect
Model: Predictions Analytical Results: Effect of Aggregation Theoretical results from comparison of two economies Finely disaggregated economy: K sectors, {αk, ω ck, ω ks } p c t = K k=1 ω ckp kt Coarse, aggregated economy: K/2 sectors, {ᾱ k, ω ck, ω k s } p c t = K/2 k =1 ω ck p k t Sectors randomly combined, with appropriate weights. Two propositions.
Model: Predictions Analytical Results: Effect of Aggregation Proposition Given no I/O linkages (δ = 0), the difference of consumption prices K/2 ω ck p c t pc t = is such that k =1 1. p c t = p c t for t = t 2. p c t < p c t for t > t [ λ k α t t +1 2k 1 + (1 λ k ) α t t +1 2k α t t +1 k ] m 3. p c t pc t is increasing in the dispersion of Calvo parameters among merged sectors 4. p c t pc t is increasing in ω ck for merged sectors with the highest dispersion of Calvo parameters
Model: Predictions Analytical Results: Effect of Aggregation Proposition When δ (0, 1) and ω sk = ω ck s, k, the amplification effect of monetary non-neutrality introduced by intermediate inputs is stronger in the finely-disaggregated economy relative to the coarsely-disaggregated economy when the dispersion of frequency of price changes is higher among the merged sectors. K/2 p c t p c 1 δ ( t = ω 1 δ (1 α) ck λ k α t t +1 k 2k 1 =1 t t δ K/2 [ ) + λ ω k (1 α 2k 1 1 δ (1 α) ck τ=1 k ( 1 α =1 k + ( ) t t 1 λ +1 k α 2k α t t ) +1 k m α τ 2k 1 + ( ) ( ) 1 λ k 1 α2k α τ 2k ) α τ k ] p c t τ (2)
Model: Predictions Analytical Results: Effect of Aggregation Allowing for full, unrestricted heterogeneity such that ω sk ω ck can lead to even larger amplification. How large are these effects? Empirical question.
Calibration Calibration Calibration goal: Which type of heterogeneity matters most? 6 cases with incremental degrees of heterogeneity Role of monetary policy? Does the level of aggregation matter? Decrease aggregation from 350 to 8 sectors Value-added sectoral output shares from BEA 2002 I-O tables from BEA to get industry-to-industry linkages Stickiness from BLS PPI micro data What is the role of heavy-tailed price stickiness?
Calibration Calibration K (8, 350) β =.9975 σ = 1 ϕ = 2 δ =.7 η = 2 θ = 6 φ π = 1.24 φ c =.33/12 ρ =.9 : Number of sectors : Monthly discount factor to get 3% annual risk-free rate : Relative risk aversion : Inverse of Frisch elasticity : Intermediate inputs share in production function : Elasticity of substitution across sectors : Elasticity of substitution across firms within sectors : Responsiveness of monetary policy to inflation : Responsiveness of monetary policy to GDP variations : Persistence of shocks Monetary shock: µ t = 1
Calibration Calibration Overview of Calibration Cases Prices Consumption Weights Input-Output Linkages Case 1 flexible homogeneous homogeneous Case 2 sticky, homogeneous homogeneous homogeneous Case 3 sticky, heterogeneous homogeneous homogeneous Case 4 sticky, heterogeneous heterogeneous heterogeneous (size weights) Case 5 sticky, heterogeneous heterogeneous homogeneous Case 6 sticky, heterogeneous heterogeneous heterogeneous
Calibration Calibration Overview of Calibration Cases Prices Consumption Weights Input-Output Linkages Case 1 flexible homogeneous homogeneous Case 2 sticky, homogeneous homogeneous homogeneous Case 3 sticky, heterogeneous homogeneous homogeneous Case 4 sticky, heterogeneous heterogeneous heterogeneous (size weights) Case 5 sticky, heterogeneous heterogeneous homogeneous Case 6 sticky, heterogeneous heterogeneous heterogeneous
Calibration Calibration Overview of Calibration Cases Prices Consumption Weights Input-Output Linkages Case 1 flexible homogeneous homogeneous Case 2 sticky, homogeneous homogeneous homogeneous Case 3 sticky, heterogeneous homogeneous homogeneous Case 4 sticky, heterogeneous heterogeneous heterogeneous (size weights) Case 5 sticky, heterogeneous heterogeneous homogeneous Case 6 sticky, heterogeneous heterogeneous heterogeneous
Calibration Results Calibration Which heterogeneity matters most? Heterogeneity of price stickiness most important driver of real effects. Lesser role for heterogeneous consumption shares and even less for input-output linkages.
Percentage Deviation from SS Percentage Deviation from SS Percentage Deviation from SS The Propagation of Monetary Policy Shocks in a Heterogeneous Production Economy Calibration Results 0 Consumption -1-2 -3-4 -5-6 0 5 10 15 20 25 30 Period 0.5 In.ation 0-0.5-1 -1.5-2 -2.5-3 0 5 10 15 20 25 30 Period 0 Real MC -1-2 -3 case1-4 case2 case3 case4-5 case5 case6-6 0 5 10 15 20 25 30 Period
Calibration Results 1 350 Sectors 0.9 0.8 0.7 Sector Frequency 0.6 0.5 0.4 0.3 0.2 0.1 0 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 Sector Size
Calibration Results 0.9 58 Sectors 0.8 0.7 Sector Frequency 0.6 0.5 0.4 0.3 0.2 0.1 0 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 Sector Size
Calibration Results Role of monetary policy: Large effect of endogenizing demand through monetary policy. Large effect of more systematic response to inflation.
Percentage Deviation from SS Percentage Deviation from SS Percentage Deviation from SS The Propagation of Monetary Policy Shocks in a Heterogeneous Production Economy Calibration Results 1 Consumption 0-1 -2-3 -4-5 0 5 10 15 20 25 30 Period 0.5 In.ation 0-0.5-1 -1.5-2 0 5 10 15 20 25 30 Period 1 Real MC 0-1 -2-3 -4 Endog. Nom. Demand Exog. Nom. Demand -5-6 0 5 10 15 20 25 30 Period
Calibration Results Increase systematic response of monetary policy (φ π = 2.5) :
Percentage Deviation from SS Percentage Deviation from SS Percentage Deviation from SS The Propagation of Monetary Policy Shocks in a Heterogeneous Production Economy Calibration Results 0 Consumption -0.5-1 -1.5-2 -2.5-3 0 5 10 15 20 25 30 Period 0-0.1-0.2-0.3-0.4-0.5-0.6-0.7 In.ation -0.8 0 5 10 15 20 25 30 Period 0 Real MC -0.5-1 -1.5 case1 case2 case3-2 case4 case5 case6-2.5 0 5 10 15 20 25 30 Period
Calibration Results Finer granularity of calibration increases real effects: 25% (34%) larger cumulative consumption response for 350 vs. 58 (8) sectors Steepest gradient between 148/60, and 60/20 sector aggregations Similar impact response for inflation.
Percentage Deviation from SS Percentage Deviation from SS Percentage Deviation from SS The Propagation of Monetary Policy Shocks in a Heterogeneous Production Economy Calibration Results 0 Consumption -1-2 -3-4 -5 0 5 10 15 20 25 30 Period 0.5 In.ation 0-0.5-1 -1.5-2 0 5 10 15 20 25 30 Period 0 Real MC -1-2 -3-4 58 Sectors 350 Sectors -5-6 -7 0 5 10 15 20 25 30 Period
Percentage Deviation from SS Percentage Deviation from SS Percentage Deviation from SS The Propagation of Monetary Policy Shocks in a Heterogeneous Production Economy Calibration Results 0 Consumption -1-2 -3-4 -5 0 5 10 15 20 25 30 Period 0.5 In.ation 0-0.5-1 -1.5-2 0 5 10 15 20 25 30 Period 0 Real MC -1-2 -3-4 n=350 n=245-5 n=148 n=60-6 n=20 n=8-7 0 5 10 15 20 25 30 Period
Calibration Results Role of fat tails in frequency of price changes: Experiment 1: cut right tail Censor 20% of upper tail Assign mean to the right censored sectors Shift entire distribution to the right to preserve mean Experiment 2: heavier left tail Right-censor at f=18% Mirror at 0.18 Put uniform mass to the left to preserve mean
Percentage Deviation from SS Percentage Deviation from SS Percentage Deviation from SS The Propagation of Monetary Policy Shocks in a Heterogeneous Production Economy Calibration Results 0 Consumption -1-2 -3-4 -5 0 5 10 15 20 25 30 Period 0.5 In.ation 0-0.5-1 -1.5-2 -2.5 0 5 10 15 20 25 30 Period 0 Real MC -1-2 -3-4 -5 350 Sectors, Baseline -6 350 Sectors, 20% Right-Trimmed 350 Sectors, Left Tail -7 0 5 10 15 20 25 30 Period
Conclusion Conclusion: Convolution of heterogeneity of price stickiness with sector size and intput-output linkages creates rich set of theoretical predictions. Empirically: Heterogeneity of price stickiness most important driver of real effects; lesser role for heterogeneous consumption shares and even less for input-output linkages. More granular calibration yields up to 34% larger real effects but similar impact response for inflation, steep gradient. Results highly sensitive to monetary policy specification. Heavy tails of frequency of price changes affect real effects. Ongoing work: idiosyncratic shocks, oil price shocks, optimal monetary policy.