Business Cycle Comovements in Industrial Subsectors

Transcription

1 Business Cycle Comovements in Industrial Subsectors Michael T. Owyang 1 Daniel Soques 2 1 Federal Reserve Bank of St. Louis 2 University of North Carolina Wilmington The views expressed here are those of the individual authors and do not necessarily reflect official positions of the Federal Reserve Bank of St. Louis, the Federal Reserve System, or the Board of Governors.

2 Motivation A common way of modeling the business cycle is through phases of expansions and recessions.

3 Motivation A common way of modeling the business cycle is through phases of expansions and recessions. Hamilton & Owyang (2012, REStat): Extended the regime-switching model of Hamilton (1989, Ecta.) to a panel setting.

4 Motivation A common way of modeling the business cycle is through phases of expansions and recessions. Hamilton & Owyang (2012, REStat): Extended the regime-switching model of Hamilton (1989, Ecta.) to a panel setting. Model looks at business cycle differences across space and time.

5 Motivation A common way of modeling the business cycle is through phases of expansions and recessions. Hamilton & Owyang (2012, REStat): Extended the regime-switching model of Hamilton (1989, Ecta.) to a panel setting. Model looks at business cycle differences across space and time. Found that states comove around the national cycle in small subsets, or clusters.

6 Motivation A common way of modeling the business cycle is through phases of expansions and recessions. Hamilton & Owyang (2012, REStat): Extended the regime-switching model of Hamilton (1989, Ecta.) to a panel setting. Model looks at business cycle differences across space and time. Found that states comove around the national cycle in small subsets, or clusters. Industrial mix is an important determinant of state-level comovement.

7 Motivation A common way of modeling the business cycle is through phases of expansions and recessions. Hamilton & Owyang (2012, REStat): Extended the regime-switching model of Hamilton (1989, Ecta.) to a panel setting. Model looks at business cycle differences across space and time. Found that states comove around the national cycle in small subsets, or clusters. Industrial mix is an important determinant of state-level comovement. Relevant questions: Is there a similar degree of comovement across industrial subsectors around the aggregate cycle?

8 Motivation A common way of modeling the business cycle is through phases of expansions and recessions. Hamilton & Owyang (2012, REStat): Extended the regime-switching model of Hamilton (1989, Ecta.) to a panel setting. Model looks at business cycle differences across space and time. Found that states comove around the national cycle in small subsets, or clusters. Industrial mix is an important determinant of state-level comovement. Relevant questions: Is there a similar degree of comovement across industrial subsectors around the aggregate cycle? Do recessions propagate up and down the production stream, or across a broad industrial classification?

9 Overview We investigate the comovement of industrial sectors by looking at similar business cycle phase shifts.

10 Overview We investigate the comovement of industrial sectors by looking at similar business cycle phase shifts. We control for trend by casting the regime-switching model of HO into an unobserved components framework.

11 Overview We investigate the comovement of industrial sectors by looking at similar business cycle phase shifts. We control for trend by casting the regime-switching model of HO into an unobserved components framework. Our measure of industrial comovement is similar recession timing in clusters.

12 Overview We investigate the comovement of industrial sectors by looking at similar business cycle phase shifts. We control for trend by casting the regime-switching model of HO into an unobserved components framework. Our measure of industrial comovement is similar recession timing in clusters. Regress comovement on input-output variable and broad industry classification. Main finding: - Recessions spread across broad industry classifications, rather than up or down the production stream.

13 Literature Industrial Subsector Comovement: Hornstein (2000) shows that industries comove both within and across sectors. Comin & Phillipon (2005) attribute a decline in aggregate volatility to a decline in the synchronization of industries. Foerster, Sarte, & Watson (2011, JPE) attributes aggregate IP variability to common factors, not sectoral ones. Stella (2015, JEDC) find that firm-level shocks explain littel of U.S. business cycles, even after accounting for IO-linkages. Industrial Comovement as Phase Shifts: Camacho & Lieva-Leon (2014) investigate when idiosyncratic business cycle shocks lead to aggregate fluctuations. Chang & Hwang (2015, REStat) looks at common cyclical turning points across industries.

14 Empirical Model Let y n,t represent the log of industrial production for industry n = 1,..., N. Each industry has two unobserved components: y n,t = τ n,t + c n,t,

15 Empirical Model Let y n,t represent the log of industrial production for industry n = 1,..., N. Each industry has two unobserved components: y n,t = τ n,t + c n,t, where τ n,t is the trend: τ n,t = δ n + τ n,t 1 + η n,t, η n,t N(0, σ 2 n)

16 Empirical Model Let y n,t represent the log of industrial production for industry n = 1,..., N. Each industry has two unobserved components: y n,t = τ n,t + c n,t, where τ n,t is the trend: τ n,t = δ n + τ n,t 1 + η n,t, η n,t N(0, σ 2 n) and c n,t is the cycle: c n,t = µ n,t + p l=1 φ n,l c n,t l + ε n,t, ε n,t N(0, σ 2 n)

17 The Cyclical Component c n,t = µ n,t + p l=1 φ n,l c n,t l + ε n,t, ε n,t N(0, σ 2 n)

18 The Cyclical Component c n,t = µ n,t + p l=1 µ n,t : regime-switching intercept φ n,l c n,t l + ε n,t, ε n,t N(0, σ 2 n) µ n,t = µ n,0 + µ n,1 s n,t

19 The Cyclical Component c n,t = µ n,t + p l=1 µ n,t : regime-switching intercept φ n,l c n,t l + ε n,t, ε n,t N(0, σ 2 n) µ n,t = µ n,0 + µ n,1 s n,t s n,t : regime (recession) indicator s n,t = { 0 expansion in industry n 1 recession in industry n

20 The Cyclical Component c n,t = µ n,t + p l=1 φ n,l c n,t l + ε n,t µ n,t = µ n,0 + µ n,1 s n,t

21 The Cyclical Component c n,t = µ n,t + p l=1 φ n,l c n,t l + ε n,t µ n,t = µ n,0 + µ n,1 s n,t Friedman Plucking Model [Kim & Nelson (1999, JMCB)]: µ n,0 is the average growth rate during expansion µ n,0 + µ n,1 is the average growth rate during recession Identification assumption: µ n,0 = 0 & µ n,1 < 0 During expansion, y n,t is close to trend. During recession, y n,t gets plucked downwards away from trend.

22 Hamilton (1989) Recession Source: Figure 1, Kim & Piger (2002, JME)

23 Plucking Recession Source: Figure 2, Kim & Piger (2002, JME)

24 Panel Setting We consider all industries jointly in a single state space.

25 Panel Setting We consider all industries jointly in a single state space. Let y t = [y 1,t,..., y N,t ], c t = [c 1,t,..., c N,t ],...

26 Panel Setting We consider all industries jointly in a single state space. Let y t = [y 1,t,..., y N,t ], c t = [c 1,t,..., c N,t ],... Panel UC Model: y t = τ t + c t, τ t = δ + τ t 1 + η t, c t = µ t + p l=1 φ l c t l + ε t, E (η t η t ) = Σ E (ε t ε t) = Σ

27 Comovement in the Model We assume both shocks to the trend and cycle are uncorrelated across industries: Σ = diag[ σ 2 1,..., σ 2 N] Σ = diag[σ 2 1,..., σ 2 N]

28 Comovement in the Model We assume both shocks to the trend and cycle are uncorrelated across industries: Σ = diag[ σ 2 1,..., σ 2 N] Σ = diag[σ 2 1,..., σ 2 N] Industrial comovement is isolated to common recession timing in µ t. µ 1,0 + µ 1,1 s 1,t µ 2,0 + µ 2,1 s 2,t µ t =. = µ 0 + µ 1 s t µ N,0 + µ N,1 s N,t

29 Regime-Switching Dynamics Consider two extreme cases for s t = [s 1,t,..., s N,t ] :

30 Regime-Switching Dynamics Consider two extreme cases for s t = [s 1,t,..., s N,t ] : 1. Independent Cycles

31 Regime-Switching Dynamics Consider two extreme cases for s t = [s 1,t,..., s N,t ] : 1. Independent Cycles Each industry has its own cycle dynamics.

32 Regime-Switching Dynamics Consider two extreme cases for s t = [s 1,t,..., s N,t ] : 1. Independent Cycles Each industry has its own cycle dynamics. Number of regimes = 2 N

33 Regime-Switching Dynamics Consider two extreme cases for s t = [s 1,t,..., s N,t ] : 1. Independent Cycles Each industry has its own cycle dynamics. Number of regimes = 2 N Infeasible to allow each industry to have their own idiosyncratic cycle.

34 Regime-Switching Dynamics Consider two extreme cases for s t = [s 1,t,..., s N,t ] : 1. Independent Cycles Each industry has its own cycle dynamics. Number of regimes = 2 N Infeasible to allow each industry to have their own idiosyncratic cycle. 2. Fully Dependent Switching

35 Regime-Switching Dynamics Consider two extreme cases for s t = [s 1,t,..., s N,t ] : 1. Independent Cycles Each industry has its own cycle dynamics. Number of regimes = 2 N Infeasible to allow each industry to have their own idiosyncratic cycle. 2. Fully Dependent Switching Each industry follows the same cycle: s 1,t = s 2,t =... = s N,t

36 Regime-Switching Dynamics Consider two extreme cases for s t = [s 1,t,..., s N,t ] : 1. Independent Cycles Each industry has its own cycle dynamics. Number of regimes = 2 N Infeasible to allow each industry to have their own idiosyncratic cycle. 2. Fully Dependent Switching Each industry follows the same cycle: s 1,t = s 2,t =... = s N,t Number of regimes = 2 (Aggregate Expansion & Recession)

37 Regime-Switching & Time-series Clustering We opt for an intermediate case between the two cases.

38 Regime-Switching & Time-series Clustering We opt for an intermediate case between the two cases. We restrict the possible values s t can take:

39 Regime-Switching & Time-series Clustering We opt for an intermediate case between the two cases. We restrict the possible values s t can take: 2 Aggregate Regimes All industries in expansion (s t = 0 N 1 ) All industries in recession (s t = 1 N 1 )

40 Regime-Switching & Time-series Clustering We opt for an intermediate case between the two cases. We restrict the possible values s t can take: 2 Aggregate Regimes All industries in expansion (s t = 0 N 1 ) All industries in recession (s t = 1 N 1 ) κ Idiosyncratic Regimes

41 Regime-Switching & Time-series Clustering We opt for an intermediate case between the two cases. We restrict the possible values s t can take: 2 Aggregate Regimes All industries in expansion (s t = 0 N 1 ) All industries in recession (s t = 1 N 1 ) κ Idiosyncratic Regimes In these regimes, only a subset (or cluster ) of industries is in recession, while the rest are in expansion.

42 Regime-Switching & Time-series Clustering We opt for an intermediate case between the two cases. We restrict the possible values s t can take: 2 Aggregate Regimes All industries in expansion (s t = 0 N 1 ) All industries in recession (s t = 1 N 1 ) κ Idiosyncratic Regimes In these regimes, only a subset (or cluster ) of industries is in recession, while the rest are in expansion. Each industry can only be a member of one idiosyncratic cluster.

43 Regime-Switching & Time-series Clustering We opt for an intermediate case between the two cases. We restrict the possible values s t can take: 2 Aggregate Regimes All industries in expansion (s t = 0 N 1 ) All industries in recession (s t = 1 N 1 ) κ Idiosyncratic Regimes In these regimes, only a subset (or cluster ) of industries is in recession, while the rest are in expansion. Each industry can only be a member of one idiosyncratic cluster. Feasibile to estimate restricted K-state model, where K = 2 + κ << 2 N.

44 Regime-Switching & Time-series Clustering We opt for an intermediate case between the two cases. We restrict the possible values s t can take: 2 Aggregate Regimes All industries in expansion (s t = 0 N 1 ) All industries in recession (s t = 1 N 1 ) κ Idiosyncratic Regimes In these regimes, only a subset (or cluster ) of industries is in recession, while the rest are in expansion. Each industry can only be a member of one idiosyncratic cluster. Feasibile to estimate restricted K-state model, where K = 2 + κ << 2 N. So, there exists a national cycle where all industries move together, but some industries deviate from this cycle with their cluster.

45 Logit Regression Common cluster membership is our measurement of comovement.

46 Logit Regression Common cluster membership is our measurement of comovement. Let R m,n be an indicator variable for when industries m and n are in the same cluster.

47 Logit Regression Common cluster membership is our measurement of comovement. Let R m,n be an indicator variable for when industries m and n are in the same cluster. { 1 if R R m,n = m,n > 0 0 otherwise

48 Logit Regression Common cluster membership is our measurement of comovement. Let R m,n be an indicator variable for when industries m and n are in the same cluster. { 1 if R R m,n = m,n > 0 0 otherwise R m,n = α + β IO IO mn + β C Class m,n + e m,n,

49 Logit Regression Common cluster membership is our measurement of comovement. Let R m,n be an indicator variable for when industries m and n are in the same cluster. { 1 if R R m,n = m,n > 0 0 otherwise R m,n = α + β IO IO mn + β C Class m,n + e m,n, where IO m,n : input-output variable measuring industry interdependence

50 Logit Regression Common cluster membership is our measurement of comovement. Let R m,n be an indicator variable for when industries m and n are in the same cluster. { 1 if R R m,n = m,n > 0 0 otherwise R m,n = α + β IO IO mn + β C Class m,n + e m,n, where IO m,n : input-output variable measuring industry interdependence Class m,n : indicator if industries m and n are in the same broad industry classification

51 Estimation Method We utilize the Bayesian method of Gibbs Sampling.

52 Estimation Method We utilize the Bayesian method of Gibbs Sampling. Trend-cycle decomposition done via the forward-backward filter of Carter & Kohn (1994).

53 Estimation Method We utilize the Bayesian method of Gibbs Sampling. Trend-cycle decomposition done via the forward-backward filter of Carter & Kohn (1994). Regime drawn using the multi-state extension to the filter outlined by Hamilton (1989).

54 Estimation Method We utilize the Bayesian method of Gibbs Sampling. Trend-cycle decomposition done via the forward-backward filter of Carter & Kohn (1994). Regime drawn using the multi-state extension to the filter outlined by Hamilton (1989). Posterior distribution constructed by 10,000 draws after burn-in of 20,000.

55 Estimation Method We utilize the Bayesian method of Gibbs Sampling. Trend-cycle decomposition done via the forward-backward filter of Carter & Kohn (1994). Regime drawn using the multi-state extension to the filter outlined by Hamilton (1989). Posterior distribution constructed by 10,000 draws after burn-in of 20,000. Estimate logit regression every 4th run of the sampler.

56 Estimation Method We utilize the Bayesian method of Gibbs Sampling. Trend-cycle decomposition done via the forward-backward filter of Carter & Kohn (1994). Regime drawn using the multi-state extension to the filter outlined by Hamilton (1989). Posterior distribution constructed by 10,000 draws after burn-in of 20,000. Estimate logit regression every 4th run of the sampler. BIC used to determine the optimal number of clusters κ Priors

57 Data Unobserved Components Model: Economic activity measure (y t ): seasonally-adjusted industrial production 83 industrial sectors at the four-digit NAICS level Time period: 1972Q1-2014Q4

58 Data Unobserved Components Model: Economic activity measure (y t ): seasonally-adjusted industrial production 83 industrial sectors at the four-digit NAICS level Time period: 1972Q1-2014Q4 Logit Regression: Input-output data from BEA; average Broad industry classification: three-digit NAICS code

59 Results Average recession growth rate: µ n,1 = 3.06 Average trend drift: δ n = 0.48 Optimal number of clusters: κ = 4 Cluster Composition: - Cluster 1: Mining, paper products, computer and electronic products - Cluster 2: Textiles, wood products, wholesale trade - Cluster 3: Energy, food, medical equipment, transportation - Cluster 4: Conglomerate of industries

60 Aggregate Recession Probabilities Agg. Rec (Left) IP Growth (Right)

61 Cluster 1 Idiosyncratic Recession Probabilities Agg. Rec Cluster 1

62 Cluster 2 Idiosyncratic Recession Probabilities Agg. Rec Cluster 2

63 Cluster 3 Idiosyncratic Recession Probabilities Agg. Rec Cluster 3

64 Cluster 4 Idiosyncratic Recession Probabilities Agg. Rec Cluster 4

65 Z t 1 Z t Agg. Exp. Agg. Rec. Cluster 1 Cluster 2 Cluster 3 Cluster 4 Agg. Exp Agg. Rec Cluster Cluster Cluster Cluster Table: Transition Probabilities. This table shows the posterior median draw of the transition probabilities for the aggregate state variable (Z t ). Zeros in bold indicate transitions that were restricted ex ante.

66 Logit Regression R m,n : indicator variable for when industries m and n are in the same cluster { 1 if R R m,n = m,n > 0 0 otherwise where R m,n = α + β IO IO mn + β C Class m,n + e m,n, IO m,n : input-output variable measuring industry interdependence Class m,n : indicator if industries m and n are in the same broad industry classification

67 R m,n = α + β IO IO mn + β C Class m,n + e m,n, Parameter Post. Mean Post. SD α β IO β C Do recessions spread across industries based on the production stream or similar industry classification?

68 R m,n = α + β IO IO mn + β C Class m,n + e m,n, Parameter Post. Mean Post. SD α β IO β C Do recessions spread across industries based on the production stream or similar industry classification? Evidence in favor of similar industry classification.

69 R m,n = α + β IO IO mn + β C Class m,n + e m,n, Parameter Post. Mean Post. SD α β IO β C Do recessions spread across industries based on the production stream or similar industry classification? Evidence in favor of similar industry classification. Comovement arises due to common shocks across a broad industry class as opposed to up or down the production stream.

70 Conclusion We investigate industrial sector comovement in a cross-sectional unobserved components framework. Estimate comovement based on similar recession timing. Do recession propagate up and down the production stream, or across a similar industrial class? - Similar industrial class

71 Priors Parameter Prior Distribution Hyperparameters µ 1n N ( m, σ 2 M ) m = 2 ; M= 1 n σn 2 Γ ( ν 2, ι ) 0 2 ν 0 = 10 ; ι 0 = 1 n σ n 2 Γ ( ν 0 2, ι ) 0 2 ν 0 = 100 ; ι 0 = 0.1 n P D (ff) α i = 0 i δ n N (d 0, D 0 ) d 0 = [2, 0] ; D 0 = I 2 n φ n N (g, G) g = 0 p ; G = I p n h nk Pr(h nk = 1) = 1 κ (1 p 0) p 0 = 0.01 n, k Table: Priors for Estimation. Estimation Method