Whats News In Business Cycles? Stephanie Schmitt-Groh e Mart n - PowerPoint PPT Presentation

What’s News In Business Cycles? Stephanie Schmitt-Groh´ e Mart ´ ın Uribe Columbia University April 19, 2010 1

News as a Source of Business Cycles • Theoretical papers: – Barro and King, (QJE, 1984); Beaudry and Portier (JET, 2007); Jaimovich and Rebelo (AER, 2009) • Empirical papers: VAR estimation of anticipated shocks: – Cochrane (CRCSPP, 1994); Beaudry and Portier (AER, 2006); Beaudry and Lucke (NBERMA, 2009); Eric Sims (2009) • This paper: Likelihood-based estimation of News shocks in the context of an optimizing DSGE model 2

The Model Preferences: ∞ β t ζ t U ( C t − bC t − 1 − ψh θ � E 0 t S t ) t =0 S t = ( C t − bC t − 1 ) γ S 1 − γ t − 1 Capital accumulation: � � �� I t K t +1 = (1 − δ ( u t )) K t + z I 1 − S t I t I t − 1 Production technology: Y t = z t F ( u t K t , X t h t , X t L ) 3

Resource constraint: C t + A t I t + G t = Y t An exogenous wage markup: ∂U ′ ( V t ) = Λ t W t ζ t ∂h t 1 + µ t

Introducing Anticipated Shocks ln x t = ρ ln x t − 1 + µ t µ t = ǫ 0 x,t + ǫ 4 x,t − 4 + ǫ 8 x,t − 8 ǫ i x,t ∼ i.i.d. N (0 , σ i x ) , i = 0 , 4 , 8 4

Autoregressive Representation of Anticipated Shocks x t +1 = M ˜ ˜ x t + ην t +1 ; ν t ∼ i.i.d. N (0 , I )  x t +1   x t  ǫ 4 ǫ 4 σ 0     x,t 0 0 x,t +1 ρ 0 0 0 1 0 0 0 0 0 0 0 1 x  ǫ 4   ǫ 4  σ 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 x,t x,t − 1     x ǫ 4 ǫ 4    0 1 0 0 0 0 0 0 0 0 0 0 0      0 0 0 x,t − 1 x,t − 2         0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ǫ 4 ǫ 4         x,t − 2 x,t − 3 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 � ν 0         ǫ 8 ǫ 8 �    0 0 0 0 0 0 0 0 0 0 0 0 0   x,t   σ 8  x,t +1 0 0 t +1 x ǫ 8 ǫ 8         ν 4 = 0 0 0 0 0 1 0 0 0 0 0 0 0 + 0 0 0 x,t x,t − 1         t +1 ǫ 8 ǫ 8 0 0 0 0 0 0 1 0 0 0 0 0 0 ν 8 0 0 0         x,t − 1 x,t − 2 t +1    0 0 0 0 0 0 0 1 0 0 0 0 0      ǫ 8 0 0 0 ǫ 8         x,t − 3 x,t − 2 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0  ǫ 8     ǫ 8    0 0 0 0 0 0 0 0 0 1 0 0 0 x,t − 4  x,t − 3       0 0 0  ǫ 8 ǫ 8      0 0 0 0 0 0 0 0 0 0 1 0 0    0 0 0 x,t − 4 x,t − 5     0 0 0 0 0 0 0 0 0 0 0 1 0 ǫ 8 ǫ 8 0 0 0     x,t − 5 x,t − 6 ǫ 8 ǫ 8 x,t − 6 x,t − 7 Note: A k -period anticipated shock generates k additional latent state variables. 5

Seven Exogenous Driving Forces: 1. Stationary Neutral Productivity Shocks: z t Y t = z t F ( u t K t , X t h t , X t L ) ln z t = ρ z ln z t − 1 + µ z,t µ z,t = ǫ 0 z,t + ǫ 4 z,t − 4 + ǫ 8 z,t − 8 ǫ i z,t ∼ i.i.d. N (0 , σ i z ) , i = 0 , 4 , 8 6

2. Non-stationary Neutral Productivity Shocks: X t Y t = z t F ( u t K t , X t h t , X t L ) X t µ x t ≡ X t − 1 ln( µ x t /µ x ) = ρ x ln( µ x t − 1 /µ x ) + ǫ 0 x,t + ǫ 4 x,t − 4 + ǫ 8 x,t − 8 ǫ i x,t ∼ i.i.d. N (0 , σ i x ) , i = 0 , 4 , 8 . 7

3. Stationary Investment-Specific Productivity Shocks: z I t � � �� I t K t +1 = (1 − δ ( u t )) K t + z I 1 − S t I t I t − 1 ln z I t = ρ z I ln z I t − 1 + µ z I ,t µ z I ,t = ǫ 0 z I ,t + ǫ 4 z I ,t − 4 + ǫ 8 z I ,t − 8 ǫ i z I ,t ∼ i.i.d. N (0 , σ i z I ) , i = 0 , 4 , 8 8

4. Non-stationary Investment-Specific Productivity Shocks: A t C t + A t I t + G t = Y t A t = A t − 1 µ a t ln( µ a t /µ a ) = ρ a ln( µ a t − 1 /µ a ) + ǫ 0 a,t + ǫ 4 a,t − 4 + ǫ 8 a,t − 8 ǫ i a,t ∼ i.i.d. N (0 , σ i a ) , i = 0 , 4 , 8 . 9

5. Government Spending Shocks: G t C t + A t I t + G t = Y t g t = G t X G t � 1 − ρ xg ; � ρ xg � t = A α/ ( α − 1) X G � X G X Y X Y t = X t t − 1 t − 1 t ln( g t /g ) = ρ g ln( g t − 1 /g ) + ǫ 0 g,t + ǫ 4 g,t − 4 + ǫ 8 g,t − 8 ǫ i g,t ∼ i.i.d. N (0 , σ i g ) , i = 0 , 4 , 8 . 10

6. Wage Markup Shocks: µ t An exogenous wage markup: ∂U ′ ( V t ) = Λ t W t ζ t 1 + µ t ∂h t ln µ t /µ = ρ µ ln µ t − 1 /µ + µ µ,t µ µ,t = ǫ 0 µ,t + ǫ 4 µ,t − 4 + ǫ 8 µ,t − 8 ǫ i µ,t ∼ i.i.d. N (0 , σ i µ ) , i = 0 , 4 , 8 11

7. Preference Shock: ζ t ∞ β t ζ t U ( C t − bC t − 1 − ψh θ � t S t ) E 0 t =0 ln ζ t = ρ ζ ln ζ t − 1 + µ ζ,t µ ζ,t = ǫ 0 ζ,t + ǫ 4 ζ,t − 4 + ǫ 8 ζ,t − 8 ǫ i ζ,t ∼ i.i.d. N (0 , σ i ζ ) , i = 0 , 4 , 8 12

Interpretation as Technological Diffusion Consider the technological diffusion ∞ (1 − φ i ) ν t − i � ln X t = i =0 It can be written as ln( X t /X t − 1 ) = φ ln( X t − 1 /X t − 2 ) + (1 − φ ) ν t − 1 This is a special case of our assumed process with ρ x = φ σ 1 x = (1 − φ ) σ ν σ k x = 0; for k = 0 , 2 , 3 13

Functional Forms U ( V ) = V 1 − σ − 1 1 − σ F ( a, b, c ) = a α k b α h c 1 − α k − α h , S ( x ) = κ 2( x − µ I ) 2 δ ( u ) = δ 0 + δ 1 ( u − 1) + δ 2 2 ( u − 1) 2 Calibration µ y µ a β σ α k α h δ 0 u G/Y h µ 0.99 1 0.23 0.67 0.025 1 1.0045 0.9957 0.2 0.2 1.15 14

Sample: 1955Q1-2006Q4 Seven Observables. 1. ∆ ln Y t = Output Growth 2. ∆ ln C t = Consumption Growth 3. ∆ ln( I t A t ) = Investment Growth 4. ∆ ln h t = Hours Growth 5. ∆TFP = TFP Growth 6. ∆ ln G t = Government Consumption Growth 7. ∆ ln A t = Growth Rate of the Price of Investment 15

Prior Parameter Distributions • All σ i j are gamma (m,m) distributions. • The unanticipated innovation has variance of 3 × the sum of the anticipated components: ( σ 0 w ) 2 w = z, x, z I , a, g, µ, ζ . w ) 2 = 0 . 75; w ) 2 + ( σ 4 w ) 2 + ( σ 8 ( σ 0 • The Jaimovich-Rebelo parameter γ has a uniform prior over the unit interval. • All serial correlations beta prior distributions. 16

Model Predictions g y g c g i g h g g g tfp g pa Statistic Standard Deviations Data 0.91 0.51 2.28 0.84 1.14 0.75 0.41 Model – Bayesian Estimation 0.73 0.58 2.69 0.85 1.13 0.79 0.40 Model – ML Estimation 0.67 0.53 2.28 0.79 1.01 0.76 0.36 Correlations with Output Growth Data 1.00 0.50 0.69 0.72 0.25 0.40 -0.12 Model – Bayesian Estimation 1.00 0.58 0.69 0.42 0.33 0.28 0.01 Model – ML Estimation 1.00 0.60 0.67 0.38 0.34 0.22 0.04 Autocorrelations Data 0.28 0.20 0.53 0.60 0.05 -0.01 0.49 Model – Bayesian Estimation 0.43 0.39 0.60 0.14 0.02 0.03 0.47 Model – ML Estimation 0.36 0.34 0.52 0.09 0.03 0.05 0.48 Note: Bayesian estimates are medians of 500,000 draws from the posterior distri- butions of the corresponding population second moments. 17

Variance of Output Growth Variance of Consumption Growth 5 2.5 4 2 3 1.5 density density 2 1 1 0.5 0 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 share explained by anticipated shocks share explained by anticipated shocks Variance of Investment Growth Variance of the Growth Rate of Hours 4 10 8 3 6 density density 2 4 1 2 0 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 share explained by anticipated shocks share explained by anticipated shocks 18

Share of Variance Explained by Anticipated Shocks g Y g C g I g h Specification 1. Bayesian Estimation 0.41 0.50 0.33 0.77 2. Maximum Likelihood Estimation 0.49 0.70 0.41 0.72 3. Stock Prices Observable 0.68 0.83 0.69 0.55 4. HP Filtered Predictions 0.48 0.59 0.49 0.84 5. Parsimonious Model 0.68 0.68 0.69 0.69 19

To which extend are government spending shocks, g t , anticipated? Variance Decomposition Bayesian MLE g Y g g g Y g g Innovation Total 0.09 0.95 0.11 0.96 ǫ 0 0.03 0.37 0.03 0.25 g ǫ 4 0.04 0.35 0.08 0.71 g ǫ 8 0.02 0.23 0.00 0.00 g Note: For the Bayesian estimation figures correspond to the mean of 500,000 draws from the posterior distribution of the variance decomposition. 20

How important are shocks to the price of invest- ment? • Our estimates: share of var( g y ) explained by ǫ i a is zero • Justiniano et al.: share of var( g y ) explained by ǫ i a > 60%. • What explains the difference in results? Observability of rel. price of investment. Observable in our paper but not in JPT. 21

Relation To VAR Evidence on Anticipated Pro- ductivity Growth Shocks: Beaudry and Portier (BP), AER 2006 � � � ǫ 1 � ∆ ln TF P t t = C ( L ) ǫ 2 ∆ ln SP t t A BP News Shock Satisfies Simultaneously: • It does not affect TFP contemporaneously • It does affect TFP in the long run. Note: Our model does not have a BP-style bivariate VAR representation. 22

Beaudry-Portier-Style VAR Regressions: Parsimonious Model IR of TFP, LR identification IR of Value of Firm, LR identification 2.5 12 10 2 8 1.5 % % 6 1 4 0.5 2 0 0 0 5 10 15 20 0 5 10 15 20 quarters quarters IR of TFP, SR identification IR of Value of Firm, SR identification 1.5 12 10 1 8 % % 0.5 6 4 0 2 −0.5 0 0 5 10 15 20 0 5 10 15 20 quarters quarters 23