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Whats News In Business Cycles? Stephanie Schmitt-Groh e Mart n 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,

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SLIDE 1

What’s News In Business Cycles?

Stephanie Schmitt-Groh´ e Mart ´ ın Uribe Columbia University April 19, 2010

1

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SLIDE 2

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

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SLIDE 3

The Model Preferences: E0

∞

  • t=0

βtζtU(Ct − bCt−1 − ψhθ

tSt)

St = (Ct − bCt−1)γS1−γ

t−1

Capital accumulation: Kt+1 = (1 − δ(ut))Kt + zI

t It

  • 1 − S
  • It

It−1

  • Production technology:

Yt = ztF (utKt, Xtht, XtL)

3

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SLIDE 4

Resource constraint: Ct + AtIt + Gt = Yt An exogenous wage markup: ζt ∂U′(Vt) ∂ht = ΛtWt 1 + µt

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SLIDE 5

Introducing Anticipated Shocks

ln xt = ρ ln xt−1 + µt µt = ǫ0

x,t + ǫ4 x,t−4 + ǫ8 x,t−8

ǫi

x,t ∼ i.i.d. N(0, σi x),

i = 0, 4, 8

4

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SLIDE 6

Autoregressive Representation of Anticipated Shocks ˜ xt+1 = M˜ xt + ηνt+1; νt ∼ i.i.d. N(0, I)

                 

xt+1 ǫ4

x,t+1

ǫ4

x,t

ǫ4

x,t−1

ǫ4

x,t−2

ǫ8

x,t+1

ǫ8

x,t

ǫ8

x,t−1

ǫ8

x,t−2

ǫ8

x,t−3

ǫ8

x,t−4

ǫ8

x,t−5

ǫ8

x,t−6

                 

=

             

ρ 1 1 1 1 1 1 1 1 1 1 1 1

                               

xt ǫ4

x,t

ǫ4

x,t−1

ǫ4

x,t−2

ǫ4

x,t−3

ǫ8

x,t

ǫ8

x,t−1

ǫ8

x,t−2

ǫ8

x,t−3

ǫ8

x,t−4

ǫ8

x,t−5

ǫ8

x,t−6

ǫ8

x,t−7

                 

+

             

σ0

x

σ4

x

σ8

x

              ν0

t+1

ν4

t+1

ν8

t+1

  • Note: A k-period anticipated shock generates k additional latent state variables.

5

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Seven Exogenous Driving Forces:

  • 1. Stationary Neutral Productivity Shocks: zt

Yt = ztF (utKt, Xtht, XtL) ln zt = ρz ln zt−1 + µz,t µz,t = ǫ0

z,t + ǫ4 z,t−4 + ǫ8 z,t−8

ǫi

z,t ∼ i.i.d. N(0, σi z),

i = 0, 4, 8

6

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SLIDE 8
  • 2. Non-stationary Neutral Productivity Shocks: Xt

Yt = ztF (utKt, Xtht, XtL) µx

t ≡

Xt Xt−1 ln(µx

t /µx) = ρx ln(µx t−1/µx) + ǫ0 x,t + ǫ4 x,t−4 + ǫ8 x,t−8

ǫi

x,t ∼ i.i.d. N(0, σi x),

i = 0, 4, 8.

7

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SLIDE 9
  • 3. Stationary Investment-Specific Productivity Shocks: zI

t

Kt+1 = (1 − δ(ut))Kt + zI

t It

  • 1 − S
  • It

It−1

  • ln zI

t = ρzI ln zI t−1 + µzI,t

µzI,t = ǫ0

zI,t + ǫ4 zI,t−4 + ǫ8 zI,t−8

ǫi

zI,t ∼ i.i.d. N(0, σi zI),

i = 0, 4, 8

8

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SLIDE 10
  • 4. Non-stationary Investment-Specific Productivity Shocks: At

Ct + AtIt + Gt = Yt At = At−1µa

t

ln(µa

t /µa) = ρa ln(µa t−1/µa) + ǫ0 a,t + ǫ4 a,t−4 + ǫ8 a,t−8

ǫi

a,t ∼ i.i.d. N(0, σi a),

i = 0, 4, 8.

9

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SLIDE 11
  • 5. Government Spending Shocks: Gt

Ct + AtIt + Gt = Yt gt = Gt XG

t

XG

t =

  • XG

t−1

ρxg

XY

t−1

1−ρxg ;

XY

t = Aα/(α−1) t

Xt ln(gt/g) = ρg ln(gt−1/g) + ǫ0

g,t + ǫ4 g,t−4 + ǫ8 g,t−8

ǫi

g,t ∼ i.i.d. N(0, σi g),

i = 0, 4, 8.

10

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SLIDE 12
  • 6. Wage Markup Shocks: µt

An exogenous wage markup: ζt ∂U′(Vt) ∂ht = ΛtWt 1 + µt ln µt/µ = ρµ ln µt−1/µ + µµ,t µµ,t = ǫ0

µ,t + ǫ4 µ,t−4 + ǫ8 µ,t−8

ǫi

µ,t ∼ i.i.d. N(0, σi µ),

i = 0, 4, 8

11

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SLIDE 13
  • 7. Preference Shock: ζt

E0

∞

  • t=0

βtζtU(Ct − bCt−1 − ψhθ

tSt)

ln ζt = ρζ ln ζt−1 + µζ,t µζ,t = ǫ0

ζ,t + ǫ4 ζ,t−4 + ǫ8 ζ,t−8

ǫi

ζ,t ∼ i.i.d. N(0, σi ζ),

i = 0, 4, 8

12

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Interpretation as Technological Diffusion

Consider the technological diffusion ln Xt =

∞

  • i=0

(1 − φi)νt−i It can be written as ln(Xt/Xt−1) = φ ln(Xt−1/Xt−2) + (1 − φ)νt−1 This is a special case of our assumed process with ρx = φ σ1

x = (1 − φ)σν

σk

x = 0;

for k = 0, 2, 3

13

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Functional Forms U(V ) = V 1−σ − 1 1 − σ F (a, b, c) = aαkbαhc1−αk−αh, S(x) = κ 2(x − µI)2 δ(u) = δ0 + δ1(u − 1) + δ2 2 (u − 1)2 Calibration β σ αk αh δ0 u µy µa 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

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Seven Observables. Sample: 1955Q1-2006Q4

  • 1. ∆ ln Yt = Output Growth
  • 2. ∆ ln Ct = Consumption Growth
  • 3. ∆ ln(ItAt) = Investment Growth
  • 4. ∆ ln ht = Hours Growth
  • 5. ∆TFP = TFP Growth
  • 6. ∆ ln Gt = Government Consumption Growth
  • 7. ∆ ln At = Growth Rate of the Price of Investment

15

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Prior Parameter Distributions

  • All σi

j are gamma (m,m) distributions.

  • The unanticipated innovation has variance of 3× the sum of

the anticipated components: (σ0

w)2

(σ0

w)2 + (σ4 w)2 + (σ8 w)2 = 0.75;

w = z, x, zI, a, g, µ, ζ.

  • The Jaimovich-Rebelo parameter γ has a uniform prior over

the unit interval.

  • All serial correlations beta prior distributions.

16

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Model Predictions

Statistic gy gc gi gh gg gtfp gpa 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

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

18

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Share of Variance Explained by Anticipated Shocks Specification gY gC gI gh 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

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To which extend are government spending shocks, gt, anticipated?

Variance Decomposition Bayesian MLE Innovation gY gg gY gg Total 0.09 0.95 0.11 0.96 ǫ0

g

0.03 0.37 0.03 0.25 ǫ4

g

0.04 0.35 0.08 0.71 ǫ8

g

0.02 0.23 0.00 0.00

Note: For the Bayesian estimation figures correspond to the mean of 500,000 draws from the posterior distribution of the variance decomposition. 20

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SLIDE 22

How important are shocks to the price of invest- ment?

  • Our estimates: share of var(gy) explained by ǫi

a is zero

  • Justiniano et al.: share of var(gy) explained by ǫi

a > 60%.

  • What explains the difference in results? Observability of rel.

price of investment. Observable in our paper but not in JPT.

21

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SLIDE 23

Relation To VAR Evidence on Anticipated Pro- ductivity Growth Shocks:

Beaudry and Portier (BP), AER 2006

  • ∆ ln TF Pt

∆ ln SPt

  • = C(L)
  • ǫ1

t

ǫ2

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

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Beaudry-Portier-Style VAR Regressions: Parsimonious Model

5 10 15 20 −0.5 0.5 1 1.5 IR of TFP, SR identification quarters % 5 10 15 20 2 4 6 8 10 12 IR of Value of Firm, SR identification quarters % 5 10 15 20 0.5 1 1.5 2 2.5 IR of TFP, LR identification quarters % 5 10 15 20 2 4 6 8 10 12 IR of Value of Firm, LR identification quarters %

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Summary of Main Findings

  • 1. In the context of our estimated model anticipated shocks

explain about half of the movements in aggregate variables at business-cycle frequency.

  • 2. In a parsimonious model, the most important anticipated

shocks are innovations to TFP.

  • 3. The estimated importance of shocks to the price of invest-

ment is zero when this variable is treated as an observable in the estimation.

  • 4. Government spending shocks have an important anticipated

component.

24

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EXTRAS

25

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Identification of Anticipated Shocks: An Illustrative Example

  • Model: xt = 0.9xt−1 + ǫ0

t + ǫ1 t−1 + ǫ2 t−2

yt = 0.5yt−1 + ǫ1

t

zt = ǫ2

t

  • Observables: xt and vt ≡ yt + zt
  • Case 1: True values: (σ0, σ1, σ2) = (0.2, 0.4, 0.8), prior are

gamma(.5,.2), posterior means (0.24, 0.4, 0.79) posterior stan- dard deviations (0.06, 0.02, 0.04).

  • Case 2: True values: (σ0, σ1, σ2) = (0.8, 0.8, 0.8), prior are

gamma(.5,.2), posterior means (0.75, 0.73, 0.77) posterior stan- dard deviations (0.07, 0.04, 0.05).

26

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0.5 1 2 4 6 σ0 0.5 1 5 10 15 σ1 0.5 1 5 10 σ2 0.5 1 2 4 6 σ0 0.5 1 5 10 σ1 0.5 1 2 4 6 8 σ2 10 20 0.5 1 Impulse Responses of xt 10 20 0.5 1 Impulse Responses of vt ε0

t

ε1

t

ε2

t