Discussion of: Chari-Kehoe-McGrattan: Are Structural VARs Useful …lchrist/research/CKM/overhe… · Chari-Kehoe-McGrattan: Are Structural VARs Useful Guides for Developing Business

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Discussion of:Chari-Kehoe-McGrattan:

Are Structural VARs Useful Guides for DevelopingBusiness Cycle Theories?

by Larry Christiano

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Chari-Kehoe-McGrattan:Are Structural VARs Useful Guides for Developing

Business Cycle Theories?• Jordi Gali Estimated the Dynamic Effects of Technology Shocks By Exploiting

Three (Identification) Assumptions:a. Tech Shocks Are a Linear Combination of a Finite Number of Lags of Past

Data.b. Tech Shocks Are Orthogonal to Other Structural Shocks.c. Tech Shocks are the Only Shocks that Have Long Run Effects on Labor

Productivity.

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Productivity.

• Technically, CKM’s Paper is a Critique of Jordi Gali’s Paper:– Argue that Gali’s Methods Produce Severely Distorted Estimates of Impulse

Response Functions.

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Productivity.


Response Functions.• CKM Do Not Think of This as a Narrow Comment on Gali Alone.

– They Conjecture that their Critique Applies to VAR Methods MoreGenerally.

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Productivity.


Response Functions.• CKM Do Not Think of This as a Narrow Comment on Gali Alone.

– They Conjecture that their Critique Applies to VAR Methods MoreGenerally.

• So, the Answer to the Question in the title of the Paper is NO!

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• CKM Conclusion: Identified VARs Are of No Use As A Guide for DevelopingBusiness Cycle Theories.– Based On Three Numerical Examples.

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• CKM Conclusion: Identified VARs Are of No Use As A Guide for DevelopingBusiness Cycle Theories.– Based On Three Numerical Examples,

• The Examples Fail to Establish CKM’s Case.

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• The Examples Fail to Establish CKM’s Case.• In Two Examples: Distortions Occur Because Gali’s Identification Assump-

tions Do Not Hold.– They Illustrate the Principle:

If You Make the Wrong Identification AssumptionThen You Get the Wrong Answer

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– Problem: Simply Pointing Out this Principle Does Not Establish That GaliActually Did Make the Wrong Assumption, or that He Got the WrongAnswer.

– The Examples are Not New or Surprising.

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– Problem: Simply Pointing Out this Principle Does Not Establish That GaliActually Did Make the Wrong Assumption, or that He Got the WrongAnswer.

– The Examples are Not New or Surprising.• A Third Example:

– Numerical Example In Which Gali’s Assumptions Are True, and EstimationIs Nevertheless Distorted.

– This Example Potentially Interesting, Is it a Problem in Practice?– Distortions Not Present in a Recent VAR Analysis.

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Outline• Overview (done!)• Long Run Identification• Equilibrium Model Used in Examples.• The Three Examples• Conclusion

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Long-Run Identification• Data:

DSVAR: Yt =

"∆ log

³ytlt

´∆lt

#, LSVAR: Yt =

"∆ log

³ytlt

´lt

#

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DSVAR: Yt =

"∆ log

³ytlt

´∆lt

#, LSVAR: Yt =

"∆ log

³ytlt

´lt

#• Vector Autoregression:

Yt = B(L)Yt−1 + ut, Eutu0t = V.

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DSVAR: Yt =

"∆ log

³ytlt

´∆lt

#, LSVAR: Yt =

"∆ log

³ytlt

´lt



• Assumption about Fundamental Economic Shocks, εt :ut = Cεt, CC

0 = V,

εt =

µεtechnology,tεother,t

¶• In General:

limj→∞

Et log

µyt+jlt+j

¶= a× εtechnology,t + b× εother,t.

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...


DSVAR: Yt =

"∆ log

³ytlt

´∆lt

#, LSVAR: Yt =

"∆ log

³ytlt

´lt



• Assumption about Fundamental Economic Shocks, εt :ut = Cεt, CC

0 = V,

εt =


¶• In General:

limj→∞

Et log

µyt+jlt+j

¶= a× εtechnology,t + b× εother,t.

• Long Run Identification Assumption:b = 0.

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Examples Constructed Using Variants of FollowingModel

• Resource Constraint:ct +Gt + kt+1 = kαt (Ztlt)

1−α + (1− δ)kt

• Intratemporal Euler equation:Uleisure,t

Uc,t= (1− τ lt)Fl,t

• Intertemporal Euler equation:Uc,t(1 + τxt) = βEtUc,t+1 [Fk,t+1 + (1− δ) (1 + τx,t+1)]

• Exogenous Processes:Zt, τ lt, τ xt, Gt

• Three Examples: Alternative Specifications of Exogenous Processes.

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Examples• Example #1: DSVAR Analysis Distorted by ‘Invertibility Problems’• Example #2: An RBC Model Fit by Maximum Likelihood Methods to US Data

Implies Identification Based on Long-Run Restrictions Severely Distorted.• Example #3: Even when Identifying Restrictions Correct, Estimates of Impulse

Response Functions Hopelessly Imprecise.

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Example #1 Invertibility• Exogenous Shocks:µ

∆ logZt

τ lt

¶=

∙0 00 0.938

¸µ∆ logZt−1

τ lt−1

¶+


¶• Model Prediction: DSVAR Analysis Finds Hours Fall After Positive Shock To

Technology, Even Though In Data Generating Mechanism Hours Rises.

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• (Partial) Explanation:– RBC Model Implies lt Stationary. So, there is NO VAR representation for

Yt =

"∆ log

³ytlt

´∆lt

#.

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Yt =

"∆ log

³ytlt

´∆lt

#.

– Example: Suppose hours stationary in levels -lt = ρlt−1 + εt, − 1 < ρ < 1

so,∆lt = ρ∆lt−1 + εt − εt−1.

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Yt =

"∆ log

³ytlt

´∆lt

#.


so,∆lt = ρ∆lt−1 + εt − εt−1.

Try and ‘invert’ this, i.e., express εt as function of current and past ∆lt’s:∆lt = (ρ− 1) [∆lt−1 +∆lt−2 +∆lt−3 + ...] + εt

Can’t do it...Not Invertible.

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Yt =

"∆ log

³ytlt

´∆lt

#.


so,∆lt = ρ∆lt−1 + εt − εt−1.


Can’t do it...Not Invertible.– VAR For Yt Is Misspecified, Regardless of Lag Length.

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Yt =

"∆ log

³ytlt

´∆lt

#.


so,∆lt = ρ∆lt−1 + εt − εt−1.


Can’t do it...Not Invertible.– VAR For Yt Is Misspecified, Regardless of Lag Length.– In Practice, This Problem Need not be Fatal. There Exist Methods That Can

be Used to Assess Whether Hours Worked Should Be Differenced, Or Not(see recent literature).

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Yt =

"∆ log

³ytlt

´∆lt

#.


so,∆lt = ρ∆lt−1 + εt − εt−1.


Can’t do it...Not Invertible.– VAR For Yt Is Misspecified, Regardless of Lag Length.– In Practice, This Problem Need not be Fatal. There Exist Methods That Can

be Used to Assess Whether Hours Worked Should Be Differenced, Or Not(see recent literature).

– Findings of Example #1 Closely Related to Similar Findings in Altig,Christiano, Eichenbaum and Linde (2002), Christiano, Eichenbaum andVigfusson (2004a,2004b).

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Example #1 Invertibility, cont’d• Source of Non-Invertibility Explored Here: Data Overdifferencing

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Example #1 Invertibility, cont’d• Source of Non-Invertibility Explored Here: Data Overdifferencing• Other Sources of Non-Invertibility

– Lippi-Reichlin: Technology Growth Follows Diffusion Process:∆ log (Zt) = εtechnology,t + 2× εtechnology,t−1.

May Not Be Able to Recover εtechnology,t From Past Data.

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May Not Be Able to Recover εtechnology,t From Past Data.– Can Generate Other Examples (Hansen and Sargent).

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May Not Be Able to Recover εtechnology,t From Past Data.– Can Generate Other Examples (Hansen and Sargent).– Often: More Data in VAR Solves the Problem (Hansen-Sargent, Reichlin).

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May Not Be Able to Recover εtechnology,t From Past Data.– Can Generate Other Examples (Hansen and Sargent).– Often: More Data in VAR Solves the Problem (Hansen-Sargent, Reichlin).

• These Sources of Non-Invertibility Deserve More Attention, But CKM areSilent About Them.

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Example #2: A Model Estimated By MaximumLikelihood Implies Gali-Style VAR Identification

Misleading• Exogenous Shocks:

logZt = αt + log zt,

logGt = βt + log gt⎛⎜⎜⎝log ztτ ltτxtlog gt

⎞⎟⎟⎠ = P

⎛⎜⎜⎝log zt−1τ lt−1τxt−1log gt−1

⎞⎟⎟⎠+Q

⎛⎜⎜⎝ηz,tητ l,tηx,tηg,t

⎞⎟⎟⎠ .

• The matrix, Q Lower Triangular, QQ0 = V.

• Enormous Persistence. Eigenvalues of P :0.9952± 0.0019i, 0.9927, 0.9598

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0 50 100 150 200 250 300 350 400-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1Response in Log, Labor Productivity to 1 std dev. Technology Shock

Quarters

Response to Shocks in CKM's Preferred Model

0 50 100 150 200 250 300 350 400-0.2

0

0.2

0.4

0.6

0.8

1

1.2Response in Log, Labor Productivity to 1 std dev. Labor Tax Rate Shock

Quarters

...

• Gali’s Long Run Identification Assumptions Wrong in This Example– No Shock Has A Truly Permanent Effect– Two Shocks Do Have Highly Persistent Effects On Labor Productivity– No Surprise that Gali’s Identification Assumptions Could Produce Highly

Distorted Results In this Case.

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Distorted Results In this Case.• Reader is Asked to take the Model Seriously Because it is Estimated Using

Maximum Likelihood Methods.

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Maximum Likelihood Methods.– A Literal Interpretation of the Model is Hard to Take Seriously∗ Positive Innovation to Labor Tax⇒ Labor Productivity Up Persistently.∗ Positive Innovation to Technology⇒ Labor Productivity Down.

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– Could Interpret CKM Model As Reduced Form of Another Model

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– Could Interpret CKM Model As Reduced Form of Another Model∗ In That Deeper Structural Model, Gali’s Assumption May Well Be Valid.

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– Could Interpret CKM Model As Reduced Form of Another Model∗ In That Deeper Structural Model, Gali’s Assumption May Well Be Valid.∗ Possibility: There Could Be Just One Shock That Has A Permanent

(or, Highly Persistent) Effect on Labor Productivity, Which Drives BothlogZ and τ lt.

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– Could Interpret CKM Model As Reduced Form of Another Model∗ In That Deeper Structural Model, Gali’s Assumption May Well Be Valid.∗ Possibility: There Could Be Just One Shock That Has A Permanent

(or, Highly Persistent) Effect on Labor Productivity, Which Drives BothlogZ and τ lt.

• Without Further Analysis, Not Clear What this Example Implies For Gali, orVAR Methods Generally.

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Example #3: Impulse Response Functions Hard ToPin Down Even If Identification Assumptions Are

Correct• Exogenous Shocks:µ

∆ logZt

τ lt

¶=

∙0 00 0.938

¸µ∆ logZt−1

τ lt−1

¶+


¶• Do LSVAR Analysis, with

Yt =

"∆ log

³ytlt

´lt

#.

• No Over Differencing!• Seems As Though There Should Be No Problem.

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• Findings:a. In Small Samples, Estimated Impulse Responses Have Very Large

Sampling VarianceAnalysis in Erceg, Guerrieri and Gust (2004) Suggests this May Be

Because of High Persistence of τ ltb. Bias in Large Samples. Goes Away With Longer Lags in VAR.

• Would the Analyst Using Standard Diagnostic Tests for Lag Lengths Discoverthat Lag Lengths Need to Be Very Long?– If ‘Yes’ then the Example is Perhaps Less Worrisome.

• Do the Problems Go Away With More Data? Here is an Example WhichSuggests that Maybe The Answer is ‘yes’.

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Example #3, Cont’d• Model Laboratory: Altig-Christiano-Eichenbaum-Linde Model, to be Pre-

sented and Defended Tomorrow by Marty.• Model Parts:

– Consumption, Investment, Employment, Transactions Motive for HoldingMoney Balances.

– Investment Adjustment Costs, Wage Setting Frictions, Variable CapitalUtilization.

– Monetary Policy Shock, Neutral Shock to Technology (i.e., Zt), InvestmentSpecific Shock to Technology.

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• Basic Business Cycle Properties of the Model:Comparison of Model and Data: Kydland-Prescott Statistics

(Rel.) Std. Dev. Corr. w/YVariable Model US Data Model US DataOutput 1.3 1.6 1 1Hours 0.8 1.1 1.0 0.9Productivity 0.3 0.5 0.8 0.07Wage 0.2 0.5 0.4 0.1Consumption 0.5 0.5 0.8 0.7Investment 2.7 3.9 1.0 0.9All Statistics Computed on Logged, HP-filtered Data

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• Experiment:– Report Impulse Responses of 10 Model Variables to Three Shocks (This is

‘Truth’, for Purposes of Experiment)– Simulate Artificial Data From Model– Estimate a 10-Variable, 4-Lag VAR (with a little measurement error, for

non-singularity) in Artificial Data.– Use Long-Run Identifying Restrictions and Monetary Policy Shock

Identification to Estimate Impulse Response Functions∗ Large Sample∗ Small Sample

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0 5 10 15−0.1

0

0.1

0.2

0.3

Output

0 5 10 15

0

1

2

MZM Growth

0 5 10 15−0.05

0

0.05

0.1

0.15

Inflation

0 5 10 15

−0.4

−0.2

0

Fed Funds

0 5 10 15

−0.2

−0.1

0

0.1

0.2

Capacity Util

0 5 10 15−0.1

0

0.1

0.2

0.3

Avg Hours

0 5 10 15

0

10

20x 10

−3 Real Wage

0 5 10 15

0

0.05

0.1

Consumption

0 5 10 15

0

0.5

1

Investment

0 5 10 15

−0.4

−0.2

0

0.2

Velocity

Dynamic responses to a monetary policy shock: true model

0 5 10 15−1

−0.5

0

0.5

1Price of Inv.

0 5 10 15−0.1

0

0.1

0.2

0.3

Output

0 5 10 15

0

1

2

MZM Growth

0 5 10 15−0.05

0

0.05

0.1

0.15

Inflation

0 5 10 15

−0.4

−0.2

0

Fed Funds

0 5 10 15

−0.2

−0.1

0

0.1

0.2

Capacity Util

0 5 10 15−0.1

0

0.1

0.2

0.3

Avg Hours

0 5 10 15

0

10

20x 10

−3 Real Wage

0 5 10 15

0

0.05

0.1

Consumption

0 5 10 15

0

0.5

1

Investment

0 5 10 15

−0.4

−0.2

0

0.2

Velocity

Dynamic responses to a monetary policy shock: true model (.) vs. VAR on simulated data (o)

0 5 10 150

1

2

3x 10

−3 Price of Inv.

0 5 10 15−0.1

0

0.1

0.2

0.3

Output

0 5 10 15

0

1

2

MZM Growth

0 5 10 15−0.05

0

0.05

0.1

0.15

Inflation

0 5 10 15

−0.4

−0.2

0

Fed Funds

0 5 10 15

−0.2

−0.1

0

0.1

0.2

Capacity Util

0 5 10 15−0.1

0

0.1

0.2

0.3

Avg Hours

0 5 10 15

0

10

20x 10

−3 Real Wage

0 5 10 15

0

0.05

0.1

Consumption

0 5 10 15

0

0.5

1

Investment

0 5 10 15

−0.4

−0.2

0

0.2

Velocity

Dynamic responses to a monetary policy shock: true model

0 5 10 15−1

−0.5

0

0.5

1Price of Inv.

0 5 10 15

−0.2

0

0.2

0.4

Output

0 5 10 15−1

0

1

2

MZM Growth

0 5 10 15−0.1

0

0.1

0.2Inflation

0 5 10 15

−0.4

−0.2

0

Fed Funds

0 5 10 15

−0.2

0

0.2

Capacity Util

0 5 10 15

−0.1

0

0.1

0.2

0.3

Avg Hours

0 5 10 15

−0.05

0

0.05

Real Wage

0 5 10 15

−0.1

0

0.1

Consumption

0 5 10 15

−0.5

0

0.5

1

Investment

0 5 10 15

−0.4

−0.2

0

0.2

Velocity

Dynamic responses to a monetary policy shock: true model (.) vs. VAR on simulated data (o)

0 5 10 15−0.05

0

0.05Price of Inv.

0 5 10 15

0.25

0.3

0.35

0.4

0.45

Output

0 5 10 150

0.2

0.4

0.6

0.8

MZM Growth

0 5 10 15

−0.02

0

0.02

0.04

Inflation

0 5 10 15−0.15

−0.1

−0.05

0

Fed Funds

0 5 10 15

0.2

0.25

0.3

0.35

Capacity Util

0 5 10 15

0.05

0.1

0.15

0.2

0.25

Avg Hours

0 5 10 15

0.1

0.2

0.3

Real Wage

0 5 10 150.2

0.3

0.4

Consumption

0 5 10 15

0.3

0.4

0.5

Investment

0 5 10 15

−0.1

−0.05

0

Velocity

Dynamic responses to a neutral technology shock: true model

0 5 10 15−1

−0.5

0

0.5

1Price of Inv.

0 5 10 15

0.250.3

0.350.4

0.45

Output

0 5 10 150

0.5

1

MZM Growth

0 5 10 15

−0.02

0

0.02

0.04

Inflation

0 5 10 15−0.15

−0.1

−0.05

0

Fed Funds

0 5 10 15

0.2

0.25

0.3

0.35

Capacity Util

0 5 10 15

0.05

0.1

0.15

0.2

0.25

Avg Hours

0 5 10 15

0.1

0.2

0.3

Real Wage

0 5 10 150.2

0.3

0.4

Consumption

0 5 10 15

0.3

0.4

0.5

0.6

Investment

0 5 10 15

−0.1

−0.05

0

Velocity

Dynamic responses to a neutral technology shock: true model (.) vs. VAR on simulated data (o)

0 5 10 15

−8

−6

−4

−2

0x 10

−3 Price of Inv.

0 5 10 15

0.25

0.3

0.35

0.4

0.45

Output

0 5 10 150

0.2

0.4

0.6

0.8

MZM Growth

0 5 10 15

−0.02

0

0.02

0.04

Inflation

0 5 10 15−0.15

−0.1

−0.05

0

Fed Funds

0 5 10 15

0.2

0.25

0.3

0.35

Capacity Util

0 5 10 15

0.05

0.1

0.15

0.2

0.25

Avg Hours

0 5 10 15

0.1

0.2

0.3

Real Wage

0 5 10 150.2

0.3

0.4

Consumption

0 5 10 15

0.3

0.4

0.5

Investment

0 5 10 15

−0.1

−0.05

0

Velocity

Dynamic responses to a neutral technology shock: true model

0 5 10 15−1

−0.5

0

0.5

1Price of Inv.

0 5 10 15

0

0.2

0.4

0.6

Output

0 5 10 15

0

0.5

1

MZM Growth

0 5 10 15

−0.1

0

0.1

0.2

Inflation

0 5 10 15−0.2

−0.1

0

0.1

Fed Funds

0 5 10 15−0.2

0

0.2

0.4

Capacity Util

0 5 10 15−0.2

0

0.2

0.4

Avg Hours

0 5 10 15

0.1

0.2

0.3

0.4

Real Wage

0 5 10 150.1

0.2

0.3

0.4

0.5

Consumption

0 5 10 15−0.5

0

0.5

1

1.5Investment

0 5 10 15

−0.2

0

0.2

Velocity

Dynamic responses to a neutral technology shock: true model (.) vs. VAR on simulated data (o)

0 5 10 15

−0.1

−0.05

0

0.05

0.1Price of Inv.

0 5 10 150

0.2

0.4

Output

0 5 10 15

0

0.1

0.2

MZM Growth

0 5 10 15

0

0.1

0.2

Inflation

0 5 10 15

0.05

0.1

0.15

Fed Funds

0 5 10 15−0.2

0

0.2

0.4

Capacity Util

0 5 10 15−0.1

0

0.1

0.2

0.3

Avg Hours

0 5 10 15

0.04

0.06

0.08

0.1Real Wage

0 5 10 150.06

0.08

0.1

0.12

0.14

0.16

Consumption

0 5 10 150

0.5

1

1.5

Investment

0 5 10 15

0

0.2

0.4

Velocity

Dynamic responses to an embodied technology shock: true model

0 5 10 15

−0.23

−0.22

−0.21

−0.2

−0.19

Price of Inv.

0 5 10 150

0.2

0.4

Output

0 5 10 15

0

0.1

0.2

MZM Growth

0 5 10 15

0

0.1

0.2

Inflation

0 5 10 15

0.05

0.1

0.15

Fed Funds

0 5 10 15−0.2

0

0.2

0.4

Capacity Util

0 5 10 15−0.1

0

0.1

0.2

0.3

Avg Hours

0 5 10 15

0.04

0.06

0.08

0.1Real Wage

0 5 10 150.05

0.1

0.15

Consumption

0 5 10 150

0.5

1

1.5

Investment

0 5 10 15

0

0.2

0.4

Velocity

Dynamic responses to an embodied technology shock: true model (.) vs. VAR on simulated data (o)

0 5 10 15−0.24

−0.22

−0.2

Price of Inv.

0 5 10 150

0.2

0.4

Output

0 5 10 15

0

0.1

0.2

MZM Growth

0 5 10 15

0

0.1

0.2

Inflation

0 5 10 15

0.05

0.1

0.15

Fed Funds

0 5 10 15−0.2

0

0.2

0.4

Capacity Util

0 5 10 15−0.1

0

0.1

0.2

0.3

Avg Hours

0 5 10 15

0.04

0.06

0.08

0.1Real Wage

0 5 10 150.06

0.08

0.1

0.12

0.14

0.16

Consumption

0 5 10 150

0.5

1

1.5

Investment

0 5 10 15

0

0.2

0.4

Velocity

Dynamic responses to an embodied technology shock: true model

0 5 10 15

−0.23

−0.22

−0.21

−0.2

−0.19

Price of Inv.

0 5 10 15

−0.2

0

0.2

0.4

0.6

Output

0 5 10 15

−0.5

0

0.5

MZM Growth

0 5 10 15−0.1

0

0.1

0.2

0.3

Inflation

0 5 10 15

0

0.1

0.2

Fed Funds

0 5 10 15−0.4

−0.2

0

0.2

0.4

0.6

Capacity Util

0 5 10 15−0.2

0

0.2

0.4

Avg Hours

0 5 10 15−0.2

0

0.2

Real Wage

0 5 10 15

−0.2

0

0.2

Consumption

0 5 10 15

0

1

2Investment

0 5 10 15−0.2

0

0.2

0.4

0.6

Velocity

Dynamic responses to an embodied technology shock: true model (.) vs. VAR on simulated data (o)

0 5 10 15−0.25

−0.2

−0.15

−0.1

Price of Inv.

...

• In the Example, Performance of VAR Seems Adequate:– Little Large or Small Sample Bias,– Sampling Variation, Though Large in Some Cases, Not Out of Line With

Standard Estimates of Sampling Uncertainty.• Perhaps Different Result From CKM Has to do With Presence of Many More

Variables in VAR.

43

...

Concluding Remarks• CKM Hope to Induce Researchers to Stop Working With Identified VARs.

44

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Concluding Remarks• CKM Hope to Induce Researchers to Stop Working With Identified VARs.• Their Case is Built Around Three Examples.

45

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Concluding Remarks• CKM Hope to Induce Researchers to Stop Working With Identified VARs.• Their Case is Built Around Three Examples.• Two Examples Show How a Researcher Who Makes a Wrong Assumption

Will Reach the Wrong Conclusion.– This Does Not Imply that Actual Researchers Have Made Wrong Assump-

tions or Reached the Wrong Conclusions.– In Practice, There are Things the Researchers Can Do To Guard Against

Mistakes.

46

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Mistakes.• One Example is Presented in Which Impulse Responses From VARs May be

Distorted, Even Without Wrong Assumptions.

47

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Mistakes.• One Example is Presented in Which Impulse Responses From VARs May be

Distorted, Even Without Wrong Assumptions.– Not Clear that this Poses a Problem in Practice.– I Presented an Example Drawn from a Research Study in Which the

Problem Is Not Present.

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• No Need to Throw Identified VAR’s Out of Economist’s Tool Kit.

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• No Need to Throw Identified VAR’s Out of Economist’s Tool Kit.– Identified VAR’s Are Known to Have Problems (Cooley-Dwyer, Faust-

Leeper, Erceg-Guerrieri-Gust, Hansen-Sargent, Lippi-Reichlin).∗ But, there are Ways to Guard Against the Problems.

50

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Leeper, Erceg-Guerrieri-Gust, Hansen-Sargent, Lippi-Reichlin).∗ But, there are Ways to Guard Against the Problems.∗ Just Because Something Isn’t Perfect Doesn’t Mean it Is Not Good, or

Useful.

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Useful.– VARs Have Proved Useful in Guiding the Construction and Estimation of

Dynamic Economic Models.– As With Any Econometric Tool, It Should Be Used With Caution.

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• The Best Proof of the Value of a Methology Lies In Whether It Helps Us LearnAbout the Data.

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• The Best Proof of the Value of a Methology Lies In Whether It Helps Us LearnAbout the Data.– Tomorrow, We Will Present a Paper Which May Convince You that

Identified VARs are Useful For Constructing Dynamic Business CycleModel.

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Documents

Discussion of: Chari-Kehoe-McGrattan: Are Structural VARs Useful …lchrist/research/CKM/overhe… · Chari-Kehoe-McGrattan: Are Structural VARs Useful Guides for Developing Business