monetary economics: empirical, theoretical and policy...

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Monetary Economics: Empirical, Theoretical andPolicy Issues

Lawrence J. Christiano1

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Questions• Why Did Inflation Take Off in Many Countries in the 1970s?

• Does Low Inflation Monetary Target Expose Economy to Collapse?– Claim -∗ Combination: Low Inflation Target and Zero Lower Bound

∗ ⇒ Risk: Fall into a Downward Spiral of Deflation and Low Output

– Does Claim Hold Water In Reasonably Constructed Models of Economy?

• Japan’s ‘Lost Decade’ of 1990s: Why?

• What is the Appropriate Monetary Policy in the Wake of a Financial Crisis?

• How Much Price Stability is Desirable? What is the ‘Optimal’ Nominal Interest Rate?

• Stock Market...– Why Did the Recent Stock Market Boom/Bust Cycle Occur?– Should (Could?) Monetary Policy Have Done Something to Prevent The Cycle?– Did Monetary Policy Inadvertently Contribute to the Amplitude of the Cycle?

15

...

Ways to Answer Questions Like These:– Look at Historical Episodes (limited use)– Experiment (not an option!)– Experiment in Model Economies.

Issues to Confront in Analysis of Model Economiesa. Empirical: Formulate and Estimate a Model

b. Analytic∗ Appropriate Equilibrium Concepts for the Issue Studied

∗ Relevant Computational Strategies

∗ Other Issues.

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...

Questions

Answers

Models

Model Selection and Construction

Model Analysis

20

Objective

• Provide Exposure to Key Aspects of Formulation, Estimation and Analysis ofEquilibrium Models

• Provide Tutorials and MATLAB Software for Analysis of a Range of Models,Which You May Find Useful as Templates for Future Research

• Target Audience:

– People with Little Exposure to this Material

– People Currently Already Actively Applying the Material in their Research.

25

Outline

• Formulating and Estimating a DSGE Model For Monetary Policy Analysis(2.0 lectures)

• Policy Analysis

– Optimal Policy (1.5 lectures)

– Evaluation of Alternative Policy Rules (1.5 lectures)

• Materials are on the Course Website,– http://www.faculty.econ.northwestern.edu/faculty/christiano/course/main.htm

26

VAR Analysis: General Background Comments

• My Focus Will Be On The Use of VARs to Learn About Construction andParameterization of Dynamic, General Equilibrium Models of Money.

• A ‘Shock-Based Approach to Estimating Models’.• Basic Idea:

– Use Minimal Restrictions From Class of Economic Models Under Consid-eration to Estimate the Dynamic Impact of Economic Shocks on EconomicVariables of Interest

– Choose Parameters and Functional Forms for a Dynamic General Equilib-rium Model to Match These Effects as Closely As Possible.

• Lucas Program for Model Selection:

‘Neet to test them (models) as useful imitations of reality by subjectingthem to shocks for which we are fairly certain how actual economies wouldreact. The more dimensions on which the model mimics the answers actualeconomies give to simple questions, the more we trust its answers to harderquestions.’

32

VAR Analysis: General Background Comments

• Alternative Strategy:– Choose Model Parameters and Functional Forms to Match Second Moment

Properties of Model and Data.– Maximum Likelihood– Must Have all the Shocks in and Without Specification Error.

35

VAR Analysis: General Background Comments

• Advantages of Shock-Based Approach– Focus of Analysis is on Objects of Specific Economic Interest:∗What Accounts for Inertia in Response of Inflation to Policy Shocks

(Mankiw, Chari-Kehoe-McGrattan)?· Need a Measure of That Inertia

∗What Fraction of Variance of Output is Due to Different Kinds ofTechnology Shocks?· Need a Measure of Different Shocks

– May Only Want a Small Number of Shocks in Model - Capturing All theSmaller Shocks May Only Generate Specification Error∗ Models are Abstractions: Small Number of Shocks May Be Enough to

Account for 75-80% of Variation in Data– Modelers Who Want All the Shocks Can Use VARs for Diagnostic Purposes

40

Outline of VAR Discussion

• The Identification Problem

• Long Run Restrictions as a Way to Solve the Problem:

– Bivariate Blanchard-Quah Example

– The Multivariate Case

• Short Run Restrictions: Identification of Monetary Policy Shocks

• Results

• Historical Decompositions of Data

41

Identification

• Vector Autoregression (VAR):

Yt = B1Yt−1 + ... +BpYt−p + ut, Eutu0t = V

Bl’s, ut’s and V Obtained by OLS Regressions.• Fundamental Economic Shocks, et:

ut = Cet, Eete0t = D, D ∼ Diagonal, CC 0 = V.

• Impulse Responses (p = 2):

Yt −Et−1Yt = Cet, EtYt+1 −Et−1Yt+1 = B1CetEtYt+2 −Et−1Yt+2 = B2

1Cet +B2Cet

42

Identification ...

• For Impulse Responses: Need Bl’s and Columns of C.• Problem: N2 Unknown Elements in C,

a. Only N(N + 1)/2 Equations in:

CC 0 = V

b. Need to Make (Identifying) Assumptions!

44

Bivariate Blanchard and Quah Example

• Identification Assumption:Technology Shock is Only Shock that Has Long-Run Impact on (Forecast of)Level of Labor Productivity:

(exclusion restriction) limj→∞

[Etyt+j −Et−1yt+j] = f (technology shock only)

(sign restriction) f 0 > 0

yt =outputhour

• Blanchard-Quah/Jordi Gali:This Assumption Makes it Possible to Estimate Technology Shock, EvenWithout Direct Observations on Technology

45

Bivariate Blanchard and Quah Example ...

• Bivariate VAR:

Yt = BYt−1 + ut, Eutu0t = V

ut = Cet

Yt =

µ∆ytxt

¶, C =

∙C11 C12C21 C22

¸, et =

µe1te2t

¶ezt ˜ Technology Shock.

• From Applying OLS To Both Equations in VAR, We Know:B, V

• Problem: CC 0 = V Provides only Three Equations in Four Unknowns in C.• Result: Assumption that e2t Has No Long Run Impact on yt Supplies the Extra

Required Equation

46

Bivariate Blanchard and Quah Example ...

• Easy to Verify:

Et[∆yt+1+∆yt]−Et−1[∆yt+1+∆yt]z | Et[yt+1]−Et−1[yt+1] = (1, 0) [B + I ]Cet

Et[yt+2]−Et−1[yt+2] = (1, 0)£B2 +B + I

¤Cet

Et[yt+j]−Et−1[yt+j] = (1, 0)£Bj +Bj−1 + ... +B2 +B + I

¤Cet

as j →∞ :

limj→∞

Et[yt+j]−Et−1[yt+j] =

limj→∞

(1, 0)£... +Bj +Bj−1 + ... +B2 +B + I

¤Cet

= (1, 0) [I −B]−1Cet

47

Bivariate Blanchard and Quah Example ...

• As j →∞ :

limj→∞

Et[yt+j]−Et−1[yt+j] = (1, 0) [I −B]−1Cet

• Identification Assumption About Technology:

[I −B]−1C =

∙number 0number number

¸• Final Result: Solve for C Using

(exclusion restriction) 1, 2 element of [I −B]−1C is zero

(sign restriction) 1, 1 element of [I −B]−1C is positiveCC 0 = V

• Conclude: Long-Run Restriction Supplies Extra Equation Needed to AchieveIdentification.

48

Arbitrary Variables, Arbitrary Lags

• More General Case of Arbitrary Number (N ) of Variables and Lags:

Xt = B1Xt−1 +B2Xt−2 + ... +BpXt−p + ut

• To Compute Impulse Response to Technology Shock,– Require: B1, ..., Bp and C1, First Column of C in CC 0 = V

– Can Obtain by OLS: B1, ..., Bp and V– Identification Problem: Find C1

• Solution: Use Restriction, as j →∞ :

limj→∞

Et[yt+j]−Et−1[yt+j] = (1, 0, ..., 0) [I −B(1)]−1Cet

B(1) ≡ B1 +B2 + ... +Bp.

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Arbitrary Variables, Arbitrary Lags ...

• VAR:

Xt = B1Xt−1 +B2Xt−2 + ... +BpXt−p + ut

• Long-Run Restriction:

(exclusion restriction) [I −B(1)]−1C =

∙number 0, ..., 0numbers numbers

¸(sign restriction) (1, 1) element of [I −B(1)]−1C is positive

CC 0 = V

• There Are Many C That Satisfy These Constraints. All Have the Same C1.

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Arbitrary Variables, Arbitrary Lags ...

• Using the Restrictions to Uniquely Pin Down C1• Let

D ≡ [I −B(1)]−1C

so, DD0 = [I −B(1)]−1 V [I −B(1)0]−1 ≡ S0 (Since CC 0 = V )

• Exclusion Restriction Requires:

D =

∙d11 0, ..., 0D21 D22

¸• So

DD0 =

∙d211 d11D

021

D21d11 D21D021 +D22D

022

¸=

∙S110 S2100S210 S220

¸.

• Sign Restriction:d11 > 0.

• Then, First Column of D Uniquely Pinned Down:

d11 =qS110 , D21 = S210 /d11

• First Column of C Uniquely Pinned Down:C1 = [I −B(1)]D1.

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Arbitrary Variables, Arbitrary Lags ...

• In the Application We Will Review Here, More Convenient to Follow Variantof Shapiro-Watson Approach.

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Arbitrary Variables, Arbitrary Lags ...

• Data :

Yt|z10×1

=

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

∆ ln (relative price of investmentt)∆ ln (GDPt/Hourst)∆ ln (GDP deflatort)capacity utilizationt

ln (Hourst)ln (GDPt/Hourst)− ln (Wt/Pt)

ln (Ct/GDPt)ln (It/GDPt)

Federal Funds Ratetln(GDP deflatort) + ln (GDPt)− ln (MZMt)

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

53

−15−10−5

05

x 10−3 p

I growth

−0.01

0

0.01

0.02

APL growth

0

0.01

0.02

Inflation

4.2

4.4

Capacity Util

−7.6

−7.4

Hours

−0.52−0.5

−0.48−0.46−0.44

APL / Real Wage

−0.32−0.3

−0.28−0.26−0.24

C / Y

−1.6

−1.4

I / Y

Q2−59 Q4−67 Q2−76 Q4−84 Q2−93 Q4−01

0.05

0.1

0.15

Fed Funds

Figure 1: data used in the analysis

Q2−59 Q4−67 Q2−76 Q4−84 Q2−93 Q4−010.6

0.8

1

1.2MZM velocity

Arbitrary Variables, Arbitrary Lags ...

• Three Identified Shocks:– Two Technology Shocks: Only Shocks that Have a Long Run Impact on

Labor Productivity∗ Neutral Shock to Technology.∗ Embodied Shock to Technology· only shock with long-run effect on investment good prices (J. Fisher)

– Monetary Policy Shock∗ Disturbance in OLS Regression:

Rt = f(Ωt) + ωeRt,

eRt ⊥ Ωt

∗ ⇒Monetary Policy Has No Contemporaneous Impact on Prices andAggregate Allocations.∗ ⇒Interest Rate Not Significantly Contemporaneously Affected by

Money Demand Shocks, Other than Via Ωt.

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Arbitrary Variables, Arbitrary Lags ...

What Is A Monetary Policy Shock? Shocks to Preferences of Monetary Authority

Technical Factors Like Measurement Error (Bernanke-Mihov):

xt(0) = xt + vt, xt(1) = xt + utSt = β0St−1 + β1xt(0) + β2xt−1(1)

orSt = β0St−1 + β1xt + β2xt−1 + εtεt = β1vt + β2ut−1.

Recursiveness Assumption: β0 = 0, or β0 6= 0, ut = 0.

55

Arbitrary Variables, Arbitrary Lags ...

What Is a Monetary Policy Rule? Literal Interpretation: Structural Policy Rule of Central Bank.

Combination of Structural Policy Rule and Other Stuff– Example (Clarida-Gertler):

‘True’ Policy Rule: St = αEtxt+1 + εt= f(all time t data used in Etxt+1) + εt

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Results for Impulse Response Functions

• Show Data, VAR Lag Length: 4, Sample Period 1959Q1-2001Q3.• Responses to Monetary Policy Shock

– Impact on Money Growth and Interest Rate Over in 1 Year, Other VariablesKeep Going

– Significant Liquidity Effect– Inflation Peaks in Roughly Two Years– Output, consumption, investment, hours worked and capacity utilization are

hump-shaped.– Velocity comoves with the interest rate

• Responses to a Positive, Neutral Technology Shock– Output, hours, investment, consumption display strong, positive, significant

responses.– Strong, immediate drop in inflation

• Responses to a Negative, Embodied Shock to Technology– Rise in Output, Hours Worked, Interest Rate, Strong Rise in Investment.

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0 5 10 15

−0.4

−0.2

0

0.2

0.4Output

0 5 10 15

−2

−1

0

1

2

MZM Growth (Cash Balances, Q)

0 5 10 15

−0.1

0

0.1

0.2

Inflation

0 5 10 15

−0.6

−0.4

−0.2

0

0.2

Fed Funds

0 5 10 15

−0.5

0

0.5

Capacity Util

0 5 10 15

−0.2

0

0.2

0.4

Avg Hours

0 5 10 15−0.2

−0.1

0

Real Wage

0 5 10 15

−0.2

0

0.2

Consumption

0 5 10 15

−1

0

1

Investment

0 5 10 15

−0.5

0

0.5

1

1.5

Velocity

0 5 10 15−0.1

0

0.1

0.2

pI

Figure 3: Benchmark model − dynamic response to a monetary policy shock

0 5 10 15 200

0.5

1

1.5Total money growth (M)

0 5 10 15

0.2

0.4

0.6

0.8

Output

0 5 10 15−1

0

1

MZM Growth (Cash Balances, Q)

0 5 10 15

−0.8

−0.6

−0.4

−0.2

0

Inflation

0 5 10 15−0.6

−0.4

−0.2

0

0.2

Fed Funds

0 5 10 15

−0.5

0

0.5

Capacity Util

0 5 10 15

0

0.2

0.4

0.6

0.8

Avg Hours

0 5 10 15

0

0.2

0.4

Real Wage

0 5 10 15

0.2

0.4

0.6

0.8

1

Consumption

0 5 10 15

0

1

2

Investment

0 5 10 15−3

−2

−1

0

Velocity

0 5 10 15

−0.4

−0.2

0

0.2

pI

Figure 4: Benchmark model − dynamic response to a neutral technology shock

0 5 10 15 200

0.5

1Total money growth (M)

0 5 10 15

−0.2

0

0.2

0.4

0.6

0.8Output

0 5 10 15

−1

0

1

MZM Growth (Cash Balances, Q)

0 5 10 15

−0.2

0

0.2

0.4

Inflation

0 5 10 15

−0.2

0

0.2

0.4

0.6

Fed Funds

0 5 10 15−1

−0.5

0

0.5

1

Capacity Util

0 5 10 15−0.4−0.2

00.20.40.60.8

Avg Hours

0 5 10 15−0.2

0

0.2

0.4

Real Wage

0 5 10 15−0.2

0

0.2

0.4

Consumption

0 5 10 15

0

1

2

3

Investment

0 5 10 15−2

−1

0

1

Velocity

0 5 10 15

−0.6

−0.4

−0.2

pI

Figure 5: Benchmark model − dynamic response to an embodied technology shock

0 5 10 15 200

0.2

0.4

0.6

0.8Total money growth (M)

Historical Decompositions

• With the Identified Shocks in Hand, we Can Ask:

– What Would have Happened if Only Monetary Policy Shocks Had Driventhe Data?

– We Can Ask This About the Other Shocks, or About a Combination ofShocks

– We Find that The Three Shocks Together Account for A Large Part (Perhapsas much as 50%) Of Fluctuations

∗ Money Has More to Do With Business Cycles

∗ Neutral Technology Has More to Do With Lower-Frequency Componentof the Data

58

Q2−60 Q2−70 Q2−80 Q2−90 Q2−00

−5

0

5

Output

Q2−60 Q2−70 Q2−80 Q2−90 Q2−00

0

20

40

60

MZM Growth

Q2−60 Q2−70 Q2−80 Q2−90 Q2−00−4

−2

0

2

4

6Inflation

Q2−60 Q2−70 Q2−80 Q2−90 Q2−00

−0.020

0.020.040.060.08

Fed Funds

Q2−60 Q2−70 Q2−80 Q2−90 Q2−00

−10

−5

0

5

Capacity Util

Q2−60 Q2−70 Q2−80 Q2−90 Q2−00

−5

0

5

Avg Hours

Q2−60 Q2−70 Q2−80 Q2−90 Q2−00

−10

−5

0

Real Wage

Q2−60 Q2−70 Q2−80 Q2−90 Q2−00

−5

0

5

Consumption

Q2−60 Q2−70 Q2−80 Q2−90 Q2−00

−20

−10

0

10

Investment

Q2−60 Q2−70 Q2−80 Q2−90 Q2−00

−10

0

10

20

Velocity

Figure 6: Historical decomposition − monetary policy shocks only

Q2−60 Q2−70 Q2−80 Q2−90 Q2−00−4

−2

0

2

4

6

8

Price of Inv.

Q2−60 Q2−70 Q2−80 Q2−90 Q2−00

−5

0

5

Output

Q2−60 Q2−70 Q2−80 Q2−90 Q2−00

0

20

40

60

MZM Growth

Q2−60 Q2−70 Q2−80 Q2−90 Q2−00−4

−2

0

2

4

6Inflation

Q2−60 Q2−70 Q2−80 Q2−90 Q2−00

−0.020

0.020.040.060.08

Fed Funds

Q2−60 Q2−70 Q2−80 Q2−90 Q2−00

−10

−5

0

5

Capacity Util

Q2−60 Q2−70 Q2−80 Q2−90 Q2−00

−5

0

5

Avg Hours

Q2−60 Q2−70 Q2−80 Q2−90 Q2−00

−10

−5

0

Real Wage

Q2−60 Q2−70 Q2−80 Q2−90 Q2−00

−5

0

5

Consumption

Q2−60 Q2−70 Q2−80 Q2−90 Q2−00

−20

−10

0

10

Investment

Q2−60 Q2−70 Q2−80 Q2−90 Q2−00

−10

0

10

20

Velocity

Figure 7: Historical decomposition − neutral technology shocks only

Q2−60 Q2−70 Q2−80 Q2−90 Q2−00−4

−2

0

2

4

6

8

Price of Inv.

Q2−60 Q2−70 Q2−80 Q2−90 Q2−00

−5

0

5

Output

Q2−60 Q2−70 Q2−80 Q2−90 Q2−00

0

20

40

60

MZM Growth

Q2−60 Q2−70 Q2−80 Q2−90 Q2−00−4

−2

0

2

4

6Inflation

Q2−60 Q2−70 Q2−80 Q2−90 Q2−00

−0.020

0.020.040.060.08

Fed Funds

Q2−60 Q2−70 Q2−80 Q2−90 Q2−00

−10

−5

0

5

Capacity Util

Q2−60 Q2−70 Q2−80 Q2−90 Q2−00

−5

0

5

Avg Hours

Q2−60 Q2−70 Q2−80 Q2−90 Q2−00

−10

−5

0

Real Wage

Q2−60 Q2−70 Q2−80 Q2−90 Q2−00

−5

0

5

Consumption

Q2−60 Q2−70 Q2−80 Q2−90 Q2−00

−20

−10

0

10

Investment

Q2−60 Q2−70 Q2−80 Q2−90 Q2−00

−10

0

10

20

Velocity

Figure 8: Historical decomposition − embodied technology shocks only

Q2−60 Q2−70 Q2−80 Q2−90 Q2−00−4

−2

0

2

4

6

8

Price of Inv.

Q2−60 Q2−70 Q2−80 Q2−90 Q2−00

−5

0

5

Output

Q2−60 Q2−70 Q2−80 Q2−90 Q2−00

0

20

40

60

MZM Growth

Q2−60 Q2−70 Q2−80 Q2−90 Q2−00−4

−2

0

2

4

6Inflation

Q2−60 Q2−70 Q2−80 Q2−90 Q2−00−0.04−0.02

00.020.040.060.08

Fed Funds

Q2−60 Q2−70 Q2−80 Q2−90 Q2−00

−10

−5

0

5

Capacity Util

Q2−60 Q2−70 Q2−80 Q2−90 Q2−00

−5

0

5

Avg Hours

Q2−60 Q2−70 Q2−80 Q2−90 Q2−00

−10

−5

0

Real Wage

Q2−60 Q2−70 Q2−80 Q2−90 Q2−00

−5

0

5

Consumption

Q2−60 Q2−70 Q2−80 Q2−90 Q2−00

−20

−10

0

10

Investment

Q2−60 Q2−70 Q2−80 Q2−90 Q2−00

−10

0

10

20

Velocity

Figure 9: Historical decomposition − monetary policy and technology shocks

Q2−60 Q2−70 Q2−80 Q2−90 Q2−00−4

−2

0

2

4

6

8

Price of Inv.

Conclusion from VAR Analysis

• Our Estimates Suggest that the Three Identified Shocks Account for ASubstantial Fraction (Around 50%) of Business Cylcle Variation.

• We have a set of Estimates of How Economy Responds to Three Types ofShocks

• Will use these to Estimate a DSGE Model.

59