The Role of Money: Empirical Evidence Money in the Short-Run

Monetary Theory University of Bern

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Money in the Short–Run

• Mostly how Central bankers view their role: Acting to stabilize the business cycle. • How does monetary policy affect the business cycle? • From simple correlation analysis to causality.

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Correlation Analysis

What are Business Cycles? • Lucas’ definition: Recurrent fluctuations of macroeconomic aggregates about trend • Various definitions of the trend: Here the Hodrick Prescott trend min t

{xTτ }τ =1

subject to

t−1 ∑ ((

t ∑ (

xτ − xTτ

)2

τ =1

) ( ))2 xTτ +1 − xTτ − xTτ − xTτ −1 ⩽c

τ =2

• Use time series and time series analysis • Start with correlation analysis (simple and informative) 3/62

Back to our business!

• Output: real Gross Domestic Product • Prices • GDP deflator • Consumer Price Index

• Interest rates • Federal fund rates • Treasury bill • 1 and 10 years constant maturity government bonds

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Back to our business!

• Monetary Aggregates • MB: monetary base (Total reserves held by banking system + currency in the hands of the public) • M1: Currency held by non banks public+traveler checks+demand deposits+other checkable deposits • M2: M1+saving accounts and small denomination time deposits + balances in retail money market mutual funds

• Sample period 1960Q1–2007Q4. • HP–filtered data. • Compute simple correlations

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Money and Output: Dynamic Correlation Analysis

• Correlation analysis hp corr(yhp t , mt+j ) with j = −8, . . . , 8

• Correlogram peaks for j < 0: Money is a leading indicator of output conditions • Correlogram peaks for j > 0: Output is a leading indicator of monetary developments

• NOT Causal

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Money and Output: Dynamic Correlation Analysis 1.0

M1 M2 M Base

0.5

0.0

0.5

1.0

8

6

4

2

0 k

2

4

6

8

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Money and Output: Dynamic Correlation Analysis

• Monetary base is positively correlated with output at all leads and lags • M1 and M2 are positively correlated at lags but negatively at leads. • Larger correlation for M2 as endogenous. • High GDP (relative to HP trend) is preceded by relatively high money, and followed by low values. =⇒ Money leads Output • Consistent with Friedman and Schwartz (1963): Monetary History of the United States

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Interest Rates and Output: Dynamic Correlation Analysis 1.0

Fed Fund Rate 3 Months 1 Year 10 Years

0.5

0.0

0.5

1.0

8

6

4

2

0 k

2

4

6

8

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Interest Rates and Output: Dynamic Correlation Analysis

• Negatively correlated at lags, positively correlated at leads. • Same pattern for short and long run rates, but weaker for LR rates. • High GDP (relative to HP trend) is preceded by relatively low interest rates, and followed by high ones. • Consistent with a liquidity effect.

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Interest Rates and Output: The Liquidity Effect i

Ms0

Ms1

i⋆0 ∆i < 0

i⋆1 ∆M > 0

Md (i)

M

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Prices and Output: Dynamic Correlation Analysis 1.0

GDP Deflator CPI

0.5

0.0

0.5

1.0

8

6

4

2

0 k

2

4

6

8

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Prices and Output: Dynamic Correlation Analysis

• Negatively correlated at lags, positively correlated at leads. • Same pattern for GDP deflator and CPI. • High GDP (relative to HP trend) is preceded by relatively low prices, and followed (much later) by high prices. • Inconsistent with correlation analysis of money! • How to reconcile the facts?

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Prices and Output: Dynamic Correlation Analysis

• A story for the impact correlation: Flexible prices =⇒ Supply shocks matter! (Kydland and Prescott, 1980) • Does not explain the negative correlation at lags • Illustrates the caveat of the approach: • Descriptive statistics • No causal explanation (despite the timing) • Needed: a more structured approach

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Towards a Causal Link

Estimating the effects of money

• Goes back to Friedman and Schwartz 1963: Monetary History of the United States • 100 years of US data • Finding: • Faster money growth is followed by output above trend; • slowdowns in money growth is followed by decline in output

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Money and Output: Is there a link?

8 6 4 2 0 2 4 6 1960

M1 M2 GDP

1970

1980

1990

2000

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Money and Output: 1960–1982

4 3 2 1 0 1 2 3 4 5 1960

M1 M2 GDP

1965

1970

1975

1980

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Money and Output: 1982–2007

8 6 4 2 0 2 4 6

M1 M2 GDP

1985

1990

1995

2000

2005

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Money and Output: Is there a link?

• Strong link between monetary aggregate and output in the 60’s, 70’s and early 80’s • Less clear link after 1982 (ex: 2000 boom, 2001 recession) • Graphical appraisal is not sufficient • Previous correlation analysis indicated a timing that resembles a causal interpretation, but IT IS NOT! • Let’s go econometrics!

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Money and Output: The Saint–Louis equation • Friedman and Meiselman (1963) ynt = c +

pa ∑ i=0

αi at−i +

pm ∑

βi mt−i +

i=0

px ∑

ζi xt−i + ut

i=0

where • • • •

ynt : Nominal output at : Autonomous expenditures mt : Monetary Aggregate xt : Over explanatory variables

• Main results: αi = 0 cannot be rejected, while βi are statistically significant • Use of this model promoted at Saint–Louis Fed. • Does not split the impact of money between Price and real output. 20/62

Money and Output: The Saint–Louis equation

• Linearly detrended US Data: 1960Q1–2007Q4 • Autonomous expenditures: GDP-C (In line with Keynesian–cross) • Money: M1, M2 • Others: Federal funds rate • 4 lags • Wald test for significance of M Agg.

Stat.

p–value

M1 M2

120.73 166.55

0 0

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Money and Output: The Saint–Louis equation M1 0.4

Data St-Louis Eq. w/o M St-Louis Eq.

0.3 0.2 0.1 0.0 0.1 0.2 0.3 1960

1970

1980

1990

2000

2010 22/62

Money and Output: The Saint–Louis equation M2 0.4

Data St-Louis Eq. w/o M St-Louis Eq.

0.3 0.2 0.1 0.0 0.1 0.2 0.3 1960

1970

1980

1990

2000

2010 23/62

Money and Output: The Saint–Louis equation: Endogeneity

• Looks awesome! • Is it as good as it seems? • Monetary policy is likely to be endogenous • If M reacts to Y: back to the Chicken and Egg problem! • More importantly: misspecification! • Creates problem to detect an effect of money!

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Money and Output: Causal relationship

• Sims (1972) proposed to estimate ynt = c +

pa ∑ i=1

αi at−i +

pm ∑ i=1

βi mt−i +

px ∑

ζi xt−i + ut

i=1

• Advantages • money does not appear contemporaneously =⇒ solves endogeneity • Allows to test for Granger causality

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Money and Output: Granger causality

• A variable x is said to Granger cause a variable y if and only if lagged values of x have marginal predictive power in predicting y • Amount to a simple Wald test in the preceding regression • Money Granger causes output if the null H0 : βi = 0 ∀i = 1, . . . , pm is rejected.

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Money and Output: Granger causality

• Sims’ original specification reduces to ynt = c +

pm ∑ i=1

βi mt−i +

px ∑

ζi ynt−i + ut

i=1

• Monetary base and M1 are found to Granger cause output. • The causal link is established! • Sims (1980): weaker evidence if interest rates are introduced in the equation • Eichenbaum and Singleton (1986): weaker evidence if variables are first–differenced. • Stock and Watson (1989) systematic treatment of the trend (cointegration): money Granger causes output even if prices and interest rates are introduced.

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The VAR Approach to Money

The VAR approach

• Once you have one dynamic equation, it is natural to extend it to a system of dynamic equations • This is the Vector AutoRegression (VAR) approach Xt =

p ∑

Ai Xt−i + ut also noted A(L)Xt = ut

i=1

where Li Xt = Xt−i . Xt is an (n × 1) vector, Ai are (n × n) matrices of coefficients. E(u) = 0 and E(uu′ ) = Σ. • a VAR featuring p lags is denoted VAR(p).

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The VAR approach

• Example a bi–dimensional VAR(2) featuring output, yt , and money, mt ( ) ( )( ) ( )( ) ( ) a211 a212 u1,t yt a111 a112 yt−1 yt−2 =C+ + + u2,t a121 a122 a221 a222 mt−1 mt−2 mt • Estimate each equation by OLS b111 yt−1 + a b112 mt−1 + a b211 yt−2 + a b212 mt−2 + u b1,t yt = b c1 + a b121 yt−1 + a b122 mt−1 + a b221 yt−2 + a b222 mt−2 + u b2,t mt = b c2 + a

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The VAR approach

• Looks like the equation we estimated for causality analysis! • What is the gain? • Full modeling of all variables! • Totally agnostic approach to the data • So what? • Enables us to recover “structural” shocks (note the quotes!) • In particular monetary policy shocks. • Will not exhaust the topic (see Christiano, Eichenbaum and Evans for a (big) survey)

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The VAR approach: Impulse Response Functions

• What does this mean? • Can study the effects of a particular “structural shock” on the variables (output,…) • Assume there is no shock prior to some date t0 . • In t0 there is a shock, and no shocks after t0 . • What will it imply for the dynamics of variables? • Compute the expected effects of the shock

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The VAR approach: Impulse Response Functions

• AR(1) example: xt = ρxt−1 + εt • Assume xt = εt = 0 for all t < t0 . • In t0 , εt raises by 1% =⇒ xt0 = 0.01 • The expected value of xt0 +1 as of time t0 , Et0 xt0 +1 is xt0 +1 = ρxt0 = 0.01ρ • The expected value of xt0 +2 as of time t0 , Et0 xt0 +2 is Et0 xt0 +2 = ρEt0 xt0 +1 = ρ2 xt0 = 0.01ρ2 • so Et0 xt0 +i = 0.01ρi

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The VAR approach: Impulse Response Functions εt ,xt

t0 Dynamics of εt

time Dynamics of xt

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The VAR approach: Identification of Shocks

• Extend it to the VAR! • Problem: Which shock? ui,t ? • Residuals are usually correlated • Assumption: Residuals are combinations of other independent shocks that can be given a structural interpretation ui,t =

n ∑

sij εj,t ⇐⇒ ut = Sεt

j=1

where E(εt ) = 0 and E(εt ε′t ) = D where D is diagonal ∑∞ • Want to obtain Xt = C(L)εt = i=0 Ci εt−i

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The VAR approach: Identification of Shocks • Example (go back to VAR in (yt , mt )): u1,t = s11 εyt + s12 εm t u2,t = s21 εyt + s22 εm t

• Problem: how to recover the εs and S? • We know that

E(uu′ ) = Σ E(εε′ ) = D ⇐⇒ SDS′ = Σ u = Sε

• Identification problems 35/62

The VAR approach: Identification of Shocks

• The VAR has n variables =⇒ n residuals. • This implies n(n + 1)/2 parameters we can use in Σ. • We are looking for n2 parameters in S and n in D: n(n + 1) • Under-identified!! • Need to place assumptions • Without loss of generality: D = I (just a rescaling of S) • we still have n2 parameters in S and n(n + 1)/2 informations • Requires n2 − n(n + 1)/2 = n(n − 1)/2 assumptions.

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The Recursive Assumption

• Initiated by Sims (1972, 1980) • Amounts to impose some restrictions on the short–run behavior of the economy • Shocks are identified based on whether or not they exert an immediate effect on some variables

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The Recursive Assumption

• Recall (X is centered) Xt = A1 Xt−1 + . . . + Ap Xt−p + Sεt • Assume that all Xs are at their mean (0) and there’s a shock in t0 Xt0 = Sεt0 • The coefficient sij therefore measures the impact effect of shock εj on variable xi . • By imposing that n(n-1)/2 sij are 0 we solve identification • The recursive assumption corresponds to this situation and assumes that the S matrix is lower diagonal (so the recursivity)

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The Recursive Assumption

• S has the structure



s11 s  21   s31   ..  .

0 s22 s32 .. .

0 0 s33 .. .

... ... ... .. .

0 0 0 .. .

sn1

sn2

sn3

...

snn

       

• n(n + 1)/2 non zero terms, and n(n + 1)/2 terms in Σ • Technically: Choleski decomposition of Σ: SS′ = Σ

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The Recursive Assumption • Consider a VAR in (Y, P, M, i) (in this order) • With the recursive assumption, we have    Yt s11 0  P  s  t   21 s22  = Mt  s31 s32 it s41 s42

0 0 s33 s43

  0 ε1t   0  ε2t     3   0 εt  s44 ε4t

• Output only responds to ε1 =⇒ ε1 is the sole shock with an impact effect on Yt (IS). • Prices respond to ε1 and ε2 =⇒ ε2 is the price shock and ε2 ⊥ ε1 . • And so on... • If M is the monetary policy instrument: M reacts to shocks to Y and P, but not to i. • Y and P are not affected by the money shock, but i is. 40/62

The Recursive Assumption • Still this does not tell us what the monetary shock is! • What is the instrument of monetary policy? • Money aggregates or interest rates? • Institutional answer: over the last 35 years, the interest rate has been the instrument • Any unforecasted shock to i is a monetary shock (Bernanke and Blinder (1992), Bernanke and Mihov (1998)) • It is usually found easier to control i than M! • Shocks to M1 or M2 mostly reflect money demand shocks (but not shock to NBR) • Most of the literature considers that a monetary shock is a shock to i! 41/62

The Recursive Assumption

• Christiano, Eichenbaum and Evans (2000) • Key paper in the literature! • Survey of most studies and own contribution • VAR featuring Output, GDP deflator, Commodity price, Federal fund rate, non–borrowed reserves, total reserves, M1 (in that order) • Monetary shock: Shock on i • Assumption: Monetary policy responds to changes in output and prices, output and prices respond to monetary policy with a lag. • Extend CEE to 1960Q1–2004Q4 (need commodity price), 4 lags, level specification.

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The Recursive Assumption Expansionary Monetary policy Shock (Decrease in FFR) Output

0.008 0.006 0.004 0.002 0.000 2

4

6

8

10

12

Non-Borrowed Reserves 0.020 0.015 0.010 0.005 0.000 0.005 0.010 0.015

2

4

6

8

10

12

0.005 0.004 0.003 0.002 0.001 0.000 0.001 0.002 0.020 0.015 0.010 0.005 0.000 0.005 0.010 0.015

Prices

2

4

6

8

10

12

Total Reserves

2

4

6

8

10

12

0.4 0.2 0.0 0.2 0.4 0.6 0.8 1.0 0.010 0.008 0.006 0.004 0.002 0.000 0.002 0.004

Interest Rate

2

4

6

8

10

12

10

12

Money (M1)

2

4

6

8

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The Recursive Assumption

1. Output responds positively with a hump–shaped pattern (peak around 10 quarters) 2. Prices respond very little in the short–run (slight non significant decrease: price puzzle) 3. Monetary aggregates increase 4. Long lasting effect of the shock on the interest rate 5. But Monetary policy shock contributes little to output volatility Quarter Contribution

1

4

8

12

0%

5%

15%

22%

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The Recursive Assumption Expansionary Monetary policy Shock (Increase in NBR) 0.004 0.003 0.002 0.001 0.000 0.001 0.002 0.003 0.004 0.5 0.4 0.3 0.2 0.1 0.0 0.1 0.2 0.3 0.4

Output

2

4

6

8

10

12

Interest Rate

2

4

6

8

10

12

0.007 0.006 0.005 0.004 0.003 0.002 0.001 0.000 0.001 0.05 0.04 0.03 0.02 0.01 0.00 0.01

Prices

2

4

6

8

10

12

Total Reserves

2

4

6

8

10

12

0.05 0.04 0.03 0.02 0.01 0.00 0.01 0.014 0.012 0.010 0.008 0.006 0.004 0.002 0.000 0.002 0.004

Non-Borrowed Reserves

2

4

6

8

10

12

10

12

Money (M1)

2

4

6

8

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The Recursive Assumption

1. Output responds positively with a hump–shaped pattern (peak around 4–6 quarters) 2. Prices respond very little in the short–run (slight non significant decrease: price puzzle) 3. Monetary aggregates increase 4. Less long lasting effect of the shock on the interest rate =⇒ Same qualitative results, quantitative differences

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The Price Puzzle

1. Variables and their ordering are not innocuous: It conditions a lot the identification 2. Move the FFR up, such that the order is (Y, P, FFR, PCOM, NBR, TR, M1) 3. Get rid off commodity prices (PCOM)

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The Price Puzzle Expansionary Monetary policy Shock 0.006 0.005 0.004 0.003 0.002 0.001 0.000 0.001

Output

2

4

6

Base CEE FFR up No Pcomm 8 10 12

Non-Borrowed Reserves 0.016 0.014 0.012 0.010 0.008 0.006 0.004 0.002

2

4

6

8

10

12

0.0020 0.0015 0.0010 0.0005 0.0000 0.0005 0.0010 0.0015 0.0020 0.009 0.008 0.007 0.006 0.005 0.004 0.003 0.002 0.001

Prices

2

4

6

8

10

12

Total Reserves

2

4

6

8

10

12

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.0065 0.0060 0.0055 0.0050 0.0045 0.0040 0.0035 0.0030 0.0025 0.0020

Interest Rate

2

4

6

8

10

12

10

12

Money (M1)

2

4

6

8

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The Price Puzzle

• Mostly the same results, but prices decrease following the money expansion • Price puzzle • Explanation: the identification does not account for the full information set available to the FED • Assume the FED raise the interest rate when it forecasts higher inflation in the future • If the FED cannot offset the factors that led to forecast higher inflation, or acts too late to prevent it from rising, then the increase in the fund rate will be followed by an increase in the prices. • Adding the commodity price (because it is sensitive to inflation forecasts) solves the problem because it adds the required information to account for the FED’s behavior.

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Taking Advantage of Money Neutrality

1. Idea: Money (NBR) should be neutral in the Long–run 2. The monetary shock does not exert an effect on real variables in the long–run 3. Based on Blanchard and Quah (1989) A(L)Xt = ut ⇐⇒ Xt = C(L)ut = C(L)Sεt The LR is given by B = C(1)S, the restriction is B12 = 0. 4. Used by Judd and Trehan (1989), Hutchinson and Walsh (1992), or Galí (1992) (in combination). 5. Not so good assumption (Faust and Leeper (1997)): In this case, the monetary policy shock can be confounded with money demand shocks!

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Taking Advantage of Money Neutrality Expansionary Monetary policy Shock (Increase in NBR) 0.010 0.008 0.006 0.004 0.002 0.000 0.002 0.004

Output

2

4

6

8

10

12

0.010 0.008 0.006 0.004 0.002 0.000 0.002 0.004

Non-Borrowed Reserves 0.06

0.06

0.05

0.05

0.04

0.04

0.03

0.03

0.02

0.02

0.01

2

4

6

8

10

12

0.01

Prices

2

4

6

8

10

12

Total Reserves

2

4

6

8

10

12

0.6 0.4 0.2 0.0 0.2 0.4 0.6 0.035 0.030 0.025 0.020 0.015 0.010 0.005 0.000

Interest Rate

2

4

6

8

10

12

10

12

Money (M1)

2

4

6

8

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Sign Restrictions

1. Idea: Impose sign restrictions on the behavior of key variables 2. Uhlig (2004) assumes that a “contractionary” monetary policy shock does not lead to • an increase in prices; • increase in non-borrowed reserves; • decreases in the federal funds rate

for a certain period following a shock. 3. Methodology: Draw the matrix S, and only keep the IRFs that satisfy the restrictions. 4. Finding: Money neutrality is not inconsistent with the data: output does not respond much.

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Sign Restrictions

1. Replicate Uhlig, using Quaterly data (He uses monthly) 2. Same variables as in previous VARs 3. Impose that following an “expansionary” monetary policy shock • prices (GDP deflator and Commodity prices) do not decrease; • non-borrowed reserves do not decrease; • the federal funds rate does not increase

for 2 quarters (he uses 6 months)

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Sign Restrictions Expansionary Monetary policy Shock 0.008 0.006 0.004 0.002 0.000 0.002 0.004 0.006 0.008

Output

2

4

6

8

10

12

Non-Borrowed Reserves 0.04 0.03 0.02 0.01 0.00 0.01 0.02

2

4

6

8

10

0.012 0.010 0.008 0.006 0.004 0.002 0.000

Prices

2

0.03

12

4

6

8

10

12

Total Reserves

0.6 0.4 0.2 0.0 0.2 0.4 0.6 0.8

0.010

0.01

0.005

0.00

0.000

0.01

0.005 2

4

6

8

2

10

12

0.010

4

6

8

10

12

10

12

Money (M1)

0.015

0.02

0.02

Interest Rate

2

4

6

8

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Sign Restrictions

• By construction, no price puzzle • Prices respond very little in the short–run • interest rate decreases (by construction) with persistence • BUT Output is basically left unaffected! • Goes back to small contribution of monetary policy shocks found in CEE!

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The VAR Approach: Summary

• Following a positive monetary policy shock 1. Monetary transmission mechanism: • Prices respond very little and increase sluggishly • Output responds positively with a hump–shaped pattern

2. Liquidity Effect: • the nominal interest rate decreases and goes back steadily to its average level (persistence) • while monetary aggregates increase

• Small contribution to output volatility of monetary policy shocks

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The VAR Approach: Concerns and Criticisms • Often do not conform with economists’ intuition! • Information problems: • Mis–specification problems: results are sensitive to the variables that are taken into account (ex: price puzzle) • The equation for the monetary instrument is a type of monetary policy rule: only backward looking! (can be mitigated) • Central bankers deal with real–time data, not last releases (revision problems)

• Identification problems: • • • •

Ordering matters a lot in recursive systems Are we so sure we recover policy shocks? (ex: LR identification) Anticipated vs unanticipated shocks ignored (matters a lot!) Shocks bear little resemblance with historical records of policy actions: what are they?

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The VAR Approach: Concerns and Criticisms Monetary policy Shocks vs contractionary monetary policy

6 5 4 3 2 1 0 1 2 3 1960 1965 1970 1975 1980 1985 1990 1995 2000 Quarters Note: Compare the monetary policy shock from CEE and contractionary monetary policy episodes as identified by Romer and Romer. A green line indicates that the CEE monetary policy shock is indeed contractionary, a red line indicates otherwise 58/62

The VAR Approach: Concerns and Criticisms

• BUT! Everything depends on what is wanted • If one wants to study the effects of a particular shock in a particular recession, VAR cannot be used (if we refer to previous criticisms) • If one just wants to understand how shocks propagated in the economy, this is fine!

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Alternative Approaches: Alternative Measures • Measures of monetary policy: Romer and Romer (1989), Boschen and Mills (1991) • Romer and Romer: use the FED’s record of policy actions and identify date at which FED conducted a contractionary monetary policy (inflation concern). Add this “dummy” variable in a VAR and study the response of the VAR to it. • Hoover and Perez (1994): Romer and romer essentially pick up oil price shocks! • Boschen and Mills (1991): build an index based on readings of the FOMC minutes • +2: strong emphasis on inflation reduction • -2: strong emphasis on promoting real growth

• Main finding: expansionary monetary policy is followed by drops in Federal fund rate, which represents well monetary policy.

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Alternative Approaches: Structural Econometric

• Estimate fully fledged models • Fully specify a theoretical model, and estimate it with various techniques. • Study the effects of monetary policy shocks in these models. • But we need to know what these models are. • This is what we will do now!

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What we will do from now on!

• Define some tools • Flexible prices case • Information Problems • Sticky prices • Monetary policy

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