econ 4325 Œmonetary policy and business fluctuations · econ 4325 Œmonetary policy and business...

ECON 4325 Monetary Policy and BusinessFluctuations

Tommy Sveen

Norges Bank

January 21, 2010

TS (NB) ECON 4325 January 21, 2010 1 / 24

IntroductionSyllabus

21/1: Introduction and empirical evidence (Sveen)Readings: Galí, ch. 1, Christiano, Eichenbaum and Evans (2005)

28/1: A simple RBC model, log-linearization (Sveen)Readings: Galí, ch. 2

4/2: The basic new Keynesian model (Sveen)Readings: Galí, ch. 3

11/2: The basic new Keynesian model (Sveen)

18/2: Interest rate rules (Sveen)Readings: Galí, ch. 4

4/3: The credit channel of monetary policy (Alstadheim)Readings: Walsh, ch. 7, Bernanke, Gertler, and Gilchrist (1999)

11/3: Monetary policy and nancial crises (Alstadheim)Readings: Borio and Disyatat (2009)


IntroductionSyllabus

18/3: Time-inconsistency (Røisland)Readings: Lecture notes

25/3: Optimal policy in the New Keynesian model (Røisland)Readings: Galí, ch. 5.

8/4: Monetary policy in Norway (Røisland)Readings: Holmsen, Qvigstad, Røisland and Solberg-Johansen (2008),Faust and Henderson (2004), Woodford (2005)

15/4: Sticky wages in the new Keynesian model (Holden)Readings: Gali, ch. 6

22/4: Welfare costs of business uctuations (Holden)Readings: Gali, Gertler, López-Salido; Gali

30/4: The nancial crisis (Holden)Readings: Diamond; Brunnermeier


IntroductionWhat is Monetary Economics?

Monetary Economics (ME) analyzes the relationship between real variables such as real GDP, real interest rates, employment or unemployment, andreal exchange rate and nominal variables such as rate of ination,nominal interest rates, nominal exchange rate, and money supply:

Relationship between di¤erent nominal variables.

Relationship between di¤erent real variables in monetary models.


IntroductionBackground

IS-LM and AD-AS models (60-70s):

Ad hoc static models. Completely xed prices.AD-AS adding a supply side: focus still on price level.ME concerned with ination.Central bank controls money supply.


IntroductionBackground

Flexible-price models:

RBC-models: new-classical models with exible prices and wages,micro-founded, productivity shocks important.Monetary models: Lucassupply curve, LPC-models, MIU-models.Generally small e¤ects from monetary disturbances.

New-Keynesian models: Most models have classical long-runproperties, microfoundation, monopolistic competition in product andfactor markets, nominal rigidities.


Empirical EvidenceSome Stylized Facts Long-Run Correlations

Correlation between the growth rate of money supply and ination isalmost 1 (varying between 0.92-0.96).

If money growth exogenous evidence that money growth causesination (one-for-one).The reverse causality equally consistent with high correlation the CBadjusts money growth to the rate of ination.Theoretical models should be consistent with this nding.

No correlation between ination and GDP growth, but this result isless robust:

Slightly positive correlation at low levels of ination.Negative correlation for high levels of ination.


Empirical EvidenceSome Stylized Facts Business Cycle


Empirical EvidenceSome Stylized Facts Business Cycle

Common features

Standard deviation of output 1.5-1.9 (except FRA).

Consumption is (often) smoother than output, while investments are2-3 times as volatile as output.

Employment smoother than output, but some di¤erences acrosscountries.

Persistence uctuations in output.

Employment, consumption and investment are pro-cyclical.


Empirical EvidenceSome Stylized Facts Short-run relationships

Have monetary policy disturbances played a role in economicuctuations?

Are the predictions from theoretical models consistent with empiricalevidence?

Friedman and Schwartz

Faster money growth tends to be followed by increases in outputabove trend slower money growth by declines in output.

Variations in money growth cause with long and variable lags variations in real activity.


Empirical EvidenceVector Autoregressions (VARs)

Proposed by Christopher Sims in 1970s, 1980s (see, e.g.,Macroeconomics and Reality, Econometrica 48, 1-48.).

Useful way to organize data.

We want to answer the following question: "How does the economyrespond to a particular shock?"

The answer can be very useful for discriminating between models, andfor estimating the parameters of a given model.VARs can not actually address such a question! We need StructuralVARs.



The Basic Set-Up

Let Yt be a N 1 vector of macroeconomic variables. A vectorautoregression (VAR) is:

Yt = B1Yt1 + B2Yt2 + ...+ BpYtp + ut ,

where the B 0s are parameters and ut is a vector of shocks. Moreoverwe have Eutu0t = Σu .It is easy to get estimates for the B 0s, the u0s, and Σu , but we areinterested in impulse response functions to fundamental shocks:

ut = Cet ,

Eete 0t = Σe = I ,CC 0 = Σu .



The structural VAR:

Yt = B1Yt1 + B2Yt2 + ...+ BpYtp + Cet .

The impulse response to the i th shock:

Yt Et1Yt = Ciei ,t ,

EtYt+1 Et1Yt+1 = B1Ciei ,t ,

...

To compute impulse responses we need B1, ...,Bp , and C .



Identication

There are n2 di¤erent terms in C , while there are only n (n+ 1) /2independent equations in CC 0 = Σu .Identication problem: not enough restrictions to pin down all theparameters in C .

We need additional n (n 1) /2 identifying restrictions.



Example

Consider a bivariate VAR in xt and πt with two lags:

xt = B1xxxt1 + B1xππt1 + B2xxxt2 + B

2xππt2 + ux ,t ,

πt = B1πxxt1 + B1πππt1 + B2πxxt2 + B

2πππt2 + uπ,t ,

and it is assumed that

ux ,t = Cxx ex ,t + Cxπeπ,t ,

uπ,t = Cπx ex ,t + Cππeπ,t ,

From the OLS estimation we get

Σu =

σ2ux σux ,uπ

σux ,uπ σ2uπ

.

We need one additional restriction.TS (NB) ECON 4325 January 21, 2010 15 / 24


Identication

Three basic approaches to solve the identication problem:

(i) Contemporaneous restrictions:

No short-run e¤ects from policy shocks to some variable(s).

E.g. monetary policy shocks do not a¤ect output within the sameperiod.

No short-run e¤ect from shocks to the policy instrument.

Monetary policy does not react within the period to certain shocksor variables.



Identication

(ii) Long-run restrictions:

Monetary neutrality.

Monetary policy disturbances have no long-run e¤ect on real variables(output, unemployment, real exchange rate, etc).Demand shocks no long-run e¤ects on output and unemployment.

(iii) Sign restrictions:

Positive demand shocks increase ination, while positive supply shocksdecrease ination.



Christiano, Eichenbaum and Evans (2005)

Use short-run restrictions to identify a monetary policy rule and thecorresponding shock to policy:

Rt = f (Ωt ) + εt ,

where Rt is the federal funds rate, f is a linear function of theinformation set Ωt , and εt is the monetary policy shock.

Let the vector of variables be Yt = [Y1,t ,Rt ,Y2,t ]0.

Variables in Y1,t (GDP, consumption, GDP deator, investments, realwage, labor productivity) do not react to monetary policy shocks.Variables in Y2,t (real prots and growth in M2) do not belong to Ωt .


5 10 15 20-0.4

-0.2

0

0.2

0.4inflation (APR)

5 10 15 20-0.3

-0.2

-0.1

0

0.1

0.2real wage

5 10 15 20-1

-0.5

0

0.5interest rate (APR)

5 10 15 20-0.5

0

0.5

1output

5 10 15 20-2

-1

0

1

2investment

5 10 15 20-0.4

-0.2

0

0.2

0.4consumption

5 10 15 20-4

-2

0

2

4profits

5 10 15 20-4

-2

0

2

4price of capital

5 10 15 20-0.4

-0.2

0

0.2

0.4productivity

Figure 1: Model and Data Impulse Responses

5 10 15 20-0.2

-0.1

0

0.1

0.2

0.3dm


Main Results

Persistent e¤ects on real variables.

Ination is slow to react.

Hump-shaped responses of real variables.

Walsh (2003): We cannot design policy without a theory of howmoney or monetary policy in general a¤ects the economy.


Log-Linearizing

Useful method to approximate and solve dynamic models.

Let xt denote the log-deviation of a variable Xt from its steady stateX :

xt = logXtX

.

Hence, we look at percentage deviations of the variable around itssteady state value:

xt Xt XX

.


Log-LinearizingA Simple Method

If Xt = F (Yt ,Zt ), how do we nd the log-linear approximation of Xt?

Let us consider a simple method:

Xt = XXtX

= Xe log(Xt/X ) = Xext

Take a rst-order Taylor approximation:

Xext ' Xe0 + Xe0 (xt 0)' X (1+ xt ) .


Log-LinearizingA Simple Method

Rewrite the function Xt = F (Yt ,Zt ):

Xext = F (Yeyt ,Zezt )

Next, take a rst-order Taylor approximation:

X + Xxt ' FYe0,Ze0

+ FY

Ye0,Ze0

Ye0 (yt 0)

+FZYe0,Ze0

Ze0 (zt 0)

xt ' FY (Y ,Z )YX

yt +FZ (Y ,Z )Z

Xzt

' εx ,y yt + εx ,zzt ,

where εx ,y ∂F∂Y

YX is the steady state elasticity of X wrt Y .


Log-LinearizingExamples

Cobb-Douglas production function: Yt = K αt N

1αt . What is

log-linearized output?

Yt = AtK αt N

1αt ,

where Yt is output, At is the level of technology, Kt is the capitalstock, and Nt is labor. Parameter α is the capital share in production.

Rewriting gives:eyt = eat+αkt+(1α)nt ,

where we have used the steady state relationship.

Next, we take a rst-order Taylor approximation:

yt = at + αkt + (1 α) nt .


Log-LinearizingExamples

The aggregate resource constraint:

Yt = Ct + It ,

where Ct is consumption and It is investment.

Rewriting:

1 =CtYt+ItYt.

Taking a rst-order Taylor approximation of the di¤erent terms gives:

1 ' CY(1+ ct yt ) +

IY(1+ it yt )

yt =CYct +

IYit .


econ 4325 Œmonetary policy and business fluctuations · econ 4325 Œmonetary policy and business...

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