Monetary Policy and a Stock Market Boom-Bust Cycle Lawrence - - PowerPoint PPT Presentation

Monetary Policy and a Stock Market Boom-Bust Cycle

Lawrence Christiano, Cosmin Ilut, Roberto Motto and Roberto Motto, and Massimo Rostagno

Asset markets have been volatile Should monetary policy react to the volatility? Is monetary policy somehow responsible for the volatility? Suppose (following Beaudry-Portier) asset price booms triggered by expectation of improved future productivity, which are not realized. A standard monetary DSGE model implies:

inflation targeting as implemented in practice inflation targeting as implemented in practice + sticky wages = suboptimal volatility hard to understand boom-busts without monetary policy

Our finding contradicts conventional wisdom: inflation stabilization also stabilizes asset markets and real economy (Bernanke-Gertler) Conventional wisdom assumes inflation rising in stock market booms market booms

Inflation and Stock Price

Inflation and Stock Price (real terms) in Interwar Period

5 1 1 5 250 350 450

Inflation and Stock Price (real terms) in 1950s to 1970s

6 8 1 1 2 800 1 200 1 600

• 1

5

• 1
• 5

1 9 2 3 1 9 2 4 1 9 2 5 1 9 2 5 1 9 2 6 1 9 2 7 1 9 2 8 1 9 2 8 1 9 2 9 1 9 3 1 9 3 1 1 9 3 1 1 9 3 2 1 9 3 3

• 1

50

• 50

50 1 50 2 4 6

1 9 5 3 1 9 5 5 1 9 5 7 1 9 5 9 1 9 6 1 1 9 6 3 1 9 6 5 1 9 6 7 1 9 6 9 1 9 7 1 1 9 7 3 1 9 7 5 1 9 7 7

400 800

Note: Inflation is computed as the year-on-year change in GNP Deflator. Stock Price is Dow Jones divided by GNP Deflator.

Inflation and Stock Price (real terms) in 1990s to 2005

Note: Inflation is computed as the year-on-year change in GDP Deflator. Stock Price is Dow Jones divided by GDP Deflator.

Inflation appears to be falling during

( )

2 3 4 5 8000 1 2000 1 6000

Inflation appears to be falling during the start-up of boom-bust episodes

1

1990 1991 1993 1994 1995 1996 1998 1999 2000 2001 2003 2004 2005

4000

Note: Inflation is computed as the year-on-year change in GDP Deflator. Stock Price is Dow J di id d b GDP D fl

Stock Price (right-hand scale) Inflation (percentage points, left-hand scale)

Jones divided by GDP Deflator.

‘Stock Market Boom-Bust Cycle’

Episode in which: p

• Stock prices, consumption, investment,
• utput employment rise sharply and then fall
• utput, employment rise sharply and then fall
• Inflation

– low during boom – tends to rise near end (Adalid-Detken, Bordo-Wheelock) )

Argument g

• We argue that it is difficult to account for

boom-bust with a non-monetary model. boom bust with a non monetary model.

– Even with ‘bells and whistles’ non-monetary Even with bells and whistles , non monetary model has a hard time accounting for duration and magnitude. – Non-monetary model has a hard time i f li l k i accounting for procyclical stock prices.

• Easy to account for in a monetized model.

Signal about future technology Signal about future technology

• Time series representation:

signal



Time series representation:

at  at−1  t  t−p at  log, technology

• If , then signal turns out to be false

tp  −t

• If , then signal turns out to be

correct

tp  0

correct.

RBC Model with Bells and Whistles

• Household preferences:



E0 ∑

t0

tlogCt − bCt−1  log1 − ht.

• Production function:

Yt  Kt

expatht1−

• Capital accumulation:

K 1 K 1 S It I

• Resource constraint

Kt1  1 − Kt  1 − S It It−1 It. Ct  It ≤ Yt

Simple RBC model

• No adjustment costs in investment:

S ≡ 0

• No habit persistence:

b  0

• Other parameters:

  0.36,   1.03−.25,  .02,   2.3.

• Signal of future improvement in technology

leads to:

– Fall in employment, investment – Rise in consumption Price of capital is constant – Price of capital is constant

• Terrible model of boom-bust cycle!

Adding bells and whistles

• Investment adjustment costs

S S′ 0 i St d St t S  S′  0 in Steady State S′′  5 in Steady State

• Habit persistence

b  0.75

• Now we have a better theory of the boom-

bust cycle bust cycle

Diagnosing the results

• Role of habit persistence: major

– Ensures that consumption rises in the boom

• Role of investment adjustment costs: major

– Ensures that investment rises in the boom – Adjustment costs in level of investment does not work work

Kt1  1 − Kt  S It Kt Kt, S′  0, S′′  0

• Puzzle: why does the theory imply a fall in the

stock market?

Some Capital Theory

• In a production economy, price of capital

(‘stock market’) satisfies two relations

– Usual present discounted value relation (‘demand id ’) side’) – Tobin’s q relation (‘supply side’) Tobin’s q relation especially useful for intuition – Tobin s q relation especially useful for intuition

• First we derive the present discounted value

First, we derive the present discounted value relation

• Then, Tobin’s q

• Lagrangian

∑ t Ct − bCt−11 − ht1−

1 −   t Ktztht1− − Ct − It   t 1 − Kt  1 − S It It−1 It − Kt1 

• Consumption first order condition

t  Ct − bCt−1−1 − ht1− − bCt1 − bCt−1 − ht11−.

• First order condition with respect to Kt1

  K −1 h 1− 1  t   t1Kt1−1zt1ht11−  t11 −  .

• Divide both sides of FONC by :

Kt1 t t    t1  Kt1−1zt1ht11−  t1  1 −  .

‘Ti t P i f C it l ’ (T bi ’ )

t  t Kt1 zt1ht1  t1 1  . K

• ‘Time t Price of Capital, ’ (Tobin’s q):

t

dUt dK

1

dCt Kt1 t t 

dKt1 dUt dCt

 dCt dKt1 ≡ Pk′,t.

• Rewrite FONC for :

Kt1  Pk′,t   t1 t Kt1−1zt1ht11−  Pk′,t11 −  .

• Repeating FONC for Kt1

epea g O C o

Pk′,t   t1 t Kt1−1zt1ht11−  Pk′,t11 −  .

t1

• Suppose households earn on bonds

t rt1

– Household FONC:

 1

• So

 t1 t  1 1  rt1 .

• So,

Pk′,t  1 1  rt1 Kt1−1zt1ht11−  Pk′,t11 −  , 1  rt1

• Repeating:

epea g

Pk′ t  1 Kt1−1zt1ht11−  Pk′ t 11 −  Pk′,t 1  rt1 Kt1 zt1ht1  Pk′,t11  ,

• Rental rate on capital under competition:
• So

rt1

k

 Kt1−1zt1ht11−

• So,

Pk′,t  1 1  rt1 Rt1

k

 Pk′,t11 − .

• Repeating,

P 1  k P 1 

• Recursive substitution yields usual present

Pk′,t  1 1  rt1 rt1

k

 Pk′,t11 − .

value relation:

1 1  Pk′,t  1 1  rt1 rt1

k

 1 −  1  rt1 Pk′,t1  1 r

1 k

 1 −  1 r

2 k

 1 −  Pk′

2

 1  rt1 rt1  1  rt1 1  rt2 rt2  1  rt2 Pk′,t2  1 1  rt1 rt1

k

 1 −  1  rt 11  rt 2 rt2

k

 1 −  1  rt1 1 −  1  rt2 Pk′,t2 1  rt1 1  rt11  rt2 1  rt1 1  rt2  ...

 i

 ∑

i1  j1

1 1  rtj 1 − i−1rti

k .

Tobin’s q (price of capital from q (p p supply side)

• Lagrangian FONC w.r.t I:

− t  t1 − S It I  − tS′ It I It I t  t1 S It−1  tS It−1 It−1  t1S′ It1 It It1 It

2

 0.

• Taking into account the definition of the

price of capital

t t

price of capital,

PK′ t  1 1 − 1 1 PK′ t1S′ It1 I It1 I

2

. PK ,t 1 − S

It It−1

− S′

It It−1 It It−1

1 1  rt1 PK ,t1S It It .

• Repeating,

It1/It  0 → this term is big

p g

PK′,t  1 1 − S

It It−1

− S′

It It−1 It It−1

1 − 1 1  rt1 PK′,t1S′ It1 It It1 It

2

.  Static Marginal Cost  Dynamic Part

• This clarifies why falls during boom

PK′,t

– Anticipated High Future Investment Implies there is an Extra Payoff to Current Investment. – Under Competition, This Extra Payoff Would Lead Sellers of Capital to Sell at a Lower Price Lead Sellers of Capital to Sell at a Lower Price.

A monetized model

• When we monetize the RBC model, get a

more promising model of the response to an ti i t d t h l h k anticipated technology shock

• Intuition is simple and can be explained in
• Intuition is simple, and can be explained in

the CGG model.

• An anticipated future technology shock in

principle drives up the real rate. Under t d d t li th t standard monetary policy, the monetary authority prevents the rise and thereby exacerbates the boom-bust in real variables, , and causes the stock market to boom too.

The standard New-Keynesian Model

at  at−1  t  t−p at  log, technology

p

rrt

∗  rr − 1 − at  t1−p (natural (Ramsey) rate)

rrt rr 1 at  t1−p (natural (Ramsey) rate)   E 

1  x

 (Calvo pricing equation) t  Ett1  xt − t (Calvo pricing equation)  E

∗

E (i t t l ti ) xt  −rt − Ett1 − rrt

∗  Etxt1 (intertemporal equation)

rt  Ett1  xxt (policy rule)

The standard New-Keynesian Model

at  at−1  t  t−p at  log, technology

p

rrt

∗  rr − 1 − at  t1−p (natural (Ramsey) rate)

rrt rr 1 at  t1−p (natural (Ramsey) rate)   E 

1  x

 (Calvo pricing equation) t  Ett1  xt − t (Calvo pricing equation)  E

∗

E (i t t l ti ) xt  −rt − Ett1 − rrt

∗  Etxt1 (intertemporal equation)

rt  Ett1  xxt (policy rule)

• Can we get a boom-bust out of this?

– Rise in output and employment, and weak inflation in boom

Response to (false) signal in period 0 that technology will jump 1% in period 1 Period 0 Periods 1 2 Period 0 Periods 1, 2, ... logAt 400  t

• 1

100  loght 0.7 100  logyt 0.7

• Can we get it in an empirically-based

  0.95,   1.5, x  0.5,   0.82

Can we get it in an empirically based model?

• Can we get a boom-bust out of this?

– Rise in output and employment, and weak inflation in boom

Response to (false) signal in period 0 that technology will jump 1% in period 1 Period 0 Periods 1 2 Period 0 Periods 1, 2, ... logAt 400  t

• 1

100  loght 0.7 100  logyt 0.7

• Can we get it in an empirically-based

  0.95,   1.5, x  0.5,   0.82

Can we get it in an empirically based model?

• Can we get a boom-bust out of this?

– Rise in output and employment, and weak inflation in boom

Response to (false) signal in period 0 that technology will jump 1% in period 1 Period 0 Periods 1 2 Period 0 Periods 1, 2, ... logAt 400  t

• 1

100  loght 0.7 100  logyt 0.7

• What happens in an empirically-

  0.95,   1.5, x  0.5,   0.82

What happens in an empirically constructed model?

Empirically-based model

• Features:

– Habit persistence in preferences – Investment adjustment costs in change of investment Calvo sticky wages and prices – Calvo sticky wages and prices

• Non-optimizers:

R b t t i f G tl T i i d l f Pit  Pi,t−1, Wj,t  zWj,t−1 – Robustness to version of Gertler-Trigari model of labor market.

• Estimation by standard Bayesian methods

Shocks and observables

• Six observables:

– output growth, – inflation, – hours worked, – investment growth, – consumption growth, – T-bill rate.

Sh k

• Shocks:

 preference

l2 Et

j ∑ l0

l  c,tl logCtl − bCtl−1 − L ltl,j

2

2 Kt1  1 − 0.02Kt  1 − S

marginal (in-) efficiency of investment

 i,t It It−1 It Y



1

Y

1  dj ss markup

 f,t

Yt  

0 Yjt

f,t dj

iid iid



iid

 at  at−1  t   t−4

4

  t−8

8

Some parameters

wage-stickiness parameter

 w  0.83,

price stickiness parameter

 f  0.77,

curvature on adjustment costs

 S′′  8.8 logRt

∗  log

ztarget  − 1  1.50Et t1 −

annualized target: 2.5%

target  0.12logYt/Ys logR 0 79logR  1 0 79logR∗  ump logRt  0.79logRt−1  1 − 0.79logRt  ut

p

Variance decompositions

Percent Variance in Row Variable due to Indicated Column Shock Technology shocks variable innovation 4 quarter advance 8 quarter advance c,t i,t f,t monetary policy ΔCt 3 25 38 12 8 10 5 ΔI 1 12 21 5 54 6 1 ΔIt 1 12 21 5 54 6 1 ΔYt 3 21 32 5 28 9 1 loght 1 7 21 23 27 21 1 t 2 11 23 23 23 18 0.5 Rt 1 10 23 24 23 18 1

Variance decompositions

Percent Variance in Row Variable due to Indicated Column Shock Technology shocks variable innovation 4 quarter advance 8 quarter advance c,t i,t f,t monetary policy ΔCt 3 25 38 12 8 10 5 ΔI 1 12 21 5 54 6 1 ΔIt 1 12 21 5 54 6 1 ΔYt 3 21 32 5 28 9 1 loght 1 7 21 23 27 21 1 t 2 11 23 23 23 18 0.5 Rt 1 10 23 24 23 18 1

big bigger!

First and second moments of posterior distribution, iid shock standard deviations (100) shock mode std dev posterior distribution

mode

shock mode std. dev., posterior distribution

std dev

innovation to technology 0.59 0.07 8.8 4-quarter advance signal, t

4

0.98 0.07 13.9 8-quarter advance signal, t

8

0.99 0.07 13.9 innovation to utility, c,t 1.55 0.23 6.7 innovation to marginal efficiency of investment, i,t 2.08 0.39 5.3 innovation to markup, f,t 1.09 0.26 4.1 innovation to monetary policy, ut

mp

7.3 0.59 12.3

• Estimated technology shock process:

Estimated technology shock process:

at  at−1  t−1

1

 t−2

2

 t−3

3

 t−4

4

 t−5

5

 t−6

6

 t−7

7

 t−8

8

 t.

Centered 5-quarter moving average of shocks NBER trough Signals 5-8 quarters in past NBER peak Current shock plus most recent F t ’ i l NBER peak Four quarters’ signals

Benchmark: Ramsey Response to Signal Shock Signal Shock

• Drop Monetary Policy Rule.
• Now, economic system under-determined. Many

equilibria. q

• We select the best equilibrium, the Ramsey

equilibrium: optimal monetary policy.

• 1. In the equilibrium,

inflation is below steady state 2 I R i fl ti

• 2. In Ramsey, inflation

has a zero steady state

Problem: monetary policy does not raise the interest rate

Price of capital (marginal cost of Price of capital (marginal cost of equity) rises in equilibrium

Sticky wages y g exacerbate the problem

Why is the Boom-Bust So Big? y g

• Most of boom-bust reflects suboptimality

p y

• f monetary policy.
• What’s the problem?

–Monetary policy ought to respond to the natural (Ramsey) rate of interest natural (Ramsey) rate of interest. Relatively sticky wages and inflation –Relatively sticky wages and inflation targeting exacerbate the problem

Policy solution

• Modify the Taylor rule to include:

– Natural rate of interest – Credit growth Credit growth – Stock market – Wage inflation instead of price inflation. g p

• Explored consequences of adding credit

p q g growth and/or stock market by adding Bernanke-Gertler-Gilchrist financial frictions.

Welfare effects of perturbations to policy

Welfare Costs of Business Cycles, In Percent of Consumption Shock Ramsey Equilibrium Rt

∗  Ett1 − 

̄   y log

Yt Yt



 Xt Xt  c$Credit Growtht  s$Net Worth Growtht Baseline c  1 s  1  replaced by w ase e c s  ep aced by w Boom-bust t 0.0520 0.3760 0.2257 0.3452 0.1289 Boom-bust signal 4) 0.0275 0.3627 0.2182 0.2664 0.1883 Boom bust signal 8 0 0243 0 3996 0 2527 0 2626 0 2114 Boom-bust signal 8 0.0243 0.3996 0.2527 0.2626 0.2114 Cost push f,t 0.00265 0.0033 0.0028 0.0032 0.0027 Discount rate shocks c,t 0.0698 0.1601 0.1793 0.1480 0.1708

lol Looking at credit growth helps

Marginal efficiency of investment i,t 0.0587 0.0965 0.0598 0.0774 0.0674

Welfare effects of perturbations to policy

Welfare Costs of Business Cycles, In Percent of Consumption Shock Ramsey Equilibrium Rt

∗  Ett1 − 

̄   y log

Yt Yt



 Xt Xt  c$Credit Growtht  s$Net Worth Growtht Baseline c  1 s  1  replaced by w ase e c s  ep aced by w Boom-bust t 0.0520 0.3760 0.2257 0.3452 0.1289 Boom-bust signal 4) 0.0275 0.3627 0.2182 0.2664 0.1883 Boom bust signal 8 0 0243 0 3996 0 2527 0 2626 0 2114 Boom-bust signal 8 0.0243 0.3996 0.2527 0.2626 0.2114 Cost push f,t 0.00265 0.0033 0.0028 0.0032 0.0027 Discount rate shocks c,t 0.0698 0.1601 0.1793 0.1480 0.1708

Replacing price inflation by wage inflation is best!

Marginal efficiency of investment i,t 0.0587 0.0965 0.0598 0.0774 0.0674

Welfare effects of perturbations to policy

Welfare Costs of Business Cycles, In Percent of Consumption Shock Ramsey Equilibrium Rt

∗  Ett1 − 

̄   y log

Yt Yt



 Xt Xt  c$Credit Growtht  s$Net Worth Growtht Baseline c  1 s  1  replaced by w ase e c s  ep aced by w Boom-bust t 0.0520 0.3760 0.2257 0.3452 0.1289 Boom-bust signal 4) 0.0275 0.3627 0.2182 0.2664 0.1883 Boom bust signal 8 0 0243 0 3996 0 2527 0 2626 0 2114 Boom-bust signal 8 0.0243 0.3996 0.2527 0.2626 0.2114 Cost push f,t 0.00265 0.0033 0.0028 0.0032 0.0027 Discount rate shocks c,t 0.0698 0.1601 0.1793 0.1480 0.1708 Marginal efficiency of investment i,t 0.0587 0.0965 0.0598 0.0774 0.0674

Replacing price inflation by wage Replacing price inflation by wage inflation is the best in all but two cases

What do real wages do in boom-bust i d ? episodes?

• We looked at three 20th century US

We looked at three 20 century US episodes.

• Great Depression (real wage low)
• 1950-1969 (real wage not low)

( g )

• 1982 2000 (real wage low)
• 1982-2000 (real wage low)

Conclusion

• Difficult to account for boom-busts in a real version

Difficult to account for boom busts in a real version

• f standard DSGE models.
• A boom-bust explanation emerges when nominal

A boom bust explanation emerges when nominal frictions are introduced and monetary authority does not (or, cannot) respond to the natural rate

– Problem is most severe when wages are sticky relative to prices.

• Robust to:

– Various treatments of indexation – Alternative models of labor market (Gertler-Trigari) that do not fall prey to Barro critique not fall prey to Barro critique.

• Explored some modifications to policy that might

help ameliorate the problem help ameliorate the problem