1 news about the future and ⁄uctuations - dspace.mit.edu file0 5 10 15 20 25 30 35 40 1.4 1.2 1...
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1 News about the future and �uctuations
� old idea: expectations drive business cycle
� uncertainty about the economy�s fundamentals, which will determine thelong run equilibrium
� partial equilibrium ideas:
� consumption: permanent income hypothesis future income expecta-tions matter for consumption decisions
� investment: high expected returns
� problem: how to �t these ideas in general equilibrium setup
1.1 Evidence
� basic fundamental for long-run growth: TFP
� can expectations about long-run TFP drive cycle?
� how to measure expectations?
� Beaudry and Portier (2006): use the stock-market
"�TFPt�St
#=
"a11 (L) a12 (L)a21 (L) a22 (L)
# ""1t"2t
#
Two identi�cation approaches:
1. Short run:
a12;0 = 0:
2. Long run:
a12 (1) = 0:
0
5 10 15 200-0.1
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0.8 11
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quarters quarters
% d
evia
tion
% d
evia
tion
Impulse responses to shocks ε2 and ε1 in the (TFP, SP) VAR
TFP Stock prices
~
Image by MIT OpenCourseWare. Adapted from Figure 2 in Beaudry, Paul, and Franck Portier. “Stock Prices, News, and Economic Fluctuations.’’ NationalBureau of Economic Research Working Paper No. 10548, June 2004.
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0 2 4 6 8 10 12 0 2 4 6 8 10 12
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Consumption (a)
quartersquarters
quarters quarters
% d
evia
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evia
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% deviation
% deviation
The figure displays the response of consumption, investment, output (measured as C + I) and hoursto a unit ε2 shock (the shock that does not have instantaneous impact on TFP in the short run identification). The unit of the vertical axis is percentage deviation from the situation without shock. (See the main text for more details)
Impulse responses to ε2 in the baseline (TFP, SP) VAR
Hoursoutput (C+I)
Image by MIT OpenCourseWare. Adapted from Figure 8 in Beaudry, Paul, and Franck Portier. “Stock Prices, News, and Economic Fluctuations.’’National Bureau of Economic Research Working Paper No. 10548, June 2004.
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quarters quarters quarters quarters
quarters quarters quarters quarters
TFP Stock prices Consumption Hours
TFP Stock prices Consumption Hours
Impulse responses to ε2 and ε1 in the (TFP, SP, H) VAR, without (upper panels) or with (lower panels) Adjusting TFP for capacity utilization.
~
Image by MIT OpenCourseWare. Adapted from Figure 17 in Beaudry, Paul, and Franck Portier. “Stock Prices, News, and Economic Fluctuations.’’ National Bureauof Economic Research Working Paper No. 10548, June 2004.
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Shar
e of
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.V.
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Shar
e of
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.V.
quarters
quarters quarters
Share of the forecast error variance of consumption (C), Investment I, Output (C+I) and hours (H) attribute to ε2 (left panel) and ε1 (right panel) in 4-variables VARs, with non adjusted TFP (top panels) or adjusted TFP (bottom panels)
C I HC+I
~
Image by MIT OpenCourseWare. Adapted from Figure 19 in Beaudry, Paul, and Franck Portier. “Stock Prices, News, and Economic Fluctuations.’’National Bureau of Economic Research Working Paper No. 10548, June 2004.
Main conclusions:
� both identi�cations give similar shocks
� response of C and Y builds up, then permanent
� response of H has hump then dies out slowly
1.2 Neoclassical growth model
Preferences
E1Xt=0
�tU (Ct; Nt)
Technology
Ct +Kt � (1� �)Kt�1 � AtF (Kt�1; Nt)
� what happens when agents receive news about future At+s?
� what type of cycles does this generate?
Basic parametrization
U (Ct; Nt) = logCt �1
1 + �N1+�t
AtF (Kt�1; Nt) = AtK�t�1N
1��t
At = eat
at = �at�1 + �t
� = 0:99
� = 1
� = 0:36
� = 0:95
� = 0:025
5 10 150
0.1
0.2a
5 10 150
0.5
1y
5 10 150
0.1
0.2c
5 10 150
0.5i
5 10 150
0.05n
Shock to current productivity
� Now introduce news about the future
� Simplest way: agents observe shock realization T periods in advance
at = �at�1 + �t�T
� What happens at the time of the announcement?
� Consumption increases, investment and hours fall!
� Danthine, Donaldson and Johnsen (1997), Beaudry and Portier (2005):nothing that looks like business cycles.
2 4 6 8 100.2
0
0.2a
2 4 6 8 101
0
1y
2 4 6 8 100
0.1
0.2c
2 4 6 8 101
0
1i
2 4 6 8 100.2
0
0.2n
1.2.1 Mechanism
Basic mechanism driven by intra-temporal optimality condition
(1� �) 1CtAtK
�t�1N
��t = N
�t
or (in terms of real wages)
1
CtWt = N
�t
together with the resource constraint
It + Ct = AtK��1t�1 N
1��t
� If At unchanged cannot have It ",Ct "
� Changing intertemporal elasticity and elasticity of labor supply can changeresponse of Ct and It, but cannot give right combination
� Adjustment costs in Kt can give It " but then Ct #
� No hope for neoclassical model with news about the future?
� Several attempts
� Jaimovich and Rebelo (2006): three ingredients
� adjustment costs in investment
� variable capacity utilization
� preferences with �weak wealth e¤ects on labor supply�
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Consumption
3
Hours
OutputInvestment
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Response to TFP News Shock, Our Model
Percentage deviations from steady state
Image by MIT OpenCourseWare. Adapted from Figure 2 in Jaimovich, Nir, and Sergio Rebelo. "Can News about the Future Drive the Business Cycle?"National Bureau of Economic Research Working Paper No. 12537, September 2006.
Preferences
X�t
�Ct �N�tXt
�1�� � 11� �
� Xt is a geometric discounted average of past consumption levels
Xt = C t X
1� t�1 :
� The parameter 2 [0; 1]: speed at which the wealth e¤ect kicks in
� Suppose Xt � 1 then quasi-linear (GHH)
Wt = �N��1t
no income e¤ect here. Inconsistent with LR growth
� Here income e¤ect that phases in slowly
� In the long run
Wt = �N��1t Ct
Simplistic interpretation:
1. quasi-linear in short run: no income e¤ect
2. log in the long run: income and substitution cancel
but 1 is wrong!
Decomposition: income e¤ect
X�t
�Ct �N�tXt
�1�� � 11� �
XR�t (Ct �WNt) = B0
� Suppose real wage constant at W , interest rate constant at R = 1=�
� e¤ects of an increase in B0
1
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0
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-0.4
-0.6
2 4 6 8 10 12 14 16 18 20 22 24Periods
% D
evia
tions
from
Ste
ady
Stat
e
Response of Hours - Income Effect
GHHgamma = 0.01 gamma = 0.5
gamma = 0.6
gamma = 0.7
gamma = 0.8
gamma = 0.9
gamma = KPR
gamma = 0.05
gamma = 0.1
gamma = 0.2
gamma = 0.3
gamma = 0.4
Image by MIT OpenCourseWare.
Mechanism
�rst order condition for labor supply in the following form
�tWt = �XtN��1t ;
and
�t =
�Ct �N�tXt
��� � �t C �1t X1� t�
Ct �N�tXt��� ;
where �t is a complicated forward looking object.
Agents forecast that work will be painful in the future, so they work more today
1.2.2 Habits and labor supply
Christiano, Ilut, Motto and Rostagno
E1Xt=0
�t log (Ct � bCt�1)�
1
1 + �N1+�t
!(habit)
Kt = (1� �)Kt�1 +
0@1� a2
It
It�1
!21A It (CEE Adj. Costs)Yt = AtK
�t N
1��t = It + Ct
At = eat
at = �at�1 + �t�T
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2 24 46 68 8
Output Investment Consumption
Pk
Perc
ent
Perc
ent
Perc
ent
Perc
ent
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-0.62 4 6 8
Perc
ent
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0
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-200
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-0.5
Hours workedRiskfree rate with payoff in
t+1 (annual)B
ass p
oint
s
t t t
ttt
Perturbed RBC ModelBaseline RBC Model
Real business cycle model with habit and CEE investment adjustment costs baseline - tech shock not realized, perturbation - tech shock realized in period 5
Image by MIT OpenCourseWare. Adapted from Figure 3 on p. 78 in Christiano, Lawrence, Cosmin Ilut, Roberto Motto, and Massimo Rostagno.“Monetary Policy and Stock Market Boom-Bust Cycles.’’ European Central Bank Working Paper No. 955, October 2008.
Perc
ent
0.05
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0.15
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Output
t2 4 6 8
Perturbed RBC Model Baseline RBC Model
2
Perc
ent
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0.250.3
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4
Hours worked
t6 8
Bas
is p
oint
s
0
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600
800
1000
Riskfree rate with payoffin t+1 (annual)
t2 4 6 8
Perc
ent
-0.8
-0.7
-0.5-0.6
-0.2
-0.3
-0.4
Pk
t2 4 6 8
Real Business Cycle Model without Habit and with CEE Investment Adjustment CostsTechnology Shock not Realized in Period 5
Perc
ent
0.150.2
0.25
0.350.3
0.40.45
0.5
Investment
t2 4 6 8 2
Perc
ent
-0.15
-0.1
0
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0.05
-0.05
0.15
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4
Consumption
t6 8
Image by MIT OpenCourseWare. Adapted from Figure 4 on p. 79 in Christiano, Lawrence, Cosmin Ilut, Roberto Motto, and Massimo Rostagno.“Monetary Policy and Stock Market Boom-Bust Cycles.’’ European Central Bank Working Paper No. 955, October 2008.
Perc
ent
-0.1-0.05
00.050.1
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Output
t2 4 6 8
2
Perc
ent
-0.1
0
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0.5
4
Hours worked
t6 8
Perc
ent
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00.10.20.30.40.5
Investment
t2 4 6 8 2
Perc
ent
-0.05
0
0.05
0.1
0.15
0.2
4
Consumption
t6 8
Bas
is p
oint
s
0
200
400
600
800
1000
Riskfree rate with payoffin t+1 (annual)
t2 4 6 8
Perc
ent
-0.8
-0.6
-0.4
-0.2
0
0.2Pk
t2 4 6 8
Perturbed RBC Model Baseline RBC Model
Real Business Cycle Model with Habit and Without Investment Adjustment Costs TechnologyShock not Realized in Period 5
Image by MIT OpenCourseWare.Adapted from Figure 5 on p. 80 in Christiano, Lawrence, Cosmin Ilut, Roberto Motto, and Massimo Rostagno.“Monetary Policy and Stock Market Boom-Bust Cycles.’’ European Central Bank Working Paper No. 955, October 2008.
Conclusions:
� model with both habits and CEE adjustment costs produces right comove-ment of quantities
� but not of prices: interest rate and asset prices
� looking for real interest rate that responds less!models with nominalrigidities
Importance of habit formation
�tWt = N�t
�t =1
Ct � bCt�1� �bEt
"1
Ct+1 � bCt
#
� high consumption in the future increases incentive to work today.
� wealth e¤ects here? See problem set
1.3 Nominal rigidities
� two period economy
� households of consumers-producers
� monopolistic competition, price-setting
� uncertainty about productivity
� preferences2Xt=1
�t logCit �
�
1 + �N1+�it
!;
Cit is the CES aggregate
Cit =
Z 10C��1�ijt di
! ���1
;
with � > 1
� Technology
Yit = AtNit:
� productivity shocks AtAt = e
at
a1 = x+ �1;
a2 = x+ �2
� x and �t mean-zero, i.i.d., normal
� A signal about long-run productivity
s = x+ e
� nominal balances with central bank at nominal rate R
� household set Pit then consumers buy
� intertemporal BC
(P2Ci2 � Pi2Yi2) +R � (P1Ci1 � Pi1Yi1) � 0;
� Pt is the price index
Pt =�Z
P 1��it di
� 11��
:
Flexible price equilibrium
� optimality for price-setting
(1� �) 1
PtCit
PitYitPit
+ ��1
At
YitPitN�it = 0:
� symmetric equilibrium, Yt = AtNt, this condition gives
Nt =�� � 1��
� 11+�
= 1
(choosing � = (� � 1) =�).
� quantitiesCt = Yt = At:
� what about consumers�decisions?
� consumer Euler equation
1
C1= RE
"P1P2
1
C2ja1; s
#
� Ct = At log-normal
r + p1 � E [p2ja1; s] = E [a2ja1; s]� a1 �1
2V ar [a2ja1; s] :
� all changes in E [y2] go to the real interest rate
� notice role of p1: neutralizes r
Fixed prices in period 1
� price-setting before any shock observed
E
"(1� �) 1
P1Ci1
Pi1Yi1Pi1
+ ��1
A2N�i1Yi1Pi1
#= 0:
� rearranging this gives
EhN1+�1
i= 1
� this will pin down averages but not responses to shocks
� quantities: equilibrium in period 2 identical
� in period 1 now Euler equation (set p2 = 0)
c1 = E [a2ja1; s]�1
2V ar [a2ja1; s]� r � p1:
� suppose r �xed, p1 �xed by assumption
� now �sentiment shocks�a¤ect consumption
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Perc
ent
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Perc
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1
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Perc
ent
Hours worked
Investment
RBC and Simple Monetary Model Expectation of Technology Shock in Period 13 Not Realized
0
500
1000
5 10 15 20B
asis
poi
nts
Pk'
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0
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Perc
ent
Consumption
Simple Monetary Model Real Business Cycle Model
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00.2
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Inflation (APR)
-80-60-40-20
020
5 10 15 20
Basis
poi
nts
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00.2
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Perc
ent
Real wage
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-0.2
-0.1
0
5 10 15 20
Perc
ent
Nominal rate of interest(Rt+1, annual)e
Ex post realized realRt+1/πt+1 (annual)e
eNote: Subscript on nominal rate of interest indicates date of payoff. Rt+1 is graphed at date t.πt indicatesgross change in price level from t-1 to t.
Image by MIT OpenCourseWare. Adapted from Figure 8 on p. 83 in Christiano, Lawrence, Cosmin Ilut, Roberto Motto, and Massimo Rostagno.“Monetary Policy and Stock Market Boom-Bust Cycles.’’ European Central Bank Working Paper No. 955, October 2008.
� pin down p1EhN1+�1
i= E
he(1+�)(y1�a1)
i= 1;
� thanks to log-normality this equation can be solved explicitly and gives
�r � p1 �1
2V ar [a2ja1; s] +
1
2(1 + �) (� + � � 1)2 �2x +
+1
2(1 + �) (� � 1)2 �2� +
1
2(1 + �) �2�2e = 0
� where
E [a2ja1; s] = �a1 + �s
� simple implication anticipated changes in r are neutral
� if instead we follow rule, e.g.
r = �0 + �1y1
then economy response changes
� we�ll go back to monetary policy
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14.461 Advanced Macroeconomics IFall 2009
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