Download External Shocks, Banks and Monetary Policy in an Open Economy

External Shocks, Banks and Monetary Policy in
an Open Economy
Yasin Mimir*
Enes Sunel
Central Bank of the Republic of Turkey
CBRT and BOE Joint Workshop on
International Monetary and Financial System: short-term challenges,
long-term solutions
June 14, 2015
The ideas in this talk are solely authors’ and do not reflect the official views or the policies of
the Central Bank of the Republic of Turkey.
Macroeconomic dynamics in EMEs around 2007-09 crisis
EMBI Spreads
Capital Flows to Emerging Economies (Million $)
25,000
Real Economic Activity
500
4
20,000
8
Gross Domestic Product
Private Consumption
Investment (right axis)
3
15,000
400
10,000
5,000
300
0
-5,000
200
-10,000
4
1
2
0
0
-1
-2
-2
-4
-3
-15,000
100
I
II
III IV
I
II
2007
III IV
I
II
2008
III IV
I
II
2009
III IV
I
2010
II
III IV
I
II
III IV
I
2007
II
III IV
I
2008
Lending Spreads
II
III IV
I
2009
II
III IV
I
2010
II
III
Lending Spread (Domestic)
Lending Spread (Foreign)
900
4
1.6
2
1.2
0
0.8
-2
-4
0.0
-6
-0.4
600
500
-8
400
300
Change in REER
C.A. Balance to GDP Ratio (right axis)
-10
I
II III IV
2008
I
II III IV
2009
III IV
I
I
II III IV
2010
I
II III
2011
II
III IV
I
2008
II
III IV
I
2009
II
III IV
I
2010
II
III
2011
Policy Instruments
9
11
Policy Rate
Avg. Reserve Req. Ratio (right axis)
8
10
7
9
6
8
5
7
0.4
700
II III IV
2007
II
2007
800
I
-8
I
2011
External Side
1,100
1,000
-6
-4
2011
6
2
I
II III IV
2007
I
II III IV
2008
I
II III IV
2009
I
II III IV
2010
I
II III
2011
-0.8
-1.2
4
6
3
5
I
II III IV
2007
I
II III IV
2008
I
II III IV
2009
I
Cross-country means of 20 EMEs.
I
Sources: BIS, Bloomberg, EPFR, IFS, country central banks.
I
II III IV
2010
I
II III
2011
Research Questions
I
What are the macroeconomic and financial effects (transmission
channels) of external shocks on EMEs?
I
We consider four types of external shocks observed:
I
I
Country risk premium ⇒ Lehman Brothers (September 2008), Taper
tantrum (May 2013)
I
US interest rate ⇒ FED’s policy normalization (expected late(?)
2015)
I
Policy uncertainty ⇒ Magnitude of FED’s interest rate hike
I
Export demand ⇒ Exogenous disturbance in the income of the rest
of the world
Should monetary policy respond to financial variables over and
above their effect on inflation in an open economy?
Theoretical Framework
I
A New Keynesian small open economy with banking.
I
Workers consume, supply labor and save in domestic currency
deposits.
I
Bankers collect domestic and foreign funds, and lend to production
firms.
I
I
Financial frictions à la Gertler and Kiyotaki (2011) between bankers
and depositors ⇒ countercyclical lending spreads.
I
Frictions are asymmetrically more intense on foreign investors ⇒
differentiation in domestic/foreign lending spreads.
Costly price adjustment framework à la Rotemberg (1982).
I
Imperfect exchange rate pass through due to sticky import prices.
Methodology
I
Quantitatively investigate how alternative Taylor type monetary
policy rules might perform in terms of
I
I
I
Macroeconomic stability ⇒ inflation and output
Domestic financial stability ⇒ inflation and credit growth
External financial stability ⇒ inflation and RER depreciation.
I
Construct optimized monetary policy rules based on alternative
policy mandates using loss function approach.
I
Impulse-response experiments that intend to reflect on the impact of
“Taper tantrum” and “(uncertain) policy normalization” shocks.
Main Findings
Literature Review
I
Risk premium shocks have more explanatory power than TFP, world
interest, and export demand shocks for most macro aggregates.
I
Negative external shocks trigger an adverse feedback loop of real
depreciation, capital flow reversal, tightening in credit conditions and
reduced real economic activity, alongside inflation.
I
The credit-augmented IT rule outperforms classical and RER
augmented IT rules in minimizing losses that depend on price,
output and/or credit growth (or real exchange rate) stability.
I
I
monetary policy can lean against the wind to reduce the
procyclicality in the financial system.
Augmenting a strict IT rule with a RER stabilization objective does
not contribute to macroeconomic stabilization.
Bankers
I
Banker j borrows from worker i 6= j and foreigners to finance loans.
∗
Qt ljt = (1 − rrt )Bjt+1 + (1 − rrt )St Bjt+1
+ Njt ,
I
For R̂t+1 =
njt+1
Rt+1 −rrt
1−rrt ;
net worth evolution
i
h
∗
∗
bjt+1 + R̂t+1 njt
= Rkt+1 − R̂t+1 qt ljt + Rt+1 − Rt+1
b∗
I
For Ψt = F ( yt+1
)ψt , F 0 (.) > 0;
t
Pt
∗
∗ St+1 Pt
Rt = Et (1 + rnt )
Rt = Et Ψt (1 + rnt )
Pt+1
St Pt+1
I
External shocks are assumed to follow AR(1) processes:
Country risk premium:
U.S. interest rate:
U.S. policy uncertainty:
ln(ψt+1 ) = ρψ ln(ψt ) + ψ
t+1
∗
∗
∗
∗
ln(Rt+1
) = ρR ln(Rt∗ ) + σtR Rt+1
∗
R∗
∗
R∗
∗
R∗
R
σt+1
= (1−ρσ )σ R +ρσ σtR +σt+1
Workers
Bankers’ profit maximization
Vjt =
max
∗
ljt+i ,bjt+1+i
Et
∞
X
Optimization Problem
(1 − θ)θi Λt,t+1+i njt+1+i
(1)
i=0
I
Bankers survive with a likelihood of 0 < θ < 1 and are subject to
Vjt ≥ λ qt ljt − ωl bjt+1
(2)
I
Financial frictions, λ > 0 and ωl = 0 reduce the magnitude of
intermediated funds
I
I
Loan-deposit spreads emerge due to limited external finance.
Domestic and foreign debt are perfect substitutes.
b∗
b+b ∗
I
In the data,
= 40% in Turkey between 2002-2010.
I
If domestic depositors have a comparative advantage in monitoring
banks, i.e. 0 < ωl < 1 a fraction of domestic debt becomes
non-divertable
Asymmetry in financial frictions
Spreads
I
λ > 0 and ωl = 0 reduce the magnitude of intermediated funds ⇒
n
o
∗
Et {Λt,t+i+1 Rkt+i+1 } > Et Λt,t+i+1 R̂t+i+1 = Et Λt,t+i+1 Rt+i+1
I
If domestic lenders monitor better, i.e. 0 < ωl < 1, part of domestic
debt is non-divertable ⇒
n
o
∗
Et {Λt,t+i+1 Rkt+i+1 } > Et Λt,t+i+1 R̂t+i+1 > Et Λt,t+i+1 Rt+i+1
I
Competition for funds in the domestic deposit market bids up real
deposit rates.
I
The credit spread over real deposit rates becomes smaller.
I
Can pick 0 < ωl < 1 to hit
b∗
b+b ∗
in the data.
Symmetric equilibrium
Capital Producers
qt ljt − ωl bjt+1 =
Final-Goods Producers
Intermediate-Goods Producers
νt − νt∗
njt = κjt njt
λ − ζt
(3)
where ζt = νtl + νt∗ .
I
Divertable assets cannot exceed an endogenous multiple of bank
capital, i.e.,
qt lt − ωl bt+1 = κt nt
I
I
Substitute (4) into (7), we get
n
o
∗
∗
net+1 = θ Rkt+1 − Rt+1
κt + Rt+1
nt
New entrants are endowed with
assets
1−θ
nnt+1 = (1 − θ)
(4)
(5)
fraction of exiting bankers’
qt lt = qt lt
1−θ
nt+1 = net+1 + nnt+1 .
(6)
(7)
Monetary authority
I
log
log
1 + rnt
1 + rn
1 + rnt
1 + rn
log
Central bank conducts monetary policy using three types of Taylor
rule configurations and discretionary changes in reserve requirements.
= ρrn log
1 + rnt
1 + rn
= ρrn log
1 + rnt−1
1 + πt+1
qt lt
+(1−ρrn ) ϕπ Et log
+ ϕl log
1 + rn
1+π
qt−1 lt−1
= ρrn log
H yt
1 + rnt−1
1 + πt+1
+ ϕy log
+(1−ρrn ) ϕπ Et log
1 + rn
1+π
y
1 + rnt−1
1 + πt+1
st
+(1−ρrn ) ϕπ Et log
+ ϕs log
1 + rn
1+π
st−1
log(1 + rrt ) = (1 − ρrr ) log(1 + rr ) + ρrr log(1 + rrt−1 ) + rr
Parametrization and calibration
Description
Parameter
Value
Target
Financial Intermediaries
Fraction of the revenues that can be diverted
Fraction of domestic deposits that cannot be diverted
Survival probability of the bankers
Proportional transfer to the entering bankers
λ
ωl
θb
b
0.598
0.822
0.925
0.0015
Commercial loan/domestic deposits spread
Banks’ liability composition (foreign funds)
Leverage ratio of 7.5 for commercial banks
1.33% of aggregate net worth
rr
ϕy
ϕl
ϕs
gH
0.06
2.2564
0.2280
1.4268
0.1
Required reserve ratio for 2002 - 2013
Estimated from the Turkish data
Estimated from the Turkish data
Estimated from the Turkish data
average share of government spending in GDP
ρΨ
σΨ
ρRn∗
σRn∗
0.9628
0.0032
0.977
0.00097
Estimated
Estimated
Estimated
Estimated
Monetary Authority and Government
Domestic and foreign currency required reserve ratios
Reaction parameter to output gap in Taylor rule
Reaction parameter to credit growth in Taylor rule
Reaction parameter to change in RER in Taylor rule
Steady state government expenditure to GDP ratio
Shock Processes
Persistence of risk premium process
Standard deviation of risk premium shocks
Persistence of U.S interest rate process
Standard deviation of U.S. interest rate shocks
R∗
Persistence of U.S policy uncertainty process
ρσ
Standard deviation of U.S. policy uncertainty shocks
σσ
Other
R∗
0.15
0.0015
from
from
from
from
the
the
the
the
Turkish EMBI data
Turkish EMBI data
US data
US data
N/A
Estimated from the US data
Inefficiencies and external shocks
I
Monopolistic competition → Higher mark-up → Lower employment
and output
I
Price rigidity → Increased import prices due to ER pass through and
higher price dispersion → Higher inflation → Increased menu costs
→ lower output
I
Financial friction (λ > 0) → Insufficient substitution of foreign debt
with domestic deposits → Less intermediated funds → Larger credit
∗
spreads Et [Rkt+1 − Rt+1 ], Et [Rkt+1 − Rt+1
] ↑ → Reduced
investment and output
I
Asymmetry in the financial friction (ω > 0) → Differentiates
domestic and foreign funding rate, and partly eliminates the
arbitrage between loan-domestic deposit rates i.e.,
∗
Et [Rkt+1 − Rt+1
] > Et [Rkt+1 − Rt+1 ] > 0.
Variance decomposition (%)
TFP
Country Risk Premium
U.S. Interest Rate
Export Demand
49.31
21.11
8.14
28.41
65.48
76.92
4.92
10.99
12.60
17.35
2.42
2.33
37.38
30.51
18.28
17.21
2.90
9.73
51.53
41.30
46.38
49.46
82.56
47.00
7.92
6.81
7.38
7.95
11.78
7.70
3.17
21.37
27.97
25.39
2.77
35.56
52.08
52.27
38.90
39.71
6.24
6.14
2.78
1.87
Real Variables
Output
Consumption
Investment
Financial and External Variables
Credit
Liability Composition (Foreign)
Domestic lending spread
Foreign Lending spread
Real Exchange Rate
C.A. Balance to GDP ratio
Nominal Variables
CPI inflation rate
Policy Rate
Loss function values for alternative policies and mandates
2
σπ
+ σy2
TFP
Risk prem.
US int. rate
Export dem.
All
Loss
TR1
ϕπ
ϕy
Loss
TR2
ϕπ
ϕl
Loss
TR3
ϕπ
ϕs
1.428e-05
4.551e-06
5.358e-07
3.149e-06
2.357e-05
1.51
1.01
1.01
1.26
2.01
1
2.5
2.5
2.5
2.5
9.782e-06
4.695e-06
5.123e-07
5.497e-06
2.237e-05
1.76
2.26
2.01
1.01
2.01
2
2.25
2
1.75
2.25
2.7695e-05
6.4040e-06
7.262e-07
7.234e-06
3.875e-05
1.01
1.01
1.01
1.01
1.01
0
0
0
0
0
7.478e-05
2.735e-05
2.791e-06
8.666e-06
1.994e-04
4.76
1.01
1.01
1.26
4.76
1.5
2.5
2.5
0.25
2.25
7.928e-05
2.275e-05
2.596e-06
7.174e-06
1.259e-04
3.26
1.01
1.01
1.01
2.51
2.5
1.75
1.50
2.00
2.5
1.314e-04
2.783e-05
2.965e-06
9.789e-06
1.999e-04
2.01
1.01
1.01
1.01
1.26
0
0.25
0
0
0
1.544e-04
0.0025
2.360e-04
1.284e-04
0.0028
1.01
4.76
4.76
4.76
4.26
0
0
0
0
0.25
1.212e-04
0.0024
2.286e-04
1.258e-04
0.0026
3.51
4.76
4.76
4.76
4.76
2.5
0.75
0.75
0.50
1.5
1.544e-04
0.0025
2.360e-04
1.284e-04
0.0028
1.01
4.76
4.76
4.76
3.51
0
0
0
0
0
2
2
σπ
+ σy2 + σql
TFP
Risk prem.
US int. rate
Export dem.
All
2
σπ
+ σy2 + σs2
TFP
Risk prem.
US int.
Export dem.
All
Taper tantrum shock
(100 bp increase in risk premium)
Current Account Balance−to−GDP
Real Exchange Rate
4
%Ch.
0.2
3
0.15
2
0.1
1
0.05
2
4
6
8
10
12
0
14
2
4
Nominal Depreciation Rate
4
3
%Ch.
6
8
10
12
14
10
12
14
8
10
Quarters
12
14
Liability Structure
0
−1
2
−2
1
0
2
4
6
8
10
12
−3
14
2
4
6
0.6
0.4
0.2
0
2
4
6
8
10
Quarters
8
Policy Rate
Ann. Bs. Pt. Ch.
Ann. % Pt. Ch.
CPI Inflation
12
14
Taylor
30
20
10
2
Credit augmented
4
6
Taper tantrum shock ctd.
(100 bp increase in risk premium)
Output
Consumption
%Ch.
0.02
0
−0.02
Investment
−0.05
−0.2
−0.1
−0.4
−0.15
−0.6
−0.2
−0.04
5
10
15
Credit
10
15
5
Bank Net Worth
0
1
−0.1
−0.2
0
−0.2
−0.3
−1
−0.3
−0.4
−2
5
10
15
5
Loan−Foreign Deposits Spread
10
15
Asset Price
0
2
−0.1
%Ch.
−0.8
5
10
15
−0.4
Loan−Domestic Deposits Spread
5
10
15
Country Risk Premium
Ann. Bs. Pt. Ch.
100
80
10
60
80
40
5
60
20
0
5
10
Quarters
15
0
5
Taylor
10
Quarters
15
Credit augmented
40
5
10
Quarters
15
US interest rate shock
(25 bp increase)
Current Account Balance−to−GDP
Real Exchange Rate
0.08
1
%Ch.
0.06
0.04
0.5
0.02
0
2
4
6
8
10
12
0
14
2
4
Nominal Depreciation Rate
6
8
10
12
14
10
12
14
8
10
Quarters
12
14
Liability Structure
0
%Ch.
1
−0.5
0.5
0
−1
2
4
6
8
10
12
14
2
4
6
0.2
0.15
0.1
0.05
0
2
4
6
8
10
Quarters
8
Policy Rate
Ann. Bs. Pt. Ch.
Ann. % Pt. Ch.
CPI Inflation
12
14
Taylor
12
10
8
6
4
2
2
4
Credit augmented
6
US interest rate shock ctd.
Output
(25 bp increase)
Consumption
Investment
0.01
%Ch.
−0.02
0
−0.04
−0.01
−0.02
−0.05
−0.1
−0.15
−0.2
−0.25
−0.06
5
10
15
−0.08
Credit
5
10
15
5
Bank Net Worth
10
15
Asset Price
0
0
−0.05
0
−0.1
−0.5
5
10
15
−0.1
5
Loan−Foreign Deposits Spread
Ann. Bs. Pt. Ch.
%Ch.
0.5
−0.05
10
15
5
Loan−Domestic Deposits Spread
30
10
15
Country Risk Premium
0
3
−2
20
2
−4
10
1
−6
0
5
10
Quarters
15
0
5
Taylor
10
Quarters
15
Credit augmented
5
10
Quarters
15
Policy uncertainty shock
(59 bp variation in FOMC 2015 projections)
Current Account Balance−to−GDP
Real Exchange Rate
0.3
%Ch.
3
0.2
2
0.1
0
1
2
4
6
8
10
12
0
14
2
4
%Ch.
Nominal Depreciation Rate
6
8
10
12
14
10
12
14
8
10
Quarters
12
14
Liability Structure
3
0
2
−1
−2
1
−3
0
2
4
6
8
10
12
−4
14
2
4
6
CPI Inflation
Ann. Bs. Pt. Ch.
Ann. % Pt. Ch.
0.6
0.4
0.2
0
2
4
6
8
10
Quarters
8
Policy Rate
0.8
12
14
Taylor
40
30
20
10
2
4
Credit augmented
6
Policy uncertainty shock ctd.
Output
(59 bp variation in FOMC 2015 projections)
Consumption
Investment
0.02
0
−0.05
−0.1
−0.15
−0.2
−0.25
%Ch.
0
−0.02
−0.04
−0.06
−0.08
5
10
15
−0.5
−1
5
Credit
10
15
5
Bank Net Worth
10
15
Asset Price
%Ch.
0
−0.1
−0.2
−0.3
−0.4
−0.5
2
−0.2
0
−0.3
5
10
15
−2
Loan−Foreign Deposits Spread
Ann. Bs. Pt. Ch.
−0.1
5
10
15
12
80
−0.4
Loan−Domestic Deposits Spread
10
−5
60
8
−10
40
6
−15
4
−20
20
5
10
Quarters
15
2
5
10
15
Country Risk Premium
0
−25
5
Taylor
10
Quarters
15
Credit augmented
5
10
Quarters
15
Conclusion
I
A New Keynesian small open economy model with financial frictions
is able to generate the adverse macroeconomic and financial
repercussions of external shocks that EMEs face.
I
The credit-augmented IT rule outperforms classical and RER
augmented IT rules in minimizing losses that depend on price,
output and/or credit growth (or real exchange rate) stability.
I
I
Augmenting IT rules with external financial stability objective might
overwhelm monetary policy.
I
I
monetary policy can lean against the wind to reduce the
procyclicality in the financial system.
A strict IT rule with a RER stabilization objective does not
contribute to macroeconomic stabilization.
Further research calls for determining (Ramsey) optimal and
implementable rules and conducting the normative comparison of
policy rules, accordingly.
THANK YOU
Discretionary increase in reserve requirements
Current Account Balance−to−GDP
(1 % point)
Real Exchange Rate
1.5
%Ch.
0
1
0.5
−0.5
0
−1
−0.5
2
4
6
8
10
12
14
2
4
%Ch.
Nominal Depreciation Rate
6
1.5
1
1
0.5
0.5
0
0
−0.5
10
12
14
10
12
14
8
10
Quarters
12
14
−1
−0.5
2
4
6
8
10
12
14
2
4
6
0.2
0.1
0
2
4
6
8
10
Quarters
8
Policy Rate
Ann. Bs. Pt. Ch.
CPI Inflation
Ann. % Pt. Ch.
8
Liability Structure
12
14
Taylor
30
20
10
0
2
4
Credit augmented
6
Discretionary increase in reserve requirements ctd.
Output
Consumption
Investment
0
0
0.02
−0.1
%Ch.
−0.02
−0.2
0
−0.04
−0.02
10
15
−0.4
5
Credit
10
15
5
Bank Net Worth
0.2
%Ch.
−0.3
−0.06
5
0.1
2
0.2
0
0.1
−2
0
−0.1
−4
−0.1
−6
5
10
15
5
10
15
20
0
−0.2
Loan−Domestic Deposits Spread
Loan−Foreign Deposits Spread
10
15
Asset Price
0
−0.2
Ann. Bs. Pt. Ch.
(1 % point)
5
10
15
Country Risk Premium
10
0
−20
−200
5
−40
−400
−60
−600
5
10
Quarters
15
−80
5
Taylor
10
Quarters
15
Credit augmented
0
5
10
Quarters
15
Literature review
I
Recent global financial crisis has brought up the issue of
macroeconomic and macroprudential policy coordination.
I
I
Angeloni and Faia (2009), Angelini et al. (2012), Alpanda et al.
(2014) and others.
Additional policy tools are explored in order to target financial
stability.
I
I
Back
Christensen et al. (2011), Glocker and Towbin (2012), Mimir et al.
(2013).
Financial frictions in emerging economies bring additional burden on
monetary authorities.
I
I
Transmission of country borrowing premium shocks to business
cycles and domestic deposit and lending rates. Uribe and Yue (2006)
and Akinci (2013).
Adjusting short term policy rates triggers fear of
appreciation/depreciation.
Workers
max
ct ,ht ,Bt+1 ,mt
I
Back
E0
∞
X
t=0
β
(ct − hc ct−1 )
1−σ
1−σ
−1
χ 1+ξ
−
h
+ υ log
1+ξ t
Mt
Pt
#
Mt
Wt
(1 + rnt−1 )Bt
Mt−1
Tt
Bt+1
+
=
ht +
+
+ Πt −
Pt
Pt
Pt
Pt
Pt
Pt
c is a CES aggregate of home and foreign goods consumption,
γ
h 1
i γ−1
γ−1
γ−1
1
ct = ω γ (ctH ) γ + (1 − ω) γ (ctF ) γ
I
Workers save only in domestic currency deposits and hold cash.
ct +
I
"
t
Leading to the domestic CPI,
1
h
i 1−γ
Pt = ω(PtH )1−γ + (1 − ω)(PtF )1−γ
Optimality conditions of workers’ problem
Back
Lagrange multiplier of the BC:
−σ
ϕt = (ct − hc ct−1 )
−σ
− βhc Et (ct+1 − hc ct )
CS optimality condition:
Pt
ϕt = βEt ϕt+1 (1 + rnt )
Pt+1
H-F goods optimal consumption demand:
H −γ
ctH
ω
Pt
=
1 − ω PtF
ctF
CL optimality condition:
Wt
χhtξ
=
Pt
ϕt
CM optimality condition:
υ/mt
rnt
=
ϕt
1 + rnt
Financial frictions and spreads
Back
Bankers’ profit maximization
I
Back
∗
+ ν n and solve the Lagrangian
Conjecture Vjt = νtl qt ljt + νt∗ bjt+1
t jt
with the multiplier µt s.t. Vjt ≥ λ qt ljt − ωl bjt+1 to obtain
n
h
io
νtl = Et Ξt,t+1 Rkt+1 − R̂t+1
o
n
νt = Et Ξt,t+1 R̂t+1
and
n
o
∗
νt∗ = Et Ξt,t+1 Rt+1 − Rt+1
∗
where Ξt,t+1 = Λt,t+1 [1 − θ + θ(ζt+1 κt+1 + νt+1 − νt+1
)]
and Λt,t+1+i = β i+1 Uct+1+i
Uct .
I
λ, µt , ωl > 0 ⇒ νt∗ > 0.
Solution to bankers’ problem
∗
max L = νtl qt ljt + νt∗ bjt+1
+ νt njt
∗
ljt ,bjt+1
qt ljt − njt
∗
l
∗ ∗
− bjt+1
+µt νt qt ljt + νt bjt+1 + νt njt − λ qt ljt − ωl
1 − rrt
First Order Conditions:
νtl (1 + µt ) = λµt 1 −
ljt :
b∗jt+1 :
µt :
νtl qt ljt + νt∗
ωl 1 − rrt
νt∗ (1 + µt ) = λµt ωl
qt ljt − njt
− bt+1 + νt njt − λ(qt ljt − ωl bjt+1 ) ≥ 0
1 − rrt
Capital goods producers
I
Buy the deprecited capital at
production firms at qt ,
Back
PI ,t
Pt ,
repair it, and sell it to the
∞
X
n
h
PI ,t io
it
t
qt it −
it
max
E0 β Λt,t+1 qt it − Φ
it
it−1
Pt
t=0
I
subject to the evolution of physical capital
it
kt+1 = (1 − δt )kt + 1 − Φ
it
it−1
Q-investment Condition for Capital Goods:
h
h
0
0
it
it
it i
it+1 it+1 i
PI ,t
= qt 1−Φ
−Φ
+βEt Λt,t+1 qt+1 Φ
Pt
it−1
it−1 it−1
it
it
Home - Foreign Goods Optimal Investment Demand:
H −γi
itH
Pt
ωi
=
1 − ωi PtF
itF
Final goods producers
I
Back
Repackage a continuum of intermediate goods in a competitive
market.
1−1 1
Z 1
j
j
1− 1
di
yt =
yt (i)
.
0
where j denotes Home (H) and Foreign (F) intermediate goods.
max
ytj (i)
Ptj
Z
1
1
ytj (i)1− di
0
1−1 1
Z
−
1
Ptj (i)ytj (i)di
0
Iso-elastic demand for each good i of type j:
!−
Ptj (i)
j
ytj ,
yt (i) =
Ptj
Price of each good i of type j:
1
Z 1
1−
j
j
1−
Pt =
Pt (i) di
.
0
Intermediate goods producers (Home)
Foreign
Back
I
They use capital and labor in the production of intermediate goods
and they can vary capital utilization.
α
ytH (i) = At ut (i)kt (i) ht (i)1−α
(8)
I
Total factor productivity follows an AR(1) process:
ln(At+1 ) = ρA ln(At ) + At+1
I
(9)
They incur convex price adjustment costs as in Rotemberg (1982).
Pt
2
ϕH PtH (i)
−
1
H (i)
2 Pt−1
(10)
Intermediate goods producers (Home) ctd.
max Et
PtH (i)
H
Dt+j
(i)
ptH
∞
X
"
Λt,t+j
j=0
H
(i)
Dt+j
Pt+j
#
(11)
I
They maximize real profits by choosing the sales price:
=
H
H
H∗ H∗
Pt+j
(i)yt+j
(i)+St+j Pt+j
ct+j (i)−MCt+j yt+j (i)−Pt+j
I
Optimal sales price is given by
ϕH πtH (πtH − 1)
ϕH
rmct −
Et
=
+
H
−1
−1
−1
yt
I
"
#2
H
(i)
ϕH Pt+j
−1
H
2 Pt+j−1
(i)
(12)
π H (π H − 1)
Λt,t+1 t+1 t+1
ytH
ϕH → 0 ⇒ home goods prices are flexible and reflect a constant
markup of −1
over the marginal cost.
(13)
Intermediate goods producers (Home) ctd.
I
Factor demands are determined by their marginal products,
pI ,t δ 0 (ut )kt = α
α
Rkt =
ytH
kt
t
ut
rmct
(14)
rmct − pi,t δ(ut ) + qt
(15)
qt−1
wt = (1 − α)
with
δ(ut ) = δ +
and δ, d, % > 0.
yH yH t
rmct
(16)
d
u 1+%
1+% t
(17)
ht
Intermediate goods producers (Foreign)
Back
I
Importers of foreign goods incur similar rigidities with
MCtF = St PtF ∗ .
F
F
(πt+1
− 1)
πt+1
ϕF πtF (πtF − 1)
ϕF
F
pt =
st −
Et Λt,t+1
+
−1
−1
−1
ytF
ytF
(18)
I
Exporters do not have monopoly power, i.e.,
"
−Γ #ν H
PtH∗
H∗
H∗ 1−ν H
ct =
yt∗
(ct−1
)
Pt∗
with PtH∗ = Pt∗ = 1, and yt∗ taken as given.
(19)
Parametrization and calibration ctd.
Description
Parameter Value
Target
Preferences
Quarterly discount factor
Relative risk aversion
Habit persistence
Labor supply elasticity
Relative utility weight of labor
Relative utility weight of money
Relative weight of domestic goods in consumption basket
Intra-temporal elasticity of substitution for consumption composite
Intra-temporal elasticity of substitution for investment composite
β
σ
hc
ξ
χ
υ
ω
γ
γi
0.9821
2
0.7
5
4x103
0.35
0.4
1
1
Average annualized real deposit rate (7.48%)
Literature
Literature
Literature
steady state hours worked of 0.33
M2 to GDP ratio.
average consumption to GDP ratio
Gertler et al. (2007)
Gertler et al. (2007)
α
ωi
δ
u
%
ψ
ϕH
ϕF
0.4
0.87
0.035
1
1
11
4
120
120
Labor share of output (0.6)
average share of investment in GDP (0.15)
Average annual ratio of investment to capital (14.8%)
Literature
Gertler et al. (2007)
Steady state mark-up of 1.1
Elasticity of price of capital w.r.t. investment-capital ratio
Frequency of price change per quarter
Frequency of price change per quarter
Firms
Share of capital in output
Share of domestic goods in the investment composite
Depreciation rate of capital
Steady-state utilization rate
Elasticity of marginal depreciation with respect to the utilization rate
Elasticity of substitution between varieties
Investment adjustment cost parameter
Price adjustment cost for domestic intermediate goods producers
Price adjustment cost for domestic intermediate goods producers
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