2014  OriginalPaper  Buchkapitel
Interactions Between Fiscal and Monetary Authorities in a ThreeCountry NewKeynesian Model of a Monetary Union
Autoren: Tomasz Michalak, Jacob Engwerda, Joseph Plasmans
Verlag: Springer Berlin Heidelberg
2014  OriginalPaper  Buchkapitel
Autoren: Tomasz Michalak, Jacob Engwerda, Joseph Plasmans
Verlag: Springer Berlin Heidelberg
\(J_{U}^{\ast}(t_{0})\)



\(v_{0S}^{\pi}\)

\(v_{0A}^{\pi}\)

\(v_{0S}^{y}\)

\(v_{0A}^{y}\)


Benchmark

C
PNF

C456
NF

\(P\hat{C}\mathit{NF}\)

CN456
F

κ
_{ i,y/π }≈0.5

\(\mathbf{C}\check{F}\mathbf{P}N\)

\(\mathbf{C6}\check{F}\mathbf{45}N\)

C
P
F
N

C645
F
N

κ
_{ i,y/π }≈0.8

CP
NF

C645
NF

C
PNF

C645
NF

γ
_{ i }≈0.45

C
PNF

C45
6
NF

\(N\hat{C} \mathit{PF} \)

CN456
F

γ
_{ i }≈0.55

C
PNF

C45
6
NF

\(N\hat{C}\mathit{PF}\)

CN456
F

η
_{ i }≈0.65

CP
NF

C456
NF

\(\hat{C}\mathit{PNF}\)

CN45
6
F

η
_{ i }≈1

C
PNF

C456
NF

\(P\hat{C}\mathit{NF}\)

CN456
F

ρ
_{ ij }≈0.4

C
PNF

C456
NF

\(N\hat{C}\mathit{PF}\)

CN456
F

ρ
_{ ij }≈0.5

CPNF

C456
NF

CPNF

CN456
F

δ
_{ ij }≈0.075

C
PNF

C45
6
NF

\({P}\hat{C}\mathit{NF}\)

C45
N6
F

δ
_{ ij }≈2/3

C
PNF

C456
NF

\(N\hat {C} \mathit{PF} \)

CN456
F

ξ
_{ i }≈0.03

CP
NF

C645
NF

C
PNF

\(\check{C}\mathbf{6}4\mathbf{5}\mathit{NF}\)

ξ
_{ i }≈0.125

CP
NF

C45
6
NF

C
PNF

\(\check{C}\mathbf{P}N\mathbf{F}\)

ς
_{ ij }≈0.025

C
PNF

C456
NF

\(N\hat{C}\mathit{PF}\)

\(\check{\mathbf{C}}\mathbf{6}N45F\)

ς
_{ ij }≈0.1

C
PNF

C456
NF

C
PNF

\(\check{\mathbf{C}}\mathbf{6}N45F\)

\(( sc_{1},v_{0S}^{\pi} ) \)

N

C

F

[1234]

[1324]

[1234]

N
^{ F }


C1

4.2650

3.5500

3.5033

3.7917

3.7917

3.4779

4.0750

C2

4.2650

3.5500

3.5033

3.7917

3.4779

3.7917

4.0750

C3

4.2650

3.5500

3.5033

3.4779

3.7917

3.7917

4.0750

CB

11.7566

6.9454

8.5717

10.1221

10.1221

10.1221

12.3601

J
_{ U }(
t
_{0})

24.5516

17.5957

19.0817

21.1836

21.1836

21.1836

24.5859

\(J_{U}^{\ast}(t_{0})\)

13.9057

8.9598

10.3530

11.8533

11.8533

11.8533

13.7293

\(\beta_{F,C1}\hat{y}_{C1}^{2}\)

1.7332

2.1976

2.0190

2.0272

2.0272

1.4935

1.4647

\(\alpha_{F,C1}\hat{\pi}_{C1}^{2}\)

1.7692

1.0961

1.3181

1.5834

1.5834

1.5980

2.4136

\(\chi_{F,C1}\widehat{\hat{f}}^{2}_{C1}\)

0.7625

0.2562

0.1661

0.1810

0.1810

0.3863

0.1966

\(\beta_{F,C2}\hat{y}_{C2}^{2}\)

1.7332

2.1976

2.0190

2.0272

1.4935

2.0272

1.4647

\(\alpha_{F,C2}\hat{\pi}_{C2}^{2}\)

1.7692

1.0961

1.3181

1.5834

1.5980

1.5834

2.4136

\(\chi_{F,C2}\widehat{\hat{f}}^{2}_{C2}\)

0.7625

0.2562

0.1661

0.1810

0.3863

0.1810

0.1966

\(\beta_{F,C3}\hat{y}_{C3}^{2}\)

1.7332

2.1976

2.0190

1.4935

2.0272

2.0272

1.4647

\(\alpha_{F,C3}\hat{\pi}_{C3}^{2}\)

1.7692

1.0961

1.3181

1.5980

1.5834

1.5834

2.4136

\(\chi_{F,C3}\widehat{\hat{f}}^{2}_{C3}\)

0.7625

0.2562

0.1661

0.3863

0.1810

0.1810

0.1966

\(\beta_{CB}\hat{y}_{CB}^{2}\)

0.3466

0.4395

0.4038

0.3677

0.3677

0.3677

0.2929

\(\alpha_{CB}\hat{\pi}_{CB}^{2}\)

8.8462

5.4808

6.5908

7.9414

7.9414

7.9414

12.0680

\(\chi_{CB}\widehat{\hat{\imath}}_{U}^{2}\)

2.5637

1.0251

1.5770

1.8128

1.8128

1.8128

0

\(( sc_{1},v_{0S}^{\pi} ) \)

N

C

F

[1234]

[1324]

[1234]


LQDGE

158

1

1

140

140

140

PUNE

1

1

1

13

13

13

\(J_{U}^{\ast}(t_{0})/J_{U}(t_{0})\)



\(v_{0S}^{\pi}\)

\(v_{0A}^{\pi}\)

\(v_{0S}^{y}\)

\(v_{0A}^{y}\)


Benchmark

\(\mathbf{C}\check{F}\mathbf{P}N\)

\(\mathbf{C6}\check{F} \mathbf{45}N\)

CPF
N

C645
F
N

γ
_{ i }≈0.45

CF456
N

CF645
N

C456F
N

\(\check{C}\mathbf{645F}N\)

γ
_{ i }≈0.66

CF456
N

CF645
N

C
NF456

\(\check{C}\mathit{NF}456\)

η
_{ i }≈0.65

CF456
N

CF456
N

\(\mathbf{C}N \hat{F}456\)

\(\check{C}\hat{F}N456\)

η
_{ i }≈1

CF456
N

CF645
N

C456F
N

\(\check{C}\mathbf{45F}N\mathbf{6}\)

ρ
_{ ij }≈0.35

CF456
N

CF645
N

C456F
N

C645F
N

ρ
_{ ij }≈0.55

CF456
N

CF645
N

C
FN456

\(\check{C}\mathbf{64}5\hat{F}N\)

δ
_{ ij }≈0.075

CF456
N

CF645
N

C456
FN

\(\check{C}45\hat{F}N\mathbf{6}\)

δ
_{ ij }≈0.5

CF456
N

CF645
N

C645F
N

\(\check{C}\mathbf{456F}N\)

ξ
_{ i }≈0.03

CF456
N

CF456
N

\(\mathbf {C456}\check{F}N\)

\(\check{C}\mathbf{6}\check {F}N\mathbf{4}5\)

ξ
_{ i }≈0.125

CF456
N

CF645
N

CF456
N

C645F
N

ς
_{ ij }≈0.02

CF456
N

CF645
N

C456F
N

C645F
N

ς
_{ ij }≈0.1

CF456
N

CF645
N

C645F
N

\(\check{C}\mathbf{456F}N\)

\(r_{F/CB}^{\pi/y}\)

\(J_{U}^{\ast}(t_{0})\)



\(v_{0S}^{\pi}\)

\(\overline{J_{U}^{\ast}}\)

\(v_{0A}^{\pi}\)

\(\overline{J_{U}^{\ast}}\)

\(v_{0S}^{y}\)

\(10^{2}\overline{J_{U}^{\ast}}\)

\(v_{0A}^{y}\)

\(10^{2}\overline {J_{U}^{\ast}}\)


0

C
PNF

17.16

\(\check{C}645\mathit{NF}\)

1.93

CNPF

4.23

CN456
F

3.17

0.1

C
PNF

13.14

\(\check{C}645\mathit{NF}\)

1.54

\(\hat {C}\mathit{NPF}\)

7.78

CN456
F

3.38

0.2
^{a}

C
PNF

10.58

C456
NF

1.23

\(P\hat{C}\mathit{NF}\)

7.37

CN456
F

3.32

0.3

C
PNF

8.97

C456
NF

1.06

\(\mathbf {P}\hat{C}\mathit{NF}\)

7.13

C45
N6
F

3.31

0.4

C
PNF

8.05

C45
6
NF

0.96

\(\mathbf{P}\hat{C}\mathit{NF}\)

6.98

CN456
F

3.28

0.5

P
C
NF

7.58

45
C6
NF

0.91

\(\mathbf {P}\hat{C}\mathit{NF}\)

6.90

\(\hat{C}45\mathit{NF}\mathbf{6}\)

3.27

0.6

P
C
NF

7.11

45
C6
NF

0.84

\(\mathbf {P}\hat{C}N\hat{F}\)

6.85

\(\hat{C}\hat{F}45N \mathbf{6}\)

3.28

0.7

P
C
NF

6.80

45
6C
NF

0.81

\(\mathbf {P}\hat{F}N\hat{C}\)

6.84

\(\hat{C}\hat{F}N45 \mathbf{6}\)

3.24

0.8

PCF
N

6.66

45
6CF
N

0.79

\(\mathbf {FP}N\hat{C}\)

6.82

\(\mathbf{F}\hat{C} \mathbf{4}5N6\)

3.28

0.9

FPC
N

6.58

F645
C
N

0.79

\(\mathbf{FP}N\hat{C}\)

6.82

\(\mathbf{F}45\hat{C}N \mathbf{6}\)

3.29

1.0

FPC
N

6.61

F645
C
N

0.79

\(\mathbf{FP}N\hat{C}\)

6.85

F45
CN
6

3.26

\((sc_{1},v_{0S}^{\pi}) \)

NC

C

F

[1234]

[1324]

[1234]


C1

6.3331

5.0871

5.8439

6.3071

6.3071

5.4947

C2

6.3331

5.0871

5.8439

6.3071

5.4947

6.3071

C3

6.3331

5.0871

5.8439

5.4947

6.3071

6.3071

CB

6.9370

6.5147

5.5070

6.2236

6.2236

6.2236

J
_{ U }(
t
_{0})

25.9363

21.7763

23.0388

24.3328

24.3328

24.3328

\(J_{U}^{\ast}(t_{0})\)

7.0018

6.9906

6.1134

6.5194

6.5194

6.5194

\(\beta_{F,C1}\hat{y}_{C1}^{2}\)

1.0667

1.1640

1.0812

1.3336

1.3336

0.6526

\(\alpha_{F,C1}\hat{\pi}_{C1}^{2}\)

5.2015

3.4472

4.1563

4.6365

4.6365

4.7429

\(\chi_{F,C1}\widehat{\hat{f}}^{2}_{C1}\)

0.0648

0.4758

0.6063

0.3369

0.3369

0.0992

\(\beta_{F,C2}\hat{y}_{C2}^{2}\)

1.0667

1.1640

1.0812

1.3336

0.6526

1.3336

\(\alpha_{F,C2}\hat{\pi}_{C2}^{2}\)

5.2015

3.4472

4.1563

4.6365

4.7429

4.6365

\(\chi_{F,C2}\widehat{\hat{f}}^{2}_{C2}\)

0.0648

0.4758

0.6063

0.3369

0.0992

0.3369

\(\beta_{F,C3}\hat{y}_{C3}^{2}\)

1.0667

1.1640

1.0812

0.6526

1.3336

1.3336

\(\alpha_{F,C3}\hat{\pi}_{C3}^{2}\)

5.2015

3.4472

4.1563

4.7429

4.6365

4.6365

\(\chi_{F,C3}\widehat{\hat{f}}^{2}_{C3}\)

0.0648

0.4758

0.6063

0.0992

0.3369

0.3369

\(\beta_{CB}\hat{y}_{CB}^{2}\)

1.0667

1.1640

1.0812

1.0688

1.0688

1.0688

\(\alpha_{CB}\hat{\pi}_{CB}^{2}\)

5.2015

3.4472

4.1563

4.6717

4.6717

4.6717

\(\chi_{CB}\widehat{\hat{\imath}}_{U}^{2}\)

0.6686

1.9034

0.2695

0.4831

0.4831

0.4831

\(r_{CB}^{\pi/y}=0\)

\(J_{U}^{\ast}(t_{0})\)



\(v_{0S}^{\pi}\)

\(\overline{J_{U}^{\ast}}\)

\(v_{0A}^{\pi }\)

\(\overline{J_{U}^{\ast}}\)

\(v_{0S}^{y}\)

\(10^{2} \overline{J_{U}^{\ast }}\)

\(v_{0A}^{y}\)

\(10^{2}\overline{J_{U}^{\ast}}\)


\(r_{F}^{\pi/y}=0\)

C
PNF

17.16

\(\check{C}645\mathit{NF}\)

1.93

CNPF

4.23

CN456
F

3.17

\(r_{F}^{\pi/y}=0.1\)

C
PNF

13.29

\(\check{C}645\mathit{NF}\)

1.53

\(\check{C}\mathit{PNF}\)

7.83

C45
N6
F

3.31

\(r_{F}^{\pi/y}=0.2\)

C
PNF

10.72

C645
NF

1.25

\(\check{C}\mathit{PNF}\)

7.77

C45
N6
F

3.33

\(r_{F}^{\pi/y}=0.3\)

C
PNF

9.35

C645
NF

1.10

C
PNF

7.65

\(\check{C}45N6F\)

3.32

\(r_{F}^{\pi/y}=0.4\)

C
PNF

8.63

C645
NF

1.02

C
PNF

7.50

C645
NF

3.31

\(r_{F}^{\pi/y}=0.5\)

C
PNF

8.17

C645
NF

1.00

CP
NF

7.21

C45
6
NF

3.30

\(r_{F}^{\pi/y}=0.6\)

P
C
NF

7.93

645C
NF

0.99

CP
NF

7.24

C645
NF

3.29

\(r_{F}^{\pi/y}=0.7\)

P
C
NF

7.66

645C
NF

0.96

PC
NF

7.13

C45
6
FN

3.27

\(r_{F}^{\pi/y}=0.8\)

P
C
NF

7.62

645C
NF

0.94

PC
NF

7.14

C45
6
FN

3.27

\(r_{F}^{\pi/y}=0.9\)

P
C
NF

7.41

645C
NF

0.88

PCF
N

7.14

64
5CF
N

3.27

\(r_{F}^{\pi/y}=1\)

P
C
NF

7.29

645C
NF

0.86

\(\mathbf{P}\check{C}\mathbf{F}N\)

7.15

645CF
N

3.27

\(\theta_{\pi}^{U}=1.25\)

−0

−0.1

−0.3

−0.5

−0.8

−1.0


C1,
C2,
C3

2.9554

5.8427

9.0471

3.3611

2.8931

2.8148

CB

6.3700

4.2528

19.2972

12.7490

12.5669

13.0460

J
_{ U }(
t
_{0})

15.2364

21.7811

46.4388

22.8324

21.2463

21.4904

\(J_{U}^{\ast}(t_{0})\)

8.3235

9.1524

25.6551

14.1157

13.3184

13.5231

\(\beta_{F,C1}\hat{y}_{C1}^{2}\)

1.1145

1.6788

0.8843

0.4886

0.3842

0.3234

\(\alpha_{F,C1}\hat{\pi}_{C1}^{2}\)

0.7790

0.6073

2.5124

1.8967

2.0648

2.2729

\(\chi_{F,C1}\widehat{\hat{f}}^{2}_{C1}\)

1.0618

3.5565

5.6504

0.9757

0.4440

0.2184

\(\beta_{CB}\hat{y}_{CB}^{2}\)

0.2229

0.3357

0.1768

0.0977

0.0768

0.0646

\(\alpha_{CB}\hat{\pi}_{CB}^{2}\)

3.8953

3.0368

12.5621

9.4835

10.3240

11.3648

\(\chi_{CB}\widehat{\hat{\imath}}_{U}^{2}\)

2.2517

0.8801

6.5582

3.1677

2.1659

1.6165

\(\theta_{\pi}^{U}=1.50\)

−0

−0.1

−0.3

−0.5

−0.8

−1.0


C1,
C2,
C3

2.4891

2.3665

2.2435

2.1948

2.4202

2.9156

CB

4.2403

4.5948

5.4647

6.2456

8.0400

9.8299

J
_{ U }(
t
_{0})

11.7078

11.6945

12.1955

12.8300

15.3007

18.5770

\(J_{U}^{\ast}(t_{0})\)

5.7327

5.9191

6.5302

7.1445

8.9168

11.0600

\(\beta_{F,C1}\hat{y}_{C1}^{2}\)

1.7336

1.5703

1.2982

1.0880

0.8648

0.7523

\(\alpha_{F,C1}\hat{\pi}_{C1}^{2}\)

0.6500

0.7282

0.9183

1.0782

1.3704

1.5350

\(\chi_{F,C1}\widehat{\hat{f}}^{2}_{C1}\)

0.1054

0.0679

0.0269

0.0285

0.1848

0.6282

\(\beta_{CB}\hat{y}_{CB}^{2}\)

0.3467

0.3140

0.2596

0.2176

0.1729

0.1504

\(\alpha_{CB}\hat{\pi}_{CB}^{2}\)

3.2501

3.6410

4.5919

5.3912

6.8523

7.6753

\(\chi_{CB}\widehat{\hat{\imath}}_{U}^{2}\)

0.6434

0.6397

0.6131

0.6367

1.0147

2.0041

\(\theta_{\pi}^{U}=1.75\)

−0

−0.1

−0.3

−0.5

−0.8

−1.0


C1,
C2,
C3

3.4359

3.1001

2.8075

2.6060

2.4825

2.4264

CB

4.1017

3.9972

4.4681

5.0434

6.0023

6.5807

J
_{ U }(
t
_{0})

14.4096

13.2978

12.8907

12.8614

13.4500

13.8602

\(J_{U}^{\ast}(t_{0})\)

6.5822

6.1072

6.1979

6.4953

7.1816

7.5970

\(\beta_{F,C1}\hat{y}_{C1}^{2}\)

2.3617

2.1732

1.8597

1.6176

1.3284

1.1784

\(\alpha_{F,C1}\hat{\pi}_{C1}^{2}\)

0.4830

0.5555

0.7057

0.8305

1.0375

1.1745

\(\chi_{F,C1}\widehat{\hat{f}}^{2}_{C1}\)

0.5911

0.3714

0.2419

0.1578

0.1165

0.0735

\(\beta_{CB}\hat{y}_{CB}^{2}\)

0.4723

0.4346

0.3719

0.3235

0.2656

0.2356

\(\alpha_{CB}\hat{\pi}_{CB}^{2}\)

2.4154

2.7777

3.5289

4.1525

5.1879

5.8725

\(\chi_{CB}\widehat{\hat{\imath}}_{U}^{2}\)

1.2139

0.7848

0.5672

0.5673

0.5486

0.4725

\(( sc_{1},v_{0S}^{\pi} ) \)

N

N
^{ I }

N
^{ II }

N
^{ III }

C

C
^{ I }

C
^{ II }

C
^{ III }


C1,
C2,
C3

2.19

4.22

6.18

4.73

2.12

2.23

2.22

2.31

CB

6.24

8.65

16.82

12.88

5.33

3.66

3.64

3.65

J
_{ U }(
t
_{0})

12.80

21.30

35.36

27.07

11.70

10.35

10.31

10.57

\(J_{U}^{\ast}(t_{0})\)

7.14

11.60

21.67

16.05

6.37

5.02

4.99

5.05

\(J_{U}^{A\ast}(t_{0})\)

7.14

11.60

20.48

14.84

6.37

5.02

4.93

4.89

\(\beta_{F,C1}\hat{y}_{i}^{2}\)

1.09

1.57

1.60

1.71

1.06

1.47

1.47

1.47

\(\alpha_{F,C1}\hat{\pi}_{i}^{2}\)

1.08

0.94

1.01

1.22

0.88

0.58

0.57

0.61

\(\chi_{F,C1}\widehat{\hat{f}}^{2}_{i}\)

0.03

1.71

2.38

0.60

0.19

0.18

0.12

0.08

\(\chi_{F,C1}^{new,I/II}\widehat{\hat{f}}^{2}_{i}\)

–

–

3.57

1.80

–

–

0.18

0.23

\(\beta_{CB}\hat{y}_{CB}^{2}\)

0.22

0.31

0.32

0.34

0.22

0.29

0.29

0.29

\(\alpha_{CB}\hat{\pi}_{CB}^{2}\)

5.40

4.72

5.06

6.10

4.37

2.89

2.87

3.05

\(\chi_{CB}\widehat{\hat{\imath}}_{U}^{2}\)

0.64

3.62

11.44

6.43

0.76

0.47

0.47

0.30

\(( sc_{1},v_{0S}^{\pi} ) \)

F

F
^{ I }

F
^{ II }

F
^{ III }


C1

9.30

13.48

9.05

5.61

C2

9.30

13.48

9.05

5.61

C3

9.30

13.48

9.05

5.61

CB

22.00

29.30

14.20

6.66

J
_{ U }(
t
_{0})

50.00

69.73

41.30

23.50

\(J_{U}^{\ast}(t_{0})\)

30.00

41.84

22.30

11.30

\(J_{U}^{A\ast}(t_{0})\)

30.00

41.48

20.70

20.01

\(\beta_{F,C1}\hat{y}_{C1}^{2}\)

1.06

1.48

1.49

1.50

\(\alpha_{F,C1}\hat{\pi}_{C1}^{2}\)

1.00

0.63

0.65

0.67

\(\chi_{F,C1}\widehat{\hat{f}}^{2}_{C1}\)

7.00

11.37

4.61

1.15

–

–

6.91

3.44


\(\beta_{CB}\hat{y}_{CB}^{2}\)

0.20

0.30

0.30

0.30

\(\alpha_{CB}\hat{\pi}_{CB}^{2}\)

5.00

3.17

3.27

3.36

\(\chi_{CB}\widehat{\hat{\imath}}_{U}^{2}\)

16.00

25.83

10.60

3.00
