Simulation, Estimation and Welfare Implications of

Monetary Policies in a 3-Country NOEM Model

Joseph PlasmansUniversity of Antwerp and Tilburg University

Tomasz Michalak Jorge Fornero Universities of Antwerp and Liverpool University of Antwerp

NBB 4th biannual ConferenceNBB 4th biannual Conference

““Price and Wage Rigidities in an Open Price and Wage Rigidities in an Open Economy”Economy”

12 – 13 October 200612 – 13 October 2006

2

Objectives of the Project

• To develop a three-country NOEM model with asymmetric countries in size: a small and a large open economy, being members of a monetary union (MU) and the third (large) country being the rest of the world (RoW);

• To conduct numerical simulations, econometric estimations and welfare implications of alternative monetary policies (MPs), taking account of nominal price and wage rigidities.

• Application: NL, RoEMU and the RoW (USA).

3

Related literature on two-country MU models

Practically all up-to-date NOEM models of an MU are two-country settings. Interestingly:

• Benigno (2004) shows that the Common CB’s MP must take account of (relative) rigidities in the regions when designing a welfare maximizing MP rule.

• Pytlarczyk (2005) develops a two-region model for the euro area with a particular focus on analyzing the German economy within the EMU. The interesting element of his work is the utilization of disaggregated information, i.e. national accounts data, for econometric estimation along with "synthetic" euro area data.

4

Basic characteristics of the model:

• New-Keynesian open-economy model with habit formation in consumption

• Savings carry over between periods via domestic and foreign assets

• Asset markets are incomplete • Tradable and non-tradable goods• Final and intermediate goods • Separate modeling of intermediate goods sectors• Multi-level (nested) CES consumption and production

functions• Staggered Calvo price and wage settings in each level of

production.

5

Consumer i, aggregate consumption

Nested CES consumption in 2 levels:

( )

,( ) ( ) ( )1 1 1, , ,1 1

( ) ( ) ( ) ( ), , ,,

( ) , ( ), , ,( ) ( ) 1 ( ) ,

iC h

i i iC h C h C h

i i i iC h C h C hC h

h i T h i Nt T h t T h h tC i C i C i

Aggregate consumption - 1st level

Dom. tradable consumption - 2nd level

( )

( ) ( ) ( ) ( )1 1 1 11 1 1( ) ( ) ( ) ( ) ( ) ( ), ( ) , ( ) , ( ) ( ) ,

, , , , , , ,( ) ( ) ( ) 1 ( )

ih

i i i ih h h h

i i i i i ih h h h h h

T h i T h i T h i i T ht h h h t U h U t U h W h W tC i C i C i C i

6

Consumer i , budget constraint

Consumer i´s budget constraint (CBC):

Risk premium faced by the small open economy when buying foreign assets:

where is an appropriate function, e.g.: t.

P tC,hiC thi E t Qh,t,t 1

h Bh,t 1h i Q U,t,t 1

h BU,t 1h i StQ W,t,t 1

h BW,t 1h i Mt 1

h i

1 h Wh,tiLh,ti Th,th i Bh,t

h i BU,th i StBW,t

h i Mthi Bh,ti, #

11, , 1 , , 1 , 1 , 1

11, , 1 , , 1 , 1 , 1

ˆ ˆ(1 ) (.)(1 )

ˆ ˆ(1 ) (.)(1 )

h h hU t t U t t U t t t

h h h WW t t W t t W t t t

Q r F r

Q r F r

1 ( )( )(.) exp exp 1

( ) ( )t t

t t C Ct

S B iSB iv

P i P i

F

7

Consumer i, expected utility function

Consumer i´s period utility function:

1

1,

111

( ),

( ), , ,

, 11

( )( )1

( )1 1 1( )

hhh htC ht

h

h

m M ih h t

P im FT FN VT VNh tt M h

hh ht

L iC i

U iC i

•Variables are in per capita terms.

•Countries’ size is found computing the real GDP of each region (h, RoMU and RoW) with corresponding accumulated shares: n1, n2 and n3 = 1.

•These shares are used in building a common MP rule for the MU.

8

Consumer i, FOCs

1

1

1 1 1, ,1

,, , ,

,

, , 1 1

( ) ( )( ) ,

( ) ( ) ( ) ( )

( ) ( ) 1 ( ) for , , , ,1

( ) ( ) 0,

ˆ( )

h h

h h h h

h

h ht th

t t h hC h h C h ht t t t

Lm h h mh t t h t h t

Lm h

h h ht t h t t h t

ht t

C i C ii E

P i C i P i C i

L i i W i m FT FN VT VN

E i Q i

E i Q

1

, , 1 1

, , 1 1 1

, 11, ,

( ) 0,

ˆ( ) ( ) 0,

( )( ) ( )

( ) ( )

h

h hU t t h t

h h ht t W t t t h t t

hM h h ht

t h t tC h C ht t

i

E i Q S i S

M ii E i

P i P i

9

Final goods firm j´s production function

• Nested CES production function with tradable and non-tradable final goods (i.e. sectors m = FT, FN):

,

,,1 1 1, , ,1 1

, , , ,

,, ,

,,

, ,,

( ( ))

1( ,) ( )

m h

h mm hm h m h m h

m h m h m h m hm m

m m m hh t h t t

mh t Lm h Lm

hh thtL j

Y j Z

V

j

j

,1 1 1, , ,1 1

, ,, ,

1 1, ,1 1, , , ,

, , , ,1, , 2, ,

, , , ,3, , 1, 2, 3,

,

,

( ) ( )

( ) 1 (

( )

)

m hm h m h m h

m h m hm h m h

m h m h

m h m h m h m h

T m h N m hm h h t m h h t

T m h T m hm h U t m h m h m h W

m ht

t

V jV j

V j

V j V j

where:

10

Illustration of the structure of the 2nd level of aggregation: sectoral flows of intermediate goods

FNh FTh

VNh VTh

FTU FNU

VTU VNU

FNW FTW

VNW VTW

11

Intermediate goods firms

Intermediate goods modeling:1. Literature approach – in most of the papers a fraction of

imported final goods is used as an input in the production process. In other words, there is no separate modeling of intermediate goods sectors as e.g. Smets and Wouters (2002), Erceg et al. (2000) and Corsetti and Dedola (2002).

2. Alternative approach –intermediate goods are explicitly modeled as in Dellas (2005).

DIFFERENCE: the literature approaches exchange rate movements as a result of the expenditure switching effect in intermediate goods, which operates on the same level as final goods. Our model allows for expenditure switching effects on two different levels, i.e. FT and VT goods.

12

Firms j , intermediate goods production function

,,,, , , ,( ( )) ( )

m hm hm m m h m mh t h t t h t h tV j Z j L j

Firm j, which produces intermediate goods, uses labor as input. The production functions for sectors m = VT and VN are:

We assume full employment; therefore, the whole endowment of labor is allocated in FT, FN, VT and VN sectors:

, , , , ,( ) ( ) ( ) ( )supply FT FN VT VNTh t h t h t h t h tL L j L j L j L j

13

Price and Wage Stickiness

Each firm in each production sector FT, FN, VT and VN sets prices in a staggered way (in the Calvo-scheme). Also, the same pricing is assumed for the non-producing importers in the MF and MV sectors.

Also wages in each production sector FT, FN, VT and VN are sticky.

Imperfect pass-through is introduced by assuming different Calvo price-setting parameters in the import sectors MF and MV on both final and intermediate goods levels.

14

Taylor MP rules in the MU

1. Rule I: standard Taylor rule for an MU, extended with weighted tradable and non-tradable outputs:

2. Rule II: Rule I + smoothing:

(4) (4)1 2 1, ,

2, 1

2

1 2 1 1 2 1, , , ,

2 2 2 2

0 1

2 3 ,

h t U t

T T NT NTh t U t h t U t

I It t

I It

n n n

n n

n n n n n ny y y y

n n n n

r

(4) (4)1 2 1 1 2 1, 1 0 1 , , 2 , ,

2 2 2 2

1 2 13 , , 4 1,

2 2

,

II II II T Tt t h t U t h t U t

II NT NT IIh t U t t t t

n n n n n nr y y

n n n n

n n ny y r

n n

15

Taylor MP rules in the MU (con´t)

Rule III: Rule II + annualized wage inflation

(4) (4) (4) (4)1 2 1 1 2 1, 1 0 1 , , 2 , ,

2 2 2 2

1 2 1 1 2 13 , , 4 , , 5 1,

2 2 2 2

,

III III III W Wt t h t U t h t h t

III T T III NT NT IIIh t U t h t U t t t t

n n n n n nr

n n n n

n n n n n ny y y y r

n n n n

16

Net Foreign Assets (NFAs) (1)

• Merging the CBC with the government budget constraint (GBC) (assuming zero deficit).

• Disaggregating total consumption and canceling terms we obtain 3 NFAs and 6 real bilateral NFAs positions (6 variables, e.g. ).

• We deflate them and we get 2 independent NFAs equations and 3 real NFAs variables (net exports):

BhU,t BhU,t 1 BhW,t BhW,t 1 NXh,tU NXh,t

W

BhU,t BhU,t 1 BUW,t BUW,t 1 NXU,th NXU,t

W

, , ,h U

hU t U t h tB B B

17

NFAs (2)

• However, note that the risk premium in the UIP condition

depends on NFAs positions between h and RoW and between U

and RoW. • Hence, we cancel intra-MU terms from both NFAs:

BhW,t BhW,t 1 NXh,tW

BUW,t BUW,t 1 NXU,tW

E t st 1 rt,t 1 rt,t 1W BhW,t BUW,t

18

Welfare maximizing monetary policy rules

Two alternatives approaches are:1. Ortega and Rebei (2006), who focus on

unconditional welfare maximization, and 2. Levin et al. (2005) estimate an historical MP

rule, but focus on a conditional welfare maximizing rule (“conditional” means that the model acts a restriction). The optimal MP rule is a function that depends on endogenous variables of the model and on the Lagrange multipliers.

19

Unconditional approach

• Unconditional maximization implies using a grid search algorithm

where the consumer i ’s utility is approximated by a second order Taylor expansion

0 1 2 4 5 1 ,, , , , arg max ( , , )h ht t h tE U C M L

E UC th ,M th ,L h,t UCh ,Mh ,Lh U EC th ,M th ,L h,t 12EC th ,M th ,L h,tU EC th ,M th ,L h,t

20

Simulations (1)

2 main structural asymmetries in our 3-country setting:

(a) the economies differ in size (next slide):

home economy (NL) 2.6 % of the world,

the RoEMU 38.07 %,

RoW (US) accounts for 59.33 %.

(b) Home economy + the Ro(E)MU create an MU, hence, they are asymmetric w.r.t. the RoW with own monetary policy.

(c) additionally, we took into account more sclerotic characteristics of the European economy assuming that the RoW (the USA) features faster adjustment of prices and wages (lower prior means for Calvo parameters, 3rd column of table on slide 32).

21

Simulations (2) back

Shares of NL, RoEMU and US in the "reduced" World Economy

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

19

79

Q1

19

79

Q4

19

80

Q3

19

81

Q2

19

82

Q1

19

82

Q4

19

83

Q3

19

84

Q2

19

85

Q1

19

85

Q4

19

86

Q3

19

87

Q2

19

88

Q1

19

88

Q4

19

89

Q3

19

90

Q2

19

91

Q1

19

91

Q4

19

92

Q3

19

93

Q2

19

94

Q1

19

94

Q4

19

95

Q3

19

96

Q2

19

97

Q1

19

97

Q4

19

98

Q3

19

99

Q2

20

00

Q1

20

00

Q4

20

01

Q3

20

02

Q2

20

03

Q1

20

03

Q4

20

04

Q3

20

05

Q2

NL NL+RoMU US

Average 1979-2005: NL 2.6%; NL+RoEMU 38.07%; and US (RoW) 61.93Average 1987-2005: NL 2.602%; NL+RoEMU 38.08%; and US (RoW) 61.92

n3-n2

n2-n1

n1

22

Simulations (3)

We perform simulations for the following cases:1. Technological shock

2. Exchange rate shock (in the UIP condition)3. Money demand shock4. A preference shock to consumption (changing the

willingness to work w.r.t. consumption). The latter shock is reported in the paper.

in FT goods sector;in VT and VN goods sectors

23

Simulations (5)Productivity enhancing shocks

In particular, it is interesting that both monetary policies are expansionary (loosening) after positive technological shocks which increase outputs next slide. This happens because output increase is offset by deflation.

A similar behavior of central banks is noticed after a positive technological shock in intermediate goods sectors.

24

Simulations (4). Worldwide and country-specific productivity enhancing shocks

0 10 20 30 40 50-0.01

0

0.01

0.02

0.03c1

0 10 20 30 40 50-0.01

0

0.01

0.02

0.03c2

0 10 20 30 40 50-5

0

5

10

15x 10

-3 c3

0 10 20 30 40 50-6

-4

-2

0

2x 10

-3 inflation1

0 10 20 30 40 50-6

-4

-2

0

2x 10

-3 inflation2

0 10 20 30 40 50-6

-4

-2

0

2x 10

-3 inflation3

0 10 20 30 40 50-0.1

-0.05

0

0.05

0.1NFAsEMU

0 10 20 30 40 50-0.05

0

0.05

0.1

0.15NFAshome

0 10 20 30 40 50-0.1

-0.05

0

0.05

0.1NFAsRoMU

(1a)

(1b)

(1c)

(1d)

A positive technological shock hitting all the economies at the same time has a much stronger impact than similar country-specific technological shocks. back

25

Simulations (5)Positive technological shocks

effects on control variables

0 10 20 30 40 50-0.02

-0.01

0

0.01

0.02ER

0 10 20 30 40 50-4

-2

0

2x 10

-3 R2

0 10 20 30 40 50-3

-2

-1

0

1x 10

-3 R3

0 10 20 30 40 50-5

0

5x 10

-4 ER

0 10 20 30 40 50-2

-1

0

1

2x 10

-4 R2

0 10 20 30 40 50-4

-2

0

2x 10

-4 R3

Shocks in FT sector

Shocks in both VT and VN goods sectors

26

Simulations (6) Exchange rate shock model with trade in intermediates

vs. model without trade in intermediates With exchange rate shock (€ depreciation), we demonstrate

the influence of tradable intermediate goods modeling on the behavior of the model.

To do that, we construct a very similar setting with: intermediate goods are all non-tradable and are used as inputs in the production process of the domestic country.

Our simulations confirm the proposition of Dellas (2005), saying that the presence of intermediate goods can have important (negative) consequences for the ability of monetary authorities to manipulate nominal exchange rates (in our model via the UIP condition). (next slide)

Our model with tradable intermediate goods seems to be more stable after an exchange rate shock than the model with all non-tradable intermediate goods.

27

Simulations (7) Exchange rate shock Model with trade in intermediates

vs. Model without trade in intermediates

0 10 20 30 40 50

-0.02

0

0.02

0.04

0.06c1

0 10 20 30 40 50-0.02

0

0.02

0.04

0.06c2

0 10 20 30 40 50-0.06

-0.04

-0.02

0

0.02c3

0 10 20 30 40 50-5

0

5x 10

-3 inflation1

0 10 20 30 40 50-4

-2

0

2

4x 10

-3 inflation2

0 10 20 30 40 50-2

0

2

4

6x 10

-3 inflation3

0 10 20 30 40 50-1

-0.5

0NFAsEMU

0 10 20 30 40 50-0.8

-0.6

-0.4

-0.2

0NFAshome

0 10 20 30 40 50-0.8

-0.6

-0.4

-0.2

0NFAsRoMU

(2a) With VT sector

(2b) Without VT sector

back

28

Simulations (8)Money demand shock (loosening)

Comparison of 3 MP rules

Overall, the response of all endogenous variables have a more volatile evolution when the committed rule smoothes the nominal interest rate (Rules (II) and (III)).

Moreover, considering smoothing in the nominal interest rule, the one that includes wage inflation leads to lower deviations from the equilibrium after the shock. Therefore, Rule (III) stabilizes the economy more than Rule (II).

29

Simulations (9)Shock to monetary policy (loosening)

Comparison of 3 rules

0 10 20 30 40 50

0

0.01

0.02

0.03

0.04c1

0 10 20 30 40 500

0.01

0.02

0.03

0.04c2

0 10 20 30 40 50-0.01

-0.005

0

0.005

0.01c3

0 10 20 30 40 500

0.01

0.02

0.03inflation1

0 10 20 30 40 500

0.01

0.02

0.03inflation2

0 10 20 30 40 50-4

-2

0

2x 10

-3 inflation3

0 10 20 30 40 500

0.05

0.1NFAsEMU

0 10 20 30 40 500

0.02

0.04

0.06NFAshome

0 10 20 30 40 50-0.04

-0.02

0

0.02

0.04NFAsRoMU

(3a) Rule I

(3b) Rule II

(3b) Rule III

30

Estimation - data set

• The Netherlands (small open economy) vs. the Rest of the EMU and the US (big economies).

• We proximate the Rest of the Euro-zone by Euro12 minus the Netherlands.

• Data at 2000 prices from 1991 to 2005 (OECD Statistical Compendium) and from 1970 to 1990 it is backwardly completed with data from Eurostat. Hence, the quarterly sample runs from 1970 Q2 to 2005 Q4.

• We utilized Bayesian system estimation - see e.g. Smets and Wouters (2003) and Lubik and Schorfheide (2005).

31

Estimations Rule II

Results from Bayesian estimation back

NL

RoEMU

US

Rule (II) estimated parameters

Consumption parameters

yNT

yT

Stickiness

32

Estimation Results

• For FT and FN goods, NL goods prices are sticky during 2.5 quarter, while in the US these are found to sticky during 1.5 quarter.

• Stickiness in V goods sectors is about one quarter less than in the final goods sectors and very similar among countries. It is less sticky in the NL than in the RoEMU.

• The same ordering as in the final goods sectors occurs w.r.t. wages.

FT & FN

VT & VN

WT,WN,WVT & WVN

NL 2.44 1.53 1.9

RoEMU 2.18 1.65 1.8

RoW 1.53 1.63 1.56

33

Conclusions• We construct a 3-country asymmetric NOEM model:

detailed treatment of the consumption and production sectors.

• Comparing different specifications of CB MP rules, the simplest rule stabilizes more endogenous variables.

• FT, FNT, VT and VNT goods prices and also sectoral wages are assumed to be sticky. We find evidence that final goods present more stickiness.

• We find evidence that intermediate good markets are more competitive than final goods markets.