Internal imbalances in the monetary union with asymmetric openness

Author’s Accepted Manuscript Internal Imbalances in the Monetary Union with Asymmetric Openness Shih-Fu Liu, Yu-Ning Hwang, Ching-Chong Lai

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To appear in: International Review of Economics and Finance Cite this article as: Shih-Fu Liu, Yu-Ning Hwang and Ching-Chong Lai, Internal Imbalances in the Monetary Union with Asymmetric Openness, International Review of Economics and Finance, http://dx.doi.org/10.1016/j.iref.2017.03.012 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Internal Imbalances in the Monetary Union with Asymmetric Openness

Shih-Fu Liua*, Yu-Ning Hwanga, Ching-Chong Laia,b,c a

Department of Economics, National Chengchi University, Taiwan b

c

Institute of Economics, Academia Sinica, Taiwan

Institute of Economics, National Sun Yat-Sen University, Taiwan

*Correspondence to: Shih-Fu Liu, Department of Economics, National Chengchi University, 64, Sec. 2, Tzu-nan Rd., Taipei 116, Taiwan. Tel: +886 2 27822791#664; Email: [email protected]

Abstract This paper develops a two-country, two-sector model under both monetary union and flexible exchange rate regimes featured with trade openness differentials, and then uses it to examine the relative macroeconomic effects of trade openness under both regimes.

Some main

results emerge from our analysis regarding an adverse shock of either country-wide productivity or country-wide government expenditure.



First, the decline in output is greater

We would like to thank the discussant of this paper, Prof. Jenn-Hong Tang, at the 2016 Taipei

IREF Workshop on “Trade, Finance, and Growth” held on May 19th at Academia Sinica, Taipei, Taiwan for his helpful comments. We also wish to acknowledge the workshop organizers, Institute of Economics, Academia Sinica, and College of Business, Feng Chia University, for their efforts in support of this workshop. This paper has benefited from helpful suggestions and insightful comments by an anonymous referee, Cheng-wei Chang, Kuan-jen Chen, Ping-ho Chen, Hsun Chu, Mei-ying Hu, Wei-chi Huang, Chih-hsing Liao and Shine-hung Lin. Any errors or shortcomings are, however, the authors’ responsibility.

for a country with low openness under both regimes. Second, the monetary union will result in a greater decline in output if the monetary authority attaches a higher weight to output stabilization. Third, the high elasticity of substitution results in a greater difference in output between the two regimes.

Keywords: Flexible exchange rates; monetary union; monetary policy JEL classification: E52, F31, F45

1. Introduction Since the global recession in 2008, the economic performance of the Euro area has declined significantly, and has not shown evident recovery. In particular, there have been great differences in the economic performance of different countries. In the leading country, Germany, as an example, GDP declined by 5.64% in 2009, but recovered relatively quickly after 2009. On the contrary, Portugal, Italy, Greece and Spain have sunk into long-term recession. GDP continued to decline in these four countries from 2012 to 2013. As a result, the economic characteristics that cause the different reactions of the regions of the monetary union to the same external shock become the main focus of concerns. McKinnon (1963), following Mundell (1961), analyzes how openness differentials may affect the external and internal economy and stability of prices for a region.1 He finds that, when an economy with a high degree of openness employs flexible exchange rates to dampen the external deficit, it is likely to suffer from greater price instability. Thus, a group of open areas which trade extensively with each other would find it beneficial to form a monetary union. Based on this view, this study attempts to analyze whether or not the economic openness differential can be one of the causes of the different responses of regions in a monetary union to the same shock. An alternative question that we are interested in concerns whether or not a country would perform better under the external shock if it did not participate in the monetary union. In the past decade, there have been many studies focusing on the possible benefits and losses from a monetary union based on the DSGE model. For example, Benigno (2004) and Ferrero (2009) show the optimal macro policies in the Euro area. Eghgertsson et al. (2014) analyze whether structural reforms are helpful in boosting output and regaining competitiveness in the Euro area. However, many issues remain obscure. In particular, the literature analyzing the influence of economic openness on a monetary union using DSGE models is relatively rare.

1

McKinnon (1963) defines “openness” as the share of tradable goods in consumption. setting.

1

We also follow the same

Table 1 The openness of the Euro area. Country

Openness

Belgium

0.834

Austria

0.763

Netherlands

0.759

Germany

0.705

Portugal

0.697

Spain

0.621

France

0.622

Italy

0.551

Greece

0.53

Finland

0.487

Source: Lombardo and Ravenna (2014).

However, countries in a monetary union can significantly differ in their degree of openness. Take the Euro area as an example. The degrees of economic openness of countries in the Euro area do differ. Lombardo and Ravenna (2014) have shown that the openness across regions in the Euro area is asymmetric. According to the input-output data that they use, Lombardo and Ravenna (2014) estimate the share of tradable goods in consumption of 25 OECD countries. Table 1 shows the degree of openness of the main regions in the Euro area, as estimated by Lombardo and Ravenna (2014).2 It is shown that the degree of openness of Belgium is the highest (0.834) while the degree of openness of Finland is the lowest (0.487). The difference in the openness, from the highest to the lowest, is 0.346. The degrees of openness of Germany, France, Italy and Spain, which are the four largest economies of the Euro area, are 0.705, 0.622, 0.551 and 0.622, respectively, which also exhibit significant differences. Panels (a) and (b) in Fig. 1 depict the relationship between the degree of economic openness and the average economic growth rate both before and after the great recession (2000-2007 vs. 2008-2013). It can be clearly seen that the five countries with lower degrees of economic openness were strongly affected by the global recession. The empirical observations exhibited in Panels (a) and (b) of Fig. 1 indicate that the different degrees of openness play a crucial role in affecting macroeconomic performance.

2

Our study only uses the data for 10 countries, and excludes the data for Ireland and Luxembourg, as the ratios of GDP of these two countries are less than 3% of the overall GDP of the Euro area.

2

(a)

(b)

Fig. 1. The coefficient of the average economic growth rate against the degree of openness. Source: World Development Indicators, World Bank.

The degree of openness remains an important issue in monetary policy studies. Using a small open economy with tradable goods, Faia and Monacelli (2008) analyze the relationship between the degree of openness and the volatility of the optimal exchange rate. Duarte and Obstfeld (2008) show that a two-country model with non-tradable goods, rather than home bias, generates asymmetric responses of the home and foreign consumptions to shocks, and results in exchange rate volatilities. With the estimated degrees of openness for the 25 countries, Lombardo and Ravenna (2014) measure the welfare loss under shocks for countries with different levels of openness. Using a two-country model with tradable goods only, Corsetti (2006) deals with the relationship between openness and exchange rate volatility under an optimal stabilization policy, and shows that the volatility increases with the positive degree of home bias. However, none of these studies analyze the monetary union regime of countries with different degrees of openness. Thus, in this paper, we attempt to bridge this gap in the literature by examining the macroeconomic effects of openness on the monetary union countries. Our analytical framework consists of a two-country (Home and Foreign countries), two-sector (tradable and non-tradable sectors) economy with sticky prices. The presentation of our model is similar to that in Eggertsson et al. (2014). To highlight the macroeconomic effects of the monetary union regime on the regions with different degrees of openness, we compare the impacts of the productivity and fiscal shocks on countries with different degrees of openness under 3

the monetary union regime, and under a flexible exchange rate regime with independent monetary policies.3 While the optimal policy appears to be the focus of monetary union studies,4 some studies also emphasize the regional differentials of regions in the monetary union. Duarte and Wolman (2008) deal with the relationship between fiscal policies and regional inflation differentials in a monetary union. When the labor income tax is taken into account, the regional fiscal policy does affect the volatility of the inflation differentials, but the volatility of output of each country remains roughly unchanged under this fiscal policy. Altissimo et al. (2011) use a two-country, two-sector (tradable and non-tradable) model to explore the effects of productivity shocks of the tradable and non-tradable sectors on the regional inflation differentials. They find that there are greater output differentials under the productivity shock arising in the tradable sector, but inflation differentials can be higher under the productivity shock arising in the non-tradable sector. However, these studies assume that the degrees of openness of countries in the monetary union are identical. The monetary union studies, which use the two-country model with asymmetric degrees of openness, focus on one specific country within the Euro area. For example, Rabanal (2009) and Forni et al. (2010) explore the relationship between Spain and the Euro area and the relationship between Italy and the Euro area, respectively. Lama and Rabanal (2014) discuss whether or not the U.K. should enter the monetary union, by focusing on the trade and financial linkages. Veld et al. (2014) use an estimated three-country New Keynesian model of the Spanish economy with financial frictions to show that, under strong capital inflows which led to booms in housing prices, tightening collateral constraints of households and firms, will eventually result in a collapse in housing prices that lead to a sharp reduction in capital inflows, and in turn cause the slump in Spain's economic activities. In this paper, the analysis of the regional differentials is similar to the approach in Duarte and Wolman (2008) and Altissimo et al. (2011). Moreover, we extend their analyses to compare the macroeconomic effects across regimes. We find that the monetary union regime helps moderate regional inflation differentials as compared to the flexible exchange rate regime. Shocks to different sectors result in different effects on the regional output differentials. 3

4

Most of the studies on monetary union use the two-country framework. With a two-country DSGE model, Benigno (2004) has analyzed the optimal policy for the monetary union. Beetsma and Jensen (2005) as well as Ferrero (2009) explore the optimal fiscal policy and monetary policy in the monetary union. Some studies use the multiple-country framework to analyze the monetary union issues. For example, following Gali and Monacelli (2008), Leith and Wren-Lewis (2011) use a monetary union model with infinitely small economies, where each country has its own fiscal policy maker but one common monetary authority for the union, to analyze the interaction between the country-specific government debt and the common monetary policy of the union. In addition, their paper compares the across-regime differentials under the debt shock. The studies on the optimal policy for the monetary union include Benigno (2004), Beetsma and Jensen (2005), Ferrero (2009), and many others.

4

The remainder of this paper is arranged as follows. Section 2 outlines the structure of the model. Section 3 presents the calibration, Section 4 analyzes the influence of shocks on openness, and Section 5 measures the effects of openness on welfare. Section 6 we conclude.

In

2. The Model We assume that the world economy consists of two unequally-sized countries, Home

H 

and Foreign

F  .

The world economy is populated by a continuum of agents

on the interval 0, 1 . The population on the segment 0, n  belongs to country H , while the population on segment n, 1 belongs to country F. There is a continuum of households of measure one in the Home country.

Each

household derives utility from the consumption of tradable and non-tradable goods, but obtains disutility from work hours. We assume that labor is immobile across countries. Therefore, firms produce tradable and non-tradable goods using labor that is country-specific. The production process is a two-stage process: firstly, a representative perfectly competitive retailer combines the differentiated intermediate goods to produce the final goods. Secondly, monopolistically competitive intermediate goods producers set the price of each differentiated intermediate good under a staggered price setting. This paper explores the effects of monetary mechanisms under both monetary union and flexible exchange rate regimes. Under the monetary union regime, the common monetary authority formulates monetary policies that are union-wide which means that they share the same interest rate level. In economies with a flexible exchange rate regime, each monetary authority sets respective monetary policies over only one country which has its own interest rate level. 2.1. Households Each country has its representative household that provides labor inputs for tradable and non-tradable sectors within his own country. The representative household’s decision problem consists of two steps: the first step regarding its decisions consists of maximizing lifetime utility subject to a budget constraint, and the second step regarding its decisions consists of minimizing the costs of composite consumption goods.

5

2.1.1. The representative household’s utility maximization problem The expected lifetime utility of household h in country H is given by  Ct h 1 Lt h 1  E0     , 1  t 0  1 

t

(1)

where Ct  h  denotes consumption from household h at time t , Lt  h  denotes labor supply, the parameter  denotes the intertemporal discount factor,  denotes the coefficient of relative risk aversion, and the parameter  denotes the inverse of the labor supply elasticity. Under the flexible exchange rate regime where these two countries implement separate monetary policies, we assume that the households belonging to country H divide up their wealth for the domestic currency and two nominal risk-free bonds with a maturity of one period, denominated in domestic and Foreign currency respectively. A household h maximizes the expectation of Eq. (1) subject to a budget constraint as follows:

Pt Ct h   BH , t h  

St BF , t h 

 B, t

 Wt Lt h   1  it 1 BH , t 1 h   St 1  it*1 BF , t 1 h   t h   Tt h  , where

BH ,t h  and

(2)

BF ,t h  are households’ holdings of nominal risk-free

one-period bonds that pay one unit of Home and Foreign currency when they mature.

it and it* are the nominal interest rates for bonds. price level and the nominal wage in country H . taxes Tt  h  .

Pt and Wt are the aggregate The household pays lump-sum

t h  is the profit of the intermediate-goods producers.

By

following Benigno (2001), Erceg et al. (2006) and Eggertsson et al. (2014), the intermediation cost  B , t that the domestic household’s holdings of foreign bonds incurs guarantees a stationary net foreign asset position in this model.

St is the

nominal exchange rate, defined as the Home-currency price of one Foreign currency. The intermediation cost is given by Eq. (3) with  B  0 . We assume that only the domestic household has to pay the intermediation cost which depends on the ratio of economy-wide holdings of net foreign assets to nominal output.5 5

The setting for the intermediation cost follows the work of Benigno (2001). There are some restrictions on  B , t () :  B, t (0)  1 and  B , t () equals 1 only if BtF  0 ;  B , t () is a differentiable and decreasing function that is close to zero. There are two purposes behind these restrictions: the net foreign assets can avoid the unit root problem, which is characterized by stationarity. Besides, given that steady-state net foreign assets are set to zero, they have no influence on the dynamics of the log-linearized model. This will be useful in arriving at a well-defined steady state for consumption and assets.

6

  St nBF ,t  h    (3)    PY t t     On the other hand, the households from country F allocate their wealth only between foreign currency and one nominal risk-free bond denominated in a unit of

 B ,t  exp   B 

their own currency. Without facing any intermediation cost, they can lend and borrow at a risk-free nominal interest rate i * . Similarly, the budget constraint of households in country F can be written as Pt*Ct*  f   BF* ,t h   Wt* L*t  f   1  it*1 BF* ,t 1  f   t*  f   Tt*  f 

(4)

The representative household for each country decides the consumption, bonds and labor supply in both the tradable and non-tradable sectors. The labor supply decisions of the Home and Foreign households are given by Eq. (5) and Eq. (6) respectively:   W   Ct h   t   Lt h  ,  Pt 

(5)

*   W   Ct*  f   t*   L*t  f  , (6)  Pt  Optimization implies that the Home and Foreign consumption Euler equations are

   Ct 1 h    Pt         1 ;  1  it Et  C h    Pt 1     t 

(7)

 *   Ct 1  f    Pt*     1  i  Et  *   *    1; C  f    Pt 1     t 

(8)

   Ct 1 h    Pt  St 1          1 ,  1  i  B ,t Et  C h    Pt 1  S t     t 

(9)

* t

* t

Eqs. (7) and (8) represent the Home and Foreign Euler equations, which are obtained by optimally choosing the holding of nominal bonds that are denominated in their own currencies. Eq. (9) represents the Euler equation of households in country H , which is the optimal condition associated with the holding of Foreign-currency-denominated nominal bonds. Following Benigno (2001), we assume that Home-currency-denominated bonds are in zero-net supply within a specific country. Thus, the budget constraint of Home household can be written as:

Pt Ct h  

St BF , t h 

 B, t

 Wt Lt h   St 1  it*1 BF , t 1 h   t h   Tt h  .

(10)

Under the monetary union regime where one common currency is used across the union, net Foreign bonds are denominated in the common currency across countries. 7

At time t , the household’s budget constraints in countries H and F are expressed as Eq. (11) and Eq. (12), respectively:

Pt Ct h  

BF , t h 

 BMU ,t

 W t L t h   1  itMU 1 BF , t 1 h   t h   Tt h  ;

(11)

* * * Pt* Ct*  f   BF* , t  f   Wt* L*t  f   1  itMU 1 BF , t 1  f   t  f   Tt  f  ,

(12)

where itMU is the common interest rate prevailing within the monetary union. MU The intermediation cost  B,t is given by

 nBF , t  h      ,  Pt Yt  

  

 BMU , t  exp   B  

(13)

Optimization implies that the consumption Euler equation of the household in the Home and Foreign countries can be expressed as

 1  i

MU t



MU B ,t

   Ct 1 h    Pt         1 Et  C h    Pt 1     t 

(14)

 * *   Ct 1  f    Pt      *    1  1  i Et  * (15) Ct  f    Pt 1       Eqs. (14) and (15) represent the Home and Foreign Euler equations respectively, MU t

which are obtained by optimally choosing common-currency-denominated nominal bonds.

the

holding

of

the

2.1.2. The representative household’s cost minimization problem The Home aggregate consumption buddle Ct h  comprises the consumption of tradable goods and non-tradable goods which is defined in the form of a CES production function with a constant elasticity of substitution   0 , 

 1 1  1  1  1 Ct  h    CT , t  h    1    CN , t  h    ,  

(16)

where  represents the proportion of tradable goods in the overall consumption, with 0    1 . This proportion may be different for the household in country F , which is denoted with asterisks as  * . In our study,  and  * denote the degree of openness across countries, as in McKinnon (1963). In the following analyses, we will examine how the openness differentials in  and  * will generate regional economic differentials. The consumption of tradable goods consists of both domestic and imported goods with a constant elasticity of substitution   0 ,

8



 1 1  1   1  1 (17) CT , t h    CH , t h    1    CF , t h    ,   where  represents the home bias, measured by the proportion of Home-produced tradable goods in the consumption of tradable goods, with 0    1 . This

proportion may be different for households in country F , and is denoted by  * .6 The commodity demand of the domestic household sector derived from cost minimization is given by 



 PT , t CT , t h      Pt

 P   Ct h  ; CN , t  h   1     N , t  Ct  h  ,  Pt  

 PH , t CH , t  h      PT , t 

 PF , t   CT , t  h  ; CF , t  h   1      PT , t 



(18)



  CT , t  h  . 

(19)

In the same spirit, the commodity demand of the Foreign household sector is expressed as  PT*, t  f     *  Pt

* H,t

 P*  f     H*, t  P T ,t

C

C

*

*



 P*   C *t  f  ; C N* , t  f   1  *  N*, t  P   t 

* T,t





  C *t  f  ,  

 P*   C *T ,t  f  ; C F* , t  f   1   *  F , t   P*   T ,t

(20)



  C *T ,t  f  .  

(21)

Given the above specification, the associated price indexes for country H and F are defined as 1



1



Pt   PT1,t  1    PN1, t 1 ; Pt*   * PT*, t1  1   * PN*, t 1  1 ,  

PT , t

  P

1  H ,t

 1   PF1, t 1 ; 1

* T,t

P

 

*

P

* 1  H ,t

 1   P  *

1 * 1  1  F, t

(22) ,

(23)

where Pt and Pt* represent the consumption price index in countries H and F, respectively.

PT ,t and PT*,t represent the overall price index for tradable goods in

countries H and F, respectively. goods in country H and F.

PH ,t and PF ,t represent the prices of tradable

PN ,t and PN* ,t represent the prices of non-tradable goods

in countries H and F.

6

This is a common specification in the existing literature such as Benigno and Thoenissen (2003), Corsetti et al. (2008), and Eggertsson et al. (2014). The degree of trade openness which is measured by the share of tradable goods in the overall consumption  is consistent with the definition as Lombardo and Ravenna (2014) indicate. With this specification, when   1 and  *  1 , we have the result: exports = imports = 0. In the extreme case, this economy remains open, but there is complete home bias and consumers make consumption of domestic tradable goods only.

9

While there are two currencies and the nominal exchange rate is freely determined, we assume that the law of one price holds for differentiated goods, which implies

PH , t  St PH* , t ,

(24)

PF , t  St PF*, t ,

(25)

PT , t  St PT*, t ,

(26)

Under the monetary union where goods are denominated in the common currency, the associated prices of the Home and Foreign countries:

PH ,t  PH* , t

(27)

PF , t  PF*, t .

(28)

and

2.2. Retailers

k  H 

In the tradable

and non-tradable

k  N 

sectors, a representative

retail producer combines raw goods according to a CES production function with a constant elasticity of substitution k  0 , k

1   k 1 k k  k 1   1 (29) Yk , t     Yk , t  j  k dj  ,  k  0    where j denotes an intermediate goods producer. The segments 0, H  and H ,1 are labor inputs of the tradable and non-tradable sectors where H   and N  1   be the tradable and non-tradable sectors’ sizes, respectively.

The representative retailer of sector k maximizes profits subject to its technological constraint as follows: k

max Pk , t Yk , t   Pk , t  j  Yk , t  j dj .

Yk , t  j 

(30)

0

The first-order condition of Eq. (30) yields the standard demand function as follows 1  Pk , t  j  Yk , t  j     k  Pk , t 

 k

Yk , t ,

(31)

where Pk , t  j  indexes the price of the j th variety of the good produced in sector k.

The zero profit condition implies that the price index in sector k is as follows:

Pk , t

1   k

1



k

0

Pk , t  j 

1k

 1k dj  

(32) 10

2.3. Intermediate goods producers In each sector, intermediate goods producer j uses the following technology Yk , t  j   Z t Ak , t Lk , t  j  ,

(33)

where k  H , N . Lk ,t  j  is the labor demand of firm j of the sector k at time t .

Z t is an exogenous country-wide productivity shock in the Home country at time t , which will be identical across the tradable and non-tradable sectors. Ak ,t is the sector-specific productivity shock to sector k at time t . country-wide productivity shock follows an AR (1) process:

We assume that the

Zt  ZtZ1 Z 1 Z exp  Z ,t  .

(34)

The sector-specific productivity shock to sector k follows an AR (1) process: A

1  A k

Ak ,t  Ak ,t k1 A





exp  A k ,t ,

(35)





where  Z  1 ,  Ak  1 ,  tZ ~ N 0,  Z  and  Ak ,t ~ N 0,  Ak . Intermediate goods producers are imperfectly competitive, and they choose the price

Pk ,t  j  to maximize profits subject to their technology constraint Eq. (33). By following Calvo (1983), we assume that the intermediate goods producers change their price on a staggered basis. The firm j in sector k cannot change its price with probability  k in each period.

According to the technology, the marginal cost

can be obtained from the intermediate goods producers’ cost minimization subject to their technology constraint:

MCk , t  j   MCk , t 

Wk , t Z t Ak , t

,

(36)

where MCk ,t  j  denotes the nominal marginal cost of firm j in sector k at time

t .7

Wt denotes the nominal wage of firm j in sector k .

According to the demand function (31) and the production function (33), the aggregate production function of intermediate goods, by aggregating the production of all firms can be written as Yk , t d k , t  Z t Ak , t Lk , t

(37)

where the labor market equilibrium implies that k

Lk , t   Lk , t  j dj , and

(38)

0

7

The marginal cost is identical across firms, regardless of firm-specific characteristics.

11

d k , t denotes a price dispersion index as

dk, t 

1

k



k

0

 Pk , t  j    dj .  Pk , t 

(39)

Then, for a given marginal cost function, the intermediate goods producers decide their optimal price subject to their respective demand functions (31). The optimal price setting problem of firm j at time t is defined as

  max Et ks Qt ,t  s  pk , t  j   MCk , t  s  Yk , t  s  j   , pk , t  j   s 0  where Qt ,t  s   s Ct  s Ct 



 Pt

(40)

Pt  s  is the stochastic discount factor for nominal

assets between t and t  s , Yk ,t  s  j  is given by Eq. (31) which is the demand at

pk ,t that remains effective at t  s . t  s conditional on the optimal price reset at t , ~

 k , lying between 0,1 , is the probability that firms will not change the price in each period.

~ ~ In equilibrium, all firms set pk , t  j   pk , t .

The optimality condition is

expressed as ~ pk , t Pk , t

  s  Et   ks Qt , t  s   kk, t h  MCk , t  sYk , t  s  s 0  h 1   k ,  s k  1  k 1  s Et   k Qt , t  s    k , t h  Pk , t  sYk , t  s s 0  h 1 

(41)

where  k , t 1  ( Pk , t 1 Pk , t ) denotes the inflation rate between t and t  1 in sector In sector k , since the firms who do not change their price at period t , on average, will maintain their price at the previous period, the price index Eq. (32) yields a non-linear relation between the optimal price (relative to the aggregate price level) and the inflation rate: k.

1

 1   k kk, t 1  1k (42)  .  Pk , t  1   k  According to the price index in Eq. (32) and the staggered price setting, we derive the law of motion for the index of price dispersion: ~ pk , t

k

d k , t   k d k , t 1 kk, t

 1   k kk, t 1  k 1  .  1   k   1  k  

12

(43)

2.4. Monetary policy In this section, we introduce two different specifications of the monetary policy framework. Monetary policy is conducted with a Taylor rule that targets the CPI inflation and output deviating from their steady-state values. Under the flexible exchange rate regime, the monetary authority in each country acts separately and sets its own interest rate according to the economic situation of its own country. The interest rate levels in the domestic and foreign asset markets are different. i denotes the Home interest rate and i * denotes the Foreign interest rate. The Taylor rules of the country H and F are given by

 t    

1  it  1  i 

1  it 1 

1  it*  1  i

 1  i 

1 



* 1 

* t 1



1  1

 *t   *   

 Yt    Y 

1  1*

1 2

 Yt*   *  Y 

exp  Hm ,t ,

1   2*

exp  Fm, t  .

(44)

(45)

where  Hm ,t and  Fm,t are i.i.d monetary policy shocks in the Home and Foreign countries, respectively, and 1 (1* ) and 2 (2* ) are policy parameters determined by the monetary authority.8 Under the monetary union regime, the common monetary authority sets the common interest rate ( i MU ) according to the union-wide economic situation, which prevails in the monetary union: 1 i

MU t

 1  i

 1  i 

MU 1 

MU t 1



  tMU   MU   

1  1

 Yt MU   MU  Y 

1  2

m exp  MU ,t .

(46)

m MU where  MU is the gross inflation rate ,t is an i.i.d monetary policy shock, and  t

in the monetary union as follows:

 tMU 

Pt MU , Pt MU 1

(47)

where Pt MU is the union-wide price index as a population-weighted geometric average of the CPI in these two countries and is given by:9 Pt MU  Pt n Pt*  . 1n

(48)

In the same way, Yt MU is the union-wide level of output as a population-weighted geometric average of the levels of output in countries H and F : Yt MU  Yt n Yt*  . 1n

8

9

(49)

In the following numerical analyses, we assume that the monetary policy authorities in the home and foreign countries implement the same policy parameters such that 1  1* and 2  2* . This definition is the model-equivalent of the Harmonized Index of the Consumer Price(HICP) of the Euro area.

13

2.5. Fiscal policy The governments of these two countries conduct independent fiscal policies regardless of monetary policy implementations. The government spending falls on both the tradable and non-tradable goods, with the same composition of consumption goods. The levels of government expenditure on tradable goods GH ,t

and

non-tradable goods GN ,t are given by GH , t  Gt ,

(50)

GN , t  1    Gt .

(51)

where Gt is an exogenous government expenditure shock.

The country-wide

government expenditure follows an AR (1) process: Gt  GtG1G1 G exp  tG  .

(52)

where G  1 and  tG ~ N 0, G  . The government’s budget constraint can be written as: PG t t  Tt   Tt  h  dh . n

(53)

0

2.6. Market Clearing The market clearing conditions for tradable goods, non-tradable goods and labor are given by YH , t  CH , t  CH* , t  GH ,t * F, t

Y

 CF , t  C

* F, t

G

* F, t

(54) ,

(55)

YN , t  CN , t  GN , t ,

(56)

YN** , t  CN* * , t  GN* * , t ,

(57)

Lt  LH ,t  LN ,t ,

(58)

L L * t

* F, t

L

* N* , t

.

(59)

Finally, the asset market clearing condition requires that

Bt  Bt*  nBt h   1  n Bt* h   0 .

(60)

3. Calibration This section reports the procedure for the parameter settings used in solving the model. In order to avoid the effect of population size on the analysis and similar shares, population size n is set to 0.5 in both countries. First, we specify the degree of openness which was defined as the share of the Home tradable goods in its aggregate consumption  , and the share of the Foreign tradable goods in the Foreign aggregate consumption  * , following the empirical studies by Lombardo and Ravenna (2014). 14

From the results that they report, we divide the member countries of the Euro area into two groups based on the degree of openness. The countries with the degree of openness greater than or equal to 0.697 are classified as the high-openness country, and the countries with the openness lower than 0.697 are classified as the low-openness country.10 , 11 Within either group, we use the GDP as the share to compute the weighted average of degree of openness, which is 0.7283 and 0.5897 for the high-openness and low-openness countries respectively. Therefore, we specify the degree of openness of the high-openness and low-openness countries as 0.73 and 0.59 respectively. Furthermore, the shares of the Home tradable goods in the Home and Foreign consumption bundles,  and  * , are assumed to be 0.57 and 0.43, respectively, to capture the home bias in consumption, which is consistent with Eggertsson et al. (2014). The subjective discount factor  is set to 0.99, which implies a 4% annual real rate in the steady state. Following the estimation of Hansen and Singleton (1983), the coefficient of relative risk aversion  is set to 0.5. The inverse of the labor supply elasticity  is set to 6, which is commonly used in the New-Keynesian literature. Based on Quint and Rabanal (2014), the elasticity of substitution between the Home and Foreign tradable goods  is set to 1.9, and the elasticity of substitution between tradable and non-tradable goods  is set to 0.5, which is consistent with Mendoza (1991). To ensure the stationarity of the net Foreign asset position, the intermediation cost  B is set to 4  106 , as in Erceg (2006). As for the firm sector, we establish the probabilities of holding the price fixed in a certain period  k equal to 0.66 which implies an average frequency of price changes of 3 quarters, which is consistent with the calibration of Eggertsson et al. (2014). The elasticity of substitution  in sector k across regions is set to 6

k  6 ,

which implies a steady-state markup of 1.2. The share of government

expenditure in GDP is set to 0.2, as in Rabanal (2009). In addition, we assume that both the productivity and government expenditure shocks follow an AR (1) process. The autocorrelation coefficient of productivity shock is set to 0.9, following Rabanal (2009). Based on the findings of Duarte and Wolman (2008), the autocorrelation coefficient of the government expenditure shock is set to 0.42. Following Quint and Rabanal (2014), we set the policy parameters of the nominal interest rate rule 1 ,  2 and  equal to 1.56, 0.2 and 0.8, respectively, which are assumed to be identical across countries. 10

11

Following the estimation of Lombardo and Ravenna (2014), Table 1 shows that the degrees of openness of Belgium, Austria, the Netherlands and Germany are more than 0.697 (the degree of openness of Portugal is equal to 0.697), which are classed as countries with a high degree of openness. Conversely, the degrees of openness of Spain, France, Italy, Greece and Finland are less than 0.697, which are classed as countries with a low degree of openness. The share of high openness countries in the Euro area is about 43%.

15

16

4. Analyses In this section, we will examine the effects of the openness differential on the economy’s response to shocks across monetary regimes. In Section 4.1, we outline the impulse response analyses to the exogenous shocks to show how different degrees of openness may result in different macroeconomic responses to shocks. In Section 4.2, we perform the robustness analysis. In this study, we consider both the productivity shock and the government expenditure shock. There are two types of productivity shocks. One is the sector-specific productivity shock to sector k where k  H , N denotes the tradable and non-tradable sectors, respectively. The other is the country-wide productivity shock. We assume a productivity shock of 1% with an AR (1) coefficient of 0.9. A government expenditure shock is also assumed to be 1% with an AR (1) coefficient of 0.42. 4.1. Differences in the degree of trade openness across regimes To compare the impulse response analyses under different degrees of trade openness across regimes, we categorize the countries into two types. Following Lombardo and Ravenna (2014), the degrees of openness (  and  * ) are assumed to be 0.59 and 0.73 for the low-openness and high-openness countries, respectively. In all the figures for the impulse response functions, the “blue line” denotes the Home country, the “red line” denotes the Foreign country, while the “solid line” denotes the monetary union regime, and the “dashed line” denotes the flexible exchange rate regime. 4.1.1. The productivity shock in the Home tradable sector Panel (a) in Fig. 2 plots the dynamic effect of a 1% productivity shock on the Home tradable sector in the low-openness country. Under the monetary union regime (solid line), a fall in the productivity of the Home tradable sector not only reduces the Home output and consumption, but also increases the Home inflation and labor. A reduction in the Home consumption of the Foreign tradable goods results in a decrease in the Foreign output. The Foreign inflation increases due to the rise in the prices of Home tradable goods. The interest rate rises due to higher inflation and causes the intertemporal substitution effect which lowers the current consumption. The rise in inflation and interest rate lowers the Foreign consumption. The impulse responses of consumption and inflation are similar to those in Duarte and Wolman (2008), with the exception of the impulse response of the Foreign output.12 12

When we raise the elasticity of substitution between the home tradable goods and foreign tradable goods  , home and foreign households will increase their consumption of the foreign tradable goods, which increases the foreign output. This result is consistent with Duarte and Wolman (2008).

17

On the other hand, under the flexible exchange rate regime (dashed line), a rise in the prices of the Home tradable goods brings about a trade deficit, which causes the Home currency to depreciate. The Home currency depreciation helps lower the price of the Home tradable goods, and helps increase the Foreign demand for the Home tradable goods which dampens the fall in the Home output and consumption. The expenditure-switching effect from the Home currency depreciation, however, intensifies the decline in the Foreign output and consumption. This flexible exchange rate adjustment mechanism is absent from the monetary union. Thus, compared with the flexible exchange rate regime, the Home inflation rate and thereby the interest rate, which responds to the inflation rise, of the monetary union is higher, while the Foreign inflation rate and interest rate is lower. As a result, the absence of the Home currency depreciation, together with the intertemporal substitution effect of the higher interest rate, intensifies the decline in the Home output and consumption, but dampens the decline in the Foreign output and consumption. The monetary union regime widens the regional differential between the Home and Foreign countries. Furthermore, the effects of an adverse productivity shock may differ under different degrees of openness. In panel (b) in Fig. 2, the shock occurs to the Home country with higher degree of openness and leads to greater declines in output and consumption in the Home and Foreign countries, and causes greater Home currency depreciation. Thus, the result suggests that if there is an adverse productivity shock to the tradable sector in the more open country, the loss of the Home country from joining the monetary union by abandoning the flexible exchange regime which helps dampen the domestic impact, may be greater. (a) (b) High Openness (   0.73,  *  0.59 )

Percent

Percent

Low Openness (   0.59,  *  0.73 )

18

Percent Percent Percent Percent

MU Home Case Flex Home Case MU Foreign Case Flex Foreign Case

Fig. 2.

i (MU Case) i (Flex Home Case) i* (Flex Foreign Case)

The productivity shock of the tradable sector in the Home country.

.

4.1.2. The productivity shock in the Home non-tradable sector Panel (a) in Fig. 3 plots the dynamic effects of a 1% productivity shock to the Home non-tradable sector in the low-openness country. In the monetary union (the solid line), lower productivity in the non-tradable sector under sticky prices will lead to a greater demand for labor to offset the decline in productivity, which leads to a higher wage. As a result, the marginal cost of tradable goods production is higher, resulting in a lower production of tradable goods and overall production in the Home country. Thus, the income effect reduces the consumption demands for both the Home and Foreign goods, which results in lower Foreign output. The international transmission mechanism under the non-tradable shock, however, is small relative to that under the shock to the tradable sector. Thus, the Home country will bear most

19

of the adverse shock. The shock to the non-tradable sector will enlarge the regional differential, which is similar to the findings reported in Duarte and Wolman (2008). Under the flexible exchange rate regime (dashed line), on the occurrence of the productivity shock in the Home non-tradable sector, the initial exchange rate remains roughly unchanged, but the Home interest rate rises. The intertemporal substitution effect from the interest rate rise not only intensifies the decline in the Home consumption, but also that in the Home output. For the Foreign country, the flexible exchange rate regime helps dampen the decline in Foreign output. The comparison between panels (a) and (b) in Fig. 3, shows that, there are greater declines in output and consumption as well as greater increases in inflation and labor employment in the low-openness country. (b) High Openness  (  0.73,  *  0.59 )

Percent

Percent

Percent

Percent

Percent

(a) Low Openness  (  0.59,  *  0.73 )

20

Percent

MU Home Case Flex Home Case MU Foreign Case Flex Foreign Case

i (MU Case) i (Flex Home Case) i* (Flex Foreign Case)

Fig. 3. The productivity shock of the non-tradable sector in the Home country. A comparison between Fig. 2 and Fig. 3 demonstrates the effect of the monetary union on the transmission mechanism of shocks may crucially depend on the source of the shocks. The exchange rate adjustment mechanism under the flexible exchange rate regime helps transmit the shock from the tradable sector in one country to the other, but this mechanism is mute under the shock from the non-tradable sector.

Therefore, joining the monetary union does not lead to significant difference in the regional differential under the productivity shock to the non-tradable sector. Moreover, the rise in inflation caused by adverse shock to nontradable productivity remains mostly domestically and thus there rise in the Foreign inflation is smaller, compared with the shock to the Home tradeable sector. This results in lower union-wide inflation and interest rate in the monetary union.

4.1.3. Country-wide productivity shock Fig. 4 plots the dynamic effects of a  1% Home country-wide productivity shock in the low-openness country. The country-wide shock will affect both the tradable and non-tradable sectors and thus the effects can be considered as the combined effects from previous two sections. As shown above, the shock to the tradable sector can be more easily shared across countries through trades, but not the shock to the nontradable sector. As a result, the country-wide shock to the more open country with larger tradable sector can be more easily dampened. The comparison between panel (a) and (b) in Fig. 4 shows that the decline in output and consumption in the Home country with higher degree of openness is smaller under the adverse shock. This can be consistent with the observation from Fig. 1 which presents the negative relationship between the degree of openness and recessions under adverse shocks.

21

(b) High Openness (   0.73,  *  0.59 )

Percent

Percent

Percent

Percent

Percent

Percent

(a) Low Openness (   0.59,  *  0.73 )

MU Home Case Flex Home Case MU Foreign Case Flex Foreign Case

i (MU Case) i (Flex Home Case) i* (Flex Foreign Case)

Fig. 4. The country-wide productivity shock in the Home country. 22

4.1.4. Country-wide government expenditure shock Panel (a) in Fig. 5 plots the dynamic effects of a  1% country-wide government expenditure shock to the Home country with a lower degree of openness. In the monetary union, the decline in the demand for the Home goods reduces output, labor employment, inflation and thereby the interest rate. The current consumption rises due to the intertemporal substitution effect due to lower interest rate, which helps offset the decline in the government spending. The decrease in the price of the Home tradable goods causes not only an increase in the Foreign consumption of the Home tradable goods but also an increase in the Foreign consumption and deflation. The increase in the Home demand for the Foreign tradable goods also contributes slightly to the increase in the Foreign output. While the impulse response analyses of other variables are consistent with Duarte and Wolman (2008), that of the Foreign output and labor employment differ. (a) (b) Low Openness (   0.59,  *  0.73 )

High Openness

Percent

Percent

Percent

(   0.73,  *  0.59 )

23

Percent Percent Percent

MU Home Case Flex Home Case MU Foreign Case Flex Foreign Case

Fig. 5.

i (MU Case) i (Flex Home Case) i* (Flex Foreign Case)

The country-wide government expenditure shock in the Home country.

Under the flexible exchange rate regime, the Home interest rate is lower compared to the monetary union regime. The intertemporal substitution effect due to the decreased interest rate boosts an increase in the Home consumption. On the other hand, the Home currency depreciation increases the Foreign demand for the Home tradable goods, but increases the decline in the Home consumption. Thus, the flexible exchange rate regime helps moderate the decline in the Home output due to the adverse demand shock. The monetary union where this mechanism is absent may lead to a greater decline in the Home output, but lowers the decrease in Home consumption. Therefore, the monetary union dampens the regional differential in output under the adverse demand shock, but raises the regional differential in consumption.

Since the government spending is composed of only the Home goods, the impact of the decrease in the government expenditure falls more heavily on the Home production. Thus, comparing panels (a) and (b) in Fig. 5, there is a greater reduction in output and labor employment, but also greater deflation in the low-openness country. Thus, the decline in the output due to monetary union is greater for a country with lower degree of openness. 24

4.2. Robustness Check In this section, we will examine the macroeconomic dynamics across regimes and different degrees of openness under different specifications of parameters for the robustness analysis. This may help us better understand the effects of the degree of openness and monetary policy implementation on the impacts of different shocks. 4.2.1. Monetary policies Table 2 The policy parameters for the Taylor rule. Targeting

1

2

Literature

Output-gap stabilization

1.7

0.4

Forni et al. (2010)13

Benchmark

1.56

0.2

Quint et al. (2014)

Inflation stabilization

1.85

0.15

Poutineau and Vermandel (2015)

As discussed above, the monetary policy may play a crucial role in directing the macroeconomic responses to shocks. In this section, we will examine the policy parameters of the Taylor rule, based on the various calibration and estimation results from the literature on the Euro area. For a monetary authority which places emphasis on the inflation and output gap, the policy parameters can be divided into three groups: the output-gap stabilization, benchmark (as in Section 3), and inflation stabilization, as listed in Table 2. The policy parameters for the output-gap stabilization are specified as 1  1.7 and 2  0.4 , following Forni et al. (2014). The parameters of the monetary policy which emphasize the inflation rate stabilization are assumed to be 1  1.85 and 2  0.15 , based on the Bayesian estimation of the Eurozone by Poutineau and Vermandel (2015).14 The following discussion will center on two channels, exchange rate and interest rate channels, as stated above. The “exchange rate channel” indicates the exchange rate flexibility which helps dampen the negative effects from the adverse productivity shock on the Home country. The “interest rate channel” indicates the interest rate rise due to higher inflation under adverse productivity shock. These two effects play the key role under shocks but counteract each other. Fig. 6 plots the output effects of a 1% productivity shock to the Home tradable sector under these three specifications of monetary policy parameters. Column (a) in Fig. 6 shows the different output dynamics under the adverse productivity shock to the Home tradable sector of the low-openness country under different specifications of policy parameters. Column (b) considers the shock to the high-openness country. Column (c) shows the across-regime difference in the Home 13

14

As for the literature on output-gap targeting, we also refer to Lama and Rabanal (2014). Regarding the literature on inflation targeting, we refer to Amisano and Tristani (2010). As to the literature on benchmarks, we consider Benchimol and Fourcans (2012) as well as Gerali et al. (2010). In each of the cases, this policy parameter specification is used for both countries under the flexible exchange rate regime, and is also used by the monetary authority of the monetary union.

25

the analysis of Section 4.1.1. (a)

(b)

Low Openness (   0.59,  *  0.73 )

High Openness (   0.73,  *  0.59 )

(c)

Percent Percent

Percent

Benchmark (v1 = 1.56, v2 = 0.2) Inflation Stabilization (v1 = 1.85, v2 = 0.15)

Output-Gap Stabilization (v1 = 1.7, v2 = 0.4)

output. It is shown that there are greater decreases in the output of the high-openness country under all policy specifications. This result is consistent with

Fig. 6.

The output effect of a 1% productivity shock to the tradable sector under different monetary policies.

However, the way in which the monetary policy is implemented can crucially affect the across-regime differences. As shown in column (c), the monetary union results in a greater decline in output if the monetary authority attaches greater importance to output stabilization, while the monetary union may lower the decline in output if there is a bigger attempt to stabilize the inflation rate. This is because the interest rate channel approximates the exchange rate channel under the inflation stabilization policy, but the effects of the interest rate channel are still less than those of the exchange rate channel. Fig. 7 plots the output effects of a 1% productivity shock to the Home non-tradable sector under three monetary policies. Similar to Fig. 6, Column (a) 26

shows the dynamics under the shock to the low-openness country, Column (b) considers the shock to the high-openness country, while Column (c) presents the across-regime difference. It is shown that there are greater decreases in the output of the low-openness country under all policy specifications. This result is consistent with the analysis of Section 4.1.2. (b) High Openness (   0.73,  *  0.59 )

(c)

Output-Gap Stabilization (v1 = 1.7, v2 = 0.4) Percent

(a) Low Openness (   0.59,  *  0.73 )

Benchmark (v1 = 1.56, v2 = 0.2) Percent

10-3 Y(MU Case)- Y(Flex Case)

Inflation Stabilization (v1 = 1.85, v2 = 0.15) Percent



Fig. 7.

The output effect of a 1% productivity shock to the non-tradable sector under different monetary policies.

As shown in Column (c), the monetary union results in a greater decline in output if the monetary authority places greater weight on output stabilization, while the monetary union may help raise output if there is a stronger attempt to stabilize the inflation rate. This is because the interest rate channel is greater than the exchange rate channel under the inflation stabilization policy. A comparison between Fig. 6 and 7 shows that the monetary policy can influence the impacts of different types of shocks. The monetary union can also lower the output effect of a shock on the tradable productivity, but raise that on the non-tradable productivity if the benchmark 27

or inflation stabilization policy is implemented. If the output-gap stabilization policy is implemented, the monetary union can lower both the shocks to the tradable and non-tradable productivity. Fig. 8 plots the output effects of a 1% country-wide productivity shock on the Home country under three monetary policies with the same outline. It is shown that there are greater declines in the output of the low-openness country under all policy specifications. This result is consistent with the analysis of Section 4.1.3. Furthermore, the across-regime comparison in column (c) shows that the monetary union results in a greater decline in output if the monetary authority attaches greater importance to output stabilization. However, the monetary union may help raise output if there is greater attempt to stabilize the inflation rate. This is because the interest rate channel is greater than the exchange rate channel under the inflation stabilization policy. Furthermore, in the absence of an exchange rate adjustment mechanism, these effects can be stronger for the output of the low-openness country. (a) (b) (c) High Openness (   0.73,  *  0.59 )

Benchmark (v1 = 1.56, v2 = 0.2) Percent

Output-Gap Stabilization (v1 = 1.7, v2 = 0.4) Percent

Low Openness (   0.59,  *  0.73 )

Inflation Stabilization (v1 = 1.85, v2 = 0.15) Percent

10-3 Y(MU Case)- Y(Flex Case)

Fig. 8.

The output effect of a 1% country-wide productivity shock under different monetary policies. 28

Fig. 9 outlines the output effects of a 1% country-wide government expenditure shock under three different kinds of monetary policy. Similar to Fig. 8, column (a) shows the dynamics under the shock to the low-openness country, column (b) shows the dynamics under the shock to the high-openness country, while column (c) shows the across-regime difference. Similar to Section 4.1.4, output in all cases falls upon the negative demand shock, and the output declines more in the low-openness country. Furthermore, the monetary union tends to lower output under all three policy specifications, but the across-regime difference under the adverse demand shock is greater under the output stabilization policy. (a)

(b)

Low Openness (   0.59,  *  0.73 )

High Openness (   0.73,  *  0.59 )

(c)

Output-Gap Stabilization (v1 = 1.7, v2 = 0.4) Percent

10-3 Y(MU Case)- Y(Flex Case)

Benchmark (v1 = 1.56, v2 = 0.2) Percent

10-3 Y(MU Case)- Y(Flex Case)

Inflation Stabilization (v1 = 1.85, v2 = 0.15) Percent

10-3 Y(MU Case)- Y(Flex Case)

Fig. 9.

The output effect of a 1% country-wide government spending shock under different monetary policies.

4.2.2. Elasticity of substitution The elasticity of substitution between the Home and Foreign tradable goods can crucially affect the consumers’ spending on the Home and Foreign tradable goods, and thus affect the across-regime output effects under tradable productivity shocks. 29

Thus, it would be interesting for us to examine the effects of the elasticity of substitution on the output effect of the tradable productivity shock under different regimes. The first row of Figure 10 outlines the dynamics of output in the low-openness and high-openness countries across regimes under the benchmark value of an elasticity of substitution of   1.9 , when the 1% productivity shock to the Home tradable goods sector takes place. The second row of Figure 10 outlines the same dynamics under an alternative value of the elasticity of substitution of   4.43 , according to the Bayesian estimation of the Eurozone by Poutineau and Vermandel (2015). (a) (b) (c) High Openness (   0.73,  *  0.59 )

(θ = 4.43) Percent

(θ = 1.9) Percent

Low Openness (   0.59,  *  0.73 )

Fig. 10. The dynamics under a 1% productivity shock to the tradable goods sector under alternative elasticities of substitution.

A comparison between the first and second rows shows that the high elasticity of substitution results in greater output decline, and a greater across-regime differential under the adverse shock to tradable goods productivity. While the elasticity of substitution is high, the monetary union may lower output more than under the flexible exchange rate regime. This result is quite intuitive. People will consume more Foreign goods if an adverse shock affects the Home tradable goods productivity. The decline in the consumption, and thereby the production, of the Home goods can be greater under a higher elasticity of substitution. Under a flexible exchange rate regime, the Home currency may depreciate to dampen this effect. In a monetary union 30

where the exchange rate adjustment is absent, the output can decline more. The across-regime differential, however, is about the same regardless of the degree of openness. The across-regime differential under the shock to the non-tradable goods productivity is negligible, but the effects under the country-wide productivity shock and government spending shocks are similar to those of the tradable productivity shock.

5. Welfare gains across regimes Following the same approach by Schmitt-Grohé and Uribe (2007), we calculate the welfare gains across regimes. Given a set of allocations i , where i  MU case is the allocation under the monetary union regime, and i  Flex case is the allocation under the flexible exchange rate regime, the welfare gain  i is calculated as follows: 1  1     i 1 Lit h 1  i   L1  t C t h    E0    C   E0      1   1  1 1   1     100   t 0 t 0   where C and L are the steady-state values of consumption and labor. 

t

(61)

The (net) welfare gain across regimes  is obtained as follows: (62)    MU case   Flex case If the resulting value  is positive, there will be a (net) welfare gain entering a monetary union regime. On the other hand, if  is negative, a country will be better off maintaining a flexible exchange rate regime. This section examines the welfare gains (losses) of entering the monetary union under a 1% Home and Foreign country-wide productivity shock and government spending shock for the Home country with different degrees of trade openness. Since the welfare gain can be sensitive to the value of the monetary policy responses and the elasticity of substitution, we outline the results under different output responses of the Taylor rule in Fig. 11, and under different values of the elasticity of substitution between the tradable goods in Fig. 12. As shown in panel (a) in Fig. 11, under a 1% Home country-wide productivity shock, the Home country, regardless of the degree of openness, is indifferent across regimes where   0 when 2  0.05 . When the output response of the monetary policy is less than 0.05, the Home country can experience a welfare loss by entering the monetary union. The stronger output response helps lower the welfare loss, and results in the welfare gain from entering the monetary union when the output response exceeds 0.05. The welfare gain under the monetary union (relative to the flexible exchange rate regime) is smaller for a country with a low degree of openness. As shown in panel (b) in Fig. 11, if the adverse shock comes from the Foreign country, the Home country may benefit from entering the monetary union if the output response is small (this can be considered as the Home country shock’s impact 31

on the Foreign country). The Home country with a low degree of openness can be indifferent across regimes if 2  0.04 , and the welfare gain from joining a monetary union decreases with the increase in the policy’s response to the output gap. The welfare gain or loss associated with each policy parameter is greater for the high-openness country, and the cutoff point of  2 is also higher. (b) Home Country Foreign Country-Wide Productivity Shock Welfare Gain

Home Country-Wide Productivity Shock Welfare Gain

(a) Home Country

2

2

Fig. 11. The welfare gain  under alternative monetary policy responses to the output-gap. Note:  2 is the output-gap parameter of the Taylor rule.

Under the flexible exchange rate regime, the exchange rate flexibility helps stabilize the (Home) economy under the Home shock, and it is not necessary to stabilize the (Home) economy with the output-gap stabilization policy. A bigger attempt to stabilize the output with this policy may lower the welfare instead.15 However, while the exchange rate adjustment is absent, the greater the output stabilization that the policy entails, the more that it can help stabilize the (Home) economy and raise the (Home) welfare. Thus, the monetary policy with greater output-stabilization can welfare-dominate the policy under the flexible exchange rate regime in the Home country, but welfare is dominated in the Foreign country. The flexible exchange rate regime with less emphasis on the output-stabilization policy, nevertheless, will reverse the welfare measure. As depicted in panel (a) in Fig. 12, following a 1% Home country-wide productivity shock, the welfare gain of the Home country increases at first with the rise in  , and then decreases when  is less than 2.3 in the monetary union. When  is equal to 2.3, the welfare gain from entering the monetary union is maximized. As is obvious, the welfare gain is greater for a country with a high 15

Please refer to Kollmann (2002), Bergin et al. (2007) and Gali and Monacelli (2008).

32

degree of openness. In panel (b) in Fig. 12, if the adverse shock comes from the Foreign country, the Home welfare loss from the monetary union will increase at first with the rise in  , and then decline when  is greater than 1.7 in the monetary union. When  is equal to 1.7, the welfare loss of the Home country is maximized in the monetary union. Accordingly, the welfare loss from entering the monetary union is greater for a country with a high degree of openness.

Fig. 12.

(b) Home Country Foreign Country-Wide Productivity Shock Welfare Gain

Home Country-Wide Productivity Shock Welfare Gain

(a) Home Country

θ

θ

Welfare as a function of the elasticity of substitution between the Home and Foreign tradable goods,  .

Note that, the degree of openness also leads to the welfare difference between the monetary union and flexible exchange rate regime, and thereby results the welfare gain (or loss) of monetary union relative to the flexible exchange rate, as shown in Fig. 12. The solid and dash curves correspond to the welfare gain of monetary union under the high and low openness respectively. As shown in panel (a), the Home country’s welfare gain from the monetary union is lower when the Home country where the shock originates is more open, regardless of the elasticity of substitution, since its loss under the monetary union where the exchange rate flexibility is missing can be greater. Similarly, if the shock occurs to the Foreign country, the welfare loss of the Home country will be smaller if the Home country is more open.16

6. Conclusion This paper uses a two-country, two-sector model under both monetary union and flexible exchange rate regimes to examine how the macroeconomic effects of an 16

In the literature, the central bank of an open economy may tend to manipulate the exchange rate to benefit the exports, which is known for the terms-of-trade externality. However, with the common monetary authority in this study, the terms-of-trade externality can be internalized. While the terms-of-trade externality is not the focus of this study, it can be an interesting issue for the future study on the monetary union.

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adverse shock may differ with the trade openness. Two main findings are obtained from our simulation analyses regarding an adverse shock to the country-wide productivity or government expenditure. First, the decrease in output is greater for a country with a low degree of openness under both regimes. However, the exchange rate flexibility helps dampen the output declines, and thus the output of a country with lower openness declines more in a monetary union where the exchange rate flexibility is absent. Second, the macroeconomic effects of an adverse shock may vary with the degree of output stabilization of the monetary authority and elasticity of substitution between the Home and Foreign tradable goods. The declines in output are greater if the monetary authority of the monetary union attaches greater importance to output stabilization. The difference in the output decline across regimes is greater when the elasticity of substitution is greater. One extension could be considered in future research. According to Schmitz and Hagen (2011) as well as Belke and Dreger (2013), the empirical evidence reveals that the country has a current account imbalance in the Euro area compared to the extra-Euro area. It would be plausible to extend the analysis by setting up a three-country model to explore the relationship between the trade openness and current account imbalance in the monetary union when taking into account its relationship with the extra-Euro area. This extension inevitably complicates the analysis, but it deserves future study.

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References Altissimo, F., Benigno, P. & Palenzuela, D. R. (2011). Inflation Differentials in a Currency Area: Facts, Explanation and Policy. Open Economies Review, 22, 189-233. Amisano, G. & Tristani, O. (2010). Euro Area Inflation Persistence in an Estimated Nonlinear DSGE Model. Journal of Economic Dynamics and Control, 34, 1837-1858. Beetsma, R. M. W. J. & Jensen, H. (2005). Monetary and Fiscal Policy Interactions in a Micro-Founded Model of a Monetary Union. Journal of International Economics, 67, 320-352. Belke, A. & Dreger, C. (2013). Current Account Imbalances in the Euro Area: Does Catching up Explain the Development?. Review of International Economics, 21, 6-17. Benchimol, J. & Fourçans, A. (2012). “Money and Risk in a DSGE Framework: A Bayesian Application to the Eurozone. Journal of Macroeconomics, 34, 95-111. Benigno, G. & Thoenissen, C. (2003). Equilibrium Exchange Rates and Supply-Side Performance. Economic Journal, 113, 103-124. Benigno, P. (2004). Optimal Monetary Policy in a Currency Area. Journal of International Economics, 63, 293-320. Bergin, P. R., Shin, H. C. & Tchakarov, I. (2007). Does Exchange Rate Variability Matter for Welfare? A Quantitative Investigation of Stabilization Policies. European Economic Review, 51, 1041-1058. Calvo, G. A. (1983). Staggered Prices in a Utility-maximizing Framework. Journal of Monetary Economics, 12, 383-398. Corsetti, G. (2006). Openness and the Case for Flexible Exchange Rates. Research in Economics, 60, 1-21. Corsetti, G., Dedola, L. & Leduc, S. (2008). International Risk Sharing and the Transmission of Productivity Shocks. Review of Economic Studies, 75, 443-473 Duarte, M. & Obstfeld, M. (2008). Monetary Policy in the Open Economy Revisited: The Case for Exchange-Rate Flexibility Restored. Journal of International Money and Finance, 27, 949-957. Duarte, M. & Wolman, A. L. (2008). Fiscal Policy and Regional Inflation in a Currency Union. Journal of International Economics, 4, 384-401. Eggertsson, G., Ferrero, A. & Raffo, A. (2014). Can Structural Reforms Help Europe?. Journal of Monetary Economics, 61, 2-22. 35

Erceg, C., Guerrieri, L. & Gust, C. (2006). SIGMA: A New Open Economy Model for Policy Analysis. International Journal of Central Banking, 2, 1-50. Faia, E. & Monacelli, T. (2008). Optimal Monetary Policy in a Small Open Economy with Home Bias. Journal of Money, Credit and Banking, 40, 721-750. Ferrero, A. (2009). Fiscal and Monetary Rules for a Currency Union. Journal of International Economics, 77, 1-10. Forni, L., Gerali, A. & Pisani, M. (2010). Macroeconomic Effects of Greater Competition in the Service Sector: The Case of Italy. Macroeconomic Dynamics, 14, 677-708. Gali, J. & Monacelli, T. (2008). Optimal Monetary and Fiscal Policy in a Currency Union. Journal of International Economics, 76, 116-132. Gerali, A., Neri, S., Sessa, L. & Signoretti, F. M. (2010). Credit and Banking in a DSGE Model of the Euro Area,” Journal of Money, Credit and Banking, 42, 107-141. Hansen, L. P. & Singleton, K. (1983). Stochastic Consumption, Risk Aversion, and the Temporal Behavior of Asset Returns. Journal of Political Economy, 91, 249-265. in’t Veld, J., Kollmann, R., Pataracchia, B., Ratto, M. & Roeger, W. (2015). International Capital Flows and the Boom-Bust Cycle in Spain. Journal of International Money and Finance, 48, 314-335. Kollmann, R. (2002). Monetary Policy Rules in the Open Economy: Effects on Welfare and Business Cycles. Journal of Monetary Economics, 49, 989-1015. Kollmann, R. (2004). Welfare Effects of a Monetary Union: The Role of Trade Openness. Journal of the European Economic Association, 2, 289-301. Lama, R. & Rabanal, P. (2014). Deciding to Enter a Monetary Union: The Role of Trade and Financial Linkages. European Economic Review, 72, 138-165. Leith, C. & Wren-Lewis, S. (2011). Discretionary Policy in a Monetary Union with Sovereign Debt. European Economic Review, 55, 93-117. Lombardo, G. & Ravenna, F. (2014). Openness and Optimal Monetary Policy. Journal of International Economics, 93, 153-172. McKinnon, R. I. (1963). Optimum Currency Areas. American Economic Review, 53, 717-725. Mendoza, E. (1991). Real Business Cycles in a Small Open Economy. American Economic Review, 81, 797-818. Mundell, R. A. (1961). A Theory of Optimum Currency Areas. American Economic Review, 51, 657-675.

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Okano, E. (2014). How Important is Fiscal Policy Cooperation in a Currency Union?. Journal of Economic Dynamics and Control, 38, 266-286. Poutineau, J. & Vermandel, G. (2015). Cross-Border Banking Flows Spillovers in the Eurozone: Evidence from an Estimated DSGE Model. Journal of Economic Dynamics and Control, 51, 378-403. Quint, D. & Rabanal, P. (2014). Monetary and Macroprudential Policy in an Estimated DSGE Model of the Euro Area. International Journal of Central Banking, 10, 169-236. Rabanal, P. (2009). Inflation Differentials Between Spain and the EMU: A DSGE Perspective. Journal of Money, Credit, and Banking, 41, 1142-1166. Schmitt-Grohé, S. & Uribe, M. (2007). Optimal Simple and Implementable Monetary and Fiscal Rules. Journal of Monetary Economics, 54, 1702–1725. Schmitz, B. & Jürgen Von Hagen, J. (2011). Current Account Imbalances and Financial Integration in the Euro Area. Journal of International Money and Finance, 30, 1676‐1695.

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