Literature review

authority copes with shocks in a monetary union with a dynamic stochastic general equilibrium (DSGE) model whether the fund mechanism is successful to reduce the impacts of shock. In accordance with Robio and Roldan (2003) which built an explicit form of fiscal coordination to simulate its effect in a monetary union by using the data of the EMU, we set a cast of fund mechanism into a monetary union to simulate a fiscal coordination among member states.

Gali and Monacelli (2008) modeled the currency union as a continuum of small open economies in a micro-founded model in the presence of nominal rigidity. They evaluate the role of monetary and fiscal policies in the country and union level, respectively. We follow their framework and embed a fund mechanism in the union¹

Under the fund mechanism, there is a central fiscal authority that raises the constant fund payment from all member countries and redistributes it to member states. Hence, the local governments can focus on their provision of public goods and the fluctuation of output could be absorbed by the net transfer. We find that the net transfer only substitutes some parts of local government spending. This kind of fiscal coordination is not necessary for a monetary union.

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1.2. Literature review

Several papers have discussed the influence of monetary and fiscal policies together in a currency union. Beesta and Jensen (2005) addressed the interaction between monetary and fiscal policies in a two-country, micro-founded model of a monetary union with sticky prices. They discussed the mechanism of the fiscal stabilization policy and commitment and identify the gains of it. Their results

1 We refer to Chatterjee and Turnovsky (2005) developed the public capital fashion that accumulates from two sources: constant government expenditure and transfer from the rest of the world, for the fund transfer between the fiscal authority and individual countries.

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suggested that there were not trivial gains from the fiscal stabilization and commitment. Sánchez (2010) also discussed the interplay of monetary and fiscal policies in a multinational currency union and focused on the free-rider problems which lead to the failure of the fiscal coordination. Therefore, he suggested that the fiscal budget considerations as the Stability and Growth Pact could against the fluctuations caused by shocks.

In recent years, several literatures focused on the fiscal coordination among countries in a monetary union. For instance, Kirsanova, Satchi and Vines (2004) pointed out that an active fiscal policy could significantly improve welfare and provide macroeconomic stabilization in the face of asymmetric shocks in a monetary union. Oros (2008) proved that no matter the demand or supply shocks, the fiscal coordination was an optimal shock absorber in a closed monetary union with a two-country, static Keynesian model. Valeria and Pompeo (2010) found that if member countries were hit by asymmetric shocks, the fiscal cooperation and state-contingency were necessary to obtain an efficient outcome.

Robio and Roldan (2003) used the change in the unemployment rate as an indicator to redistribute funds with the monthly data of 11 countries in EMU showed that the insurance mechanism would lead a higher stabilizing effect the more asymmetric was the shock.

Gali and Monacelli (2008) assumed a common policymaker to determine the monetary and fiscal policies together in the union-wide. Therefore, the common policymaker was not only a central bank but also a central fiscal authority. Under their investigation, the fiscal policy had a country-specific stabilization role in the equilibrium.

Some empirical studies have formed the specific fashion of fiscal coordination and discuss the effects in the European Union. But there is no discussion of the form

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立 政 治 大 學

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N a tio na

l C h engchi U ni ve rs it y

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of fiscal coordination in DSGE model. Therefore, we want to capture the stabilized function of fiscal coordination in a monetary union. We include a fund mechanism in a union with a DSGE model to discuss how the central fiscal authority works in a monetary union.

The rest of this paper is structured as follows. In Section 2, we depict the model specifically. In Section 3, we derive the market clearing condition and have the dynamic equilibrium for output and inflation in country level and union-wide, respectively. Then, in Section 4, we discuss the social planner’s problems under flexible prices. We show the tradeoffs between policies under sticky prices in Section 5. In Section 6, we obtain the optimal monetary and fiscal policies and the path of the fund mechanism. Finally, Section 7 concludes.

2. Model

2.1. Goods market

In the currency union like the EMU, the majority of the countries are small relative to the whole union. The fiscal policy which is determined independently by each country itself has little influence on the other countries in the currency union. So we follow the framework of Gali and Monacelli (2008) to consider the currency union as a continuum of small open economies represented by the unit interval, which is indexed byi∈[0,1]. Later in Section 2.4, we set a fund mechanism into a monetary union so that each country gets the net transfer from the central fiscal authority. For simplicity, the member countries in the currency union are symmetric.

The household consumes the domestic goods,C and imported goods,_{i t}ⁱ_, C_{F t}ⁱ_, from

‧

the rest of the member countries in the union.

( )

whereα∈[0,1] is the weight of imported goods in the composite consumption and also represents the openness of country i . C_{i t}ⁱ_, and C_{F t}ⁱ_, are the country i ’s consumption of domestic goods and imported goods given by CES function as follow:

1 1

where j∈[0,1]denotes the type of goods. ∈>1is the elasticity of substitution between the different type of goods.

1 produced in the rest of countries in the union. Minimizing expenditure, we can obtain the demand function for domestic goods and imported goods of good j as:

, , good j which is produced in countryi and country f , respectively. Then, the Eq. (4) can be rewritten as follow:

1

, ,

0P j C_tⁱ( ) _{i t}ⁱ ( )j dj P C= _tⁱ _{i t}ⁱ

∫

^;

∫

0¹P_t^f( )j C_{f t}^f, ( )j dj=P C_t^f _{f t}^{f, (5)} Then, the optimal allocation of imported goods is ¹ _, ^* _,

0 we can obtain the optimal allocation of expenditures of domestic and imported goods

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Combining Eq. (5) and Eq. (6), we have the optimal allocation of expenditures in countryi as:

The infinitely-lived representative household in country i maximizes the discounted sum of utilities as follow:

0

whereβ∈(0,1)is the subjective discount factor of the representative household. We assume the government consumption has impact on the household’s utility. Especially,

i

G in our study includes the constant provision of public goods and the net transfer t

from the central fiscal authority. Namely, the household’s utility is also influenced by the fund mechanism.

The form of period utility based on consumption, government spending and labor is given by

where Cⁱ_t is the individual consumption and parameter χ∈[0,1) is the share of government spending relative to individual consumption in the utility. Notice that, the government spending,G , contains the provision of public and the net transfer. So, the _tⁱ net transfer also impacts on the household’s utility.N is the labor supply of the _tⁱ

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representative household.ϕ >0is the elasticity of the marginal disutility of labor supply. The budget constraint of the representative household is formed as follow:

1 1 1

, , , 1 1

0P j C_tⁱ( ) _{i t}ⁱ ( )j dj+ 0 0P_t^f( )j C djdfⁱ_{f t} +E Q_t{ _{t t+} D_tⁱ₊}≤D_tⁱ+W N_tⁱ _tⁱ−T_tⁱ

∫ ∫ ∫

⁽¹⁰⁾

whereD denotes the payoff of the portfolio that the representative household held at _tⁱ the end of periodt . Q_{t t,+1}is the stochastic discounted factor.

By using an optimal allocation of expenditure as Eq. (7), the household’s budget constraint becomes:

, { , 1 1}

i i i i i i i

c t t t t t t t t t t

P C +E Q ₊D₊ ≤D +W N − T (11)

Maximizing the household’s discounted sum of utility, Eq. (9) which is subjected to Eq. (11), we obtain the first-order conditions as below:

,

The household would purchase the riskless bond which the nominal return is

*

Taking log-linearization on Eq. (12) and Eq. (14), we can rewrite them as below:

, log(1 )

The bilateral terms of trade, _,

f

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bundle of goods produced in country f in terms of the goods in countryi . Accordingly, the effective terms of trade of countryi is given by

* 1 1

We can see the relationship between the CPI and the domestic price level by the definition of the terms of trade asP_{c t}ⁱ_, =P S_tⁱ( _tⁱ)^α, or in logs as follow:

The CPI inflation is influenced by the domestic inflation and the change of the terms of trade. According to Eq. (19), we find that the parameterα which denotes the openness of countryi has the positive effect on the CPI inflation. That is, the opener the countryi is, the more CPI inflations changed.

Under the symmetric assumption, we obtain the Euler equation of country f

from Eq. (13) as ^, _{, 1}

= . Combining these two equations, we derive the

international risk sharing condition:

1

( ,)

i f i

t i t f t

C =ϑC S ^−α (20)

whereϑ is the constant coefficient that depends on initial conditions. We assume _i initial conditions are symmetric so that we haveϑ ϑ_i = _f = . Integrating Eq. (20) over1

f in logs on this condition, we have:

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c =

∫

c df denotes the aggregate union-wide consumption index. We find that the terms of trade has less influence when countryi is opener.

2.3. Firm

2.3.1. Technology

We assume that each firm only hires laborsN_tⁱ( )j to produce good j in countryi so that the production function is given by

( ) ( )

i i i

t t t

Y j = A N j (22)

where ,i j∈[0,1]andA is a country-specific technology shock which we assume it _tⁱ

follows the AR(1) process in logs asa_tⁱ =ρ_aa_tⁱ₋₁+ , whereε_tⁱ a_tⁱ =logA_tⁱandε_tⁱis a white noise.

Under the assumption of technology, the real marginal cost of goods produced by firms in countryi is:

whereτⁱis the subsidy of employment to the firms.

We define total amount of labor hired to produce domestic goods in countryi is given by

1

‧

≡

∫

Y . According to Gali and Monacelli (2008) Appendix A, we can derive the relationship between the output level and the aggregate labor in logs as follows:

i i i

t t t

y = + a n (25)

2.3.2. Price setting

Following the staggered price-setting structure of Calvo (1983) model, there is a possibility, (1− , that firm j resets its price. Accordingly, we can also image that a θ) proportion of (1− firms reset their price andθ firms keep their price the same as θ) before in each period. LetP presents the price which firm j resets in period t. Firm jⁱt

adjusts its priceP in period t by maximizing its discounted profit that is given by ⁱt

0

which is subjected to the demand constraints of good j :

, ,

We can derive the optimal price setting (in log) of countryi in period t on the first-order condition as follow:

0

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2.4. Government and the fiscal coordination

In our study, we try to investigate how the fund mechanism works in the currency union. To this end, we assume that there is a central fiscal authority that raise the constant fund payment,F_tfrom all member countries and redistributes all of the receipts to member states, O . We assume that all the members pay the same amount _tⁱ to the fund in period t so that the difference of the net transfer among member countries only depends on the gains from fund, O . Thus, the net transfer from the _tⁱ central fiscal authority to each member:

i i

t t t

TR =O −F

(29)

whereTR denotes the country_tⁱ i ‘s net transfer. To the central fiscal authority, the budget should be balanced in each period, ¹

0 i

t t

F =

∫

S di^.

Following Chatterjee and Turnovsky (2005), we assumed that the public expenditure for each country is accumulated from two sources: the constant government spending which is financed domestically by the lump sum tax and the net transfer received from the central fiscal authority. We let the government spending stable to prevent the country from bankruptcy like Iceland, so we have the government spendingG constant. Thus, the government consumption fluctuation caused by shocks entirely responds to the net transfer. We can see how the fund mechanism operates in the countryi as follow,

i i i

t t t t

G = +G O −F = +G TR (30)

The budget constraint of the government sector of countryi is:

i i

t t t

G+F =T +O (31)

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The government consumption index of countryi is given by CES function as follow: purchases. Minimizing the government expenditure, we can obtain the optimal government spending of good j in countryi :

( ) ( ( ))

3. Equilibrium dynamics

3.1. Market clearing condition

The market clearing condition for good j in countryi is given by obtain the function of aggregate goods in terms of the consumption, the terms of trade and the net transfer in countryi as follow:

( )

i i i i

t t t t

Y =C S ^α + +G TR

(35)

We make use of a first-order Taylor expansion around steady state to obtain the

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market clearing condition in log-linear.

_tⁱ (1 )(_tⁱ _tⁱ) _tⁱ

y = − −γ φ c −αs +φtr (36)

where" " denotes the deviation of log variables from their steady state values which are denoted without time subscript, e.g.^ log

i denote the government spending share and the net transfer share in steady state value, respectively.

We can rewrite the domestic output equation Eq. (36) by using Eq. (21) and the definition of the terms of trade as follow:

_tⁱ _tⁱ (1 )_t^* (1 )( _tⁱ _t^*)

y =φtr + − −γ φ c − − −γ φ p − p (37) The domestic output is positively related to the net transfers and the union-wide consumption. If the union-wide consumption is more than its steady state value, the output of the countryi will increase. We also find that the output is negatively related to the domestic prices and positively to the union-wide prices. We integrate the domestic output, Eq. (37), overi∈[0,1]to have the market clearing equation in the union level as below:

^*t ^*t (1 ) ^*t balanced in each period.

Taking the difference equation of Eq. (38) and combining it with the integration of Eq. (16), the dynamic IS equation is given by

^* ^{* * *} ^*₁

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Thereby, we find that both of the union-wide transfers and the expected long-term rate have effects on output in the union level. The intensity of those effects depends on the steady state share of government spending and net transfers.

3.2. Inflation dynamics

Under the staggered price-setting of Calvo (1983) model, we can obtain the domestically dynamic inflation equation in terms of the marginal cost by making use of the difference to Eq. (28) as below:

1 

state value that is defined below.

We can derive the real marginal cost equation by combining Eq. (16) with the Eq.

(23) in logs as follow: derive the deviation of the real marginal cost from its steady state is in terms of output and net transfer.

 1  

Substituting Eq. (43) into Eq. (41), we obtain the new Keynesian Phillips curve (NKPC) as a function of the net transfers in the country level:

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By integrating the country’s NKPC overi∈[0,1], we obtain the new Keynesian Phillips curve of the union:

^* ^* inflation is stable under the common monetary policy, the shocks were offset by the net transfer in order to stabilize the output level.

In this section, we obtain the dynamic equilibrium equations of output and inflation in the country level, Eq. (37) and Eq. (44) and in the union level, Eq. (40) and Eq. (45) in this section. The difference between Gali and Monacelli (2008) and our study is the setting of government sector. Therefore, the equilibrium dynamics of the output and the inflation in our study are the functions of the net transfer instead of the government spending in Gali and Monacelli (2008).

4. The social planner’s problem

In this section, we want to discuss what the efficient allocation is to the social planner as a whole union under flexible prices (i.e., there is no market power distortion). The social planner seeks to maximize the utility of the whole union as follow:

1

max

∫

0U C N G di( _tⁱ, _tⁱ, _tⁱ) ⁽⁴⁶⁾

which is subjected to the technology and resource constraints:

1

Under the preference formed as Eq. (9), we obtain the optimal first-order

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condition of labor, consumption and government spending as below:

1

Substituting Eq. (50) and Eq. (51) into Eq. (1), we can have the optimal consumption for the social planner as follow:

1 *

We let the” ”present the efficient equilibrium under flexible prices. The following conditions must be satisfied to obtain the efficient allocation with no distortion.

Substitute Eq. (49), Eq. (50) and Eq. (52) into Eq. (54), we find that the subsidy

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must set a level as follow to eliminate the market power distortion:

1 τi =

∈ (55)

Based on the previous conditions, Eq. (54) and Eq. (55), we obtain the country-specific optimal allocation for alli∈[0,1]as follow:

i 1

By using Eq. (58), we can find that the government spending equilibrium in the country level is affected by country-specific shocks. Under our setting of the fund mechanism, the expenditure of public goods is constant so that the shocks influence on the net transfer instead.

According to Eq. (57) and Eq. (58), we can derive the constant weight of government spending is:

i i

In the union level, we obtain the optimal allocation by integrating Eq. (49), Eq.

(52) and Eq. (53) overi∈[0,1] as below:

We find that the efficient variables in the union level are affected by the union-wide shocks. In the next section, we discuss the variables under sticky prices

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based on the flexible price equilibrium.

5. The policy tradeoffs in the currency union under sticky prices

In this section, we discuss the tradeoffs under sticky prices. The tradeoffs arise for two reasons here: (1) the sticky prices and (2) the common currency. In the presence of the staggered price setting following Calvo (1983), the sluggish price adjustment leads the variables to deviate from their efficient level under flexible price equilibrium we derive in the last section. On the other hand, the member countries in the monetary union use the common currency. This situation implies that the nominal exchange rate is fixed and the terms of trade is unable to adjust for achieving the efficient level. Because of these two reasons, the policymakers have to make choices depending on the country-specific and the union-wide tradeoffs, respectively. Then, we derive the tradeoffs in terms of the fiscal gap and the output gap.

5.1. Union members’ tradeoffs

Letting the”  ”denotes the variables’ log deviation from their flexible prices equilibrium, i.e.,^xⁱt ≡ −xtⁱ xⁱt, for all variables,x. We define the fiscal gap as follow:

fⁱ_t ≡trⁱ_t−yⁱ_t (64)

where the tr andⁱt ^yⁱ_tare the transfer gap and the output gap of the countryi .

Under the fact thatyⁱt −yⁱ =gⁱt−gⁱ =trⁱt −trⁱ =atⁱand Eq. (43), we can have the real marginal cost in terms of output gap and fiscal gap:

 1   1  

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We can rewrite the inflation dynamic equation, Eq. (41), by substituting the Eq.

(65) with the real marginal cost term as follow:

 

By this new Keynesian Phillips curve for each union member, we can find that if the inflation is stabilized by the union-wide monetary policy, then the fluctuation of the output gap must reflect on the fiscal gap (i.e., the net transfer would cope with the fluctuation of output ). Notice that, the local government's public spending is constant so that only the net transfer from the fund mechanism responds to the output fluctuation²

Combining the differential market clearing conditions, Eq. (37) and Eq. (38) and substituting Eq. (6) and Eq. (17) with consumption, we can derive that the change in output gap is in terms of the change in fiscal gap, inflation and shocks.

. asymmetric shocks in the union, the inflation or the fiscal gap will respond to the shocks for keeping the output stable.

5.2. Union-wide tradeoffs

We can obtain the new Keynesian Phillips curve in the union level by integrating Eq. (65) overi∈[0,1]as

2 In contrast with Gali and Monacelli (2008), the output gap responds to the the government spending.

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We derive the union-wide output gap function by the dynamic equation, Eq. (39):

^* ^{* * * *} ^*₁

whererr is the union’s natural rate of interest as follow, ^*t

* * * * *

By combining Eq. (68) and Eq. (69), we can have the interaction of fiscal gap and inflation as:



According to the interaction among the fiscal gap, the inflation and the interest rate determined by the central bank, we can find that the union-wide inflation rises when the fiscal gap is positive in order to against the depression. Then, the central bank of union needs to dampen the inflation by means of raising the interest rate in the future. The contractionary monetary policy leads to a decline in output so that the common fiscal authority would run a positive fiscal policy again. Thereby, we discuss

According to the interaction among the fiscal gap, the inflation and the interest rate determined by the central bank, we can find that the union-wide inflation rises when the fiscal gap is positive in order to against the depression. Then, the central bank of union needs to dampen the inflation by means of raising the interest rate in the future. The contractionary monetary policy leads to a decline in output so that the common fiscal authority would run a positive fiscal policy again. Thereby, we discuss

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