Price setting

2. The model

2.3. Firm

2.3.2. Price setting

≡

∫

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

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:

‧

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)

‧

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

‧

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

‧

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:

‧

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:

max

∫

0U C N G di( _tⁱ, _tⁱ, _tⁱ) ⁽⁴⁶⁾

which is subjected to the technology and resource constraints:

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

‧

condition of labor, consumption and government spending as below:

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

‧

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

‧

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  

‧

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.

‧

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 the optimal monetary and fiscal policy of a currency union simultaneously in next section.

6. The optimal monetary and fiscal policies in the currency union

In this section, we have a common policymaker who determines the optimal monetary and fiscal policy together in a currency union. The objective of this

‧

policymaker is to minimize the average utility loss function of the whole union. We use the second order approximation of the utility formed in Eq. (9) to obtain the loss function as follow:

 

Then, we choose the optimal fiscal policy{^fⁱ_t}and the optimal monetary policy { }r_t* which can be determined by{ ,^yⁱ_t π by minimizing Eq. (70) which is subjected to _tⁱ} Eq. (66), Eq. (67) and the aggregate constraints given by

* 1 obtain the first-order conditions as follow:

Integrating Eq. (72), and then substituting it with Eq. (75), we obtain

* 1

Integrating Eq. (73), and then substituting it with Eq. (76), we obtain

‧

Integrating Eq. (74), and then substituting it with Eq. (77), we obtain

^* ^*

,_t 0

ft +λψ_π = (80)

We can derive the relationship between the fiscal gap and the output gap of the union by integrating Eq. (74) and combining it with Eq. (77) as

^* 1 ^* Using the dynamic IS-type equation, Eq. (69) and the optimal condition, Eq. (78), Eq. (79), Eq. (80) and Eq. (81), the equilibrium under the optimal policy will satisfy:

^* ^*

* 0

t yt ft

π = = = (82)

for all t . As this result, we find that the inflation, output gap and fiscal gap in the union level are zero which means the variables will be in their efficient flexible-price equilibrium value in the union level. By the outcome of Eq. (82), we have the rule of monetary policy, rt =rr^*t +ν π_π t^*as we discussed in section 5.2.

We can derive how the fund mechanism works in a country by combining Eqs.

(73), (74), (76) and (77):

By using the definition of the fiscal gap, Eq. (64), we derive the transfer's rule as:

 

If there is an undesirable shock which causes the output gap to be negative, the net transfer will be positive to reduce the fluctuation of output. Thus, the fund mechanism is countercyclical. Further, we can find that in the country level,

ⁱ_t ⁱ_t 0

y = f = cannot be equilibrium when the prices are less fully flexible, ψ_πⁱ_,_t > . 0

‧

Gali and Monacelli (2008) consider the monetary and fiscal policies in the union level simultaneously by a singular policymaker. Under this cast of fiscal coordination, the output’s fluctuation entirely affects on the government spending so that the local government still faces the shocks by themselves. In our model, the local government's public expenditure is constant so that the fluctuation which is caused by productive shocks is absorbed by the central fund mechanism. If we consider the multiplier term,

− as given, the path of the fiscal gap and the output gap is the same as the result of Gali and Monacelli (2008). Consequently, we can find that the net transfer only substitutes some parts of government spending in country level. This cast of fiscal coordination plays the same rule as the government sector.

7. Conclusion

In this paper, we investigate the fiscal coordination in a monetary union with micro-founded dynamic stochastic general equilibrium (DSGE) model. We follow the framework of Gali and Monacelli (2008) and set a fund mechanism to simulate a fiscal coordination under staggered price-setting. Every local government can get a net transfer from the fund and the central fiscal authority redistributes all receipts to every member state in each period. We find that if we have a common policymaker to determined monetary and fiscal policies together, the net transfer only substitutes parts of the government spending. Hence, under our design of fund mechanism which the budget of transfer is balanced in each period, this type of fiscal coordination plays the same rule as the government sector. If we set the receipts do not entirely transfer to the member countries, the fund mechanism will be inefficient.

We conclude this paper by providing some other interesting issues for future

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researches. The fund mechanism can also be considered in infinite period rather than balanced in each period. Or we can design the other form of fund, such as the net transfer is based on a proportion of output.

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Reference

Bajo-Rubio, O. and C. Díaz-Roldán (2003). Insurance mechanisms against asymmetric shocks in a monetary union a proposal with an application to EMU.

Recherches économiques de Louvain, 69, 73-96.

Beetsma, R.M.W.J. and H. Jensen (2005). Monetary and fiscal policy interactions in a micro-founded model of a monetary union. Journal of International Economics, 320-352

Calvo, G. (1983). Staggered prices in a utility-maximizing framework. Journal of Monetary Economics, 12(3), 383-398

Chatterjee, S. and S.J. Turnovsky (2005). Financing public investment through foreign aid: Consequences for economic growth and welfare. Review of International Economics, 13(1), 20-44

Gali, J. and T. Monacelli (2008). Optimal monetary and fiscal policy in a currency union. Journal of International Economics, 76(1), 116-32

Gali, J. and T. Monacelli (2005). Monetary policy and exchange rate volatility in a small open economy. Review of Economic Studies 72 (3), 707-734

Kirsanova, T., M. Satchi and D. Vines (2004). Monetary union: Fiscal stabilization in the face of asymmetric shocks. CEPR Discussion Paper (4433)

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Oros, C. (2008). Macroeconomic stabilization in a heterogeneous monetary union:

some insights into the effects of fiscal policy coordination". Economics Bulletin, 5(34), 1-12

Traficante, G. (2010). Fiscal issues in a monetary union. Rivista Bancaria-Minerva Bancaria, 66(3), 5-27

Valeria, D.B. and D.P. Pompeo (2010). On the coordination of national fiscal policies in a monetary union. Economia Internazionale/International Economics, 63(3), 273-96

Appendix

We want to rewrite the utility function to loss function in terms of output gap, fiscal gap and inflation. We have the form of utility function as follow,

Next we derive the function of consumption, labor supply and government in second order approximation, respectively.

By using Eq. (34) and the fact, ¹

0s di_tⁱ =0

∫

, we can derive the union-wide Taylor expansion of consumption as follow:

1 1 1 1

‧

φ≡ Y denote the government spending share and the net transfer share in steady state value, respectively.

The union-wide Taylor expansion of government spending is given by

1 1

The union-wide Taylor expansion of labor is given by

1 1

According to Eq. (24) and the lemma 1 in Gali and Monacelli (2008), var { ( )}

Then, we obtain the union-wide Taylor expansion of labor in terms of output gap.

 

According to the second order approximation of consumption, government spending and labor, we can rewrite the union-wide utility function as:

0 ( ⁱ, ⁱ, ⁱ)

t t t t

U ≡

∫

U C G N di

‧

Depending on lemma 2 shown in Gali and Monacelli (2008),

∑ ∑

, we can rewrite the discounted sum of utilities to the loss function as below:



在文檔中貨幣聯盟中最適的財政政策合作 - 政大學術集成 (頁 15-0)

2. The model

2.3. Firm

2.3.2. Price setting

∫

‧

∫

‧

‧

‧

‧

∫

‧

‧

‧

‧

‧

‧

‧

‧

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立 政 治 大 學

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N a tio na

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∫

‧

∫

‧

∑ ∑

立政治大學

立政治大學