Fiscal stimulus in a monetary union

E�ciency of �scal packages in a monetary union

Olfa Alouini & Aurélien Poissonnier

OFCE-Humbolt Universität & Crest-Insee

November 2010

Olfa Alouini & Aurélien Poissonnier E�ciency of �scal packages in a monetary union

Introduction

Plan

1 Introduction


Introduction

Purpose

Built a monetary union model, as simple as possible.Investigate the cross border e�ects of re�ation policies in this framework.Can a country free ride on the others' policy ?Does this free riding opportunity depends on the country size, openness,nominal rigidity ?Is "internal devaluation" an e�cient and non-cooperative strategy ?


Introduction

Modeling choices

- general equilibrium model

- only 2 countries

- no capital (to simplify)

- localized labor force

- nominal rigidities to make room for monetary policy (EMU)

- explicit government spending and public debt

∵ microfondation of government spending decision

∵ feedback between public debt and government spending decision

∵ taxes on production and consumption to diversify public intervention

channels

Related literature

Andres, Ortega, Valles, JEDC 2008Gali, Monacelli, JIE 2008Benigno, JIE 2004Corsetti, Meier, Muller, IJCB 2010


Introduction

Modeling choices


- only 2 countries








channels

Related literature



Introduction

Modeling choices


- only 2 countries








channels

Related literature



Introduction

Modeling choices


- only 2 countries








channels

Related literature



Introduction

Modeling choices


- only 2 countries








channels

Related literature



Introduction

Modeling choices


- only 2 countries








channels

Related literature



Introduction

Modeling choices


- only 2 countries








channels

Related literature



Introduction

Modeling choices


- only 2 countries








channels

Related literature



Introduction

Modeling choices


- only 2 countries








channels

Related literature



Introduction

Modeling choices


- only 2 countries








channels

Related literature



Model

Plan

2 ModelGoods aggregationHouseholdsFirmsMonetary Authority (closing the model)Government spending and debts-assetsThe augmented version of the model


Model Goods aggregation

Bundles produced in each country

n �rms in country 1 and 1− n �rms in country 2, produce di�erentiatedgoods in their country.The goods are locally aggregated (Dixit-Stiglitz)

Y 1t = K1

(1

n

∫ n

0y1(ε, t)

θ1−1

θ1 dε

) θ1θ1−1

Y 2t = K2

(1

1− n

∫ 1

n

y2(ε, t)θ2−1

θ2 dε

) θ2θ2−1

skip



Prices of production

The corresponding prices are

P1t =

1

K1

(1

nθ1

∫ n

0P1(ε, t)1−θ1dε

) 11−θ1

P2t =

1

K2

(1

(1− n)θ2

∫ 1

n

P2(ε, t)1−θ2dε

) 11−θ2



Speci�c demand for each product in a bundle

Each �rm will face a speci�c demand for its production (either locallyconsumed or exported)

y1(ε, t) =K1θ1−1

nθ1

(P1(ε, t)

P1t

)−θ1Y 1t

y2(ε, t) =K2θ2−1

(1− n)θ2

(P2(ε, t)

P2t

)−θ2Y 2t



Consumption Bundle

In each country, the consumption bundle consists in a mix of bothproductions local and imported.

C it =

C ii ,t

1−αiC ij ,tαi

(1− αi )1−αiααiiCPI it = P i

t

1−αiPjt

αi



Private demand for each product in each country

C 12,t = α1

(P1t

P2t

)1−α1

C 1t

C 11,t = (1− α1)

(P2t

P1t

)α1

C 1t

C 21,t = α2

(P2t

P1t

)1−α2

C 2t

C 22,t = (1− α2)

(P1t

P2t

)α2

C 2t


Model Households

Households' maximization program

maxC i (τ,t),Ai (τ,t),Li (τ,t)

E0

∞∑0

βt(log(C i (τ, t))− κLi (τ, t) + µlog(G i

t ))

subject to their budget constraint

Ai (τ, t) =(1 + rt−1 − ψ(ait−1))Ai (τ, t − 1) + w i (τ, t)Li (τ, t)

−CPI it (1 + νc,it )C i (τ, t) + B i (τ, t)

with ait−1 =Ait−1

P it−1Y

i


Model Households

Consumption dynamic-Euler equation

Et

β C it

C it+1

1 + rt − ψ(ait)

Πc,it+1

1+νc,it+1t

1+νc,it

= 1


Model Households

Labor supply-Wage Phillips curve

We suppose a Dixit-Stiglitz aggregation of di�erentiated labor supplies anda Calvo process on wage setting.Households focus on the purchasing power of their net revenu :

PPNR = w it

CPI it (1+νc,it )

The wages Phillips curve reads

ˆPPNRi

t − ˆPPNRi

t−1 + Πc,it +

νc,i

1 + νc,i(νc,it − ν

c,it−1) =

β

(ˆPPNRt+1 − ˆPPNRt +

νc,i

1 + νc,i

(νc,it+1 − ν

c,it

)+ Πc,i

t+1

)+

(1− βξiw )(1− ξiw )

ξiw

(C it − ˆPPNRt

)


Model Firms

Firms' production function

y i (ε, t) = ζ it(Lit(ε)

)with costs w i

t (1 + νw ,it )Lit(ε)

where ζ i is the total factor productivity in country iPrice setting, Calvo + Dixit-Stiglitz = Phillips curve

Πit =βΠi

t+1 +(1− βξi )(1− ξi )

ξi[ˆPPNR

i

t + ˆRPCi

t +νw ,i

1 + νw ,iνw ,it +

νc,i

1 + νc,iνc,it − ζ it

]


Model Monetary Authority (closing the model)

Central Banker = Taylor Rule for the whole union

Rt = Rρt−1(R∗Πrπ

t Yryt

)1−ρ


Model Government spending and debts-assets

The Governments try to maximize the utility of their citizen households butare blind to their budget constraint (i.e. to their marginal utility)

maxG it

E0

∞∑0

βt log(G it )

subject to public budget constraint

PAit =

(1 + rt−1 − ψ(pait−1)

)PAi

t−1 + νw ,it w itL

it + νc,it CPI itC

it − P i

tGit

pait−1 =PAi

t−1P it−1Y

i

=⇒ The government spending decision is not that of a central planner.



Public expenditure decision

βG it

G it+1

1 + rt − ψ( PAit

P it Y

i )−PAi

t

P it Y

i ψ′( PAi

t

P it Y

i )

Πit+1

= 1 (1)

Tax rates on consumption and wages are a priori constant and exogenous.



Asset dynamic

Public assets

PAit =

(1 + rt−1 − ψ(pait−1)

)PAi

t−1 + νw ,it w itL

it + νc,it CPI itC

it − P i

tGit

Private assets

Ai (t) = (1 + rt−1 − ψ(ait−1))Ai (t − 1) + w itL

it − CPI it (1 + ν i ,ct )C i (t) + B i (t)

NB : a spread is paid on the asset which depends on the aggregate asset ofthe country. If it is debt, the agent pays a spread to the �nancialintermediary, if it is savings, the �nancial intermediary will keep a spreadfrom the monetary policy rate.



Microfondation

Union wide �nancial market of both private and public asset/debtOn this market, �nancial intermediaries borrow, from the central bank tolend to households or governments (and vice versa)The cash needs, turnover, costs and pro�ts of �nancial intermediaries are

Cash needs = CNt = −(A1t + A2

t + PA1t + PA2

t )

Turnover =− (rt − ψ(a1t ))A1(t)− (rt − ψ(a2t ))A2(t)

− (rt − ψ(pa1t ))PA1t − (rt − ψ(pa2t ))PA2

t

Costs = rtCNt + Ξ(A1t , A

2t , PA

1t , PA

2t )

Pro�ts =ψ(a1t )A1(t) + ψ(a2t )A2(t) + ψ(pa1t )PA1t + ψ(pa2t )PA2

t

−Ξ(A1t , A

2t , PA

1t , PA

2t )



To ensure the uniqueness of the steady state, we suppose that �nancialintermediaries clear their position vis à vis the central bank so that theircash needs are

CNt = −(A1t + A2

t + PD1t + PD2

t ) = 0

assumption 1 : quadratic costs of debt/asset managementassumption 2 : perfect competition⇒ The �nancial market is orthogonal to the rest of the model.


Model The augmented version of the model

The augmented version of the model

utility in consumption and public expenditure CES (not log)

Frisch elasticity 6=∞external habit formation on consumption and labour

internal habit formation on government spending

non constant return to scale production function

partial indexation of production prices on past in�ation

partial indexation of wages on past in�ation of consumption


Model The augmented version of the model

Calibrations

Classical calibration values table

Spread elasticity with respect to the level of debt

European data of public debt and government bonds interest rate.Using Germany as a reference, we �nd that 1% increase in the public debtgenerates a 5 basis point spread on the corresponding government bond(in quaterly terms).


Simulation strategy

Plan

3 Simulation strategy


Simulation strategy

What can the government do to stimulate the economy ?

- a positive shock on G i

- negative shock on νc,i

- negative shock on νw ,i


Simulation strategy

Comparing �scal stimuli

For the �scal stimulus to be comparable, we state that the increase inpublic expenditures or the decreases in tax revenue are equal 3% of thecountry's GDP.

Public expenditures (four quarters) extra G i = 3%G i

Y i

= 10%

VAT cut (four quarters) ∆νc,i = −3%C i

Y i

≈ −2.8pt

Payroll tax cut (four quarters) ∆νw ,i = − 3%

(1+νc,i ) Ci

Y i

≈ −2.4pt


Simulation strategy

We can assess the following questions

Which �scal stimulus is the most e�cient (in terms of national GDP) ?

How can �scal policy interact with monetary policy ?

What are the cross border externalities of the �scal packages and howmuch do they depend on asymetries ?


Best �scal stimulus

Plan

4 Best �scal stimulus



Figure: Simulated output 1 following di�erent �scal shocks in country 1



Which �scal stimulus is the most e�cient ?

By increasing its demand, the government has a direct e�ect on output.By decreasing tax levels, the gov. generates disin�ation which in turnmodi�es the consumption leisure trade-o�.With usual value of the intertemporal elasticity of substitution our result isdi�erent from Mountford and Uhlig (JAE 2008) on US data=⇒ the most e�cient policy is to increase public spendings


Interaction with the central banker

Plan

5 Interaction with the central banker



Figure: Simulated interest rate following di�erent �scal shocks in country 1



How the government interacts with the central banker ?

Gov. Spendings : the government helps the central banker (in�ation)

Tax cuts : the gov. generates disin�ation which forces the centralbanker to decrease its interest rate (especially if the central bankerreact to in�ation of consumption tax included)

In this context the risk for the central banker is to be constrained by thezero lower bound when the government uses tax cuts.


Fiscal spillovers

Plan

6 Fiscal spilloversIdentifying the spilloversHow these spillovers depend on di�erences between countries ?


Fiscal spillovers

Union disymetries

Benchmark : same size, Calvo parameter 0.75

France and Netherlands : relative size 3.5, corresponding opennessdegrees 0.2 and 0.7

+ Asymetric nominal rigidities : Calvo parameter 0.63 or 0.83


Fiscal spillovers Identifying the spillovers



Fiscal spillovers Identifying the spillovers

What are the spillover e�ects ?

1 Gov Spendings : the government does not foster imports directly butthrough crowding out e�ect

2 VAT cut : reduces the price of imports directly + pulls real interestrate down for partner country

3 Payroll tax cut : triggers competition in prices across countries + pullsreal interest rate down

Positive spillovers

In the 3 cases �scal packages have a positive impact on the partner country.Strongest impact with VAT cut.


Fiscal spilloversHow these spillovers depend on di�erences between

countries ?

How these spillovers depend on di�erences between countries ?

We focus on a monetary union between a large country less �exible, andless open with a small, more open and �exible country.The large country tries to stimulate its production.



countries ?




countries ?




countries ?

Figure: Simulated interest rate following di�erent �scal shocks in country 1Olfa Alouini & Aurélien Poissonnier E�ciency of �scal packages in a monetary union


countries ?

How these spillovers depend on country size ?

Spillover e�ects are larger in this disymetric case ( +0.5 points of GDP withtax cuts) since the small country exports a larger share of its production.Also the large country has a stronger in�uence on unionwide in�ation,hence on the central banker.

How these spillovers depend on nominal �exibility ?

1 Being �exible is an advantage for the small country to compete inprices after tax cuts.

2 Yet, when the large country increases public spending, the smallcountry adjust more through prices and less through quantities.

3 The large country being less �exible, generates (twice) less disin�ationhence puts less pressure on the central banker



countries ?

How these spillovers depend on country size ?

Spillover e�ects are larger in this disymetric case ( +0.5 points of GDP withtax cuts) since the small country exports a larger share of its production.Also the large country has a stronger in�uence on unionwide in�ation,hence on the central banker.

How these spillovers depend on nominal �exibility ?

1 Being �exible is an advantage for the small country to compete inprices after tax cuts.

2 Yet, when the large country increases public spending, the smallcountry adjust more through prices and less through quantities.

3 The large country being less �exible, generates (twice) less disin�ationhence puts less pressure on the central banker


Internal devaluation

Plan

7 Internal devaluation



Figure: Simulated output following internal devaluation in country 1 and 2



Figure: Simulated public debt following internal devalution in country 1 and 2



Figure: Simulated public debt following internal devalution in country 1 and 2



Is internal devaluation unfair ?

Internal devaluation succeeds in controlling public de�citLagged e�ect on output and low e�ciency in home countrySmall positive (lagged) e�ect on the partner country's outputSmall negative externality on foreign public debt.In the short run, internal devaluation is not an evil policy for a monetaryunion and is NOT EFFICIENT.



Thank you for your attention.


Other papers investigate the same questions. They usually rely on budgetrules to model the government.We compare our model to Corsetti, Meier, Muller (2010 IJCB).The di�erence relies mainly on the reaction of the government to shocks ofmonetary policy : In our model, higher interest rates tamper thegovernment's emission of debt.In CMM, the pro or contra cyclical government rule does not have a sizableimpact on the government decision.


Figure: Comparison of our government with a budget rule : government spending


Figure: Comparison of our government with a budget rule : public asset

back Olfa Alouini & Aurélien Poissonnier E�ciency of �scal packages in a monetary union


Parameter Description Value Alternativeα Production technology parameter 0.7 -β Discount factor 0.9 -h Habit formation 0.7 -σc Inverse of intertemporal elasticity 2 0.5

of substitution of private consumptionσl , Inverse of the Frisch elasticity 2 -α1, α2 Import share 0.45 0.7, 0.2ξ1 Calvo parameter on prices and wages adjustment 0.75 0.83/0.66γ1, γ2 Price and wage indexation on past in�ation 0.2θ1, θ2 Elast. of sub. of domestic products and labour 6 -

products yielding a markup of 20% on prices and wagesνc,1, νc,2 Tax level on consumption 20% -νw,1, νw,1 Tax level on wages 19% -rπ Central Bank reaction to in�ation 1.7 -ρ Taylor rule smoothing parameter 0.8 -ry Central Bank reaction to output gap 0.25 -θ Economic size ratio Y 1/Y 2 1 3.5C/Y , Relative shares of private consumption in GDP 0.7 -ψ Financial premium on debt 0.05 -

Table: Parameters Calibration

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Fiscal stimulus in a monetary union

Economy & Finance