**Discussion** **Paper**

Deutsche Bundesbank

No 44/2016

Optimal fiscal substitutes for the

exchange rate in a monetary union

Christoph Kaufmann

(University of Cologne)

**Discussion** **Paper**s represent the authors‘ personal opinions and do not

necessarily reflect the views of the Deutsche Bundesbank or its staff.

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Non-technical summary

Research Question

Tax rate adjustments can change relative prices between countries in a similar fashion

as the exchange rate. It has therefore been debated whether member states of the European

Monetary Union (EMU) could consider ”fiscal” instead of nominal devaluations

in response to macroeconomic turmoil. This paper asks to what extent optimal, that is

welfare-maximizing, fiscal policy should substitute for the role of the exchange rate in the

EMU.

Contribution

This question is answered using a New Keynesian 2-region model that is calibrated to the

EMU. A common central bank controls monetary policy at the level of the union, while

governments in each country levy a value added tax and issue debt in order to finance

a given amount of public spending. The paper adds to the literature on the conduct of

monetary and fiscal policy in monetary unions by analysing if fiscal devaluations should

be part of optimally-designed policy.

Results

Simulating the EMU in the model shows that optimal fiscal policy can reduce the welfare

costs from giving up exchange rate flexibility by up to 86%. Fiscal devaluations can be

observed as an optimal policy response to macroeconomic shocks. As a policy recommendation,

the model suggests that whenever a nominal devaluation of a region were optimal

in the monetary union, it is optimal to raise its value added tax relative to other regions.

The reason is that this policy cheapens domestic exports relative to imports, since value

added taxes apply only to goods sold within a country.

Nichttechnische Zusammenfassung

Fragestellung

Steuersatzveränderungen können Relativpreisverhältnisse zwischen Ländern auf ähnliche

Art und Weise verändern wie der Wechselkurs. Es wird daher diskutiert, ob Mitgliedsstaaten

der Europäischen Währungsunion (EWU) als Antwort auf makroökonomische Turbulenzen

fiskalische“ anstelle von nominalen Abwertungen vornehmen könnten. Dieses

”

Papier behandelt die Frage in welchem Maße optimale, im Sinne von wohlfahrtsmaximierender,

Fiskalpolitik genutzt werden sollte, um für die Funktion des Wechselkurses

innerhalb der EWU zu substituieren.

Beitrag

Diese Frage wird mithilfe eines Neu-Keynesianischen Zwei-Regionen Modells beantwortet,

das anhand der EWU kalibriert wurde. Die Geldpolitik wird von einer gemeinsamen Zentralbank

auf Unionsebene bestimmt, während die Regierung jedes Mitgliedslandes eine

Mehrwertsteuer erhebt und Schulden aufnehmen kann, um Staatsausgaben in gegebener

Höhe zu finanzieren. Das Papier trägt zur Literatur über die Durchführung von Geldund

Fiskalpolitik in Währungsunionen bei, indem es analysiert, ob fiskalische Abwertungen

Teil einer optimal ausgestalteten Politik sein sollten.

Ergebnisse

Simulationen der EWU anhand des Modells ergeben, dass optimale Fiskalpolitik in der

Lage ist, die Wohlfahrtskosten, die sich aus dem Verlust der Wechselkursflexibilität ergeben,

um bis zu 86% zu reduzieren. Fiskalische Abwertungen können als optimale Antwort

auf makroökonomische Schocks beobachtet werden. Das Modell empfiehlt als Politikmaßnahme

für Situationen, in denen die nominale Abwertung einer Region innerhalb der

Währungsunion optimal wäre, stattdessen den Mehrwertsteuersatz der Region relativ zu

dem anderer Regionen zu erhöhen. Der Grund dafür ist, dass diese Politik heimische

Exporte relativ zu Importen verbilligt, da Mehrwertsteuern nur auf Güter anfallen, die

innerhalb eines Landes verkauft werden.

Bundesbank **Discussion** **Paper** No 44/2016

Optimal Fiscal Substitutes for the Exchange Rate in a

Monetary Union ∗

Christoph Kaufmann

University of Cologne

Abstract

This paper studies Ramsey-optimal monetary and fiscal policy in a New Keynesian

2-country open economy framework, which is used to assess how far fiscal policy can

substitute for the role of nominal exchange rates within a monetary union. Giving up

exchange rate flexibility leads to welfare costs that depend significantly on whether

the law of one price holds internationally or whether firms can engage in pricing-tomarket.

Calibrated to the euro area, the welfare costs can be reduced by 86% in the

former and by 69% in the latter case by using only one tax instrument per country.

Fiscal devaluations can be observed as an optimal policy in a monetary union: if a

nominal devaluation of the domestic currency were optimal under flexible exchange

rates, optimal fiscal policy in a monetary union is an increase of the domestic relative

to the foreign value added tax.

Keywords: Monetary union; Optimal monetary and fiscal policy; Exchange rate

JEL classification: F41; F45; E63.

∗ Contact address: Center for Macroeconomic Research (CMR), University of Cologne, Albertus-

Magnus-Platz, 50923 Cologne, Germany. Phone: +49 221 470 5757. E-Mail: c.kaufmann@wiso.unikoeln.de.

The author thanks Andreas Schabert, Klaus Adam, Benjamin Born, Christian Bredemeier,

Andrea Ferrero, Mathias Hoffmann, Mathias Klein, Michael Krause, Dominik Sachs, Thomas Schelkle, as

well as conference and seminar participants at Deutsche Bundesbank, the European Economic Association

(Geneva), the Spring Meeting of Young Economists (Lisbon), the Verein für Socialpolitik (Augsburg), and

University of Cologne for helpful comments and suggestions. **Discussion** **Paper**s represent the authors’

personal opinions and do not necessarily reflect the views of the Deutsche Bundesbank or its staff.

1 Introduction

Free floating exchange rates are generally regarded as an important shock absorber for

countries facing macroeconomic turmoil. Giving up this device by joining a monetary

union (MU) or committing to a peg clearly reduces the abilities of business cycle stabilization

policy in reacting to country-specific shocks, as an independent monetary policy

is no longer feasible anymore. The fixed exchange rate regime of the European Monetary

Union is also blamed for the slack or even missing recovery of some southern European

countries in the aftermath of the global financial crisis. 1

Within a monetary union, fiscal policy can take up the role of the exchange rate,

since taxes can in principle affect international relative prices—the terms of trade and the

real exchange rate—in a similar fashion as the exchange rate does. Policies of this type

are referred to as fiscal devaluations. Setting a theoretical benchmark, Farhi, Gopinath,

and Itskhoki (2014) show that the effects of the nominal exchange rate on the allocation

of an economy can be replicated entirely using a sufficient number of tax instruments.

Following a related approach, Adao, Correia, and Teles (2009) conclude that the exchange

rate regime can be completely irrelevant for stabilization policy.

In this paper, I show that even under a minimum set of fiscal instruments being in

a monetary union does not have to be unduly painful. In a common New Keynesian

2-country open economy framework, optimal use of only one tax instrument per country

reduces the welfare costs of giving up exchange rate flexibility in a MU already significantly.

Fiscal devaluation policies are not only viable, but can be observed as the optimal

policy response to country-specific shocks.

The 2-country model features complete international capital markets and staggered

price setting a là Calvo (1983). I differentiate between the case where prices are sticky

in the country of the producer only such that the law of one price (LOOP) holds internationally,

and the case where firms are capable of pricing-to-market (PTM), implying

an additional sticky price friction for imported goods. 2 This is important as the welfare

costs of fixed exchange rates as well as the capabilities of fiscal policy to reduce these costs

depend decisively on the pricing scheme. The model allows for home bias and asymmetries

between the countries along several dimensions, such as country size, the degree of

competition, and the size of the public sector. Each country has a fiscal authority, whose

objective is to finance a given amount of public spending by collecting distortionary taxes

and issuance of debt. Only one tax instrument is available for each authority—a value

added tax (VAT) payable by firms, which is levied on all goods sold within a country. Optimal

policy is characterized using a Ramsey approach. This procedure involves to find

sequences for the policy instruments that support the welfare-maximizing competitive

equilibrium.

Calibrating the model to characteristics of the euro area, I find that optimal fiscal

policy reduces the welfare costs of pegged exchange rates by 86% in case the law of one

price holds and by 69% in case of pricing-to-market. The order of magnitude of these

results is highly robust to changes in the parametrization and also if payroll taxes are

1 See, for instance, Mankiw (2015) with a particular focus on Greece.

2 In case of a flexible exchange rate regime, these two pricing schemes are also referred to as producer

currency pricing and local currency pricing. Regarding the high empirical relevance of both schemes and

a recent overview of the literature on international price setting, see Burstein and Gopinath (2014).

1

used instead of the VAT.

Besides analysing the welfare effects, I describe the conduct of optimal stabilization

policy depending on the exchange rate regime and the way prices are set. In general,

under flexible exchange rates, taxes aim to finance public expenditures in the least distortionary

way, while at the same time they can be used for stabilizing marginal costs

of firms in response to shocks. This trade-off involves a further dimension in case of a

monetary union, where taxes can additionally substitute for the role of the nominal exchange

rate, e.g. in inducing expenditure switching effects. In this way, optimal fiscal

policy can compensate at least partially for the loss of country-specific monetary policy as

a stabilization instrument, thereby bringing the economy closer to the efficient allocation.

The intuition for the simplest form of a fiscal devaluation policy is that, say, an

increase of the domestic relative to the foreign VAT rate induces firms to charge higher

prices for goods sold at home, resulting in higher prices of domestic imports relative to

exports, for the latter are subject to the relatively reduced foreign VAT. Comparable

to a nominal devaluation, this fiscal devaluation policy leads to a deterioration of the

terms of trade. As shown by Farhi et al. (2014), reproducing the depreciation of the real

exchange rate that would emerge under a nominal devaluation and stabilizing internal

prices of domestically produced goods that are distorted by the change in the VAT requires

additional instruments, though.

In a monetary union, I find that optimal fiscal policy is indeed actively concerned with

replicating the flexible exchange rate allocation. Optimal policy favours replicating the

behaviour of the terms of trade under a free float over reproducing the response of the

real exchange rate, in line with the intuition given above. In situations where a nominal

devaluation of a region were optimal, optimal fiscal policy in a MU is a relative increase

of the VAT of that region, i.e. to conduct a fiscal devaluation. Although the transmission

of fiscal policy is different under LOOP and PTM due to the limited pass-through of tax

changes on prices in the latter case, this finding is independent of the pricing scheme.

Simulating the economy under both exchange rate regimes yields correlations between

the hypothetical optimal exchange rate response and the ratio of VAT rates in the MU

of 81% when the LOOP holds and of 59% under PTM. The reaction of the level of tax

rates depends on the specific types of shocks, though. In case of shocks for which an

efficient response could be attainable under flexible exchange rates (I consider productivity,

government spending, and demand preference shocks), replicating the effects of the

exchange rate does not conflict with marginal cost stabilization—an instance of ”divine

coincidence” for fiscal policy under fixed exchange rates. This manifests in correlations

between tax rate increases in the MU and the counterfactual nominal devaluations of

about 90%. Translated into a general policy recommendation, this implies to increase the

VAT of a MU member whenever its exchange rate should be devaluated and vice-versa. In

case of mark-up shocks, optimal policy needs to trade-off the objective of stabilizing firms’

marginal costs with the incentive to replicate the effect of the exchange rate. Correlations

between the hypothetical exchange rate and taxes also depend on the origin of the shock

in this instance.

This paper contributes to the literature on optimal stabilization policy for monetary

unions in a New Keynesian framework. 3 Benigno (2004) offers a description of optimal

3 Noteworthy, a monetary union always makes the economy worse off in this literature, as its sole focus

lies on the cost-side of giving up flexible exchange rates. For an overview of other (beneficial) aspects of

2

monetary policy in a 2-country setting. He finds that inflation should be stabilized at the

level of the union, with a higher weight attached to the country with more rigid prices.

The efficient response is generally not achievable, though. Lombardo (2006) builds on

the model of Benigno, focusing in particular on the role of different degrees of imperfect

competition for monetary policy. Beetsma and Jensen (2005) add fiscal policy to the model

in the form of lump-sum financed government spending that enters households’ utility. In

this setting, optimal monetary policy is still used to stabilize aggregate inflation, while

fiscal policy aims at affecting cross-country inflation differentials. Using a similar fiscal

setting, Galí and Monacelli (2008) study optimal policy in a monetary union consisting

of a continuum of small open economies.

The closest antecedent to my article is by Ferrero (2009). In his model, fiscal policy also

needs to finance an exogenous stream of government spending by distortionary taxes and

debt. Optimal policy is described by targeting rules using a linear-quadratic approach.

The focus of the paper lies on the question how far simple policy rules can approximate

optimal policy in a monetary union. My article assesses how far optimal fiscal policy

can reduce the welfare costs of a fixed exchange rate regime. I further show that fiscal

devaluation policies can be an optimal policy response to idiosyncratic shocks. To this

end, I generalize the modelling framework of Ferrero (2009) by adding PTM, by allowing

for asymmetries between countries, and by comparing policy scenarios that differ in terms

of the exchange rate regime and the availability of fiscal policy as a stabilization device.

This paper further contributes to the literature on fiscal devaluations. Besides the work

of Farhi et al. (2014), this entails, amongst others, Lipinska and von Thadden (2012), and

Engler, Ganelli, Tervala, and Voigts (2014), who study the quantitative effects of tax

swaps from direct (payroll taxes) to indirect taxation (VATs). In general, this literature

studies the economic effects of given fiscal policies, but it does not provide a normative

analysis. I show that in fixed exchange rate regimes it is not only viable, but indeed

optimal to use fiscal devaluations as a substitute for the exchange rate.

The rest of the paper is structured as follows. Section 2 presents the open economy

model. The setup of the Ramsey policy problem is described in Section 3, while Section

4 features a description of the calibration of the model to the euro area. All results are

provided in Section 5, with a description of the steady state in Section 5.1, the analysis

of welfare costs of giving up exchange rate flexibility in 5.2, and results on optimal policy

conduct in 5.3. A conclusion including a discussion of the results is given in Section 6.

2 The Model

The model economy consists of two countries or regions i, labelled as the core (i = H)

and the periphery (i = F ), that can form a monetary union. The world population of

households (indexed by h) and firms (indexed by k) each sums up to one, of which a

fraction n ∈ (0, 1) of households and firms lives in the core and a fraction 1 − n in the

periphery. In each region, households choose consumption of domestic and foreign goods,

supply labour, which is mobile only within the region, and trade assets internationally.

Firms demand labour to produce tradable goods under monopolistic competition. Price

setting is subject to a Calvo-type friction. International prices are either set according

monetary unions, see Beetsma and Giuliodori (2010), and Santos Silva and Tenreyro (2010).

3

to the law of one price or taking into account local market conditions. Fiscal authorities

levy distortionary taxes and issue debt to finance an exogenously given amount of

public spending. Depending on whether the countries form a monetary union, there are

two separate or one single central bank, whose policy instrument is the nominal interest

rate. The economy operates at the cashless limit. Periphery variables are denoted by an

asterisk ( ∗ ). The following exposition focuses on the core region; the periphery economy

is modelled symmetrically.

2.1 Households

A representative household h living in region H derives utility from consumption and

disutility from work efforts. The consumption bundle C t (h) consists of tradable goods

only and is defined as a composite index over domestic- and foreign-produced consumption

goods,

C t (h) =

[

] ξ

γ 1 ξ

H C Ht(h) ξ−1

ξ

+ γ 1 ξ

F C F t(h) ξ−1 ξ−1

ξ , (1)

with ξ > 0 being the Armington elasticity of substitution between core and periphery

goods, and γ H = 1 − γ F ∈ (0, 1) the share of domestic goods in the consumption bundle.

If γ H > n, a home bias in preferences exists. Consumption of domestic and imported goods

by household h itself is given via Dixit-Stiglitz aggregators over imperfectly substitutable

individual varieties k,

C Ht (h) =

C F t (h) =

[ ( 1

ρ

n)1 ∫ n

C Ht (k, h) ρ−1

ρ

0

dk

] ρ

ρ−1

[ ( ) 1 ∫ 1

ρ ∗ 1

C F t (k, h) ρ∗ −1

ρ ∗ dk

1 − n n

, (2)

] ρ ∗

ρ ∗ −1

, (3)

where ρ, ρ ∗ > 1 are the elasticities of substitution between the varieties in each country.

To express specialization of countries in production, the elasticity of substitution between

varieties within a country is assumed to be greater than between goods of different origin,

i.e. ρ > ξ.

The corresponding price indices can be shown to equal:

P t =

P Ht =

P F t =

[

] 1

γ H P 1−ξ

Ht

+ γ F P 1−ξ 1−ξ

F t

, (4)

[( ∫ 1 n

] 1

P Ht (k)

n) 1−ρ

dk , (5)

0

[( 1

1 − n

) ∫ 1

n

] 1

P F t (k) 1−ρ∗ dk

1−ρ ∗ . (6)

P t denotes the core’s consumer price index (CPI), P Ht the producer price index (PPI) of

4

core goods, and P F t the price index of imported goods. Given the definitions of the price

indices, it is easy to show that consumer expenditures

∫

are given by P t C t (h) = P Ht C Ht (h)+

n

P F t C F t (h) with P Ht C Ht (h) = P 0 Ht(k)C Ht (k, h)dk and P F t C F t (h) =

∫ 1 P n F t(k)C F t (k, h)dk. Consumption demand functions are characterized by:

( ) −ξ ( ) −ξ PHt

PF t

C Ht (h) = γ H C t (h), C F t (h) = γ F C t (h), (7)

P t P t

C Ht (k, h) = 1 ( ) −ρ PHt (k)

C Ht (h), C F t (k, h) = 1 ( ) −ρ ∗

PF t (k)

C F t (h). (8)

n P Ht 1 − n

Each household h maximizes the utility function

U 0 (h) = E 0

∞

∑

t=0

subject to the flow budget constraint

β t [ζ c t

P F t

C t (h) 1−σ

1 − σ − N ]

t(h) 1+η

, (9)

1 + η

P t C t (h) + E t {Q t,t+1 [D t+1 (h) + B t+1 (h)]} ≤ W t N t (h) + D t (h) + B t (h) + Π t (h), (10)

where ζ c t denotes a demand preference shock, N t (h) labour supply, W t the wage rate, and

Π t (h) the profit share of a well-diversified portfolio of firms in possession of household h.

Asset markets are complete within and across countries. Q t,t+1 is the period t price of one

unit of domestic currency in a particular state of period t+1, normalized by the probability

of occurrence of that state, i.e. the stochastic discount factor. Accordingly, E t Q t,t+1 is

the price of an asset portfolio that pays off one unit of domestic currency in every state of

period t + 1 and, therefore, equals the inverse of the risk-free gross nominal interest rate,

R t = 1/E t Q t,t+1 . D t+1 (h) is the quantity of an internationally-traded state-contingent

private asset portfolio denominated in domestic currency, while B t+1 (h) denotes holdings

of government debt. It is assumed without loss of generality that sovereign debt of country

i can be held only by agents of that country. Besides its budget, the household has to

regard the transversality conditions

lim E t [Q t,s D t+s (h)] = 0 and

s→∞

lim E t [Q t,s B t+s (h)] = 0, (11)

s→∞

where Q t,s = ∏ s

z=t Q t,z denotes the stochastic discount factor from period s to period t.

The first-order conditions of the household’s problem imply the Euler equation,

Q t,t+1 = β ζc t+1

ζ c t

( ) −σ Ct+1 (h) P t

, (12)

C t (h) P t+1

as well as an intratemporal consumption-leisure trade-off, given by

N t (h) η

ζ c t C t (h) −σ = W t

P t

. (13)

Foreign households behave analogously and in particular hold a quantity D ∗ t+1(h) of

the internationally-traded asset portfolio. From the periphery’s perspective, the stochastic

5

discount factor is priced as

Q t,t+1 = β ζc∗ t+1

ζ c∗

t

( C

∗

t+1 (h)

C ∗ t (h)

) −σ

P ∗

t

P ∗

t+1

E t

E t+1

, (14)

where Pt

∗ is the CPI of the periphery, and E t is the nominal exchange rate, which is defined

as the price of one unit of periphery currency in terms of core currency (E t = [H]/[F ]).

An increase in E t accordingly implies a nominal devaluation of the core region. In case the

countries form a monetary union, the exchange rate is fixed at unity (E = 1). Combining

(12) and (14) yields the well-known condition of international risk sharing that links

consumption of the two countries and determines their (real) exchange rate:

q t = ζc∗ t

ζt

c

( ) C

∗ −σ

t (h)

κ. (15)

C t (h)

The real exchange rate is defined as the nominal exchange rate weighted ratio of the

CPIs, q t = (E t Pt ∗ )/P t , while κ = q 0 (C 0 /C0) ∗ −σ is a positive constant that depends on

preferences and the initial asset distribution. As pointed out, amongst others, by Faia

and Monacelli (2004), κ = 1 if markets are complete, the initial net foreign indebtedness

is zero (D t+1 (h) = Dt+1(h) ∗ = 0 ∀h), and preferences are symmetric across countries.

2.2 Firms and Price Setting Assumptions

In the core a continuum of firms k ∈ [0, n] operates under monopolistic competition. Each

firm produces a variety k according to the production plan

Y t (k) = A t N α t (k), (16)

where Y t (k) is total supply of variety k, A t a country-specific stochastic productivity level,

and N t (k) the firm’s labour demand. Labour is the sole input of production, and α is the

input elasticity of production. Labour supply by households is perfectly mobile across

firms within the country, but immobile between countries. Total demand for the good

produced by firm k is given by the demand of domestic (C Ht (k)) and foreign (C ∗ Ht (k))

households as well as public demand by the domestic government (G t (k)):

Y t (k) =

∫ n

0

C Ht (k, h) dh +

The period t profit function of firm k reads

∫ 1

[∫ n

]

Π t (k) = (1 − τt v ) P Ht (k) C Ht (k, h) dh + G t (k)

0

+ (1 − τt

v∗ ) E t PHt(k)

∗

n

∫ 1

n

C ∗ Ht(k, h) dh + G t (k). (17)

C ∗ Ht(k, h) dh − W t N t (k), (18)

where PHt ∗ (k) is the price of core good k abroad. τ t

v and τt

v∗ are country-specific valueadded

taxes (VAT) in region H and F respectively. As common in existing tax systems,

τt

v is levied on all goods sold within the Home country, but not on exports. The latter

6

are taxed at the border with the foreign VAT rate τ v∗

t .

Price setting of firms is impaired by Calvo-type price stickiness. Each period t, a firm

can adjust prices with probability 1−θ, independent of the date of previous price changes.

With probability θ the firm has to maintain last period’s prices. Optimal prices are set

as to maximize the net present value of future profits

∞∑

θ s−t E t [Q t,s Π s (k)] (19)

s=t

subject to the production technology and demand. Prices always include taxes. The

price of domestic goods sold within the core, P Ht (h), is always set in domestic currency.

The setting of export prices for the periphery, PHt ∗ (k), is conducted according to the

assumption of either the law of one price or pricing-to-market.

2.2.1 Law of One Price (LOOP)

Under this pricing scheme, firms set a price for their good in domestic currency, while the

price in the other region satisfies the law of one price, adjusted for tax rates:

s=t

(1 − τt

v∗ ) E t PHt(k)

∗

!

= (1 − τt v ) P Ht (k)

1

P Ht (k). (20)

E t

⇔ P ∗ Ht(k) = (1 − τ v t )

(1 − τ v∗

Following Farhi et al. (2014), this expression is derived from the assumption that one unit

of sales should yield the same revenue to the firm, independent of the origin of the buyer.

(20) implies complete and immediate pass-through of both exchange rates and taxes on

international prices. A relative increase of the core’s VAT rate has the same effect on

prices abroad as a nominal devaluation.

The optimality condition for the price set in period t, P Ht (k), is derived in Appendix

A.1 and reads

∑ ∞ ( ) −1−ρ [

]

P

E t θ s−t Ht (k) Ys ρ

Q t,s

P Hs P Hs ρ − 1 µ sMC Hs (k) − (1 − τs v ) P Ht (k) = 0, (21)

where MC Ht (k) = W t / [ αA t Nt

α−1 (k) ] denotes marginal costs, and µ t a stochastic markup

shock. The equation shows the standard result that the optimal price is set equal to

a mark-up over a weighted average of current and future marginal costs.

2.2.2 Pricing-to-Market (PTM)

Under the alternative assumption of PTM, firms set separate prices at home, P Ht (k), and

abroad, P ∗ Ht(k), each of them subject to a Calvo friction. As a result, there is only limited

direct pass-through of exchange rates and taxes on international prices, and the law of

one price can be violated. Optimal price setting is now described by two conditions, also

derived in Appendix A.1:

t )

7

E t

∞

∑

s=t

( ) −1−ρ [ P

θ s−t Ht (k) (nC Hs + G s ) ρ

Q t,s

P Hs P Hs

∞

( )

∑

E t θ s−t P ∗ −1−ρ [

Q

Ht(k) CHs

∗ ρ

t,s

PHs

∗ PHs

∗

s=t

]

ρ − 1 µ sMC Hs (k) − (1 − τs v ) P Ht (k)

ρ − 1 µ sMC Hs (k) − (1 − τs

v∗ ) E s P ∗ Ht(k)

= 0, (22)

]

= 0.(23)

A devaluation of the domestic currency has the same effect on the firm’s pricing

decision for exports as a reduction in marginal costs, since every unit sold abroad leads to

higher revenues than selling on the domestic market. Note that reducing the periphery’s

VAT rate τ v∗ induces, ceteris paribus, the same effect on import prices in the periphery

as a rise in E t .

2.2.3 Foreign Firms

Foreign firms are modelled symmetrically. Under the LOOP, they set a price P ∗ F t(k) at

which periphery goods are sold in F . The price at which goods are sold internationally

is again determined by the law of one price, adjusted for taxes:

P F t (k) = (1 − τ v∗ )

(1 − τ v ) E tP ∗ F t(k). (24)

In case of PTM, firms in the periphery can also set separate prices for their domestic

and the international market. Optimal prices are implicitly given by:

E t

∞

∑

s=t

θ ∗s−t Q ∗ t,s

(

[ ρ

∗

·

)

P ∗ −1−ρ ∗

F t (k) ((1 − n) CF ∗ s + G∗ s)

PF ∗ s

PF ∗ s

]

ρ ∗ − 1 µ∗ sMCF ∗ s(k) − (1 − τs

v∗ ) P ∗ F t (k)

∑ ∞ ( P F t (k)

E t

s=t

θ ∗s−t Q ∗ t,s

P F s

) −1−ρ ∗

CF s

P ∗ F s

[ ρ

∗

·

ρ ∗ − 1 µ∗ sMCF ∗ s(k) − (1 − τ ]

s v )

P F t (k)

E s

= 0, (25)

= 0, (26)

where MC ∗ F t (k) = W ∗

t / [ αA ∗ t N ∗α−1

t (k) ] .

2.3 Monetary and Fiscal Authorities

The public sector consists of separate fiscal authorities and central banks at the country

level. The policy instruments of the central banks are their nominal interest rates, R t

and Rt ∗ . If the regions share the same currency, only one central bank for the union as a

whole exists, whose policy instrument is denoted by Rt MU .

The task of the fiscal authorities is to finance an exogenously given stochastic amount

of public spending G t . In each country, government spending consists of an index of

8

locally produced goods only,

[( ∫ 1 n

G t = G t (k)

n) ρ−1

ρ

with corresponding demand functions for each variety k, given by

G t (k) = 1 n

0

] ρ

dk

ρ−1

, (27)

(

PHt (k)

P Ht

) −ρ

G t . (28)

These expenditures are financed by distortionary value-added taxes and state-contingent

public debt. The budget constraint of the domestic government reads

P Ht G t + B t ≤ E t Q t,t+1 B t+1 + τ v t

+τ v t

∫ 1 ∫ n

n

0

∫ n

0

(∫ n

)

P Ht (k) C Ht (k, h) dh + G t (k) dk

0

P F t (k)C F t (k, h) dh dk. (29)

Note that the VAT is not only levied on domestically produced goods, but also on imports

C F t .

2.4 Aggregation and Equilibrium

Due to symmetry among agents within a country, households and firms, respectively, will

in each situation come to the same decisions. In the process of aggregation, one can,

therefore, drop indices h and k.

By the law of large numbers, today’s PPIs consist of the prices set today and last

period’s price index, weighted with the probabilities of adjustment and non-adjustment,

respectively. As shown in Appendix A.2, the law of motion for P Ht can be expressed as

˜p Ht = P Ht

P Ht

=

( 1 − θπ

ρ−1 ) 1

1−ρ

Ht

, (30)

1 − θ

where π Ht = P Ht /P Ht−1 denotes the PPI inflation rate of domestically produced goods in

H.

(21) gives an expression for the Philips curve of core goods inflation under the LOOP.

In order to solve the model, it is required to rewrite the Philips curve in a recursive way,

which avoids the use of infinite sums. To do so, I follow Schmitt-Grohé and Uribe (2006)

and restate (21)by defining two auxiliary variables, X1 Ht and X2 Ht (for a derivation, see

Appendix A.3), such that

where

ρ

ρ − 1 µ tX1 Ht = X2 Ht , (31)

9

( )

X1 Ht = ˜p −1−ρ

ζ c −σ

t+1 Ct+1 π 1+ρ

Ht

Y t mc Ht + θβE t

ζt

c C t

X2 Ht = ˜p −ρ

Ht Y t (1 − τ v t ) + θβE t

ζ c t+1

ζ c t

(

Ct+1

C t

(

Ht+1 ˜pHt

π t+1

) −1−ρ

X1 Ht+1 , (32)

˜p Ht+1

) −σ

π ρ ( ) −ρ

Ht+1 ˜pHt

X2 Ht+1 , (33)

˜p Ht+1

with π t = P t /P t−1 being the CPI inflation rate of the core, and mc Ht = MC Ht /P Ht being

real marginal costs.

The resource constraint of the economy can be obtained by integrating the production

function (16) over firms. The result differs depending on whether pricing follows the law

of one price or firms can engage in pricing-to-market: 4

π t+1

A t nN α t = ∆ Ht (nC Ht + (1 − n)C ∗ Ht + G t ) (34)

A t nN α t = ∆ Ht (nC Ht + G t ) + ∆ ∗ Ht(1 − n)C ∗ Ht (35)

The first equation holds under the LOOP, the latter one under PTM. ∆ Ht and ∆ ∗ Ht are

indices of price dispersion that render inflation costly in efficiency terms. They are defined

as

∆ Ht = 1 n

∫ n

0

∫ n

( ) −ρ PHt (k)

dk, (36)

P Ht

( ) P

∗ −ρ

Ht (k)

dk. (37)

∆ ∗ Ht = 1 n

Their laws of motion are given by

0

P ∗ Ht

∆ Ht = (1 − θ)˜p −ρ

Ht + θπρ Ht ∆ Ht−1, (38)

∆ ∗ Ht = (1 − θ)˜p ∗−ρ

Ht

+ θπ ∗ρ

Ht ∆∗ Ht−1. (39)

As clarified by Schmitt-Grohé and Uribe (2006), price dispersion is irrelevant for the

allocation if the non-stochastic (steady state) level of inflation is zero and only a firstorder

approximation to the equilibrium conditions is used.

An equilibrium in this economy is characterized by prices and quantities that fulfil

the optimality conditions of households and firms in both countries such that all markets

clear, given stochastic processes for all shocks, and sequences for the policy instruments.

Goods markets under LOOP and markets for private assets clear at the international

level; goods markets under PTM, government bond, and labour markets clear at national

levels. A complete list of all equilibrium conditions under both LOOP and PTM is given

in Appendix B.

The following definition of the terms of trade will be useful for the rest of the analysis.

The terms of trade indicate how much of exports the economy has to give for one unit of

4 For derivations, see Appendix A.4.

10

imports,

z t = P F t (LOOP )

=

P Ht

(1 − τ

v∗

t )

(1 − τ v t )

} {{ }

F D t

E t

P ∗ F t

P Ht

, (40)

where the second equality sign holds under the law of one price. In this case of complete

pass-through only, exchange rate and tax adjustments translate directly into changes

of the terms of trade. The formula shows that under LOOP an increase of H’s VAT

relative to F ’s has the same effect on z t as a nominal devaluation. The term F D t =

(1 − τt

v∗ )/(1 − τt v ) will, therefore, also be referred to as the fiscal devaluation factor.

In case of pricing-to-market, the pass-through of the exchange rate and taxes on the

terms of trade is limited by their effect on P F t and P Ht . The price setting conditions

(23) and (26) make clear that the tax rates can have the same effect on import prices

as the nominal exchange rate. The speed of pass-through depends on the degree of price

stickiness, with the law of one price and, so, the second part of (40) only holding in the

long-run. The short-run efficacy of fiscal devaluation policies to affect the terms of trade

will, therefore, be higher under LOOP than under PTM.

3 The Ramsey Problem

Optimal monetary and fiscal policy is determined using a Ramsey approach. This procedure

involves to find the sequences of the available policy instruments that support the

welfare-maximizing competitive equilibrium. All policy authorities can credibly commit

to their announced policies, and I assume full cooperation between all entities. The objective

of the Ramsey planner is a utilitarian world welfare function that weights utility

of core and periphery households according to their population size:

W 0 = E 0

∞

∑

t=0

(

β

{n

t ζt

c

Ct

1−σ

1 − σ − N 1+η )

t

1 + η

(

+ (1 − n)

ζ c∗

t

C ∗1−σ

t

1 − σ − N ∗1+η

t

1 + η

)}

. (41)

If prices were flexible, the optimal policy problem could be described by maximizing

(41) subject to one implementability and one resource constraint for each country only.

Using this so-called primal approach to the Ramsey problem, proposed by Lucas and

Stokey (1983) also in the context of optimal stabilization policy, the planner directly

chooses an equilibrium allocation, from which prices and instruments can be backed out

afterwards. In presence of a sticky price friction, this reduction of the problem to just

two constraints per country is generally not possible anymore, as the Philips curves now

effectively constrain the evolution of prices. 5 The dual approach to the Ramsey problem,

which involves choosing prices and instruments directly, has to be used instead.

In the following analysis, I compare optimal policy under various scenarios to assess

the consequences of being in a monetary union. The scenarios differ by the type of

price setting (LOOP vs. PTM) and by the availability of different policy instruments:

5 The work of, for instance, Schmitt-Grohé and Uribe (2004), and Faia and Monacelli (2004) is also

subject to this issue.

11

flexible exchange rates vs. monetary union, and monetary and fiscal policy vs. monetary

policy only. In all of these scenarios, the dual solution to the policy problem is found by

maximizing (41) subject to the relevant equilibrium conditions, described in Appendix B.

If fiscal policy is an instrument to the Ramsey planner, the time path of the VAT rates,

{τt v , τt

v∗ } ∞ t=0

, has to ensure solvency of the fiscal authorities in both countries. To this

end, the problem is augmented with the intertemporal fiscal budget constraints of both

countries. As an example, I describe the solution to the Ramsey problem by means of its

first-order conditions for the case of a monetary union, where the law of one price holds,

with fiscal policy in detail in Appendix C. 6

4 Calibration

I calibrate the model to characteristics of the euro area using quarterly data between

2001:1 and 2014:4 from Eurostat. In the calibration, the core (region H) comprises Austria,

Belgium, Finland, France, Germany, the Netherlands, and Slovakia. The periphery

(region F ) consists of Greece, Ireland, Italy, Portugal, and Spain. This leads to a population

share of the core of 60%; hence, n = 0.6. In total, these 12 countries cover 98% of

euro area GDP in 2014.

Table 1: Parameter Values

Parameter Core Periphery

Size of region n = 0.6 (1 − n) = 0.4

Discount factor β = 0.99

Risk aversion σ = 2

Inverse Frisch elasticity η = 2

Home bias γ H = 0.72 γF ∗ = 0.48

Armington elasticity (Home-Foreign goods) ξ = 1.2

Elasticity of substitution between varieties ρ = 6 ρ ∗ = 4

Labor input elasticity of production α = 1

1 – Probability of price adjustment θ = 0.75 θ ∗ = 0.75

Gov. spending ratio to GDP in steady state G/Y = 0.21 G ∗ /Y ∗ = 0.19

Annual gov. debt to GDP ratio in steady state B/Y = 0.78 B ∗ /Y ∗ = 1.08

The discount factor β is set to 0.99, which is the standard value in the business-cycle

literature for quarterly data, implying an annual real interest rate of about 4% in steady

state. Risk aversion and the inverse Frisch elasticity are both set equal to 2, also following

conventions of the literature. A mild home bias in demand preferences of 20% exists in

both countries, yielding γ H = 1.2n = 0.72 and γF ∗ = 1.2(1 − n) = 0.48. Following

estimates by Feenstra, Luck, Obstfeld, and Russ (2014), I set the Armington elasticity

between goods of different origin to ξ = 1.2. Initial international private debt in steady

state is set to match the average trade balance surplus relative to GDP of the core of 2%

between 2001 and 2014.

The elasticities of substitution between individual goods varieties, ρ and ρ ∗ , are set

to match aggregate mark-ups. Høj, Jimenez, Maher, Nicoletti, and Wise (2007) provide

6 Solutions to all other scenarios are available on request.

12

estimates for several OECD countries that suggest a mark-up of 1.2 in the core and 1.3 in

the periphery, which implies ρ = 6 and ρ ∗ = 4. The labour input elasticity of production

is set to one, which implies that the production technology is linear in labour. Following

empirical evidence by ECB (2005), the probability of price stickiness is set to θ, θ ∗ = 0.75

so that price contracts last on average 4 quarters. 7 Cross-country evidence by Druant,

Fabiani, Kezdi, Lamo, Martins, and Sabbatini (2012) confirms that the frequency of price

adjustments is similar across core and periphery countries.

The ratio of government spending to GDP in steady state (G/Y ) is set to the average

values between 2001 and 2014, which are 21% for the core and 19% for the periphery. The

government debt to GDP ratio in annualized steady state (B/Y ) matches the 2010-2014

average debt-to-GDP-ratios of the core (78%) and the periphery (108%). This calibration

requires a steady state primary surplus relative to quarterly GDP of 3.1% in the core and

of 4.3% in the periphery. Balanced public budgets imply steady state VAT rates of 24.6%

and 22.6%, respectively. Table 1 summarizes all parameter values.

Table 2: Shock Processes

Parameter Core Periphery

Persistence of productivity shocks (ϕ A , ϕ A∗ ) 0.9301 0.9434

Persistence of demand preference shocks (ϕ C , ϕ C∗ ) 0.8135 0.8990

Persistence of government spending shocks (ϕ G , ϕ G∗ ) 0.7731 0.6439

Std. dev. of productivity shocks (σ A , σ A∗ ) 0.0034 0.0032

Std. dev. of demand preference shocks (σ C , σ C∗ ) 0.0139 0.0209

Std. dev. of government spending shocks (σ G , σ G∗ ) 0.0071 0.0194

Std. dev. of mark-up shocks (σ µ , σ µ∗ ) 0.0057 0.0140

Note: Parameters calibrated to match autocorrelations and standard deviations of GDP, government

spending, private consumption, and wage data between 2001:1 and 2014:4.

The evolution of the economy outside steady state is driven by region-specific stochastic

processes for productivity A t and government spending G t , the demand preference

shocks ζt c , and the mark-up shocks µ t in both countries. All but the mark-up shocks are

modelled as AR(1)-processes, while the latter are assumed to be white noise. 8 Persistence

and Variance of the shocks are calibrated to match autocorrelations and standard

deviations of seasonally adjusted and quadratically detrended data on GDP, government

spending, private consumption, and average wage rates of the core and periphery between

2001:1 and 2014:4. The resulting parameters are given in Table 2. Details on the used

data, including the target moments, are shown in Appendix D.

7 The average time until a firm gets a chance to adjust its price is given by 1/ (1 − θ), as Calvo-type

price stickiness implies a Poisson process, where time until next adjustment is an exponentially-distributed

random variable.

8 Allowing the mark-up shock to follow an AR(1)-process as well yields persistence parameters of

(µ t , µ ∗ t ) close to zero and does not affect the moments of the other processes significantly, which is in line

with results of Smets and Wouters (2003).

13

5 Results

The solution to the Ramsey problem, calibrated to the euro area, is quantitatively assessed

in this chapter. Section 5.1 provides a brief description of the steady state. Section 5.2

analyses to what extent optimal fiscal policy reduces the welfare costs of giving up flexible

exchange rates within the European Monetary Union. The conduct and mechanisms of

optimal policy are subsequently described in Section 5.3.

5.1 The Allocation in Steady State

Gross inflation rates in all sectors, domestic goods and imports, are equal to one in the

Ramsey-optimal steady state, since price dispersion that would arise otherwise impairs an

efficient bundling of individual goods. Given this result, optimal price setting of domestic

firms in steady state when the LOOP holds is described by

ρ 1

ρ − 1 (1 − τ v ) MC H = P H , (42)

while under PTM the following condition for export prices additionally holds:

ρ 1 1

ρ − 1 (1 − τ v∗ ) E MC H = PH. ∗ (43)

Combining (42) and (43) immediately yields the law of one price (20). Hence, there are

no long-run deviations from the law of one price, which would distort the composition of

consumption between domestic and imported goods.

Also visible from (42) and (43), the distortions that render the long-run allocation

different from its first-best level are the reduction in activity due to monopolistic competition

and the necessity to use distortionary taxation to finance public expenditures. As

taxes have to be positive in steady state, they cannot be used for mark-up elimination.

Instead, taxes exacerbate the wedge driven by the mark-up between prices and marginal

costs. The steady state is, therefore, in general not efficient.

5.2 The Welfare Costs of Giving up Exchange Rate Flexibility

The welfare comparison of the various policy scenarios is discussed next. The welfare

measure used to assess the scenarios is units of steady state consumption that households

are willing to give up in order to live in the deterministic steady state economy instead

of a stochastic economy—that is a percentage amount of steady state consumption ω E I

satisfying

{ ([ ( )]

1 C 1 + ω

E 1−σ

n

I

1 − β

1 − σ

) ([

− N ( )] 1+η

C

∗

1 + ω E 1−σ

I

+ (1 − n)

1 + η

1 − σ

)}

− N ∗1+η !

= W E,I

0 ,

1 + η

where W E,I

0 is the expected net present value of aggregate welfare as defined by (41) for a

given exchange rate regime E ∈ {MU, F LEX} and a given set of policy instruments I ∈

{MP, MF P }. To evaluate welfare, the model is solved by a second-order approximation

14

to the policy functions and simulated for T = 1000 periods. 9 I average the welfare measure

over J = 100 simulations with different stochastic seeds to obtain ergodic means.

Results are given in Table 3. The evaluated scenarios differ along 3 dimensions. A first

distinction is made in terms of the pricing scheme, law of one price or pricing-to-market.

Second, the two columns, headed MU and FLEX, indicate whether the exchange rate

regime is a monetary union or flexible. Third, rows mark if only monetary policy is available

for stabilization purposes (abbreviated by MP) or if both monetary and fiscal policy

can be used (MFP). To allow for comparisons between these scenarios, the underlying

steady state is calibrated to be identical across all 8 scenarios. This implies for the MP

scenarios that VAT rates in steady state have to be set on the optimal values obtained

under MFP.

As is well-known, absolute numbers calculated for the welfare costs of business cycles

are in general small in representative agent models. 10 The focus of this analysis, yet,

lies on the comparison across different scenarios, which yields more expressive outcomes.

Results for the benchmark calibration are given in Panel (A) of the table. Under LOOP

and exclusive availability of monetary policy, households are willing to give up ωMP MU =

5.16 ∗ 10 −2 % of steady state consumption (hereafter c%) to avoid living in the stochastic

economy of a monetary union and ωMP

F LEX = 4.53 ∗ 10 −2 c% with flexible exchange rates.

The difference between these two numbers, ∆ω MP = ωMP MU LEX

− ωF MP = 0.63 ∗ 10 −2 c%,

given in the last column, shows the welfare costs of giving up exchange rate flexibility in

a monetary union. Allowing for the VAT rates of both countries as a stabilization tool

reveals that fiscal policy is almost irrelevant under flexible exchange rates—welfare costs

are reduced from ωMF MU

P = 4.45 ∗ 10−2 c% to ωMF F LEX

P = 4.36 ∗ 10−2 c%. By contrast, fiscal

policy is an effective instrument in a monetary union: welfare costs of entering a MU are

reduced by 85.76% from ∆ω MP = 0.63 ∗ 10 −2 c% to ∆ω MF P = 0.09 ∗ 10 −2 c%.

Engel (2011) shows that optimal exchange rate volatility is lower in presence of pricingto-market

since in this case exchange rate movements do not directly translate into changes

of international relative prices as they would under the LOOP, but merely distort price

mark-ups of firms, thereby making inefficient deviations from the law of one price to

occur. 11 Welfare costs of fixed exchange rate regimes are, therefore, strictly lower with

PTM than under LOOP, a point also raised by Corsetti (2008). Additionally, as shown in

Section 2, fiscal policy can potentially be much more effective in manipulating the terms of

trade when the LOOP holds due to the assumption of full pass-through than under PTM.

To take into account the effect of the pricing scheme on the welfare costs of exchange

rate pegs on the one hand, and to avoid an overestimation of the beneficial effect of fiscal

policy because of full pass-through on the other hand, the reduction of welfare costs is

studied next for the case of PTM. The welfare costs of entering a MU are now about

∆ω MP = 0.099 ∗ 10 −2 c% under monetary policy only, which is about 6.4 times smaller

than when the law of one price holds. Adding fiscal policy to the set of instruments also

9 I use the Dynare toolbox to solve the model. The second-order simulations are obtained using the

pruning algorithm proposed by Kim, Kim, Schaumburg, and Sims (2008).

10 An exemption is the analysis of Schmitt-Grohé and Uribe (2016), which relies on downward nominal

wage rigidity.

11 Under very specific conditions, it can even be optimal to completely stabilize the nominal exchange

rate in presence of PTM, as shown by Devereux and Engel (2003). Duarte and Obstfeld (2008) emphasize

that this extreme result holds only under a restrictive set of assumptions. Among these are one period

in advance price stickiness and the absence of home bias.

15

Table 3: Welfare Costs of Fixed Exchange Rates

(A) Benchmark

LOOP MU FLEX Difference

Monetary Policy (MP) 10 −2 ∗ -5.1612 -4.5269 0.6343

Monetary+Fiscal Policy (MFP) 10 −2 ∗ -4.4485 -4.3582 0.0903

Reduction of Welfare Costs: 85.76%

PTM

Monetary Policy 10 −2 ∗ -5.1593 -5.0605 0.0988

Monetary+Fiscal Policy 10 −2 ∗ -4.9095 -4.8785 0.0310

Reduction of Welfare Costs: 68.66%

(B) Productivity, Preference, Gov. Spending Shocks

LOOP

Monetary Policy 10 −2 ∗ -4.1227 -3.6759 0.4468

Monetary+Fiscal Policy 10 −2 ∗ -3.7696 -3.6983 0.0713

Reduction of Welfare Costs: 84.03%

PTM

Monetary Policy 10 −2 ∗ -4.1212 -4.0689 0.0523

Monetary+Fiscal Policy 10 −2 ∗ -4.0826 -4.0593 0.0233

Reduction of Welfare Costs: 55.42%

(C) Mark-up Shocks

LOOP

Monetary Policy 10 −2 ∗ -0.9617 -0.7742 0.1875

Monetary+Fiscal Policy 10 −2 ∗ -0.6064 -0.5868 0.0194

Reduction of Welfare Costs: 89.58%

PTM

Monetary Policy 10 −2 ∗ -0.9613 -0.9148 0.0465

Monetary+Fiscal Policy 10 −2 ∗ -0.7505 -0.7428 0.0077

Reduction of Welfare Costs: 83.43%

Note: Welfare measure: consumption equivalents between deterministic and stochastic world economy.

Exchange rate regime either monetary union (MU) or flexible (FLEX). Panel (A): productivity, demand

preference, government spending, & mark-up shocks in both countries. Panel (B): all but mark-up shocks.

Panel (C): mark-up shocks only. Second-order approximation to policy functions. T = 1000, J = 100.

helps to reduce welfare costs considerably by 68.66%. Hence, even under PTM, fiscal

policy is capable of reducing the welfare costs of fixed exchange rates substantially.

The two bottom panels, (B) and (C), of Table 3 decompose the shocks into those,

for which the efficient response is attainable by the use of monetary policy only when

the law of one price holds and exchange rates are fully flexible (productivity, demand

preferences, and government spending shocks), and the mark-up shocks, which cannot be

fully stabilized. While the size of the welfare costs in the various cases naturally depends

on the type and number of shocks considered, the percentage reduction of the welfare

costs of the fixed exchange rate regime is of comparable magnitude as in the benchmark

(Panel A). Under the law of one price, using the tax instruments for stabilization policy

purposes reduces the welfare costs of the monetary union by 84% in Panel (B) and by

almost 90% in presence of the mark-up shocks. Under pricing-to-market, the reduction

16

in welfare costs depends to a larger extent on the type of shock. Allowing for active fiscal

policy reduces welfare costs by 55.42% in Panel (B) and by 83.43% in Panel (C). The

cause for the effective stabilization of mark-up shocks can directly be understood from

the firms’ first-order conditions (21) to (23). The VAT rates can directly offset the effect

of the mark-up shocks µ t on the firms’ price setting.

Various sensitivity checks confirm that the results of Table 3 are very robust to changes

in the parametrization of the model. Table 7 in Appendix E provides results, where standard

deviations of all shocks are doubled compared to the benchmark calibration. Increasing

the shock size naturally raises the shares of steady state consumption that households

are willing to give up to avoid living in the stochastic economy. The percentage reduction

of the welfare costs of fixed exchange rates by using fiscal policy, however, remains

virtually the same. Optimal exchange rate volatility and the costs of pegs also depend

on the structural parameters of the model. For instance, Lombardo and Ravenna (2014)

and Faia and Monacelli (2008) emphasize the role of trade openness for the exchange

rate, while De Paoli (2009) analyses the impact of the Armington elasticity. Results in

Table 8 show that the findings of this section regarding the reduction of welfare costs

are qualitatively fully maintained for changes in all structural parameters as well as the

amount of government spending and debt.

Instead of VAT rates, policymakers could in principle also use payroll taxes as the fiscal

instrument to substitute for the effect of the exchange rate. 12 A change in the labour tax

implies that the prices of all goods produced within a country are affected equally, while

changes of the domestic VAT alter only prices of goods sold at home, but not of exports.

To analyse whether these differences influence the capability of fiscal policy to reduce the

welfare costs of a fixed exchange rate regime, I repeat the welfare analysis of Table 3 with

a payroll tax in each country levied on firms instead of a VAT.

Table 9 in Appendix E presents the results of that exercise. To ensure comparability, I

use the same calibration as before. Most importantly, the reduction of welfare costs by the

additional use of fiscal policy remains to be high with payroll taxes. Under the benchmark

calibration, welfare costs of a peg can be reduced by about 60% under the LOOP and

by 80% under PTM. The relatively smaller reduction of welfare costs under the LOOP is

driven by the low reduction for productivity, demand preference, and government spending

shocks in Panel (B) of 41% only compared to 84% with VATs. The main reason for these

different results is that, in opposition to VATs, payroll tax changes do not directly pass

through on the terms of trade via the law of one price (recap equations 20 and 40). In

case of mark-up shocks, on the other hand, the welfare costs of fixed exchange rates can

be avoided almost completely—by 99% under LOOP and 97% under PTM. A change in

the domestic payroll tax suffices to neutralize the effect of a domestic mark-up shock,

while with VATs the rates of both countries would have to adjust for stabilization of the

shock along all relevant margins.

In sum, these results suggest that optimal use of only one fiscal instrument per country

could substantially reduce welfare costs in the euro area that arise from the fixed exchange

rate regime.

12 If a payroll tax τ n t is levied on the employers, profits of firm k become

Π t (k) = (1 − τt v ) P Ht (k) [nC Ht (k, h) + G t (k)] + (1 − τt

v∗ ) E t PHt(k)C ∗ Ht(k, ∗ h) − (1 + τt n )W t N t (k).

17

5.3 Optimal Fiscal Substitutes for the Exchange Rate

This section describes the conduct of optimal policy and shows how taxes should be used

to substitute for the nominal exchange rate inside the euro area. Optimal fiscal policy

in the monetary union depicts a fiscal devaluation policy: in case it would be optimal to

devalue the exchange rate of a region, it is optimal to increase its VAT relative to the

other region of the monetary union.

Figure 1: Productivity Shock in Core, LOOP

Note: Comparison of impulse responses to 1% productivity shock in the core under the law of one

price. Solid lines: monetary union. Dashed diamond lines: flexible exchange rate. Blue lines:

core. Red lines: periphery. Unit of y-axis is % deviation from steady state (p.p. deviation in Panels

3 & 6). X-axis indicates quarters after impulse.

5.3.1 Dynamic Response to a Productivity Shock

To gain intuition for the findings of the welfare analysis, Figure 1 compares the impulse

response to a 1% productivity shock in the core under LOOP in the monetary union (solid

lines) with the counterfactual response under flexible exchange rates (dashed diamond

lines). As shown by Corsetti, Dedola, and Leduc (2010), the latter case constitutes the

benchmark of ”divine coincidence” in open economies, where stabilizing PPI inflation by

monetary policy in both regions is sufficient to obtain the efficient allocation in presence

of the shock.

18

The increase of productivity implies that it is efficient to produce a larger share of

world output in the core. Y t increases strongly, while Yt

∗ declines on impact (Panel 1). To

induce the required expenditure-switching towards core goods, the terms of trade of the

core have to deteriorate (i.e. z t has to increase). According to (40), this can be achieved by

changes of the PPIs (P Ht ,PF ∗ t ), by nominal or by fiscal devaluation. As long as exchange

rates are flexible (dashed diamond lines), this shift in the terms of trade is generated

by the nominal exchange rate due to its feature of immediate pass-through under LOOP

(see Panel 8), while PPI inflation rates are kept constant to avoid welfare-reducing price

dispersion among goods (Panel 4). The adjustment of the exchange rate leads to strong

effects on the prices of imports (Panel 5). As imports behave as under flexible prices,

inflation in that sector does not have to be minimized to avoid welfare losses. The VAT

rates are basically unused under flexible E t (Panels 6 and 9) since the efficient response

to the shock can in this case be brought about by monetary policy alone.

These dynamics change altogether in the monetary union (solid lines). Monetary

policy on its own is not able to reach the efficient response any more. The reaction of the

nominal interest rate is now in between the responses of core and periphery under flexible

exchange rates, which implies a rate too low for the periphery and rate too high for the

core (Panel 3). As a consequence, deviations of PPI inflation from steady state are now

slightly larger than under exchange rate flexibility. The reaction is somewhat stronger

in the periphery due to its relatively lower weight in the welfare function of the Ramsey

planner. Even though E t is now fixed, the efficient response of the terms of trade can again

be reached (the brown solid and dashed lines in Panel 8 cover up each other perfectly).

The way the reaction of the terms of trade is induced is completely different, though. The

VAT rates are now used actively to substitute for the effect of E t on the terms of trade.

Panel 9 shows that the response of the fiscal devaluation factor, F D t , in the monetary

union is very close to the counterfactual flexible exchange rate response. On impact, 93%

of the response of z t in the monetary union are due to a fiscal devaluation policy. Only the

remaining 7% are due to changes in PPIs. To implement the fiscal devaluation, the VAT

of the core increases, while the VAT of the periphery decreases. Besides its effect on the

terms of trade, these tax responses at the same time help to stabilize firm mark-ups. The

increase of τt

v supports monetary policy in fighting back deflationary pressures in the core

that arise from the increased productivity, while the decrease of τt

v∗ reduces inflationary

pressures in the periphery, which are the result of the relatively loose monetary policy for

that region.

Under the free floating regime, the real exchange rate q t depreciates because the devaluation

of the core’s currency dominates the relative increase of the core’s CPI (Panel 7).

In the monetary union, the real exchange rate appreciates instead. The fiscal devaluation

also increases the CPI of the core relative to the periphery by making core imports more

expensive, but the relative currency value between the regions now remains fixed. As a

result, in case of the monetary union consumption in the periphery increases by more

than in the core due to international risk sharing (Panel 2).

Taken together, the optimal fiscal devaluation policy focusses on replicating the behaviour

of the terms of trade under flexible exchange rates to induce exenditure switching

effects, but it does not reproduce the response of the real exchange rate that affects levels

of consumption via the international risk sharing condition (15). The policymaker thereby

favours production efficiency over an efficient allocation of aggregate consumption in the

19

monetary union. Adressing the latter would require an additional instrument to affect

the real exchange rate. Farhi et al. (2014) show that a consumption subsidy payable to

households could succeed to that task. They also prove that a complete replication of

the allocation under flexible exchange rates lacks even further instruments. A payroll

subsidy to firms would be needed to stabilize internal prices of domestically produced

goods, which are distorted by the VAT, while a labour income tax levied household would

be required to neutralize distortions by the consumption subsidy on wages. 13

Figure 2: Productivity Shock in Core, PTM

Note: Comparison of impulse responses to 1% productivity shock in the core under pricing-to-market.

Solid lines: monetary union. Dashed diamond lines: flexible exchange rate. Blue lines: core.

Red lines: periphery. Unit of y-axis is % deviation from steady state (p.p. deviation in Panels 3 &

6). X-axis indicates quarters after impulse.

Figure 2 compares impulse responses of the monetary union with the flexible exchange

rate scenario for the case of pricing-to-market. Engel (2011) shows for the case of flexible

exchange rates and PTM that CPI inflation (as the weighted average of PPI and import

price inflation) instead of PPI inflation only ought to be stabilized, since the import

sector is now also subject to a sticky price friction. However, avoiding inflation and

closing output gaps is not sufficient to obtain the efficient allocation, because deviations

of the terms of trade from their efficient level and deviations from the law of one price

13 Depending on the specific model setting, still more instruments may be required. See also Adao et al.

(2009) on that point.

20

can still occur. These wrong price signals translate into inefficient shifts in the level and

composition of consumption between the regions. Accordingly, in opposition to the LOOP

case, the response to the productivity shock under flexible exchange rates and PTM does

not reach the efficient allocation.

Beginning the description with the case of flexible exchange rates again (dashed diamond

lines), PPI inflation is more pronounced under PTM, but import inflation is decisively

weaker, leading to a terms of trade deterioration which falls short of its efficient

response. Under PTM, z t rises by 0.36% in the first quarter, while the efficient response

under the LOOP renders 1%. Expenditure switching from periphery to core is, therefore,

not sufficient. The reason for the dampened reaction of the terms of trade is that exchange

rate pass-through on international prices is now limited by the sticky price friction in the

import sector, visible in the low co-movement between z t and E t (Panel 8). Policymakers

generate a weaker devaluation of the nominal exchange rate under PTM (0.7% on impact)

than under LOOP (1.1% on impact), for they now have to trade off the costs of additional

import price dispersion against the benefits of deteriorated terms of trade due to higher

import prices P F t . Taxes have a comparable effect on prices as monetary policy (confer

equations 22 and 26 for the perspective of the core). Increasing the domestic VAT, τ v t ,

dampens the deflationary pressure on the core’s PPI, but incentivizes higher import prices

also. As long as exchange rate flexibility is given, taxes are used only to a limited extent

for stabilization purposes.

In the monetary union (solid lines), the response of the terms of trade under flexible

exchange rates can again be replicated entirely by fiscal policy. The VAT rates are used

to induce the same price setting behaviour as the flexible exchange rate would. Relative

VAT rates, i.e. the fiscal devaluation factor, are highly correlated with the counterfactual

exchange rate (Panel 9), in order to shift relative prices and to reduce deviations from

the law of one price. On impact, F D t even overshoots the response of E t by 7%. The

pass-through of these tax changes on prices and the terms of trade remains, however,

limited again.

Fiscal policy in the monetary union is successful in replicating the path of the terms

of trade under flexible exchange rates, but again the fiscal devaluation policy does not

keep track of the respective real exchange rate path. Since CPIs are implicitly stabilized

under PTM, q t barely moves in the monetary union (Panel 7), leading to almost perfectly

correlated reactions of consumption in the core and periphery because of international

risk sharing. Under flexible exchange rates instead, the real exchange rate follows the

depreciation of E t closely. Consumption in the core, hence, increases by more than in the

periphery in this case.

5.3.2 Business-Cycle Properties of the Ramsey Allocations

In this section, I show to what extent the findings and intuitions obtained under the

productivity shock generalize to the other shocks as well. To do so, I analyse second

moments of key variables, generated from simulated business cycle data.

Table 4 presents correlations between the counterfactual flexible exchange rate and

various tax measures in the monetary union for both types of price setting and different

types of shocks. Correlations are calculated with the fiscal devaluation factor, F D t , and

with the tax rates in levels, τt

v and τt v∗ .

21

Table 4: Correlations between Exchange Rates and Taxes

LOOP Benchmark No Mark-up Shocks Mark-up, Core Mark-up, Periphery

Corr(E t , F D t ) 0.81 0.89 0.52 0.52

Corr(E t , τt v ) 0.03 0.81 0.43 -0.49

Corr(E t , τt v∗ ) -0.41 -0.91 0.40 -0.50

PTM

Corr(E t , F D t ) 0.59 0.89 0.86 0.65

Corr(E t , τt v ) 0.11 0.88 0.90 -0.73

Corr(E t , τt v∗ ) -0.31 -0.86 0.93 -0.69

Note: Correlations between tax measures obtained in monetary union scenario and counterfactual flexible

exchange rate. Columns indicate shock processes used for simulation: ’Benchmark’ includes productivity,

demand preference, government spending, & mark-up shocks in both countries. ’No Mark-up’ includes all

but mark-up shocks. Last two columns include mark-up shocks in the respective region only. Second-order

approximation to policy functions. T = 1000, J = 100.

The correlation between F D t and E t is generally found to be high. In the benchmark

scenario with all shocks, it reads 81% when the LOOP holds and 59% under PTM. It is

even higher at 89% for both pricing schemes when looking at the productivity, demand

preference, and government spending shocks, and it ranges between 52% and 86% for the

mark-up shocks. These results indicate that the policymaker actively uses fiscal policy to

replicate the path of the terms of trade in absence of a flexible exchange rate.

The results regarding tax rates in levels do not allow for general conclusions in the

benchmark scenario, both under the LOOP and PTM. 14 A more detailed inspection reveals

that the correlations—and, hence, the exact conduct of tax policy—depend decisively

on the type of shocks. With the productivity, demand preference, and government

spending shocks, the correlations with taxes under the LOOP (PTM) read 81% (88%)

and -91% (-86%), respectively. Whenever it were optimal to devalue the exchange rate

of a region in the monetary union, its VAT ought to be increased, while the tax of the

other (re-valuing) region should decrease. Fiscal devaluation policies as outlined in the

introduction can accordingly be observed, independent of the type of price setting.

Under mark-up shocks, the tax responses additionally depend on the origin of the

shock. The VAT rates of both regions are now positively correlated with the exchange

rate of that region which experiences a mark-up shock. 15 In response to a positive mark-up

shock, e.g., in the core, it is efficient to shift production to the periphery, which requires

an appreciated exchange rate (i.e. a decline of E t ) for the core. The optimal response

in a monetary union is to decrease taxes in both regions. Under the LOOP, this policy

attenuates the higher mark-up in the core and fosters the expenditure-switch by reducing

prices for periphery goods, while still taking heed of solvency of the fiscal authority. In

order to achieve a decline of F D t nevertheless, the VAT of the periphery should decline

by less than its core counterpart. Under PTM, it is clear from (23) that a rise in τt

v∗

aimed at replicating the decline in E t , would even exacerbate the mark-up distortion for

14 The asymmetry between the correlations of τt v and τt

v∗ is mainly driven by the different shock sizes

in core and periphery.

15 Note that E t denotes the exchange rate from the perspective of the core. Correlations are, therefore,

negative for a mark-up shock in the periphery.

22

the periphery’s import goods. τt

v∗ , therefore, also declines instead, which explains the

positive correlation of τt v∗ with E t .

Altogether, policymakers in the monetary union always adjust the ratio of tax rates

between the regions to induce relative price shifts in a similar fashion as the exchange

rate would. The behaviour of tax rates in levels and their correlation with the exchange

rate crucially depends on the type of shocks.

Table 5: Standard Deviations over the Business-Cycle

(A) Benchmark

LOOP q t z t E t F D t τt v τt

v∗

Monetary Union (MU) 0.89 1.69 1.19 1.46 1.73

Flexible Exchange Rate (FLEX) 0.49 1.68 1.84 0.26 1.52 1.53

PTM

Monetary Union 0.11 1.29 1.67 1.43 1.95

Flexible Exchange Rate 0.69 1.27 0.81 1.33 1.43 1.87

(B) Productivity, Preference, Gov. Spending Shocks

LOOP

Monetary Union 0.75 1.44 1.00 0.32 0.46

Flexible Exchange Rate 0.46 1.42 1.58 0.17 0.11 0.09

PTM

Monetary Union 0.10 1.21 0.56 0.26 0.17

Flexible Exchange Rate 0.63 1.19 0.77 0.15 0.09 0.13

(C) Mark-up Shocks

LOOP

Monetary Union 0.47 0.87 0.64 1.43 1.67

Flexible Exchange Rate 0.14 0.88 0.89 0.19 1.52 1.53

PTM

Monetary Union 0.03 0.39 1.57 1.41 1.94

Flexible Exchange Rate 0.28 0.39 0.39 1.33 1.42 1.86

Note: Standard deviations are measured in percentage points. Exchange rate regime either monetary

union (MU) or flexible (FLEX). Panel (A): productivity, demand preference, government spending, &

mark-up shocks in both countries. Panel (B): all but mark-up shocks. Panel (C): mark-up shocks only.

Second-order approximation to policy functions. T = 1000, J = 100.

Table 5 compares standard deviations of international relative prices and of taxes in

the monetary union and the flexible exchange rate regime, for both types of price setting

and different shock compositions. The following observations stand out.

In all scenarios, standard deviations of the terms of trade, z t , in the monetary union

are found to be close to their counterpart under flexible exchange rates, e.g. 1.69% versus

1.68% in the benchmark with LOOP. The volatility of real exchange rates, instead, differs

markedly between MU and FLEX. This indicates a generalization of the finding, obtained

from the productivity shock, that optimal fiscal devaluation policies focus on replicating

the time path of the terms of trade, but not of the real exchange rate.

23

Confirming Engel’s (2011) result, nominal exchange rate volatility is in all panels found

to be lower under PTM than under the LOOP, at least by a factor of two.

Also in line with the results obtained from the analysis of the productivity shock,

volatilities of the fiscal devaluation factor are smaller under flexible exchange rates than

in the monetary union in all scenarios. In the benchmark (Panel A), the volatility increases

from 0.26% to 1.19% when the LOOP holds and from 1.33% to 1.67% under PTM. The

volatility of the tax rates itself is found to be of similar size in the MU as well as the

FLEX scenario in Panel (A). The decomposition into the different shock types in Panel

(B) and (C) reveals that this is primarily driven by the mark-up shocks, for the latter

require an active fiscal policy response even under flexible exchange rates. In case of

the productivity, demand preference, and government spending shocks, the intuition,

obtained from the impulse responses, is restored that taxes are used only mildly under

flexible exchange rates, but intensely in the monetary union.

The volatility of tax rates is of the same order of magnitude as the volatility of E t . In

the benchmark of panel (A), this implies that taxes on average do not have to fluctuate

more than about 2 percentage points for an optimal policy response to the business cycle—

thereby rendering fiscal devaluations as a practically implementable policy option. 16

6 Conclusion

This paper analyses to what extent fiscal policy can compensate for the absent nominal

exchange rate in a monetary union in terms of business cycle stabilization. Various

Ramsey-optimal policy scenarios are studied in a New Keynesian 2-region model, calibrated

to the euro area, that differ regarding the exchange rate regime and the availability

of fiscal policy for stabilization purposes. Optimal use of only one tax instrument per

country enables policymakers to reduce the welfare costs of giving up flexible exchange

rates in a monetary union by up to 86% when the law of one price holds for traded goods,

and up to 69% when different prices can be set for the regions. Fiscal devaluations arises

as an outcome of optimal fiscal policy. Whenever a nominal exchange rate devaluation

were optimal for a region, a relative increase of the region’s VAT is the optimal fiscal

policy in the monetary union. In particular in case of mark-up shocks, policymakers face

a trade-off between replicating the effects of the nominal exchange rate and stabilizing

firms’ costs, however. Optimal fiscal policy in the monetary union is successful in the

reproduction of the flexible exchange rate path of the terms of trade, but not of the real

exchange rate.

The analysis of optimal policy studies the relevant benchmark of full cooperation between

the central bank(s) and the fiscal authorities at the region level. The strategic

interactions in form of a dynamic Nash game between the different entities are not considered

so far. This constitutes a probably fruitful exercise. Fiscal policy, as considered

in the model, requires tax changes at a business cycle frequency, whose implementation

16 Naturally, the standard deviations of both exchange rates and taxes increase with the size of the

underlying shocks. The seemingly small volatility of E t found in the simulations, nevertheless, does not

need to be entirely unrealistic. The model provides an optimal policy response that reacts on changes in

fundamentals only, compared to actual exchange rate data, which notoriously entails a sizeable amount

of unexplainable volatility. Regarding this point, see also the vast literature on the ”exchange rate

disconnect” puzzle following Obstfeld and Rogoff (2001).

24

surely poses political economy issues. However, first steps in direction of a unified VAT

framework for all member states of the European Union are already taken that will facilitate

a higher degree of coordination in fiscal policy in future. 17

The paper focuses on VAT-based fiscal devaluation policies. Further research could

also study the optimality of more general fiscal devaluation policies in the sense of tax

swaps from direct to indirect taxation (e.g. an increase in the VAT, paired with a reduction

of payroll taxes of employers), which can be revenue neutral to public budgets. An analysis

of such policies is, however, impeded in the present class of models due to an indeterminacy

between consumption and income taxes. The inclusion of another, untaxed, production

factor could possibly remedy this issue.

Other interesting augmentations of the model include the introduction of non-tradable

goods and downward nominal wage rigidity as an additional friction. Schmitt-Grohé and

Uribe (2016) show that the combination of these two components can lead to welfare costs

of fixed exchange rates that are more in line with conventional wisdom than those usually

obtained in representative agents models.

17 See in particular European Council Directive 2006/112/EC, which lays down a common system of

value added tax regulation for the EU. It covers aspects such as the tax base, the allowed number

of reduced tax rates besides the standard rate, and also defines which types of goods are eligible for

exemptions. It further regulates which country’s rate applies to imported goods, and even directs upper

and lower bounds for tax rates.

25

Appendix

A Derivations for Section 2

A.1 Optimal Firm Price Setting

In order to derive the conditions for optimal price setting, one first needs to derive an

aggregate demand equation Y t (k) for firm k. Consider (17), which can be rewritten as

Y t (k) = nC Ht (k) + (1 − n)CHt(k) ∗ + G t (k)

= 1 ( ) −ρ ( )

PHt (k)

(1 − n) P

∗ −ρ

(nC Ht + G t ) + Ht (k)

C ∗

n P Ht n

Ht. (44)

In the first line, I integrated over households using the fact that agents within a country

behave identically. In the second line, I applied consumption demand functions (8) of

both households and the domestic government.

Law of One Price: Using the law of one price (20) and the fact that the law also

holds for price indices under the given structure, (44) reduces to

Y t (k) = 1 n

P ∗ Ht

(

PHt (k)

P Ht

) −ρ

Y t , (45)

where Y t = nC Ht + (1 − n)C ∗ Ht + G t. By means of the law of one price again and (45),

firm profits (18) change to

Π t (k) = (1 − τ v t ) P Ht (k) 1 n

(

PHt (k)

P Ht

) −ρ

Y t − W t N t (k). (46)

The optimal price P Ht (k) is then determined by maximizing the expected present

discounted value of profits subject to the production technology (16) and demand (45):

max L LOOP

P Ht (k),N s(k)

∞

{[

∑

= E t θ s−t Q t,s P Hs (1 − τs v ) 1 ( ) 1−ρ

]

P Ht (k)

Y s − w s N s (k)

n P

s=t

Hs

[

+mc Hs (k) A s N s (k) α − 1 ( ) −ρ

]}

P Ht (k)

Y s ,

n P Hs

where w t = W t /P Ht is the producer real wage. The associated first-order conditions are:

∂L LOOP

∂P Ht (k)

∂L LOOP

∂N s (k)

= E t

∞

∑

s=t

( ) −1−ρ {

P

θ s−t Ht (k)

Q t,s Y s (1 − τs v ) (1 − ρ) P }

Ht (k)

+ mc Hs (k)ρ = 0,

P Hs P Hs

= E t θ s−t Q t,s P Hs

[

−ws + mc Hs (k)αA s N s (k) α−1] = 0.

26

Combining the two conditions and rearranging the result yields the optimal pricing condition

under LOOP (21).

Pricing-to-Market: The price setting problem of the firm under PTM implies maximizing

profits (18) subject to (16) and (44):

{

θ s−t Q t,s

max L P T M

P Ht (k),P ∗ Ht(k),N s(k)

+ (1 − τs

v∗ ) E s P ∗ Ht (k) 1 n

[

+MC Hs (k)

∑ ∞

= E t (1 − τs v ) P Ht (k) 1 n

s=t

( )

P ∗ −ρ

Ht (k)

(1 − n) CHs ∗ − W s N s (k)

A s N s (k) α − 1 n

P ∗ Hs

The associated first-order conditions are:

( P Ht (k)

P Hs

) −ρ

[nC Hs + G s ]

( ) −ρ

P Ht (k) (k)

(1 − n)

[nC Hs + G s ] −

P Hs n

(

)

P ∗ −ρ

Ht (k)

C

P

Hs]}

∗ .

Hs

∗

∂L P T M

∂P Ht (k)

∂L P T M

∂P ∗ Ht (k)

∂L P T M

∂N s (k)

= E t

∞

∑

·

s=t

θ s−t Q t,s

( P Ht (k)

P Hs

) −1−ρ

[nC Hs + G s ]

{

(1 − τ v s ) P Ht (k)

P Hs

− ρ

∞

(

∑

= E t θ s−t Q t,s

·

{

s=t

(1 − τ v∗

s ) E s

(

P ∗ Ht (k)

P ∗ Hs

P ∗ Ht (k)

P ∗ Hs

}

MC Hs (k)

= 0,

P Hs

ρ − 1

) −1−ρ

CHs

∗

)

−

ρ

ρ − 1

}

MC Hs (k)

= 0,

PHs

∗

= E t θ s−t Q t,s

[

−Ws + MC Hs (k)A s αN s (k) α−1] = 0.

Combining the conditions and rearranging the results yields the optimal pricing conditions

under PTM, (22) and (23).

A.2 Evolution of Price Indices

Price index (5) can be written as

⇔

⇔

∫ nθ

nP 1−ρ

Ht

= P 1−ρ

0

nP 1−ρ

Ht

= nθP 1−ρ

Ht−1

1 = θπ ρ−1

Ht

+ (1 − θ)

Ht−1 (k) dk + ∫ n

nθ

1−ρ

+ n (1 − θ) P Ht

( ) 1−ρ

P Ht

P Ht

P 1−ρ

Ht (k) dk

27

⇔

˜p Ht = P Ht

P Ht

=

( 1 − θπ

ρ−1 ) 1

1−ρ

Ht

,

1 − θ

which is (30) in the main text. Similar expressions hold for PF ∗ t and, under PTM, also for

P F t and PHt ∗ .

A.3 Recursive Philips Curves

The recursive form of a Philips curve is derived here by way of example for the PPI of

home goods under the LOOP. The optimal pricing condition (21) can be written as

ρ

ρ − 1 µ sE t

with

∞

∑

s=t

( ) −1−ρ

P

θ s−t Ht

∑ ∞ ( ) −ρ

P

Q t,s Y s mc Hs = E t θ s−t Ht

Q t,s Y s (1 − τs v )

P Ht P Ht

s=t

ρ

ρ − 1 µ tX1 Ht = X2 Ht

X1 Ht = E t

∞

∑

=

s=t

θ s−t Q t,s Y s

( P Ht

P Hs

) −1−ρ

mc Hs

( ) −1−ρ

P Ht

Y t mc Ht + E t

P Ht

∞

∑

s=t+1

θ s−t Q t,s

( P Ht

P Hs

) −1−ρ

Y s mc Hs

=

=

( P Ht

P Ht

) −1−ρ

Y t mc Ht

∞

∑

( ) −1−ρ

P

θ s−t−1 Ht+1

Q t+1,s Y s mc Hs

P Hs

( ) −1−ρ

P Ht

+θE t Q t,t+1 E t+1

P Ht+1 s=t+1

( ) −1−ρ ( ) −1−ρ

P Ht

P Ht

Y t mc Ht + θE t Q t,t+1 X1 Ht+1

P Ht P Ht+1

and

X2 Ht = E t

∞

∑

s=t

θ s−t Q t,s Y s

( P Ht

P Hs

) −ρ

(1 − τ v s )

=

( P Ht

P Ht

) −ρ

Y t (1 − τ v t ) + θE t Q t,t+1

( P Ht

P Ht+1

) −ρ

X2 Ht+1 .

Inserting the definition of the stochastic discount factor (12) and the law of motion of the

PPI (30) yields equation (32) and (33) in the text.

Corresponding expressions for PPIs and import price indices under PTM can be derived

accordingly from (22), (23), (25), and (26).

28

A.4 Aggregate Resource Constraint

To derive the aggregate resource constraints, combine production (16) with demand (44),

and integrate over firms:

(

PHt (k)

( P

∗

Ht (k)

) −ρ

(1 − n) C ∗ Ht

A t N α t (k) = 1 n

∫ n

A t Nt α (k) dk = 1 n

0

P Ht

∫ n

0

∫ n

) −ρ

(nC Ht + G t ) + 1 n

( ) −ρ PHt (k)

dk (nC Ht + G t )

P Ht

( ) P

∗ −ρ

Ht (k)

dk (1 − n) CHt.

∗

P ∗ Ht

+ 1 n

0

P ∗ Ht

As (P Ht (k)/P Ht ) = (PHt ∗ (k)/P Ht ∗ ) if the law of one price holds, this reduces to (34) under

LOOP, but to (35) under PTM.

The law of motion for price dispersion emerges from (36) as follows:

∫ n

∆ Ht = 1 n

[

= 1 n

0

= (1 − θ)

( ) −ρ PHt (k)

dk

P Ht

n (1 − θ)

∞∑

j=0

( P Ht

P Ht

) −ρ

+ n (1 − θ) θ

θ j ( P Ht−j

P Ht

) −ρ

( ) −ρ

P Ht

= (1 − θ) + (1 − θ)

P Ht

∞∑

j=1

( P Ht−1

P Ht

) −ρ

+ . . .

( ) −ρ

P

θ j Ht−j

P Ht

∞∑

( ) −ρ ( ) −ρ P Ht PHt−1

= (1 − θ) + θ

(1 − θ)

P Ht P Ht

= (1 − θ) ˜p −ρ

Ht + θπρ Ht ∆ Ht−1.

j=1

]

θ j−1 ( P Ht−j

P Ht−1

) −ρ

B

Competitive Equilibrium

This appendix lists equilibrium conditions for the cases of LOOP and PTM. All prices

are expressed in relative terms.

B.1 Law of One Price

Let p Ht = P Ht /P t and p ∗ F t = PF ∗ t /P t ∗ be the PPI-CPI ratios, and w t = W t /P Ht and

wt ∗ = Wt ∗ /PF ∗ t the producer real wages. A competitive equilibrium under the LOOP and

autonomous monetary policy in both countries is a set of sequences {C t , C Ht , C F t , Ct ∗ ,

CHt ∗ , C∗ F t , Y t, Yt ∗ , N t , Nt ∗ , q t , p Ht , p ∗ F t , w t, wt ∗ , π t , πt ∗ , π Ht , πF ∗ t , ∆ Ht, ∆ ∗ F t , ˜p Ht, ˜p ∗ F t , X1 Ht,

X2 Ht , X1 ∗ F t , X2∗ F t }∞ t=0, satisfying

29

• Demand for Home and Foreign goods:

C Ht = γ H p −ξ

Ht C t ,

C ∗ Ht = γ ∗ H

C F t = γ F

( (1 − τ

v∗

t )

(1 − τ v t ) p∗ F tq t

) −ξ

C t

( ) (1 − τ

v −ξ

t ) p Ht

C

(1 − τt v∗

t ∗ , CF ∗ t = γF ∗ p ∗−ξ

F t

) q C∗ t

t

• Euler equations and international risk sharing:

[ (

1

ζt+1

c Ct+1

= βE t

R t ζt

c (

1

C

∗

t+1

• Labour supply:

R ∗ t

= βE t

[

ζ c∗

t+1

q t = κ ζc∗ t

ζt

c

ζt

c∗

C t

) −σ

1

π t+1

]

C ∗ t

( C

∗

t

C t

) −σ

) −σ

1

π ∗ t+1

]

• Aggregate demand:

N η t Ct σ = ζt c w t p Ht

N ∗η

t Ct ∗σ = ζt

c∗ wt ∗ p ∗ F t

• Resource constraints:

Y t = nC Ht + (1 − n)CHt ∗ + G t

Yt ∗ = nC F t + (1 − n)CF ∗ t + G ∗ t

A t nNt α = ∆ Ht Y t

A ∗ t (1 − n)Nt ∗α = ∆ ∗ F tYt

∗

• Phillips curves:

ρ

ρ − 1 µ tX1 Ht = X2 Ht ,

X1 Ht = ˜p −1−ρ w t ζt+1

c

Ht

Y t

A t αNt

α−1 + θβE t

ζt

c

X2 Ht = ˜p −ρ

Ht Y t (1 − τ v t ) + θβE t

ζ c t+1

ζ c t

(

Ct+1

(

Ct+1

C t

(

˜pHt

) −σ

π 1+ρ ) −1−ρ

Ht+1

X1 Ht+1

C t π t+1 ˜p Ht+1

) −σ

π ρ ( ) −ρ

Ht+1 ˜pHt

X2 Ht+1

˜p Ht+1

π t+1

ρ ∗

ρ ∗ − 1 µ∗ t X1 ∗ F t = X2 ∗ F t

30

X1 ∗ F t = ˜p ∗−1−ρ∗

F t

X2 ∗ F t = ˜p ∗−ρ∗

F t

Y ∗

t

Y ∗

t

w ∗ t

A ∗ t αN ∗α−1

t

(1 − τ v∗

t

• Consumer price indices:

• Evolution of PPIs:

+ θ ∗ βE t

ζ c∗

t+1

t+1

ζt

c∗

) + θ ∗ βE t

ζ c∗

ζt

c∗

( C

∗

t+1

( C

∗

t+1

C ∗ t

C ∗ t

) −σ

π ∗1+ρ∗

F t+1

) −σ

π ∗ρ∗

F t+1

π ∗ t+1

π ∗ t+1

( ˜p

∗

F t

( ) (1 − τ

1 = γ H p 1−ξ

v∗ 1−ξ

t )

Ht

+ γ F

(1 − τt v ) p∗ F tq t

( ) (1 − τ

1 = γH

∗ v 1−ξ

t ) p Ht

+ γ

(1 − τt v∗

F ∗ p ∗1−ξ

F t

) q t

( ˜p

∗

F t

˜p ∗ F t+1

˜p ∗ F t+1

) −ρ ∗

) −1−ρ ∗

X2 ∗ F t+1

X1 ∗ F t+1

˜p Ht =

˜p ∗ F t =

( 1 − θπ

ρ−1

Ht

1 − θ

) 1

1−ρ

(

) 1

1 − θ ∗ (πF ∗ −1 1−ρ ∗

t )ρ∗

1 − θ ∗

• Evolution of price dispersion:

• Evolution of relative prices:

∆ Ht = (1 − θ) ˜p −ρ

Ht + θπρ Ht ∆ Ht−1

∆ ∗ F t = (1 − θ ∗ ) ˜p ∗−ρ∗

F t

+ θ ∗ (πF ∗ t) ρ∗ ∆ ∗ F t−1

p Ht

p Ht−1

= π Ht

π t

,

p ∗ F t

p ∗ F t−1

= π∗ F t

,

πt

∗

given the transversality conditions, sequences of the policy instruments {R t , Rt ∗ , τt v , τt v∗ } ∞ t=0

and of the shocks {A t , A ∗ t , µ t , µ ∗ t , ζt c , ζt

c∗ , G t , G ∗ t } ∞ t=0.

If the two countries form a monetary union, the equation defining Rt

∗ drops out.

Instead, an expression that restricts the evolution of the real exchange rate needs to be

added:

B.2 Pricing-to-Market

q t

q t−1

= π∗ t

π t

.

Let p F t = P F t /P t and p ∗ Ht = P Ht ∗ /P t

∗ be the import-price-to-CPI ratios. A competitive

equilibrium under PTM and autonomous monetary policy in both countries is a set of

sequences {C t , C Ht , C F t , Ct ∗ , CHt ∗ , C∗ F t , N t, Nt ∗ , q t , E t , p Ht , p F t , p ∗ Ht , p∗ F t , w t, wt ∗ , π t , πt ∗ ,

31

π Ht , π F t , π ∗ Ht , π∗ F t , ∆ Ht, ∆ HF , ∆ ∗ Ht , ∆∗ F t , X1 Ht, X2 Ht , X1 F t , X2 F t , X1 ∗ Ht , X2∗ Ht , X1∗ F t ,

X2 ∗ F t }∞ t=0, satisfying

• Demand for Home and Foreign goods:

C Ht = γ H p −ξ

Ht C t , C F t = γ F p −ξ

F t C t

CHt ∗ = γHp ∗ ∗−ξ

Ht C∗ t , CF ∗ t = γF ∗ p ∗−ξ

F t C∗ t

• Euler equations and international risk sharing:

[ (

1

ζt+1

c Ct+1

= βE t

R t ζt

c (

1

C

∗

t+1

• Labour supply:

R ∗ t

= βE t

[

ζ c∗

t+1

q t = κ ζc∗ t

ζt

c

ζt

c∗

C t

) −σ

1

π t+1

]

C ∗ t

( C

∗

t

C t

) −σ

) −σ

1

π ∗ t+1

]

• Resource constraints:

N η t Ct σ = ζt c w t p Ht

N ∗η

t Ct ∗σ = ζt

c∗ wt ∗ p ∗ F t

A t nNt α = ∆ Ht (nC Ht + G t ) + ∆ ∗ Ht (1 − n) CHt

∗

A ∗ t (1 − n) Nt ∗α = ∆ ∗ F t ((1 − n) CF ∗ t + G ∗ t ) + ∆ F t nC F t

• Philips curves:

X1 Ht =

X2 Ht =

( 1 − θπ

ρ−1

Ht

1 − θ

+θβE t

ζ c t+1

ζ c t

( 1 − θπ

ρ−1

Ht

1 − θ

+θβE t

ζ c t+1

ζ c t

ρ

ρ − 1 X1 Ht = X2 Ht

) ρ+1

ρ−1

(nC Ht + G t )

(

Ct+1

w t

A t αN α−1

t

1 − θπ ρ−1

Ht

) (

−σ

π 1+ρ

Ht+1

C t π t+1

) ρ

ρ−1

(nC Ht + G t ) (1 − τt v )

(

Ct+1

C t

) (

−σ

π ρ Ht+1

π t+1

ρ

ρ − 1 X1∗ Ht = X2 ∗ Ht

1 − θπ ρ−1

Ht+1

1 − θπ ρ−1

Ht

1 − θπ ρ−1

Ht+1

) ρ+1

ρ−1

X1 Ht+1

) ρ

ρ−1

X2 Ht+1

32

X1 ∗ Ht =

X2 ∗ Ht =

( 1 − θπ

∗ρ−1

Ht

1 − θ

+θβE t

ζ c t+1

ζ c t

( 1 − θπ

∗ρ−1

Ht

1 − θ

+θβE t

ζ c t+1

ζ c t

) ρ+1

ρ−1

(

Ct+1

C t

C ∗ HtE t

p Ht

q t p ∗ Ht

(

π t+1

) −σ

π ∗1+ρ

Ht+1

) ρ

ρ−1

C ∗ HtE t (1 − τ v∗

t )

(

Ct+1

C t

) (

−σ

π ∗ρ

Ht+1

π t+1

w t

A t αN α−1

t

1 − θπ ∗ρ−1

Ht

1 − θπ ∗ρ−1

Ht+1

1 − θπ ∗ρ−1

Ht

1 − θπ ∗ρ−1

Ht+1

) ρ+1

ρ−1

X1 ∗ Ht+1

) ρ

ρ−1

X2 ∗ Ht+1

ρ ∗

ρ ∗ − 1 X1∗ F t = X2 ∗ F t

X1 ∗ F t =

X2 ∗ F t =

(

) ρ ∗ +1

1 − θ ∗ π ∗ρ∗ −1 ρ ∗ −1

F t

((1 − n) C ∗

1 − θ ∗ F t + G ∗ t )

+θ ∗ ζt+1

c∗

βE t

ζt

c∗

(

( C

∗

t+1

C ∗ t

) −σ

π ∗1+ρ∗

F t+1

π ∗ t+1

(

w ∗ t

A ∗ t αN ∗α−1

t

) ρ ∗ +1

1 − θ ∗ π ∗ρ∗ −1 ρ ∗ −1

F t

1 − θ ∗ π ∗ρ∗ −1

X1 ∗ F t+1

F t+1

) ρ ∗

1 − θ ∗ π ∗ρ∗ −1 ρ ∗ −1

F t

((1 − n) C ∗

1 − θ ∗ F t + G ∗ t ) (1 − τt v∗ )

+θ ∗ βE t

ζ c∗

t+1

ζ c∗

t

( C

∗

t+1

C ∗ t

) (

−σ

π ∗ρ∗

F t+1

πt+1

∗

1 − θ ∗ π ∗ρ∗ −1

F t

1 − θ ∗ π ∗ρ∗ −1

F t+1

) ρ ∗

ρ ∗ −1

X2 ∗ F t+1

ρ ∗

ρ ∗ − 1 X1 F t = X2 F t

X1 F t =

X2 F t =

(

) ρ ∗ +1

1 − θ ∗ π ρ∗ −1 ρ ∗ −1

F t

1 − θ ∗

+θ ∗ ζt+1

c∗

βE t

ζt

c∗

(

( C

∗

t+1

C ∗ t

) ρ ∗

1 − θ ∗ π ρ∗ −1 ρ ∗ −1

F t

1 − θ ∗

+θ ∗ βE t

ζ c∗

t+1

ζ c∗

t

( C

∗

t+1

C ∗ t

C F t

E t

q t p ∗ F t

p F t

) −σ

π 1+ρ∗

F t+1

π ∗ t+1

C F t

E t

(1 − τ v t )

) (

−σ

π ρ∗

F t+1

πt+1

∗

w ∗ t

A ∗ t αNt

∗α−1

(

1 − θ ∗ π ρ∗ −1

F t

1 − θ ∗ π ρ∗ −1

F t+1

1 − θ ∗ π ρ∗ −1

F t

1 − θ ∗ π ρ∗ −1

F t+1

) ρ ∗ +1

ρ ∗ −1

X1 F t+1

) ρ ∗

ρ ∗ −1

X2 F t+1

33

• Consumer price indices:

• Evolution of price dispersion:

∆ Ht = (1 − θ)

∆ ∗ Ht = (1 − θ)

1 = γ H p 1−ξ

Ht

1 = γ ∗ Hp ∗1−ξ

Ht

( 1 − θπ

ρ−1

Ht

1 − θ

( 1 − θπ

∗ρ−1

Ht

1 − θ

+ γ F p 1−ξ

F t

+ γ ∗ F p ∗1−ξ

F t

) ρ

ρ−1

+ θπ ρ Ht ∆ Ht−1

) ρ

ρ−1

+ θπ ∗ρ

Ht ∆∗ Ht−1

∆ ∗ F t =

(

) ρ ∗

(1 − θ ∗ 1 − θ ∗ (πF ∗ −1 ρ ∗ −1

t

)

+ θ ∗ (π ∗

1 − θ ∗ F t) ρ∗ ∆ ∗ F t−1

∆ F t =

(

) ρ ∗

(1 − θ ∗ 1 − θ ∗ (π F t ) ρ∗ −1 ρ ∗ −1

)

+ θ ∗ (π

1 − θ ∗ F t ) ρ∗ ∆ F t−1

• Evolution of relative prices:

p Ht

p Ht−1

= π Ht

π t

,

p F t

p F t−1

= π F t

π t

,

p ∗ Ht

p ∗ Ht−1

= π∗ Ht

,

πt

∗

p ∗ F t

p ∗ F t−1

= π∗ F t

π ∗ t

• Evolution of the real exchange rate

q t

q t−1

=

E t

E t−1

π ∗ t

π t

,

given the transversality conditions, sequences of the policy instruments {R t , Rt ∗ , τt v , τt v∗ } ∞ t=0

and of the shocks {A t , A ∗ t , µ t , µ ∗ t , ζt c , ζt

c∗ , G t , G ∗ t } ∞ t=0, and an initial E −1 = 1. Unlike with

the LOOP, the nominal exchange rate is itself a relevant argument to the equilibrium.

If the two countries form a monetary union, the equation defining Rt ∗ drops out, and

the nominal exchange rate is fixed, i.e. E t = 1 ∀t.

C

The Ramsey Problem

C.1 Derivation of the Intertemporal Fiscal Budget Constraint

Integrating (29) over h and k, and dividing by P t yields

b t = E t Q t,t+1 π t+1 b t+1 + s t , (47)

where b t = B t /P t is real debt and the primary surplus reads

34

s t = 1 P t

[τ v t n (P Ht C Ht + P F t C F t ) − (1 − τ v t ) P Ht G t ] .

Repeatedly iterating on (47) using successive future terms of it, beginning in period

t = 0, yields the present-value fiscal budget constraint

b 0 = E 0

T∑

Q 0,t π 0,t s t + E 0 Q 0,T +1 π 0,T +1 b T +1 ,

t=0

where π 0,T +1 = P T +1 /P 0 is the product of inflation rates between t = 0 and t = T + 1.

Imposing the transversality condition

lim E 0Q 0,T +1 π 0,T +1 b T +1 = 0

T →∞

and using the definition of Q 0,t , one ends up with

∑ ∞

ζ0C c 0 −σ b 0 = E 0 β t ζt c Ct −σ s t .

C.2 The Lagrangian of the Ramsey Problem

The scenario under study assumes the law of one price, the availability of fiscal policy as

an instrument, and that the countries form a monetary union. The objective of the policy

planner is, hence, to find sequences { }

Rt

MU , τt v , τt

v∗ ∞ . t=0

V = E 0

∞

∑

t=0

+Λ H ζ c t C −σ

t

+Λ F ζt

c∗ Ct

∗−σ

+λ 1 t

+λ 3 t

(

β

{n

t ζt

c Ct

1−σ

1 − σ − N 1+η ) (

t

+ (1 − n) ζ c∗ Ct

∗1−σ

t

1 + η

1 − σ − N ∗1+η )

t

1 + η

[

)

]

τt v v∗

(1 − τt )

n

(p Ht C Ht +

(1 − τt v ) p∗ F tq t C F t − (1 − τt v ) p Ht G t

[ [

τt v∗ (1 − n) p ∗ F tCF ∗ t + (1 − τ ]

t v ) p Ht

C

(1 − τt v∗ Ht

∗ ) q

[

t

[

] ( ) ]

(1 − τ

γ H p −ξ

Ht C t − C Ht + λ 2 v∗ −ξ

t )

t γ F

(1 − τt v ) p∗ F tq t C t − C F t

[ ( ) ]

(1 − τ

γH

∗ v −ξ

t ) p

[

]

Ht

C ∗

(1 − τt v∗

t − CHt

∗ + λ 4 t γF ∗ p ∗−ξ

F t

) q C∗ t − CF ∗ t

t

t=0

+λ 5 t [N η t Ct σ − ζt c w t p Ht ] + λ 6 t [N ∗η

t Ct

∗σ − ζt c∗ wt ∗ p ∗ F t]

+λ 7 t [A t nNt α − ∆ Ht (nC Ht + (1 − n)CHt ∗ + G t )]

+λ 8 t [A ∗ t (1 − n)Nt ∗α − ∆ ∗ F t (nC F t + (1 − n)CF ∗ t + G ∗ t )]

[ ρ

+λ 9 t

+λ 10

t

]

ρ − 1 µ tX1 Ht − X2 Ht

[

˜p −1−ρ

Ht

(nC Ht + (1 − n)CHt ∗ + G t )

w t

αA t N α−1

t

]

− (1 − τt

v∗ ) p ∗ F tG ∗ t

35

(

+θβ ζc t+1 Ct+1

ζt

c

+λ 11

t

+θβ ζc t+1

+λ 12

t

+λ 13

t

(

˜pHt

˜p Ht+1

) −1−ρ

X1 Ht+1 − X1 Ht

]

) −σ

π 1+ρ

Ht+1

C t π t+1

−ρ

[˜p

Ht (nC Ht + (1 − n)CHt ∗ + G t ) (1 − τt v )

( ) −σ Ct+1 π ρ ( ) ]

−ρ

Ht+1 ˜pHt

X2

ζt

c Ht+1 − X2 Ht

C t π t+1 ˜p Ht+1

[ ]

ρ

∗

ρ ∗ − 1 µ∗ t X1 ∗ F t − X2 ∗ F t

[

˜p ∗−1−ρ∗

F t

(nC F t + (1 − n)CF ∗ t + G ∗ t )

+θ ∗ β ζc∗ t+1

+λ 14

t

ζt

c∗

[

˜p ∗−ρ∗

F t

+θ ∗ β ζc∗ t+1

+λ 15

t

+λ 17

t

+λ 19

t

ζt

c∗

[

( C

∗

t+1

C ∗ t

( C

∗

t+1

γ H p 1−ξ

Ht

) −σ

π ∗1+ρ∗

F t+1

π ∗ t+1

( ˜p

∗

F t

˜p ∗ F t+1

) −1−ρ ∗

w ∗ t

αA ∗ t N ∗α−1

(nC F t + (1 − n)CF ∗ t + G ∗ t ) (1 − τ v∗

) −σ ( )

π ∗ρ∗

F t+1 ˜p

∗ −ρ ∗

F t

Ct

∗ πt+1

∗

[ (1 − θπ

ρ−1

Ht

1 − θ

[

κ ζc∗ t

ζt

c

[

+λ 20

t (1 − θ) ˜p

−ρ

+λ 22

t

˜p ∗ F t+1

+ γ F

( (1 − τ

v∗

t )

(1 − τ v t ) p∗ F tq t

) 1−ξ

− 1

) 1

1−ρ

− ˜p Ht

]

( C

∗

t

C t

) −σ

− q t

]

[

pHt

− π ]

Ht

+ λ 23

t

p Ht−1 π t

p ∗ F t−1

+ λ 18

t

⎡(

⎣

t

X1 ∗ F t+1 − X1 ∗ F t

t )

X2 ∗ F t+1 − X2 ∗ F t

]

+ λ 16

t

[

γ ∗ H

]

) 1

1 − θ ∗ π ∗ρ∗ −1 1−ρ ∗

F t

1 − θ ∗

]

( (1 − τ

v

t )

(1 − τt v∗ )

⎤

Ht + θπρ Ht ∆ ] [

Ht−1 − ∆ Ht + λ

21

t (1 − θ ∗ ) ˜p ∗−ρ∗

F t

[ ] [ ]}

p

∗

F t

− π∗ F t

+ λ 24 qt

πt

∗ t − π∗ t

q t−1 π t

−Λ H ζ c 0C −σ

0 b 0 − Λ F ζ c∗

0 C ∗−σ

0 b ∗ 0.

C.3 First-order Conditions for t ≥ 1

− ˜p ∗ ⎦

F t

p Ht

q t

) 1−ξ

+ γ ∗ F p ∗1−ξ

F t

− 1

]

+ θ ∗ π ∗ρ∗

F t ∆∗ F t−1 − ∆ ∗ F t

The solution to the optimal policy problem can be described by the first-order conditions

with respect to all Lagrange multipliers and with respect to all endogenous variables of

the model:

• W.r.t. C t :

0 = n H ζt c Ct

−σ

[

+ σ C t

− Λ H ζt c σCt

−σ−1 s t + λ 1 t γ H p −ξ

(

λ 10

t θβ ζc t+1 Ct+1

ζt

c

Ht+1

π t+1

C t

) −σ

π 1+ρ

t )

( ) (1 − τ

v∗ −ξ

Ht + λ2 t γ F

(1 − τt v ) p∗ F tq t + λ 5 t N η t σCt

σ−1

( ) −1−ρ ˜pHt

X1 Ht+1

˜p Ht+1

]

36

• W.r.t. C Ht :

( ) −σ

− λ 10

t−1θ ζc t Ct π 1+ρ

Ht

ζt−1

c C t−1 π t

[

+ σ (

λ 11

t θβ ζc t+1 Ct+1

C t

ζ c t

C t

) −σ

π ρ Ht+1

(

˜pHt−1

˜p Ht

) −1−ρ

X1 Ht

]

π t+1

(

˜pHt

˜p Ht+1

) −ρ

X2 Ht+1

( ) −σ

−λ 11

t−1θ ζc t Ct π ρ ( ) ]

−ρ

Ht ˜pHt−1

X2

ζt−1

c Ht + λ 19

C t−1 π t ˜p Ht

t κ σ ζ t

c∗

C t

ζ c t

( C

∗

t

C t

) −σ

0 = Λ H ζt c Ct −σ τt v p Ht n H − λ 1 t − λ 7 t ∆ Ht n H + λ 10

t

˜p −1−ρ

Ht

n H w t

αA t Nt

α−1

+ λ 11

t ˜p −ρ

Ht n H (1 − τt v )

• W.r.t. C F t :

0 = Λ H ζt c Ct

−σ τt

v

• W.r.t. C ∗ t :

0 = n F ζ c∗

t

+ σ C ∗ t

C ∗−σ

t

[

λ 13

(1 − τt v∗ )

(1 − τt v ) p∗ F tq t n H −λ 2 t −λ 8 t ∆ ∗ F tn H +λ 13

t

− Λ F ζ c∗

t

t+1

ζt

c∗

t θ ∗ β ζc∗

−λ 13

t−1θ ∗ ζc∗ t

ζt−1

c∗

+ σ C ∗ t

• W.r.t. C ∗ Ht :

0 = Λ F ζ c∗

t

• W.r.t. C ∗ F t :

0 = Λ F ζ c∗

t

[

λ 14

( C

∗

t

t θ ∗ β ζc∗

−λ 14

t−1θ ∗ ζc∗ t

ζt−1

c∗

Ct

∗−σ

τ v∗

t

Ct

∗−σ τ v∗

C ∗ t−1

t+1

ζt

c∗

( C

∗

t

C ∗ t−1

(1 − τt v )

(1 − τt v∗ )

σCt

∗−σ−1

( C

∗

t+1

C ∗ t

s ∗ t + λ 3 t γ ∗ H

) −σ

π ∗1+ρ∗

F t+1

) −σ

π ∗1+ρ∗

F t

( C

∗

t+1

C ∗ t

π ∗ t

) −σ

π ∗ρ∗

F t

π ∗ t

p Ht

π ∗ t+1

( ˜p

∗

F t−1

) −σ

π ∗ρ∗

F t+1

π ∗ t+1

˜p ∗ F t

( ˜p

∗

F t−1

˜p ∗ F t

( (1 − τ

v

t )

( ˜p

∗

F t

(1 − τ v∗

˜p ∗ F t+1

) −1−ρ ∗

( ˜p

∗

F t

˜p ∗ F t+1

) −ρ ∗

˜p ∗−1−ρ∗

F t

p Ht

t )

) −1−ρ ∗

) −ρ ∗

X2 ∗ F t

n F −λ 3 t −λ 7 t ∆ Ht n F +λ 10

t

q t

t p ∗ F tn F −λ 4 t −λ 8 t ∆ ∗ F tn F +λ 13

t

˜p ∗−1−ρ∗

F t

X1 ∗ F t

]

n H wt

∗

αA ∗ t Nt

∗α−1

+λ 14

t

) −ξ

+ λ 4 t γF ∗ p ∗−ξ

F t

q t

X1 ∗ F t+1

]

X2 ∗ F t+1

− λ 19

t κ σ C ∗ t

˜p −1−ρ

Ht

n F wt

∗

αA ∗ t Nt

∗α−1

ζ c∗

t

ζ c t

n F w t

αA t Nt

α−1

+λ 14

t

( C

∗

t

C t

) −σ

˜p ∗−ρ∗

F t

n H (1 − τt v∗ )

+ λ 6 t N ∗η

t σCt

∗σ−1

+λ 11

t ˜p −ρ

Ht n F (1 − τt v )

˜p ∗−ρ∗

F t

n F (1 − τt v∗ )

37

• W.r.t. p Ht :

0 = Λ H ζ c t C −σ

t

• W.r.t. p ∗ F t :

(τ v t n H C Ht − (1 − τ v t ) G t ) + Λ F ζ c∗

t

( (1 − τ

−λ 1 t γ H ξp −ξ−1

Ht

C t − λ 3 t γH

∗ v

t )

(1 − τ v∗

+λ 15

t γ H (1 − ξ) p −ξ

Ht + λ16 t γ ∗ H

0 = Λ H ζt c Ct

−σ τt

v

p Ht

t )

(1 − τt v∗ )

(1 − τt v ) q tn H C F t + Λ F ζt

c∗

−λ 2 t γ F

( (1 − τ

v∗

t )

(1 − τ v t ) p∗ F tq t

) −ξ

ξC t

p ∗ F t

+λ 15

• W.r.t. q t :

t )

( ) (1 − τ

v∗ 1−ξ

(1 − ξ)

t γ F

(1 − τt v ) p∗ F tq t

0 = Λ H ζt c Ct

−σ τt

v

• W.r.t. π t :

C ∗−σ

t

τ v∗

t

(1 − τt v )

(1 − τt v∗ )

) −ξ

ξCt

∗ − λ 5 t ζt c w t

q t p Ht

( ) (1 − τ

v 1−ξ

t ) p Ht (1 − ξ)

(1 − τt v∗ ) q t

Ct

∗−σ

− λ 4 t γ ∗ F ξp ∗−ξ−1

F t

p ∗ F t

(1 − τt v∗ )

(1 − τt v ) p∗ F tn H C F t − Λ F ζt

c∗

( ) (1 − τ

−λ 2 v∗ −ξ

t ) ξC t

t γ F

(1 − τt v ) p∗ F tq t + λ 3 t γH

∗ q t

+λ 15

−λ 19

t

( ) (1 − τ

v∗ 1−ξ

t ) (1 − ξ)

t γ F

(1 − τt v ) p∗ F tq t − λ 16

q t

+ λ24 t

− λ 24

q

t+1β q t+1

t−1 qt

2

(

0 = −λ 10

t−1θ ζc t Ct

ζt−1

c

) −σ

π 1+ρ

Ht

C t−1

π 2 t

+ λ22 t

p Ht

n F C ∗ Ht

q t

p Ht−1

− λ 22

(τt

v∗ n F CF ∗ t − (1 − τt v∗ ) G ∗ t )

Ct ∗ − λ 6 t ζt

c∗ wt

∗

+ λ 16

t γ ∗ F (1 − ξ) p ∗−ξ

(

˜pHt−1

˜p Ht

F t

+ λ23 t

p ∗ F t−1

p Ht

n

qt

2 F CHt

∗

Ct

∗−σ τt

v∗ (1 − τt v )

(1 − τt v∗ )

( ) (1 − τ

v −ξ

t ) p Ht ξCt

∗

(1 − τ v∗ q t

t γ ∗ H

t )

q t

t+1β p Ht+1

p 2 Ht

− λ 23

t+1β p∗ F t+1

p ∗2

F t

( ) (1 − τ

v 1−ξ

t ) p Ht (1 − ξ)

(1 − τt v∗ ) q t q t

) −1−ρ

X1 Ht

−λ 11

t−1θ ζc t

ζ c t−1

(

Ct

C t−1

) −σ

π ρ Ht

π 2 t

(

˜pHt−1

) −ρ

X2 Ht + λ 22

t

˜p Ht

π Ht

π 2 t

+ λ 24 πt

∗

t

πt

2

• W.r.t. π ∗ t :

0 = −λ 13

t−1θ ∗ ζc∗ t

ζt−1

c∗

−λ 14

t−1θ ∗ ζc∗ t

ζt−1

c∗

( C

∗

t

C ∗ t−1

( C

∗

t

C ∗ t−1

) −σ

π ∗1+ρ∗

F t

πt

∗2

) −σ

π ∗ρ∗

F t

π ∗2

t

( ˜p

∗

F t−1

( ˜p

∗

F t−1

˜p ∗ F t

˜p ∗ F t

) −ρ ∗

) −1−ρ ∗

X1 ∗ F t

X2 ∗ F t + λ 23 πF ∗ t

t

πt

∗2

− λ24 t

π t

38

• W.r.t. π Ht :

( ) −σ

0 = λ 10

t−1θ ζc t Ct (1 + ρ) π ρ Ht

ζt−1

c C t−1 π t

( ) −σ Ct ρπ ρ−1

Ht

C t−1

• W.r.t. π ∗ F t :

0 = λ 13

• W.r.t. ∆ Ht :

+λ 11

t−1θ ζc t

ζt−1

c

+λ 17

t

t−1θ ∗ ζc∗ t

ζt−1

c∗

+λ 14

t−1θ ∗ ζc∗ t

ζt−1

c∗

+λ 18

t

(

( 1 − θπ

ρ−1

Ht

1 − θ

( C

∗

t

C ∗ t−1

( C

∗

t

C ∗ t−1

) ρ

1−ρ

) ρ ∗

1 − θ ∗ π ∗ρ∗ −1 1−ρ ∗

F t

1 − θ ∗

π t

) −σ

(1 + ρ ∗ ) π ∗ρ∗

F t

(

˜pHt−1

(

˜pHt−1

˜p Ht

˜p Ht

) −1−ρ

X1 Ht

) −ρ

X2 Ht

θ

1 − θ πρ−2 Ht

+ λ 20

t θρπ ρ−1

π ∗ t

) −σ

ρ ∗ π ∗ρ∗ −1

F t

π ∗ t

( ˜p

∗

F t−1

( ˜p

∗

F t−1

˜p ∗ F t

˜p ∗ F t

) −ρ ∗

θ ∗

1 − θ ∗ π∗ρ∗ −2

F t

+ λ 21

) −1−ρ ∗

Ht ∆ Ht−1 − λ22 t

X2 ∗ F t

X1 ∗ F t

t θ ∗ ρ ∗ π ∗ρ∗ −1

0 = −λ 7 t (n H C Ht + n F C ∗ Ht + G t ) − λ 20

t + λ 20

t+1βθπ ρ Ht+1

F t

π t

∆ ∗ F t−1 − λ23 t

πt

∗

• W.r.t. ∆ ∗ F t : 0 = −λ 8 t (n H C F t + n F C ∗ F t + G ∗ t ) − λ 21

t + λ 21

t+1βθ ∗ π ∗ρ∗

F t+1

• W.r.t. ˜p Ht :

0 = −λ 10 1 + ρ

t

+θβ ζc t+1

ζ c t

+λ 10

t−1

−λ 11

t

+θβ ζc t+1

ζ c t

+λ 11

t−1

˜p Ht

[

1 + ρ

˜p Ht

˜p −1−ρ

Ht

(n H C Ht + n F CHt ∗ w t

+ G t )

αA t Nt

α−1

) −σ

π 1+ρ ( ) ]

−1−ρ

Ht+1 ˜pHt

X1 Ht+1

C t ˜p Ht+1

(

Ct+1

θ ζc t

ζ c t−1

ζ c t−1

(

Ct

π t+1

) −σ

π 1+ρ

Ht

C t−1 π t

(

˜pHt−1

˜p Ht

) −1−ρ

X1 Ht

ρ −ρ

[˜p

Ht

˜p (n HC Ht + n F CHt ∗ + G t ) (1 − τt v )

Ht

( ) −σ Ct+1 π ρ ( ) ]

−ρ

Ht+1 ˜pHt

X2 Ht+1

C t π t+1 ˜p Ht+1

( ) −σ

ρ

θ ζc t Ct π ρ Ht

˜p Ht C t−1 π t

(

˜pHt−1

˜p Ht

) −ρ

X2 Ht − λ 17

t − λ 20

t

(1 − θ) ρ˜p −ρ−1

Ht

39

• W.r.t. ˜p ∗ F t :

0 = −λ 13 1 + ρ ∗

t

˜p ∗ F t

+θ ∗ β ζc∗ t+1

ζ c∗

t

+λ 13

t−1

−λ 14

t

1 + ρ ∗

˜p ∗ F t

ρ ∗

˜p ∗ F t

+θ ∗ β ζc∗ t+1

ζ c∗

t

+λ 14 ρ ∗

t−1

˜p ∗ F t

• W.r.t. X1 Ht :

0 = λ 9 t

• W.r.t. X2 Ht :

• W.r.t. X1 ∗ F t :

[

˜p ∗−1−ρ∗

F t

(n H C F t + n F C ∗ F t + G ∗ t )

( C

∗

t+1

C ∗ t

θ ∗ ζc∗ t

ζt−1

c∗

) −σ

π ∗1+ρ∗

F t+1

( C

∗

t

π ∗ t+1

C ∗ t−1

( ˜p

∗

F t

˜p ∗ F t+1

) −σ

π ∗1+ρ∗

F t

π ∗ t

) −1−ρ ∗

( ˜p

∗

F t−1

˜p ∗ F t

w ∗ t

αA ∗ t Nt

∗α−1

]

X1 ∗ F t+1

[

˜p ∗−ρ∗

F t

(n H C F t + n F CF ∗ t + G ∗ t ) (1 − τ v∗

( C

∗

t+1

C ∗ t

) −σ

π ∗ρ∗

F t+1

( θ ∗ ζc∗ t C

∗

t

ζt−1

c∗ Ct−1

∗

π ∗ t+1

( ˜p

∗

F t

) −σ

π ∗ρ∗

F t

π ∗ t

˜p ∗ F t+1

) −ρ ∗

( ˜p

∗

F t−1

˜p ∗ F t

) −1−ρ ∗

t )

X2 ∗ F t+1

) −ρ ∗

( ) −σ

ρ

ρ − 1 µ t − λ 10

t + λ 10

t−1θ ζc t Ct π 1+ρ

Ht

ζt−1

c C t−1 π t

( ) −σ

0 = −λ 9 t − λ 11

t + λ 11

t−1θ ζc t Ct π ρ Ht

ζt−1

c C t−1 π t

]

X1 ∗ F t

X2 ∗ F t − λ 18

t − λ 21

t

( ) −1−ρ ˜pHt−1

˜p Ht

( ) −ρ ˜pHt−1

˜p Ht

(1 − θ ∗ ) ρ ∗˜p ∗−ρ∗ −1

F t

0 = λ 12

t

ρ ∗

ρ ∗ − 1 µ∗ t − λ 13

t + λ 13

t−1θ ∗ ζc∗ t

ζt−1

c∗

( C

∗

t

C ∗ t−1

) −σ

π ∗1+ρ∗

F t

π ∗ t

( ˜p

∗

F t−1

˜p ∗ F t

) −1−ρ ∗

• W.r.t. X2 ∗ F t : 0 = −λ 12

t − λ 14

t + λ 14

t−1θ ∗ ζc∗ t

ζt−1

c∗

( C

∗

t

C ∗ t−1

) −σ

π ∗ρ∗

F t

π ∗ t

( ˜p

∗

F t−1

˜p ∗ F t

) −ρ ∗

• W.r.t. N t :

0 = −n H N η t +λ 5 t ηN η−1

t Ct σ +λ 7 t A t n H αN α−1

• W.r.t. N ∗ t :

0 = −n F N ∗η

t

t +λ 10

t

˜p −1−ρ

Ht

(n H C Ht + n F C ∗ Ht + G t )

+ λ 6 t ηN ∗η−1

t Ct

∗σ + λ 8 t A ∗ t n F αNt

∗α−1

(1 − α)

α

w t

A t N α t

40

+λ 13

t ˜p ∗−1−ρ∗

F t

(n H C F t + n F CF ∗ t + G ∗ t )

(1 − α)

α

w ∗ t

A ∗ t N ∗α

t

• W.r.t. w t :

0 = −λ 5 t ζ c t p Ht + λ 10

t

˜p −1−ρ

Ht

(n H C Ht + n F CHt ∗ + G t ) N t

1−α

αA t

• W.r.t. w ∗ t :

• W.r.t. τ v t :

0 = Λ H ζ c t C −σ

t

• W.r.t. τ v∗

t :

0 = −λ 6 t ζt c∗ p ∗ F t + λ 13

t

˜p ∗−1−ρ∗

F t

(p Ht (n H C Ht + G t ) +

(n H C F t + n F CF ∗ t + G ∗ t ) N t

∗1−α

αA ∗ t

)

v∗

(1 − τt )

(1 − τt v ) 2 p∗ F tq t n H C F t

−λ 2 t γ F

( (1 − τ

v∗

t )

(1 − τ v t ) p∗ F tq t

) −ξ

ξC t

(1 − τ v t ) + λ3 t γ ∗ H

−λ 11

t ˜p −ρ

Ht (n HC Ht + n F CHt ∗ + G t )

[ (

(1 − ξ) (1 − τ

+ λ 15

v∗

t )

(1 − τt v t γ F

)

0 = −Λ H ζt c Ct

−σ τt

v p ∗ F t q tn H C F t

(1 − τt v )

(1 − τ v t ) p∗ F tq t

) 1−ξ

− λ 16

(

+ Λ F ζt

c∗ Ct

∗−σ

( ) (1 − τ

+λ 2 v∗ −ξ

t )

ξC t

t γ F

(1 − τt v ) p∗ F tq t

(1 − τ v∗ ) − λ3 t γH

∗

t

− ΛF ζt

c∗

( ) (1 − τ

v −ξ

t ) p Ht

(1 − τt v∗ ) q t

t γ ∗ H

−λ 14

t ˜p ∗−ρ∗

F t

(n H C F t + n F CF ∗ t + G ∗ t )

[ ( )

(1 − ξ) (1 − τ

− λ 15

v∗ 1−ξ

t )

(1 − τt v∗ t γ F

) (1 − τt v ) p∗ F tq t − λ 16

Ct

∗−σ

t )

(1 − τ v∗

τ v∗

t

ξC ∗ t

(1 − τ v t )

( ) ]

(1 − τ

v 1−ξ

t ) p Ht

(1 − τt v∗ ) q t

p Ht

q t

n F C ∗ Ht

p ∗ F t (n F CF ∗ t + G ∗ t ) + (1 − τ )

t v ) p Ht

(1 − τt

v∗ ) 2 n F CHt

∗ q t

( ) (1 − τ

v −ξ

t ) p Ht

(1 − τt v∗ ) q t

t γ ∗ H

ξC ∗ t

(1 − τ v∗

t )

( ) ]

(1 − τ

v 1−ξ

t ) p Ht

(1 − τt v∗ ) q t

D

Data Sources and Calibration Targets

All data is taken from Eurostat (http://ec.europa.eu/eurostat/data/database). Population

shares of the core and periphery are calculated using time averages of total population

between 2001-2014 (variable name in source: [demo pjan]). Government debt over

GDP in steady state (G/Y ) is calculated as time average of general government consolidated

gross debt as percentage of GDP using annual data between 2010-2014 (variable

name in source: [gov 10dd edpt1]). Government spending and trade balance relative

to GDP in steady state are constructed analogously as time averages on quarterly data

between 2001:1 and 2014:4 (variables in source from category: [namq 10 gdp]).

41

Table 6: Empirical and Theoretical Second Moments

GDP Cons. Gov. Wage

Target Moments

Core:

Autocorrelation: 0.87 0.81 0.77

Std. Dev. (in p.p.): 1.67 0.96 1.07 0.99

Periphery:

Autocorrelation: 0.82 0.88 0.64

Std. Dev. (in p.p.): 2.06 1.78 2.42 1.78

Model-Generated Moments

Core:

Autocorrelation: 0.87 0.81 0.77

Std. Dev. (in p.p.): 0.88 1.17 1.12 1.39

Periphery:

Autocorrelation: 0.82 0.88 0.64

Std. Dev. (in p.p.): 1.11 2.11 2.54 1.96

Note: Empirical target moments (upper panel) calculated using quarterly data from Eurostat for the

period 2001:1 to 2014:4. All series in logs, seasonally adjusted and quadratically detrended. Theoretical

moments (lower panel) from calibrated model (see Tables 1 and 2). Available policy instruments:

monetary policy at union level only.

The data series used to construct the calibration targets for GDP, consumption, and

government spending also stem from [namq 10 gdp]. The variable names are ”Gross domestic

product at market prices”, ”Final consumption expenditure of households”, and

”Final consumption expenditure of general government”. The raw series are not seasonally

adjusted and measured in current prices. Data on aggregate wages are proxied by

the labour cost index (LCI) for the business economy sector (variable name in source:

[lc lci r2 q]), which provides observations for all required countries but France. The

index is given at a quarterly frequency, not seasonally adjusted, and it takes on a value

of 100 in 2012. Before calculating the target moments (autocorrelations, standard deviations)

for the calibration, the log of all series is quadratically detrended and seasonally

adjusted. An overview of the second moments generated from the data and from the

model is given in Table 6.

42

E

Sensitivity Analysis

Table 7: Welfare Costs of Fixed Exchange Rates – Increased Shock Size

(A) Benchmark

LOOP MU FLEX Difference

Monetary Policy (MP) 10 −2 ∗ -21.059 -18.530 2.5295

Monetary+Fiscal Policy (MFP) 10 −2 ∗ -18.219 -17.858 0.3604

Reduction of Welfare Costs: 85.75%

PTM

Monetary Policy (MP) 10 −2 ∗ -21.052 -20.658 0.3938

Monetary+Fiscal Policy (MFP) 10 −2 ∗ -20.058 -19.934 0.1235

Reduction of Welfare Costs: 68.64%

(B) Productivity, Preference, Gov. Spending Shocks

LOOP

Monetary Policy 10 −2 ∗ -17.069 -15.286 1.7827

Monetary+Fiscal Policy 10 −2 ∗ -15.654 -15.371 0.2836

Reduction of Welfare Costs: 84.09%

PTM

Monetary Policy 10 −2 ∗ -17.063 -16.854 0.2086

Monetary+Fiscal Policy 10 −2 ∗ -16.911 -16.818 0.0930

Reduction of Welfare Costs: 55.43%

(C) Mark-up Shocks

LOOP

Monetary Policy 10 −2 ∗ -3.8470 -3.0972 0.7498

Monetary+Fiscal Policy 10 −2 ∗ -2.4248 -2.3467 0.0781

Reduction of Welfare Costs: 89.58%

PTM

Monetary Policy 10 −2 ∗ -3.8454 -3.6595 0.1859

Monetary+Fiscal Policy 10 −2 ∗ -3.0018 -2.971 0.0308

Reduction of Welfare Costs: 83.43%

Note: Welfare measure: consumption equivalents between deterministic and stochastic world economy.

Exchange rate regime either monetary union (MU) or flexible (FLEX). Panel (A): productivity, demand

preference, government spending, & mark-up shocks in both countries. Panel (B): all but mark-up

shocks. Panel (C): mark-up shocks only. Shock standard deviations in all scenarios doubled compared

to benchmark calibration. Second-order approximation to policy functions. T = 1000, J = 100.

43

Table 8: Percentage Reduction of Welfare Costs of Fixed Exchange Rates – Parameter Changes

Benchmark σ = 4 η = 5 Home Bias 30% ξ = 3 ρ, ρ ∗ = 10 θ, θ ∗ = 0.85 G/Y, G ∗ /Y ∗ = 0.30 B/Y, B ∗ /Y ∗ = 1.80

(A) All Shocks

LOOP 85.76 93.01 90.10 85.23 89.78 93.17 87.12 87.20 85.66

PTM 68.66 84.12 49.99 65.21 83.26 67.32 63.56 78.93 68.61

(B) Productivity, Preference, Gov. Spending Shocks

LOOP 84.03 90.62 88.66 81.99 91.15 92.00 86.45 86.64 84.29

PTM 55.42 76.84 42.25 54.22 67.57 53.27 54.68 71.74 55.23

(C) Mark-up Shocks

LOOP 89.58 97.74 96.04 92.95 79.89 94.34 89.37 88.34 88.63

PTM 83.43 89.90 68.18 84.13 96.05 77.21 79.85 91.53 83.71

Note: Table shows percentage reduction of welfare costs of fixed exchange rates by using optimal fiscal policy. Underlying numbers of the welfare measure

for all policy scenarios are available on request. Welfare measure: consumption equivalents between deterministic and stochastic world economy. Column

’Benchmark’ repeats results of Table 3. Panel (A): productivity, demand preference, government spending, & mark-up shocks in both countries. Panel

(B): all but mark-up shocks. Panel (C): mark-up shocks only. Second-order approximation to policy functions. T = 1000, J = 100.

44

Table 9: Welfare Costs of Fixed Exchange Rates – Payroll Taxes

(A) Benchmark

LOOP MU FLEX Difference

Monetary Policy (MP) 10 −2 ∗ -5.0352 -4.4208 0.6144

Monetary+Fiscal Policy (MFP) 10 −2 ∗ -4.0039 -3.747 0.2569

Reduction of Welfare Costs: 58.20%

PTM

Monetary Policy (MP) 10 −2 ∗ -5.0348 -4.9412 0.0936

Monetary+Fiscal Policy (MFP) 10 −2 ∗ -4.006 -3.988 0.0180

Reduction of Welfare Costs: 80.77%

(B) Productivity, Preference, Gov. Spending Shocks

LOOP

Monetary Policy 10 −2 ∗ -4.0539 -3.6155 0.4385

Monetary+Fiscal Policy 10 −2 ∗ -3.8918 -3.6351 0.2567

Reduction of Welfare Costs: 41.45%

PTM

Monetary Policy 10 −2 ∗ -4.0531 -4.0023 0.0507

Monetary+Fiscal Policy 10 −2 ∗ -3.8749 -3.8582 0.0168

Reduction of Welfare Costs: 66.96%

(C) Mark-up Shocks

LOOP

Monetary Policy 10 −2 ∗ -0.9066 -0.7306 0.176

Monetary+Fiscal Policy 10 −2 ∗ -0.0453 -0.0442 0.0012

Reduction of Welfare Costs: 99.34%

PTM

Monetary Policy 10 −2 ∗ -0.9071 -0.8642 0.0429

Monetary+Fiscal Policy 10 −2 ∗ -0.0565 -0.0553 0.0012

Reduction of Welfare Costs: 97.11%

Note: Payroll taxes as fiscal instrument instead of VATs. Welfare measure: consumption equivalents

between deterministic and stochastic world economy. Exchange rate regime either monetary union (MU)

or flexible (FLEX). Panel (A): productivity, demand preference, government spending, & mark-up shocks

in both countries. Panel (B): all but mark-up shocks. Panel (C): mark-up shocks only. Shock standard

deviations in all scenarios doubled compared to benchmark calibration. Second-order approximation to

policy functions. T = 1000, J = 100.

45

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