Government spending, monetary policy, and the real exchange rate

Accepted Manuscript Government Spending, Monetary Policy, and the Real Exchange Rate Hafedh Bouakez, Aurélien Eyquem

PII:

S0261-5606(14)00151-X

DOI:

10.1016/j.jimonfin.2014.09.010

Reference:

JIMF 1476

To appear in:

Journal of International Money and Finance

Received Date: 29 January 2013 Revised Date:

1 September 2014

Accepted Date: 29 September 2014

Please cite this article as: Bouakez, H., Eyquem, A., Government Spending, Monetary Policy, and the Real Exchange Rate, Journal of International Money and Finance (2014), doi: 10.1016/ j.jimonfin.2014.09.010. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Highlights

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Empirical evidence suggests that an unanticipated increase in public spending in a given country appreciates its currency in real terms We propose a small-open-economy model to rationalize this result

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The model features three key ingredients: incomplete and imperfect international …nancial markets, sticky prices, and a not-too-aggressive monetary policy

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*Manuscript (without Author names)

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Aurélien Eyquemz

September 2014

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Abstract

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Hafedh Bouakezy

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Government Spending, Monetary Policy, and the Real Exchange Rate

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Both the traditional Mundell-Fleming-Dornbusch framework and standard dynamic generalequilibrium models with complete …nancial markets predict that an unanticipated increase in public spending in a given country appreciates its currency in real terms. This prediction, however, contradicts the …ndings of a number of recent empirical studies, which instead document a signi…cant and persistent depreciation of the real exchange rate following an expansionary government spending shock. In this paper, we rationalize the …ndings of the empirical literature by proposing a small-open-economy model that features three key ingredients: incomplete and imperfect international …nancial markets, sticky prices, and a not-too-aggressive monetary policy. The model predicts that in response to an unexpected increase in public expenditure, the long-term real interest rate rises less than the country’s debt elastic interest-rate premium. As a result, the long-term real interest rate di¤erential vis-a-vis the rest of the world falls, leading the domestic currency to depreciate in real terms. We establish this result both analytically, within a special version of the model, and numerically for the more general case.

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JEL classi…cation: F31, F41. Keywords: Incomplete markets, monetary policy, public spending shocks, real exchange rate, small open economy, sticky prices.

Financial support from SSHRC and FRQSC is gratefully acknowledged. We are grateful to two anonymous referees for very helpful comments and suggestions. We also thank Patrick Fève, Federico Ravenna, and Nicolas Vincent for useful discussions. y Corresponding author. HEC Montréal and CIRPÉE, 3000 chemin de la Côte-Sainte-Catherine, Montréal, Québec, Canada H3T 2A7. Tel.: 1-514-340-7003; Fax: 1-514-340-6469; E-mail: [email protected]. z GATE, UMR 5824, Université de Lyon and Université Lumière Lyon 2, France. Phone: Tel. : +33 04.37.37.62.81. E-mail: [email protected].

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1.

Introduction

Both the traditional Mundell-Fleming-Dornbusch (MFD) framework and standard dynamic generalequilibrium models with complete …nancial markets predict that an unanticipated increase in public

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spending in a given country appreciates its currency in real terms. In the MFD model, this appreciation results from the rise in aggregate demand induced by the increase in public spending, which falls more heavily on domestically produced goods, raising their relative price with respect to foreign goods. In dynamic general-equilibrium models with complete markets, the real appreciation ensues from a risk-sharing condition that relates the real exchange rate to the ratio of marginal util-

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ities of consumption across countries. As long as the composition of the consumption basket di¤ers across countries (due, for example, to home bias in preferences), an increase in public spending in the domestic country raises the tax burden of domestic households relative to the rest of the world,

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which in turn raises the relative shadow value of wealth in the domestic country and appreciates its currency in real terms.1

This prediction, however, appears to be at odds with the data. Several empirical studies indeed …nd that the real exchange rate depreciates persistently in response to an unexpected exogenous increase in government expenditures (Corsetti and Müller [2006], Kim and Roubini [2008], Müller [2008], Monacelli and Perotti [2010], Enders, Müller and Scholl [2011], Ravn, Schmitt-Grohé and

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Uribe [2011], and Bouakez, Chihi and Normandin [2011]). This result holds across di¤erent countries, sample periods, and identi…cation schemes, and is thus increasingly becoming a generally accepted stylized fact. Figure 1 provides an additional evidence of this fact. It depicts the dynamic response of the real exchange rate to a positive public spending shock, obtained from a panel structural vector auto-regression (SVAR) using quarterly data from Australia, Canada, Sweden, and the

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United Kingdom. Details about the variables used in estimation, sample period, data construction and identi…cation method are provided in the note below Figure 1 and in Appendix A. The …gure shows that the increase in public spending leads to a persistent depreciation the currency in real shock.

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terms (relative to pre-shock value), which is statistically signi…cant for the …rst 6 quarters after the To the extent that the response of the real exchange rate to public spending shocks is likely to play a critical role in determining the size of the spending multiplier in open economies, it is important to build macroeconomic models that are able to account for the empirical evidence just discussed. In this paper, we rationalize this evidence by proposing a small-open-economy model that combines three key features: (i ) incomplete and imperfect international …nancial markets, (ii ) 1 If the composition of the consumption basket is identical across countries, market completeness implies that the wealth e¤ects of an increase in public spending are shared equally across countries. In this case, the shadow value of wealth rises by an equal amount domestically and abroad but the real exchange rate remains una¤ected.

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.025 .020

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.000 -.005 10

15

20

25

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Figure 1: Dynamic response of the real exchange rate to a positive government spending shock. Notes: The …gure shows the dynamic response of the real exchange rate to a one-standard-deviation government spending shock, obtained from a panel SVAR using data from Australia, Canada, Sweden, and the United Kingdom. The solid line is the estimated response and the dashed lines delimit the 95 percent con…dence intervals. A positive response indicates a real depreciation. The sample period is 1975Q1–2013Q4. The series included in estimation are public spending, output, the long-term nominal interest rate, the current account, and the real exchange rate. Data construction and sources are described

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in Appendix A. The SVAR includes a constant and a linear-quadratic trend term. The lag length indicated by the Schwarz and Hannan-Quinn information criteria is 1. The government spending shock is identi…ed via a recursive scheme whereby public spending is predetermined with respect to all the remaining variables included in the SVAR.

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sticky prices, and (iii ) a not-too-aggressive monetary policy. Under incomplete …nancial markets, the real exchange rate is no longer pinned down by the ratio of marginal utilities of consumption, but instead by (the negative of) the long-term real interest rate di¤erential vis à vis the rest of the world.

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The interest rate di¤erential in turn involves a country premium that is assumed to be increasing in the economy’s foreign debt, as in Kollmann [2002], Schmitt-Grohé and Uribe [2003], and Senhadji [2003]. This debt-elastic premium is meant to capture frictions in international …nancial markets stemming, for instance, from the possibility of default or from agency costs. By raising demand for both domestically produced and foreign goods, an increase in public spending raises domestic in‡ation and deteriorates the current account. When prices are sticky and monetary policy does not react too aggressively to (expected) in‡ation, the resulting increase in the long-term real interest rate is smaller than the increase in the (cumulative) country premium. As a result, the long-term real interest rate di¤erential falls, leading the domestic currency to depreciate in real terms.

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We illustrate this mechanism within a special deterministic version of our model in which we abstract from capital and where we restrict the real interest rate to remain constant at its steady-state value at all times. This is achieved by assuming that the monetary authority changes

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the nominal interest rate one for one with expected in‡ation. The constancy of the real interest rate, which is only possible under sticky prices, implies that consumption also remains constant in response to transitory shocks. We can then solve the model analytically (up to a …rst-order approximation) and show that an increase in government purchases leads to a depreciation of the real exchange rate and to a fall in net foreign assets, consistent with the empirical …ndings.

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Intuitively, when the real interest rate is constant, output and the real exchange rate are determined independently of the supply side of the economy. Instead, their equilibrium paths are entirely pinned down by the equilibrium condition in the goods market (IS equation) and by the balance of

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payments (BOP) equation. By raising aggregate demand, an expansionary public spending shock shifts the IS curve outward in the output-real exchange rate space. But under a constant real interest rate, the shock causes an even larger outward shift of the BOP curve. To restore the equilibrium, the real exchange rate must depreciate, and this depreciation is larger the larger the degree of …nancial market imperfections.

We then proceed to the analysis of the general case via numerical simulations in order to quantify the relationship between the aggressiveness of monetary policy and the real exchange rate response

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to a public spending shock. We …nd that the values of the policy-rule parameter that generate a real depreciation fall in the range of empirically plausible numbers. We also perform a sensitivity analysis by varying the values of key parameters within the range of available estimates and by assuming an alternative speci…cation of consumer preferences. We …nd our main conclusion to be extremely robust to these perturbations. Finally, we provide suggestive evidence that the model’s

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main implication— that a country’s currency is more likely to depreciate in real terms the less aggressively monetary policy reacts to in‡ation— is supported by the data.

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Three closely related papers to ours are those by Kollmann [2010], Corsetti, Meier and Müller [2012], and Ravn et al. [2011]. Kollmann [2010] considers a two-country model with incomplete …nancial markets and ‡exible prices, and shows that an increase in public spending in one country can depreciate its real exchange rate, provided that labor supply is highly elastic. The values of the elasticity of labor supply needed to generate a real depreciation, however, seem to be hard to reconcile with available empirical estimates. In contrast, our explanation does not require such an extreme assumption about the elasticity of labor supply. Corsetti et al. [2012] develop a two-country model with complete markets, sticky prices and wages, and spending reversals. The latter feature refers to the assumption that debt-…nanced

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increases in government spending will cause subsequent spending to fall below its steady state level for some time. In turn, this lowers long-term real interest rates and depreciates the currency in real terms. However, while empirical studies based on structural vector autoregressions (SVAR)

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invariably …nd that the path of government spending in the U.S. is “self-correcting”, increasing for six to twelve quarters before eventually falling below trend, results for other countries do not display such a reversal, especially for long sample periods (e.g. Perotti [2005] and Bouakez et al. [2011]).

Finally, Ravn et al. [2011] also consider a two-country model with complete …nancial markets,

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but depart from time-separable preferences by assuming that consumers form deep habits, i.e. habits at the level of individual varieties of goods. The presence of deep habits induces …rms to lower their markups in markets in which aggregate demand rises. Thus, in response to an increase

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in government spending in the domestic economy, markups on domestically sold goods will be lower than markups abroad, making those goods relatively cheaper in the domestic economy, and implying a depreciation of the real exchange rate. While our explanation involves a completely di¤erent mechanism than those discussed above, we regard these di¤erent mechanisms as complementary, rather than competing or mutually exclusive, explanations for the “puzzling” real depreciation caused by an expansionary public spending shock.

The paper is organized as follows. Section 2 presents the model. Section 3 analyzes the e¤ects

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of a government spending shock …rst analytically within a simpli…ed version of the model and then numerically for the general case. It also performs an extensive sensitivity analysis with respect to key structural, and presents suggestive empirical evidence supporting the model’s main prediction. Section 4 concludes.

The Model Economy

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2.

The world consists of a continuum of identical small open economies that trade in …nal goods

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and …nancial assets. The size of each economy is small relative to the rest of the world. Each economy is populated by a continuum of identical, in…nitely lived, households, and has a continuum of monopolistically competitive …rms that produce a di¤erentiated …nal good. The number of households and …rms is normalized to one. Firms do not price discriminate between the domestic and export market, which means that the law of one price holds for all goods. Financial markets are assumed to be incomplete as households can only trade one-period non-state-contingent domestic and international bonds. Financial markets are also assumed to be imperfect in that the interest rate faced by domestic agents on their external borrowing is augmented by a premium that is increasing

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in the aggregate level of foreign debt.2 In what follows, we describe a representative small open economy, which we call “home country”, and denote by an asterisk variables pertaining to the rest of the world. Throughout the paper, variables without time subscripts denote steady-state values.

utility 1+1=

s t

ln cs

s=t

subject to the budget constraint "t Bt + Bt + Pt (ct + it +

t)

= "t

t 1 Rt 1 Bt 1

`s ! 1 + 1=

+ Rt

!

;

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Et

1 X

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Households The representative household in the home country maximizes its expected lifetime

1 Bt 1

+ Pt (wt `t + zt kt

1)

+ Dt

t;

and

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and to the appropriate no-ponzi-game conditions. In expression (1), the parameters 0 <

(1)

(2) < 1

> 0 are, respectively, the subjective discount factor and the Frisch elasticity of labor supply,

ct is a consumption index, and `t is the quantity of labor competitively supplied to the …rms. In Equation (2), Bt and Bt are the household’s nominal holdings of, respectively, international and domestic bonds at the end of period t; "t is the nominal exchange rate, de…ned as the price of a unit of the foreign currency in terms of the domestic currency; it is private investment, capital-adjustment costs, Rt

1

and Rt

1

denotes

are the nominal interest rates paid on, respectively, foreign 1 and t; Pt is the consumption-based price index (CPI

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and domestic bonds between periods t

t

hereafter), wt is the real wage rate, zt is the real rental price of capital, kt 1 is the stock of capital at R1 the beginning of period t, Dt = 0 Dt (i)di denotes the household’s claims on …rms’(indexed by i) nominal pro…ts, and

t

denotes lump-sum taxes paid to the government. The term

t

is a country

premium that increases with the economy’s aggregate level of debt as a percentage of steady-state t

has the following functional form: ! ~t "t B ; t = exp Y

where

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output. More speci…cally,

is a positive parameter,

(3)

~ is the aggregate level of foreign debt, which the household in B t

the small open economy takes as given, and Y denotes nominal GDP in the steady state. The capital stock evolves according to the following law of motion: kt = (1

) kt

2

1

+ it ;

(4)

This assumption has been used by several authors, such as Kollmann [2002] or Schmitt-Grohé and Uribe [2003]. The presence of a debt-elastic interest rate premium also induces stationarity in the log-linearized version of the model. Without it, the model’s equilibrium dynamics exhibit a unit root (see Schmitt-Grohé and Uribe [2003]).

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where 0 <

< 1 is the depreciation rate. Capital adjustment costs are assumed to be quadratic in

net investment

where

=

2

(it

kt

2 1) ;

is a positive parameter.

Denoting by qt

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t

"t Pt =Pt the real exchange rate, the household’s …rst order conditions imply 1=

!ct `t

Pt ct 1 = 0; Pt+1 ct+1 qt+1 Pt+1 Pt = 0; t Rt qt Pt Pt+1

kt

1)

Et

Rt

ct (1 ct+1

+ zt+1 + (it+1

kt )) = 0;

(5) (6) (7) (8)

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1 + (it

1 Pt+1 ct+1

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R t Et

Et

wt = 0;

in addition to the usual transversality conditions.

Taking a log-linear approximation of Equation (7) around a symmetric non-stochastic steady state yields a modi…ed interest rate parity condition (UIP) that relates the di¤erence between the domestic and the foreign real interest rate to sum of the expected rate of real depreciation of the domestic currency and a debt-elastic country premium (see Equation C2). The presence of an interest-rate premium is consistent with the extensively documented empirical failure of the stan-

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dard UIP condition. Abstracting from risk considerations (since we will be focusing on a log-linear solution of the model), violations of the UIP condition re‡ect frictions in international capital markets that may arise from information asymmetries between domestic borrowers and foreign lenders or from the possibility of default or rare events (peso problem). Information asymmetries give rise to agency costs that drive a wedge between the borrowing and the lending rate (see Bernanke and

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Gertler [1989]). Models of default typically imply that the ex ante probability of default is increasing in the level of debt (e.g. Arellano [2008] and Bi [2012]). In the open-economy macroeconomics

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literature, frictions in international …nancial markets are sometimes captured by assuming that the purchase of foreign assets is subject to portfolio-adjustment costs that are increasing and convex in the volume of transactions. Up to a …rst-order approximation, this assumption also leads to a modi…ed UIP equation whereby the interest rate di¤erential depends positively on the stock of foreign debt, just as in Equation (C2). While both portfolio-adjustment costs and the debt-elastic country premium assumed in this paper are admittedly reduced-form approaches to modelling imperfections in international …nancial markets, the resulting relationship between the interest rate di¤erential and the net foreign asset position is nonetheless strongly supported by the data. For instance, Edwards [1984] …nds that the interest rate di¤erential increases with the ratio of foreign debt to output in a sample of 19 developing countries. Bernhardsen [2000] reports that the interest 6

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rate di¤erential of 9 European countries (with respect to Germany) rises signi…cantly following a current-account deterioration. Lane and Milesi-Ferretti [2002] …nd the interest rate di¤erential of 20 industrialized countries (with respect to the U.S.) to be negatively correlated with the net

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foreign asset position.3 The consumption index, ct ; is an aggregate of consumption of goods produced in the home country (cH;t ) and goods produced in the rest of the world (cF;t ) ) (cH;t )

+

1

1

1

(cF;t )

;

(9)

2 [0; 1] measures the share of imported goods in total consumption, thus

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where the parameter

1

1

ct = (1

re‡ecting the degree of openness of the small open economy,4 and the parameter

is the elasticity

of substitution between domestic and foreign goods. The associated CPI is

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1

) (PH;t )1

Pt = (1

(PF;t )1

+

1

;

(10)

where PH;t and PF;t are the price sub-indexes associated with cH;t and cF;t ; respectively. The optimal allocation of consumption between home and foreign goods gives rise to the following demand functions:

PH;t Pt

)

ct ;

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cH;t = (1

PF;t Pt

cF;t =

ct :

(11)

The consumption sub-indexes cH;t and cF;t are bundles of di¤erentiated varieties produced domestically and abroad, and are given by, respectively cH;t =

Z

1

1

cH;t (i)

1

di

,

cF;t =

1

1

cF;t (i)

1

di

;

(12)

0

0

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Z

where cH;t (j) (respectively cF;t (j)) is consumption of a typical variety i produced in the home country (respectively in the rest of the world) and

> 1 is the elasticity of substitution between

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varieties originating in the same country. The price sub-indexes associated with cH;t and cF;t are given by, respectively

PH;t =

Z

1

1

1

PH;t (i)

1

di

,

PF;t =

Z

1

1

1

PF;t (i)

1

di

;

(13)

0

0

where PH;t (j) (respectively PF;t (j)) is the domestic-currency price of a typical variety i produced in the home country (respectively in the rest of the world). Demand functions for domestically 3

In this paper, we also provide independent evidence of a positive relationship between the interest rate di¤erential (with respect to the U.S.) and the ratio of foreign debt to GDP in Australia, Canada, Sweden, and the United Kingdom (see Appendix D). 4 The fraction (1 ) therefore measures the degree of home bias in consumption.

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produced and foreign varieties are given by cH;t (i) =

PH;t (i) PH;t

cH;t ;

PF;t (i) PF;t

cF;t (i) =

cF;t :

(14)

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Note that because the law of one price holds for all goods, we have PF;t (i) = "t PF;t (i) 8i; and thus PF;t = "t PF;t .

Firms. Each monopolistically competitive …rm is the supplier of a single variety i, produced with the following technology:

where nt (i) and kt

1 (i)

' 1 ' ; 1 (i) nt (i)

(15)

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yt (i) = kt

are labor and capital inputs used by …rm i, and 0 < ' < 1 is a parameter.

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Cost minimization implies yt (i) kt 1 (i) yt (i) ') nt (i)

' (1

zt ; mct (i) wt ; mct (i)

=

=

(16) (17)

where mct denotes real marginal cost, which satis…es

(zt )' (wt )1 '' (1 ')1

'

':

(18)

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mct (i) = mct =

Since …rms do not segment markets by country, the export price of a typical …rm i, PH;t (i); will be equal to PH;t (i)="t ; which also implies that PH;t = PH;t ="t . Prices are set à la Calvo [1983]. That is, each period, a fraction (1 …rm at period

t.5

of …rms keep their prices unchanged. Let P H;t denote the price set by a typical

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remaining fraction

) of …rms are randomly selected to set new prices while the

Assuming that private investment and government consumption are aggregated

analogously to private consumption, the total demand facing this …rm in period s (s P H;t PH;s

=

P H;t PH;s

AC C ys =

cH;s + iH;s + PH;s Ps

H;s

((1

+ gH;s + cH;s + iH;s +

) (cs + is +

s

H;s

t) is

+ gH;s

+ gs ) + qs (cs + is +

s

+ gs )) :

(19)

The optimal price, P H;t ; is chosen to maximize Dt = Et

1 X

(

)s

t

t;s

P H;t

Ps mcs y s ;

(20)

s=t

5 The optimal price does not depend on the …rm index because all the …rms that have the opportunity to change their prices at a given time choose the same price.

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where

t;s

=

Pt ct Ps cs :

The …rst-order condition for this problem yields P1 ( P s=t 1 1 s=t (

P H;t =

)s )s

t t

Et (mcs y s =cs ) : Et (y s =(Ps cs ))

(21)

1

PH;t = (1

) P H;t 1

1 + PH;t

1

1

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Aggregating across all …rms, the price index for domestically produced goods is given by :

(22)

Government Since Ricardian equivalence holds in this model, we abstract from public debt and

Pt gt =

t:

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assume that the government …nances its expenditures through lump-sum taxes. That is

(23)

gt g

ln where 0

g

1 and

g t

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Public spending is exogenous and follows the autoregressive process =

g

gt 1 g

ln

+

g t;

(24)

is a serially uncorrelated disturbance with zero mean.

Monetary authority The monetary authority in the small open economy sets the nominal interest rate according to the following rule:

where

t

= Pt =Pt

1

Rt R

Rt 1 R

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ln

=

r

ln

+ (1

r)

Et

is the CPI in‡ation rate between periods t

t+1

;

(25)

1 and t, 0

r

< 1 captures

the degree to which the monetary authority smooths out changes in the nominal interest rate, and

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1 measures the aggressiveness with which it responds to expected in‡ation. The assumption that the monetary authority responds to expected, rather than current in‡ation, is only made for tractability as it allows us to obtain analytical results in Section 3.1, but it is not essential to the

2.1

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general point made in this paper.

Equilibrium, steady-state and log-linearized model

Equilibrium Given that we consider a small open economy, we assume that domestically produced goods receive a negligible weight in the world consumption bundle. This implies that PF;t = Pt : R1 1 1 For the purpose of deriving the market clearing conditions, let yt di denote 0 yt (i) aggregate output. The goods market clearing condition is then given by yt =

PH;t Pt

((1

) (ct + it +

t

9

+ gt ) + qt (ct + it +

t

+ gt )) :

(26)

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Furthermore, aggregating the production functions of all domestic …rms (Equation 15) yields =

1

yt (i) di =

and nt

t

R1 0

R1 0

nt

1

kt

' 1 ' di 1 (i) nt (i)

0

0

where

Z

PH;t (i) di measures the dispersion of domestic PH;t (i) di.6 Labor-market clearing implies that

= kt' 1 n1t

'

;

(27) R1

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t yt

Z

producer prices, kt

nt = `t :

1

0

kt

1 (i) di;

(28)

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Since households in the domestic economy are identical, the domestic bonds market is in zero ~ =P = B =P net supply, i.e. Bt =Pt bt = 0; and B bt . Imposing these conditions and t t t t payments (BOP) equation: q t bt =

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consolidating the households’ and government budget constraints yield the following balance of

t R t 1 q t bt 1

+

PH;t yt Pt

ct

it

t

gt ;

where we have substituted the …rms’current dividends, used the fact that PH;t yt = and imposed the labor-market clearing condition.

(29) R1 0

PH;t (i) yt (i)di,

Conditionally on both monetary policy and the exogenous variables, a symmetric equilibrium for this economy is a collection of 13 sequences (ct , nt , it ; kt , yt , bt ; mct ; wt , zt; qt ; Pt , PH;t , and

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PH;t )1 t=0 satisfying the law of motion of capital (Equation 4), the households’…rst-order conditions (Equations 5–8, with Equation 28 substituted in for `t ), the de…nition of the CPI (Equation 10), the pricing condition (Equation 21), the de…nition of the price index for domestically produced goods (Equation 22), the aggregate production function (Equation 27), the …rm’s …rst-order conditions

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(Equations 16 and 17), the goods market clearing condition (Equation 26), and the balance of payments (Equation 29).

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Steady state. We de…ne a symmetric ‡exible-price initial steady state in which exogenous variables take identical values in the small open economy and in the rest of the world, and net foreign assets are zero, i.e. b = 0:7 Moreover, we assume without loss of generality that all nominal prices are equal to unity in steady state. This ensures that q = 1. The steady state is given in Appendix B, where

denotes the steady-state ratio of government spending to output.

R1 The variable yet y (i)di = t yt is the appropriate measure of GDP in this model. However, as shown by 0 t Galí and Monacelli [2005], t is of second order, which implies that GDP and aggregate output are equivalent up to a …rst order approximation. 7 This symmetric steady state is convenient to derive the analytical solution discussed in the next section, but it is not essential to the point made in this paper. Our results still hold when we log-linearize the model around a steady state with non-zero net foreign assets. 6

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Log-linearization In order to solve the model, we log-linearize its equilibrium conditions around the steady state. The log-linearized version of the model is presented in Appendix C, where a circum‡ex denotes the log-deviation of a variable from its steady-state value.8

Public Spending Shocks and the Real Exchange Rate

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3.

bt = 0), an Assume that all foreign variables remain at their steady-state values (b ct = gbt = bt = R

assumption that we shall maintain in the rest of the paper. Combining the balance of payments

gbt = bbt +

c b ct + y

1b bt 1

ib it y

+

1

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(Equation C3) and the goods market clearing condition (Equation C12) yields: ( (2

)

1) qbt :

(30)

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This equation states that for given paths of private consumption, investment, and net foreign assets, an increase in government spending implies a depreciation of the real exchange rate, provided that (2

) > 1. How plausible is this parametric restriction? Studies that use aggregate data to

estimate the elasticity of substitution between domestic and foreign goods, estimates in the neighborhood of

1.9

, generally report

In contrast, much larger estimates are found when data on

individual products groups are used.10 In the open-economy macroeconomics literature, values of 1:5 or 2 are frequently used to calibrate

(e.g., Backus, Kehoe and Kydland [1993], Smets

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and Wouters [2002], Monacelli [2005], Bouakez and Rebei [2008], Auray and Eyquem [2014], etc.). Estimates of the degree of trade openness suggest that plausible values for (0:1; 0:4). Clearly, even the conservative values of

and

are in the range of

imply that the condition

(2

)>1

is met. Therefore, the rest of the analysis will assume that this condition holds. Of course, whether the real exchange rate appreciates or depreciates in equilibrium will depend

EP

on the general-equilibrium adjustment of consumption, investment, and net foreign assets. In this paper, we show that a real depreciation occurs as long as private spending do not fall too much in

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response to the increase in government spending. In a model with no capital accumulation, this P 11 b requires that the long term real interest rate, Et 1 i=0 (Rt+i b t+1+i ), does not increase too much. b The only exception is b bt which denotes yt : See, for example, Heathcote and Perri [2002] and Bergin [2006]. 10 For example, Feenstra, Luck, Obstfeld and Russ [2014] estimate for 8 manufacturing sectors using a two-stage least squares (TSLS) and a two-step generalized method of moments (GMM) procedures. TSLS estimates range from 0:87 in Metals Products to 4:08 in Food Products, whereas GMM estimates range from 0:88 in Metals Products to 3:60 in Apparel Manufacturing. With both methods, the point estimate is larger than 1 in 7 of the 8 sectors. See also Feenstra [1994], Broda and Weinstein [2006] and Romalis [2007]. 11 Indeed, iterating equation (C1) forward yields: 8

9

b ct = lim Et b ct+T T !1

Et

1 X bt+i (R i=0

11

bt+1+i );

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Below, we illustrate this point by focusing on a special case of the model with no capital and in which the real interest rate, and hence consumption, remain constant in equilibrium. This version allows us to solve analytically for the equilibrium path of the real exchange rate. We then turn to

3.1

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the analysis of the more general version of the model using numerical simulations.

A special case

Consider a simpli…ed version of our model in which we abstract from uncertainty and from capital (' = 0); and where we set

r

= 0 and

= 1. In this case, the monetary authority changes the

SC

nominal interest rate one for one with expected in‡ation, thereby implying that the short and longbt+i bt+1+i ) = 0 bt bt+1 = P1 (R term real interest rates remain constant in every period, i.e. R i=0

for all t: This in turn implies that consumption remains constant in equilibrium if the economy is

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a¤ected by transitory shocks, i.e. b ct = 0 for all t. Note that this equilibrium exists only if prices are

sticky, as the real interest rate is independent of monetary policy and must adjust in a ‡exible-price equilibrium.

In the absence of intertemporal substitution (stemming from the constancy of the real interest rate), it can be easily seen that the dynamics of net foreign assets and the real exchange rate can be solved for independently of the rest of the model. More speci…cally, these two variables are determined by the following two-equation dynamic system:

where

1

( (2

)

1b bt 1

TE D

bb t

1) > 0:

= qbt

gbt ;

qbt = bbt ;

qbt+1

(31) (32)

AC C

respectively:

EP

A graphical solution of this system is shown in Figure 2, which depicts the phase diagram in the (bbt 1 ; qbt ) space. The loci bbt = 0 and qbt+1 = 0 are characterized by the following equations, qbt =

qbt =

The two loci are downward sloping, but the

1

1

bb t

1b bt 1

+

1

+ gbt :

gbt ;

(33) (34)

qbt+1 = 0 locus has a steeper slope. Assume that the

economy is initially at the equilibrium denoted by E; and that there is a temporary increase in government spending. The change in gbt shifts both loci upward by exactly the same amount (see

Equations 33 and 34). At the time of the shock, the real exchange rate depreciates immediately, which shows that the reponse of consumption to a transitory shock (so that limT !1 Et b ct+T = 0) is entirely determined by the (negative of) response of the long-term real interest rate.

12

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SC

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Figure 2: Illustrating the e¤ects of an increase in government spending using the phase diagram.

jumping to point E 0 in Figure 2. As the economy moves to point E 00 , the real exchange rate

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appreciates and net foreign assets fall for some time (inducing a current-account de…cit) before starting to increase. Both variables then move down the saddle path until the economy returns to its initial equilibrium.

We now provide an analytical solution to system (31)-(32). To do so, we use the method of

1

and

2

qbt =

b

1 bt 1

bt ; 2g

+

be shown that the coe¢ cient

1

solves the following second-order equation: 2 1

1

(1 +

)

1

1

The root that leads to a stable equilibrium is given by q 1 (1 + 1+ 1 = 2 The parameter

2

(35)

as a function of the deep parameters. By straightforward algebra, it can

AC C

and determine

EP

undetermined coe¢ cients. That is, we conjecture that the solution takes the form

1 2 )

= 0:

+4

(36)

1

< 0:

(37)

is thus given by 2

=

( 1

)

1

(

g

13

1

)

> 0:

(38)

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Note that

2

is unambiguously positive, which means that the real exchange rate depreciates

following a positive government spending shock. One can also easily check that the current account deteriorates following such a shock (net foreign assets fall). The reason this is the only possible

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equilibrium is that a real appreciation of the currency would imply that the decline in net foreign assets required to restore the balance-of-payments equilibrium violates the transversality condition. The increase in government spending must therefore be accompanied by a real depreciation. The e¤ects of government spending shocks in this special case with a constant real interest rate can also be understood using an IS-BOP framework. The IS curve describes the goods-market

ybt =

+

qbt + (1

1

SC

equilibrium in the small open economy, and is characterized by the following equation: ) gbt :

(39)

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Note that this curve is increasing in qbt , i.e. the relative price of foreign goods. To obtain an

equation for the BOP curve in the (b yt ; qbt ) space, we start by using (35) to solve for qbt+1 in (32). 2 g This yields bbt = 1 qbt gbt : Inserting this expression into Equation (C3), we obtain 1

1

ybt =

The slope of this curve,

1

1b bt 1

+

1

1

+

1

+

1

qbt +

2 g

gbt :

1

(40)

, is negative for su¢ ciently low values of , but even when

1

TE D

it is positive, it never exceeds that of the IS curve.12 In other words, the BOP curve is either downward sloping or is steeper than the IS curve in the (b yt ; qbt ) space.

Equations (39) and (40) show that an increase in gbt shifts both the IS and BOP curves outward.

This is shown in Figure 3, which illustrates the case of a downward sloping BOP curve. The shift in the IS curve is maximal given that it is not attenuated by a decline in private consumption

EP

(recall that b ct = 0). The shift in the BOP curve re‡ects the fact that the real exchange rate needs

to depreciate, for a given level of output, to restore the balance-of-payments equilibrium. Because the BOP curve shifts more than does the IS curve (note that

2 g

1

>

(1

)), the rise in

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government spending leads to an increase in output and to a depreciation of the real exchange rate. These e¤ects are larger the steeper the BOP curve (i.e. the larger the value of ). Recall, however, that the depreciation of the real exchange rate is necessary in this special case because the equilibrium cannot be restored through a change in consumption, or alternatively, a change in the long-term real interest rate. In the general case where monetary policy changes the nominal interest rate more than one for one with expected in‡ation, the response of the real exchange rate will depend on the magnitude of the adjustment of the long-term real interest rate. We explore this matter in the next section. 12

Indeed, lim

!1

1 1

+

1

=

1

<

+

1

:

14

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SC

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Figure 3: Illustrating the e¤ects of a government spending shock using the IS-BOP framework.

3.2

The general case

In this section, we show that the result highlighted in the special case discussed above holds under

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less restrictive assumptions about monetary policy. In particular, we show that the real exchange rate continues to depreciate in response to a positive public spending shock if monetary policy adjusts the nominal interest rate more than one for one to expected in‡ation, without being overly aggressive. When

takes on values that are strictly larger than 1, however, the linearized model

no longer admits an analytical solution and we have to proceed with numerical simulations. To do

EP

so, we need to assign values to the structural parameters. Parameter values We calibrate the model at a quarterly frequency. We start by discussing

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the parameters whose values are relatively conventional in the literature. The discount factor, ; is set to 0:99 so that the implied steady-state real interest rate is 4:1% annually. The preference parameter ! is a scaling parameter and is set to 1. We choose the elasticity of substitution across domestic varieties of …nal goods, , to equal 6, which yields a steady-state markup of 20%, as in Rotemberg and Woodford [1997]. The steady-state share of public spending in total output, ; is set to 0:25. The parameter governing trade openness, , is calibrated to 0:3 to match the average share of imports over GDP in industrialized economies. The smoothing parameter,

r,

is set to 0:8,

consistently with the estimates reported in the literature (e.g., Smets and Wouters [2005]). The quarterly depreciation rate is

= 0:025 and capital elasticity is ' = 0:36.

15

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Next, we turn to the parameters whose values are relatively more controversial. For each of those parameters, our strategy is to choose a benchmark value that lies within the range of available estimates and then perform a sensitivity analysis. Starting with the elasticity of substitution literature and set

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between domestic and foreign goods, ; we follow the bulk of the open-economy macroeconomics = 1:5 in the benchmark calibration (as in Backus et al. [1993], for example).

In the sensitivity analysis, we vary

between 1 and 2. Merz [1995] reports that existing estimates

of the Frisch elasticity of labor supply, , vary between 0:03 and 3. In general, micro estimates converge towards low values of , whereas macro estimates tend to be large. Following Galí, Gertler results to values of

SC

and López-Salido [2007], we consider a benchmark value of 0:5 and investigate the sensitivity of the between 0:2 and 1. We set the Calvo probability of not changing prices, ,

to 0:75, which implies an average duration of price spells of 4 quarters. In Section 3.3, we let this

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probability span the entire range of possible values, i.e. (0; 1). We choose the capital-adjustmentcost parameter, , to be 0:01, consistently with the estimate reported by Cooper and Haltiwanger [2006] and with the calibration used by Mendoza [1991], but consider larger values in the sensitivity analysis. We calibrate the autocorrelation coe¢ cient of the government spending process,

g

to

0:9, and study the sensitivity of the results when this parameter varies between 0:6 and 1. In our model, the parameter

measures the (negative of the) elasticity of the interest rate

di¤erential (or country premium) with respect to net foreign assets (see Equation (C2)). Lane and

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Milesi-Ferretti [2002] estimate the elasticity of the real interest rate di¤erential (in %) to the ratio of foreign debt to exports using annual data. Their estimates range between 0:83 and 3:24. In our benchmark calibration, we choose to be conservative and use Lane and Milesi-Ferretti’s lowest estimate. As we will show in the sensitivity analysis, higher values of

actually strengthen our

results. Once converted to a quarterly basis, Lane and Milesi-Ferretti’s lowest estimate implies

EP

= 0:0017.13 We also computed independent estimates of

using data from Australia, Canada,

Sweden, and the United Kingdom (see details in Appendix D). Our point estimates range from

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0:0016 for Canada to 0:0146 for Sweden, thus con…rming that the value of 0:0017 is a plausible lower bound on . The benchmark values assigned to the parameters are summarized in Table 1. 13

Denote by { the estimate reported by Lane and Milesi-Ferretti [2002]. In our model, b =y is the ratio of net foreign assets to quarterly GDP and is the steady-state share of exports in GDP. Thus, the ratio of net foreign assets to annual exports is b =( 4y). Since interest rates are quarterly in the model, Lane and Milesi-Ferretti’s estimate implies 400 (r r ) = {b =( 4y); where r and r are the (net) domestic and world real interest rates, respectively. The expression above yields the following mapping between the estimate { and our parameter : = {=(1600 ): For instance, if

= 0:3 and { = 0:83, we obtain

= 0:0017, which is the value used in our benchmark calibration.

16

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Table 1: Parameter Values

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= 0:99 !=1 =6 = 0:25 = 0:3 = 0:8 r = 0:0017 = 1:5 = 0:5 = 0:75 = 0:01 ' = 0:36 = 0:025 g = 0:9

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Discount factor Preference parameter Elasticity of substitution between varieties Steady state ratio of public spending to output Trade openness Nominal-interest-rate smoothing parameter debt-elasticity of the interest rate di¤erential Elasticity of substitution between goods Frisch elasticity of labor supply Calvo probability of not changing prices Capital-adjustment-cost parameter Capital elasticity Capital quarterly depreciation rate Autocorrelation of public spending shocks

Impulse response functions We now discuss the impulse responses generated by the model under the benchmark calibration when the economy is hit by a 1 percent positive government

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spending shock. To shed light on the importance of monetary policy for the response of the real exchange rate, we study two scenarios: one in which the monetary authority …ghts in‡ation aggressively (

= 1:5) and one in which monetary policy is moderately aggressive (

= 1:1). The

results are depicted in Figure 4.

EP

The responses of output, consumption, net foreign assets, the nominal interest rate and the CPI in‡ation rate are qualitatively similar across the two cases. The increase in public spending increases aggregate demand, thus putting pressure on production capacities and input prices and

AC C

inducing higher domestic-price in‡ation. The resulting increase in CPI in‡ation leads the monetary authority to raise the nominal interest rate, which, under the assumption that > 1 raises the P1 b long-term real interest rate, Et i=0 (Rt+i bt+1+i ). This in turn causes consumption to fall. As in the special case discussed above, net foreign assets decline. Increasing

from 1:1 to 1:5 only

changes the magnitude of these responses, but not their sign.

In contrast, the real exchange rate exhibits very di¤erent responses under the two scenarios, appreciating when

= 1:5 and depreciating when

= 1:1. In order to understand this result, it

is useful to iterate the modi…ed uncovered interest rate parity condition (Equation C2) forward to

17

Consumption

0.4

φπ=1.5

-0.04

0.2

-0.06 -0.07

0

25

5

10 15 20 Quarters -3 x 10Nom. interest rate 6

-0.1 -0.2

5 4 3

10 15 20 25 Quarters Long term real int. rate

5

10 15 20 25 Quarters Cumulative debt-elastic premium

0.05

0.03 5

EP

0.04

10 15 Quarters

20

25

10 15 20 Quarters CPI inflation

25

0.2

0.15

0.1

0.05

10 15 20 25 Quarters Long term real int. rate differential

5

0.01

5

% deviation

basis-points

0.06

5

0.25

TE D

5

25

% deviation

10 15 20 Quarters Current account / Y

% deviation

% deviation

0.01

-0.01

5

0

% deviation

0.02

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0

-0.05

SC

φπ=1.1

Real exchange rate

% deviation

0.6

% deviation

% deviation

Output

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ACCEPTED MANUSCRIPT

4.5

4

0 -0.01 -0.02

3.5 5

10 15 Quarters

20

25

5

10 15 Quarters

20

25

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Figure 4: Impulse responses to a 1 percent increase in public spending under aggressive ( and moderately aggressive ( = 1:1) monetary policy.

18

= 1:5)

ACCEPTED MANUSCRIPT

0.03

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0.025

0.02

0.015

0.01

0.005

0 1.1

1.15

1.2

1.25

φπ

1.3

1.35

1.4

1.45

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1.05

SC

Impact response of the real exchange rate

0.035

1.5

Figure 5: Initial response of the real exchange rate as a function of

express the real exchange rate as qbt = lim Et qbt+T

Et

i=0

TE D

T !1

1 X

bt+i (R

bt+1+i + bbt+i ):

:

(41)

If the shock is temporary, the term limT !1 Et qbt+T must be equal to zero, and the response of

the real exchange rate will depend (negatively) on the response of the long-term interest rate P b di¤erential, Et 1 bt+1+i + bbt+i ).14 The latter in turn can be expressed as the di¤erence i=0 (Rt+i

EP

between the response of the domestic long-term real interest rate and that of the cumulative country P premium, Et 1 bb . Figure 4 shows that under aggressive monetary policy ( = 1:5), the i=0 t+i

rise in the long-term real interest rate is larger in magnitude than the increase in the cumulative

AC C

country premium. As a result, the long-term real interest rate di¤erential increases, causing the real exchange rate to appreciate. Under less aggressive monetary policy (

= 1:1), the country

premium dominates, the the long-term real interest rate di¤erential falls initially, and the real exchange rate depreciates.

Figure 5 depicts the relationship between the initial response of the real exchange rate to a positive government spending shock and the parameter

, conditional on our benchmark calibration.

The …gure shows that this response is monotonically decreasing obtained with empirically plausible values of 14

.

bt = 0: Recall that we have assumed that bt = R

19

; and that a real depreciation is

ACCEPTED MANUSCRIPT

3.3

Sensitivity analysis

We now study the sensitivity of our results to alternative values of key parameters, namely, the elasticity of substitution between domestic and foreign goods, the Frisch elasticity of labor supply,

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the Calvo probability of not changing prices, the risk-premium parameter, the capital-adjustment cost parameter, and the autocorrelation of the government spending shock. In each case, we focus on the initial response of the real exchange when both the parameter of interest and the policy parameter,

, vary. We also consider an alternative speci…cation of households’preferences

SC

whereby government spending enters the utility function.

Elasticity of substitution between domestic and foreign goods ( ) As stated above, the necessary condition for the real exchange rate to depreciate in response to an expansionary govern(2

)

1 > 0, holds for any sensible value of : But how sensitive is

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ment spending shock, i.e.

this depreciation across the range of plausible values of ? Figure 6 depicts the initial response of the real exchange rate for values of

ranging from 1 to 2, and values of

ranging from 1 to 1:5.

It shows that the magnitude of the exchange rate response is essentially insensitive to the value of

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(within the range considered), regardless of the degree of aggressiveness of monetary policy.

0.04 0.03

EP

0.02 0.01 0

AC C

2

1.1

1.8

1.2

1.6

1.3

1.4

1.4

1.2 µ

1.5 1

φ

π

Figure 6: Initial response of the real exchange rate in the ( ;

) space.

Frisch elasticity of labor supply ( ) In the special case of no intertemporal substitution, discussed in Section 3.1, the absence of a consumption response implies that

20

1

n bt = w bt , which

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0.04

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0.03 0.02 0.01

1

SC

0

1.1

0.8

1.2

0.6

1.3

0.4

φ

π

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ζ

1.4 0.2 1.5

Figure 7: Initial response of the real exchange rate in the ( ;

) space.

means that the labor supply curve does not shift after an increase in public spending. In that version of the model, the parameter

plays no role in the determination of the real exchange rate.

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In the general case, however, changes in consumption shift the labor supply curve. An expansionary government spending shock will therefore shift the aggregate supply curve rightward through its e¤ect on labor supply, and the resulting e¤ect on the exchange rate will be larger the larger is . As pointed out by Kollmann [2010], however, under ‡exible prices, generating a real depreciation requires very large values of , which lie far outside the range of available estimates.15 In contrast,

EP

as shown in Section 3.2, our model generates a real depreciation using a value of with empirical estimates. Interestingly, Figure 7 below shows that, as

that is in line

tends towards the lower

bound of existing estimates, a real depreciation is still possible to obtain, but it requires less and

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less aggressive monetary policy.

Calvo probability of not changing prices ( ) While the equilibrium path of the exchange rate is independent of the degree of price rigidity in the special case with constant real interest rate, this is no longer true in the more general version of the model. Figure 8 indeed shows that the magnitude of the exchange rate response to a government spending shock increases exponentially with ; and that the model can generate a real depreciation even with an aggressive monetary policy if prices are su¢ ciently rigid. 15

Kollmann [2010] considers values of the Frisch elasticity equal to 2, 5 and in…nity.

21

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0.06

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0.05 0.04 0.03 0.02 0.01

SC

0

1.1

0.8

1.2

0.6

1.3

0.4 1.4

0.2 1.5

φ

π

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η

Figure 8: Initial response of the real exchange rate in the ( ;

) space.

Risk premium parameter ( ) In the special case with a constant real interest rate, higher values of

make the BOP curve steeper and lead to a larger depreciation of the real exchange rate

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following an expansionary public spending shock.16 To verify whether this result also holds in the more general case, we consider values of

that range from 0.015 to 0.15. Figure 9 shows that this is

indeed the case. For any given value of the policy parameter increasing in . Intuitively, higher values of

, the real exchange rate response is

imply a larger premium on the country’s borrowing,

for a given level of foreign debt. This translates into larger decline in the adjusted long term real

EP

interest rate and, therefore, a larger depreciation of the real exchange rate. Capital-adjustment-cost parameter ( ) The magnitude of the real exchange rate response to a

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government spending shock displays very little sensitivity with respect to ; as shown by Figure 10. This response in only slightly decreasing with

for relatively large values of

; but is essentially

when monetary policy is moderately aggressive. In other words, the mechanism that gives rise to a real depreciation in our model is robust to larger capital adjustment costs. Autocorrelation of the government spending shock ( g ) Figure 11 shows that the way in which the persistence of the public spending shock a¤ects the exchange rate response depends on the magnitude of the policy parameter, 16

One can also check that

d 2 d

=

@ 2 @

|{z} (+)

+

. For relatively small values of

@ 2 @ 1 @ @

1 |{z} |{z}

> 0:

( ) ( )

22

, this response increases

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0.08

0.06

0.04

SC

0.02

0

10 x 10

5

-3

1.5

γ

1.2

1.1

M AN U

15

1.3

1.4

φ

π

EP

0.03

) space.

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Figure 9: Initial response of the real exchange rate in the ( ;

0.02

AC C

0.01 0

-0.01

0.1

0.08

1.1 1.2

0.06 1.3

0.04 ξ

0.02 1.5

1.4 φ

π

Figure 10: Initial response of the real exchange rate in the ( ;

23

) space.

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0.1 0.08 0.06 0.04 0.02

SC

0

1.1

0.9

1.2

0.8

1.3

0.7

1.4 1.5

φ

π

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0.6 ρ

g

Figure 11: Initial response of the real exchange rate in the

17 g,

monotonically with negative for values of

g

but for larger values of

g;

space.

, the relationship becomes non-monotonic, being

that are less than 0:9 and positive for larger values: Again, this means that

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one can obtain a depreciation of the real exchange rate in response to a positive public spending shock even with an aggressive monetary policy, provided that the shock is su¢ ciently persistent. Alternative speci…cation of the utility function The model presented above predicts that consumption is crowded out following an increase in public spending, except in the special case

EP

where the real interest rate is held constant. Several empirical papers, however, …nd that consumption increases following an expansionary government spending shock. In what follows, we show that allowing for an alternative speci…cation of consumer preferences whereby public spending increases

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the marginal utility of private consumption (i.e. public and private goods are Edgeworth complements) can generate a crowding-in of private consumption in response to a positive government spending shock,18 without altering the mechanism that gives rise to a real depreciation. To see this, assume that the representative consumer maximizes the following lifetime utility: ! 1 1+1= X `s s t ; (42) Et ln (cs gs ) ! 1 + 1= s=t 17

In the special case of no intertemporal substitution ( = 1); this can be clearly seen from Equation (35) and the expression of 2 . 18 The idea that Edgeworth complementarity between private and public spending can cause private consumption to rise in response to an expansionary government spending shock has been suggested by Bouakez and Rebei [2007].

24

ACCEPTED MANUSCRIPT

where

is a parameter satisfying the condition 0 <

<

1

. The fact that

is positive ensures that

the marginal utility of consumption is increasing in g (i.e. c and g are edgeworth complements). In this case, Equations (C1) and (C9) are replaced by, respectively

w bt =

1

1

1

(1 + )

Et gbt+1 )

(b gt b ct

1

(1 + )

1

(1 + )

bt R

1 1

gbt +

Et bt+1 ;

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b ct = Et b ct+1

n bt ;

(43) (44)

whereas Equations (C2)–(C4) and (C10)–(C14) remain unchanged. In the special case where we

SC

abstract from uncertainty and where the monetary authority changes the nominal interest rate one for one with expected in‡ation, the resulting constancy of the real interest rate implies that the marginal utility of consumption remains constant, which by Equation (43) implies that

1

gbt :

(45)

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Since

b ct =

1

> 0, an increase in government spending raises private consumption by an amount that

increases linearly with . Equations (C2), (C3), (C12) and (45) yield again a two-equation system that allows us to solve for net foreign assets and the real exchange rate independently of the rest of the variables

1b bt 1

= qbt

TE D

bb t

(1 + ) gbt ;

qbt = bbt :

qbt+1

(46) (47)

The equilibrium path of the real exchange rate is again given by Equation (35), where given by

=

EP

2

1

(1 + )( ( g

2

is now

) > 0: )

1 1

That is, the real exchange rate depreciates following an expansionary government spending shock, increases (that is, as edgeworth

AC C

and this depreciation is larger the larger is . Intuitively, as

complementarity between private and public expenditures becomes stronger), the outward shift of the BOP curve exceeds that of the IS curve by a larger amount.19 This leads to a larger increase in output and a stronger depreciation of the real exchange rate, which are both necessary to accommodate the increase in private consumption. 19

Note that the IS and BOP curves are now characterized by the following two equations, respectively: ybt

ybt

= =

+

1

1b bt 1

+

qbt + (1 + ) (1 1

1

+

1

25

) gbt ;

qbt +

2 g

(1 + ) 1

gbt :

ACCEPTED MANUSCRIPT

3.4

Testing the model

Is the model’s main implication— that a country’s currency is more likely to depreciate in real terms the less aggressively monetary policy reacts to in‡ation— consistent with the data? To answer this

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question, we empirically evaluate the response of the real exchange rate to an increase in public spending in two sub-periods: before and after the adoption of in‡ation targeting. The argument underlying this exercise is the widespread belief that countries that have adopted in‡ation targeting regimes have become more aggressive in …ghting in‡ation.20 Since the four countries considered in our empirical analysis adopted in‡ation targeting in the early 1990s, with Australia being the

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latest to do so in 1993Q3, we split the sample at 1993Q4 and estimate separate panel SVARs for

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the periods before and after that date. The results are depicted in Figure 12.

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Figure 12: Dynamic response of the real exchange rate to a positive government spending shock before and after the adoption of in‡ation targeting. Notes: The …gure shows the dynamic response of the real exchange rate to a one-standard-deviation government spending

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shock, obtained from a panel SVAR using data from Australia, Canada, Sweden, and the United Kingdom, estimated over the sub-samples 1975Q1–1993Q4 (left panel) and 1994Q1–2013Q4 (right panel). The solid lines are the estimated responses and the dashed lines delimit the 95 percent con…dence intervals. A positive response indicates a real depreciation. The series included in estimation are public spending, output, the long-term nominal interest rate, the current account, and the real exchange rate. Data construction and sources are described in Appendix A. For each sub-sample, the lag length indicated by the Schwarz and Hannan-Quinn information criteria is 1. The government spending shock is identi…ed via a recursive scheme whereby public spending is predetermined with respect to all the remaining variables included in the SVAR.

20

This belief is corroborated by the observation that the mean and the volatility of in‡ation have declined signi…cantly in countries that have adopted in‡ation targeting.

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The …gure shows a stark di¤erence in the response of the real exchange rate to a public spending shock across the two sub-samples. In the period preceding in‡ation targeting, the real exchange rate depreciates sharply and persistently following an increase in public expenditures, and this

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depreciation remains statistically signi…cant for several quarters after the shock. In contrast, after 1994, the real exchange rate depreciates on impact but appreciates during the subsequent six quarters relative to its pre-shock level. Quantitatively, however, the response is relatively small and statistically insigni…cant at all horizons. The result that an expansionary public spending shock leads to a larger real depreciation before than after the adoption of in‡ation targeting might

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be viewed as suggestive evidence that the explanation put forward in this paper is empirically plausible.

Conclusion

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4.

Empirical studies conclude that the real exchange rate depreciates sharply after an expansionary public spending shock. This paper has shown that a sticky-price small-open-economy model with incomplete and imperfect …nancial markets can account for this empirical regularity, at least qualitatively, provided that monetary policy is not too aggressive in …ghting in‡ation. Admittedly, however, the magnitude of the real depreciation implied by the model is small in comparison with

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that documented in the empirical literature. Nonetheless, the mechanism highlighted in this paper can be viewed as a step forward towards a successful quantitative account of the e¤ects of …scal policy shocks on the real exchange rate. A quantitatively successful model would probably involve combining this mechanism with the alternative ingredients suggested by the literature cited in the introduction, namely, elastic labor supply, deep habits, and a non-Ricardian framework

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with realistic …scal-policy rules, potentially allowing for public spending reversals. Such a model should account not only for the conditional response of the economy to …scal policy shocks but also for the unconditional moments of the data, and in particular for the cyclical properties of public

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spending and taxes and for the high volatility and persistence of the exchange rate, a feature that open-economy macroeconomic models usually fail to replicate.

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Appendix A. Data Description and Sources

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The series used to estimate the panel SVAR discussed in the introduction and in Section 3.4 are constructed as follows. Output is measured by real GDP. The long-term nominal interest rate is the nominal rate of return on 10 year government bonds. The current account is expressed as a percentage of GDP. Government spending is measured by real public consumption expenditures. These series are taken from Economic Outlook No. 94, released by the Organization for Economic Cooperation and Development (OECD). The real exchange rate is de…ned as the consumer price index-based real e¤ective exchange rate, released by the OECD Main Economic Indicators. Output and government spending are expressed in per capita terms by dividing them by total population, which is taken from Datastream. All series, except the long-term interest rate and the current account, are expressed in logarithm. The sample period is 1975Q1–2013Q4. B. Steady State

The steady state is characterized by the following equations: R = 1= ; z = 1= 1

n=!

;

!

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mc = w=

1+ ;

z'

+1

w

'

+1

1

'

w 'z

'

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w n; 1 'z ' w y= 1 'z i = k; w c = n 1= : !

(B2) (B3)

1 1 '

;

(B4)

'

(1

)

' 1

w 'z

+1

;

(B5) (B6)

'

n;

(B7)

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k=

')1

1 '' (1

(B1)

(B8) (B9)

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C. Log-Linearized Model P

Et bt+1 )

bt (R

Et bt+1 )

c i b ct + bit + gbt + y y 1 (1 ) (1 ) = Et bH;t+1 + mc ct + 1b bt 1

b kt = (1

+ ybt

)b kt

1

+ bit ;

bit = Etbit+1 + b kt

mc ct = w bt + n bt ybt ; b mc c t = zbt + kt 1 ybt ; w bt = b ct +

bt = bH;t +

n bt ;

1 ybt = 'b kt 1 + (1 ybt = (1

bt = R

b

r Rt 1

bt 1 gg

1) ;

') n bt ;

c i b ct + bit + gbt y y

+ (1 +

qbt

g t:

+

r)

2 1

Et bt+1 ;

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gbt =

)

(b qt

qbt ;

qbt ;

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qbt +

c i b ct + bit + gbt y y

(C1) (C2) (C3) (C4) (C5)

Et b ct+1 + zEt zbt+1 ) ;

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1

1 b kt + (b ct i

1

1

bb ; t

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bb = t

bH;t

Et bt+1 );

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bt (R bt qbt = Et qbt+1 + (R b ct = Et b ct+1

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t+1 De…ning t PPt+1 and t Pt as the domestic and foreign gross in‡ation rates; the log-linearized t model is given by the following equations:

(C6) (C7) (C8) (C9) (C10) (C11) ;

(C12) (C13) (C14)

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D. Estimation of the Debt-Elasticity of the Interest Rate Di¤erential ( )

Rt

Et

"t+1 R e "t t

bt

= 0:

from the following simpli-

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Consistently with earlier empirical studies, we estimate the parameter …ed version of …rst-order condition (7):21

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bt We estimate this equation using GMM by exploiting the orthogonality of the term Rt "t+1 "t Rt e with respect to the information set available up to time t. More speci…cally, we build three moment conditions involving lagged exchange rate depreciation rates as instruments. Because there is only one parameter to estimate, an over-identi…cation test can be performed. In evaluating the moment conditions, we measure Rt and Rt by the domestic and U.S. three-month treasury bill rates, respectively, "t by the nominal exchange rate against the US dollar, and bt by net foreign assets as a percentage of GDP. The series are measured at a quarterly frequency and cover the period 1988Q3–2013Q2 for Australia and the United Kingdom, 1990Q3–2012Q3 for Canada and 1998Q4–2013Q1 for Sweden. The sample periods are determined by the availability of the time series of net foreign assets.22 Estimation results are reported in Table 2. The point estimates of are all positive and statistically di¤erent from zero at any conventional level of signi…cance. They range from 0:0016 for Canada to 0:015 for Sweden. Importantly, the estimated equation does not seem to be misspeci…ed as the p-values for the over-identi…cation test exceed 0.80 in all cases. These results support the hypothesis that the interest rate di¤erential is increasing in the stock of foreign debt.

Table 2: Estimation Results

Country Australia

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Canada Sweden

(0:000089)

J stat 0:2307 [0:8911]

0:0016

0:2881

0:0146

0:3894

0:0060

0:3660

(0:000071) (0:00032) (0:000831)

[0:8658] [0:8231] [0:8323]

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United Kingdom

Estimate of 0:0051

Notes: Figures between parentheses are standard errors. Figures between brackets are p-values. Under the assumption that the model is correctly speci…ed, J-stats are distributed as a 2 2:

21

Note that the simpli…ed …rst-order condition leads to the same log-linearized equation as (7). Net foreign assets are taken from the Australian Bureau of Statistics (Australia), Statistics Canada (Canada), Datamarket.com (Sweden) and the United Kingdom O¢ ce for National Statistics (United Kingdom). The remaining series are taken from the OECD Economic Outlook Database. 22

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