Fiscal Transfers in a Monetary Union with Sovereign Risk

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1 Fiscal Transfers in a Monetary Union with Sovereign Risk Guilherme de Almeida Bandeira June 17 Abstract This paper investigates the welfare and economic stabilisation properties of scal transfers schemes between members of a monetary union subject to sovereign spread shocks. The schemes, which consist of cross-country transfer rules triggered when sovereign spreads widen, are incorporated in a two-country model with nancial frictions estimated for Portugal and the Eurozone. The model is well suited to study shocks consistent with the sovereign debt crisis that aected the Periphery of the Eurozone. It is shown that, when domestic scal policy is carried through lump sum taxation, scal transfers are both welfare improving and reduce macroeconomic instability. However, asymmetries in the conduct of domestic scal policy can tilt the distribution of welfare gains between the two countries. On the contrary, when domestic scal policy is distortionary, scal transfers might cause welfare losses, despite stabilising the economy and reducing the scal adjustment required in the aftermath of sovereign spread shocks. JEL Classication: E6, F15, F41, F4, F45. Keywords: sovereign risk, banks, monetary union, scal transfers. 1 Introduction The debate over the architecture of a robust monetary union attracted renewed interest during the recent sovereign debt crisis in Europe. The asymmetrical nature of sovereign interest rate shocks, coupled with the inherent constraints they pose on domestic scal policy, exposed a painful fault Banco de España, dealmeida.bandeira@gmail.com This paper does not represent the views of the Bank of Spain or the Eurosystem.

2 in the design of the Euro area. This fault concerns the lack of adequate mechanisms to facilitate the adjustments of individual member states facing idiosyncratic shocks. As seen during the crisis, soaring sovereign spreads forced a number of countries, including Greece, Ireland, Italy, Portugal and Spain, to undertake sudden scal consolidations while implementing deep structural reforms. The dramatic economic toll of the crisis and the dubious response from the monetary union called into question the irreversibility of the common currency. This paper proposes and estimates a model of a monetary union where sovereign spreads aect private borrowing costs due to nancial frictions. The contribution to the current debate is twofold. First, the model is designed to provide a consistent narrative of the events that occurred during the sovereign debt crisis, introducing the link between sovereign spreads and the banking sector which was a root cause for the contraction in the supply of credit to the economy. The model also oers a useful framework to understand the need for scal adjustment during the crisis, demonstrating how scal consolidation is aected by the responsiveness of sovereign spreads to the scal stance and by the ratio of public debt to GDP. Second, this paper presents an assessment of the potential benets that scal transfers between member states have in terms of welfare and economic stability. Equipped with the appropriate model, it describes two alternative transfer schemes, discusses the importance of domestic scal conditions for the design of such schemes, and explains how the conduct of scal policy at the member states level can aect the macroeconomic outcomes of a federal scal arrangement. During the sovereign debt crisis, the fall in government bond prices and the down-grading of these assets by credit rating agencies severely weakened the balance sheets of banks. As a consequence of their exposure to sovereign risk, banks' ability to raise market-based funding was adversely aected. This increase in borrowing costs forced banks to strengthen their equity ratios and, in the process, to sharply reduce overall credit provision to rms and to raise lending rates. Credit scarcity dampened investment, which ultimately resulted in the recession. To capture this mechanism, nancial intermediaries are introduced in an otherwise standard two-country general equilibrium model of a monetary union. In the model, banks take short-term deposits from households and make long-term loans to rms and to the government. An agency problem between banks and their depositors forces the former to moderate their leverage ratios in order to attract deposits. Moreover, because banks hold sovereign bonds in their portfolios, their net worth is exposed to sovereign risk. In good times, the sovereign obtains funds at the risk-free interest rate. However, a spread can arise on top of the risk-free rate reecting the credit worthiness of the government. This deteriorates the equity value of banks and forces them to contract credit and to raise lending rates at the same time as they retain funds to build up their net worth. In the model, for a ratio of public debt to GDP of 6%, a 1% increase in sovereign spreads leads to an increase of about 3.5% in the interest rates charged to rms. The pass-through is reinforced when the public debt-to-gdp ratio equals 1%, with interest rates on private lending rising 7.5%. Together with the increase in borrowing costs, the drop in the supply of credit to rms causes investment to drop sharply and sparks a recession. At the trough, real GDP falls between % and 6%, depending on the size of the public debt-to-gdp ratio. These eects are magnied when sovereign spreads respond to the scal outlook, and more so for higher public debt-to-gdp ratios. The size of this ratio and of the feedback loop also have implications for scal policy.

3 With soaring spreads, the consolidation eort required to stabilise the scal stance is intensied for higher debt ratios and when spreads are more responsive. This is true for lump sum taxation as well as for distortionary scal policy. Moreover, because distortionary policy reinforces the fall in economic activity, raising consumption taxes or cutting productive or utility-enhancing public spending requires the scal adjustment to be larger. Completing the EMU with a federal scal arrangement is hardly a novel idea in policy and academic circles. At the time when its design was being discussed, it seemed clear that a system of scal transfers crafted to countervail idiosyncratic shocks would be crucial for the success of the single currency. 1 of optimal currency areas. The arguments in support of a transfer mechanism drew directly on the literature With the creation of the EMU, member states would no longer be able to use monetary policy or the exchange rate to buer country-specic shocks. Moreover, to the extent that production factors are immobile across countries and movements in nominal prices and wages are slow, scal policy becomes a key instrument to fuel the necessary adjustments. With this in mind, the Maastricht Treaty incorporated limits on budget decits and public debts in order to preserve sound domestic scal stances able to react when needed. Yet, the political process aimed at endowing the union with an area-wide scal capacity lay dormant for decades until the sovereign debt crisis, when domestic scal policies failed to operate the required adjustments. Faced with the inability of the EMU to respond adequately and promptly, policy leaders have recently sketched a road map towards the creation of an area-wide scal stabilization capacity. 3 examines the design, implementability and quantitative eects of a federal scal capacity. The present paper Two transfers schemes are studied: one has governments engaging in non-repayable transfers, with the government making the transfers funding them through the domestic public budget. The other scheme assumes that governments are called upon to repay the transfers they receive, but under better nancial terms than in market conditions. Both schemes are shown to have the potential to increase welfare in the two regions of the monetary union, with gains approaching 1% of life-time consumption and being relatively higher when transfers do not have to be repaid. Fiscal transfers reduce macroeconomic instability, with GDP, consumption, labour and ination volatility being reduced. When the public debt-to-gdp ratio is higher, sovereign spreads are responsive to movements to the scal stance, or when scal policy acts more quickly against those movements, scal transfers can secure higher relative welfare gains. However, the distribution of welfare gains between the two countries might not be symmetric. In fact, the asymmetry in welfare gains between countries can be a problematic factor to the implementation of scal transfers. Simple exercises show that, by changing domestic scal policy unilaterally after the agreement on a scal transfer scheme is closed, a government can tilt the distribution of welfare gains. While scal transfers can improve welfare when governments use lump sum taxation to target the scal stance, the same is not true when scal policy is distortionary. In this case, and despite the ability of scal transfers to reduce the magnitude of distortionary scal adjustments in recipient countries, the negative eects of funding the scheme cause welfare to fall. It is shown, 1 See, for instance, the MacDougall report (European Commission, 1977) as well as the Delors (1989) report. See the seminal articles by Mundell (1961), McKinnon (1963), and Kenen (1969). 3 The 5 Presidents Report (Juncker et al., 15) is the last high level policy contribution. It draws on and updates earlier proposals, namely by Van Rompuy et al. (1). The proposed mechanism, to be implemented before 5, is to be deployed when domestic scal policy cannot, on its own, counteract large asymmetric shocks. See also IMF (13) for discussion. 3

4 however, that scal transfers under distortionary domestic scal policy can still be used to stabilize the economy. For instance, when the domestic scal instrument is consumption taxation or the provision of utility-enhancing public goods, scal transfers can reduce the volatility of GDP, labour and ination, but not the volatility of consumption. On the contrary, when the provision of a productive public good is the scal instrument available to member-state governments, scal transfers have the potential to reduce the volatility of all these variables, even if reducing welfare. The aftermath of the sovereign debt crisis reopened an intense discussion over the design and implementation of a supra-national scal mechanism to aid individual member states to cope with large and idiosyncratic shocks. Unlike in previous occasions, when such a scheme was eventually dropped, it appears that the consensus among European leaders and policy makers is moving towards its construction in the near future. It is, therefore, crucial to assess the impact such mechanism can have and investigate under which conditions its implementation can succeed. This paper provides a contribution in that direction. Literature: This paper is related to two strands of the literature. On the one hand, it extends the literature on the implications of sovereign spreads for economic stability. Schabert and van Wijnbergen (11) and Bonam and Lukkezen (13), for instance, focus on the interactions between scal, monetary, and exchange rate policies, in an environment where sovereign spreads are introduced as a preemptive game between the government and speculators. The parsimonious way they model sovereign spreads is also used in the present paper. Corsetti et al. (1) study how the sovereign risk channel exacerbates cyclical shocks in an environment where monetary policy can be constrained at the zero lower bound and analyse the eects of scal retrenchment in alleviating macroeconomic uctuations. Bocola (13) and Pancrazi et al. (14) investigate the pass-through of sovereign risk to private lending rates and evaluate the eectiveness of asset purchases by the central bank in stabilizing real activity. Kollmann et al. (13) introduce a banking sector with capital requirements into an open economy model and investigate whether government provision of support to banks can stabilize the economy. The present paper draws on this literature of the pass-through of sovereign risk. On the other hand, this paper contributes to the literature on federal scal arrangements within monetary unions. There is a growing literature on optimal policy and international coordination using domestic scal instruments for countries sharing a common currency. 4 However, less attention has been given to federal scal schemes. Among the exceptions, Farhi and Werning (1) show that scal transfers can improve risk sharing even in an environment with complete asset markets. Costain and de Blas (1) compare scal policy rules that stabilize public debt through either income taxation or spending on wages and unemployment benets and nd that a policy of pro-cyclical spending on wages and transfers decided by a federal agency brings the market economy closer to the planner's solution. Kletzer and von Hagen (), Evers (1) and Kim and Kim (13) investigate dierent federal transfers schemes and their potential to achieve welfare gains for members of a monetary union. Building a model in which the banking sector and sovereign debt crisis interact, the present paper extends this literature by highlighting an important channel for scal policy in a currency area and showing that federal scal arrangements can stabilize the economy. 4 Evers (1) and Pappa and Vassilatos (7) provide references. 4

5 The remainder of the paper is structured as follows. The next section describes the model economy, motivates the non-standard features that have been introduced to match the sovereign debt crisis observed in the Periphery of the Eurozone, and summarizes the results of the estimation of the model. Section 3 starts with the analysis of the transmission of sovereign spread shocks, investigating the dierences generated by alternative scal instruments governments can use to stabilise the scal stance. It then proposes two transfer schemes between countries and discusses their welfare and economic stabilisation properties when governments use lump sum taxation. Finally, the analysis of the welfare and stability outcomes of the transfer schemes is extended to when domestic scal policy is distortionary. Section 4 concludes. The Model This section lays out a general equilibrium model of a monetary union. The union is composed of two open economies with habits in consumption, sticky prices and wages, nancial frictions, and investment adjustment costs. The two countries, which will be referred to as Periphery and Core, are of sizes n and 1 n, respectively. Households in each country deposit their savings in domestic banks and provide labour to domestic producer rms. Households in one country can also trade non-contingent bonds with households in the other country. Banks serve as nancial intermediaries between domestic households and domestic borrowers. They sell long-term loans to wholesale rms and to the government, but have their intermediation activity constrained by their leverage ratios. Each country produces a continuum of tradeable intermediate goods that are aggregated into a nal non-tradeable good, with the latter being consumed by households, the government, and used for investment. Each national government can raise taxes and issue long-term bonds to nance public expenditure, while the area-wide central bank sets the nominal interest rate according to a feed-back rule targeting aggregate ination and output growth. The following subsections describe the economy of the Periphery in more detail. The description of the Core is omitted for brevity since its structure is analogous to the Periphery. All variables are in per capita terms, the conventional denotes foreign variables or parameters (i.e., those of the Core), and the subscript h (f) denotes goods produced in the Periphery (Core) and respective prices..1 Households There is one innitely lived household composed of a continuum of measure 1 of household members: a fraction 1 f are workers and a fraction f are bankers. The former supply labour to non-nancial rms and receive wages, while the latter manage a nancial intermediary for prots. Household members switch between the two occupations but keep the relative proportion of each type constant. While a banker remains active in the following period with probability λ f, a fraction (1 λ f ) f of bankers retire and become workers. Conversely, each period the same number of workers randomly become bankers. Household members are assumed to pool consumption risk perfectly. Their life-time utility 5

6 is given by: E β t u (c i,t, l i,t ) for i [, n] t= with instantaneous utility of the form: u (c i,t, l i,t ) = log (c i,t ϱc t 1 ) ζ (l i,t) 1+ϕ 1 + ϕ E denotes the expectations operator conditional on the information available up to t = and β (, 1) is the household's discount factor. Households derive utility from consumption, which is subject to external habit formation ϱ (, 1), and disutility from labour, where ϕ > is the inverse elasticity of labour supply and ζ > its relative weight. Households can deposit their savings with domestic banks and can trade foreign bonds in international nancial markets. The budget constraint of the household, in real terms, is given by: c i,t + b i,b,t + e t r f,t 1 b i,f,t 1 w i,t l i,t + r h,t 1 b i,b,t 1 + e t b i,f,t Ψ (e t b i,f,t ) + V t T t (1) where b i,b denotes deposits with domestic banks, which pay the real interest rate r h,t 1, and b i,f denotes bonds traded with households abroad and which pay the real interest rate r f,t 1. For ease of exposition, the budget constraint is written such that b i,b > implies positive savings from the households, while b i,f > implies that the household is a net borrower in international markets. The term Ψ ( ) denotes convex costs incurred on holdings of bonds traded in international markets. As a consequence of being in a monetary union, the nominal exchange rate between the two countries is xed and therefore the real exchange rate, e t, is simply equal to the ratio of consumer prices in each country. Households receive labour income, at the real wage rate w i,t, real prots from rms, which is denoted by V t, and pay lump-sum taxes to the government, T t. The rst-order conditions for consumption and for nancial asset holdings are: 5 ς t = 1 c t ϱc t 1 () 1 = βλ t,t+1 r h,t (3) 1 = βλ t,t+1 e t+1 e t r f,t 1 Ψ (4) where ς t is the multiplier on the budget constraint and Λ t,t+1 = ς t+1 /ς t is the ratio of marginal utilities of consumption between t and t + 1. Nominal wage rigidities are introduced as in Erceg et al. () by assuming that households are monopolistic suppliers of dierentiated labour services, having market power to negotiate wages with intermediate good producers. In turn, intermediate good producers use a composite labour 5 The subscript i has been dropped since, due to perfect risk sharing, the rst-order conditions are common across household members. 6

7 input in production, l t, which they obtain by aggregating the dierentiated labour services according to: l t = ( n ) µw (l i,t ) µw 1 µw 1 µw di The demand curve for labour services from household i is thus given by: l i,t = ( wi,t w t ) µw l t (5) where w i,t is the real wage household i charges in order to supply l i,t, and the real price index of the ( 1 1/(1 µw) composite labour input is given by w t = (w i,t) di) 1 µw. The elasticity of substitution between labour services supplied by dierent households is given by µ w. In each period, only a fraction 1 λ w of households can re-optimize their posted nominal wage. When able to so, household i solves: Max w i,t E t s= ( ) 1+ϕ ] (βλ w ) [log s li,t+s t (c i,t+s ϱc t+s 1 ) ζ 1 + ϕ subject to (1) and (5). The rst-order condition with respect to the optimal nominal wage, w t, is given by: [ E t (βλ w ) s ς t+s l i,t+s t s= w t P t+s τ w τ w 1 ζ ( ) ϕ ] l i,t+s t ς t+s = (6) where l i,t+s t (w t /w t+s ) τw l t+s is the labour supplied in period t + s for those households that last negotiated their nominal wage at t.. Banks The banking sector described in Gertler and Karadi (11) is extended in this paper, with banks also providing funds to the government. Banks raise deposits from domestic households and lend to domestic non-nancial rms and to the government. It is assumed that the domestic banking sector holds the total amount of public debt issued by the government. As in Lama and Rabanal (14), bankers do not engage in cross-border deposits or investment activities. I motivate these two assumptions with the following stylized facts. In 11, at the height of the sovereign debt crisis, around 8% of sovereign debt claims on countries in the Periphery of the Eurozone were held by domestic banks. Moreover, domestic government bond holdings in the Periphery accounted for 93% of banks' equity. This home bias in sovereign bond holdings, although not as high, was also present in the Core of the monetary union. These gures had been markedly rising since 9. On the other hand, national banks represented roughly 75% of external nancing to domestic private rms. Consistent with the theory proposed in this paper, when sovereign spreads started to widen in the Periphery, from 8 to 13, the volume of newly issued loans fell by more than 5%. 6 6 The gures are taken from Uhlig (13), Acharya et al. (14), and Bocola (13). A report by the Bank for International Settlements, BIS (11), provides a comprehensive discussion on the link between sovereign credit risk 7

8 Every period a fraction f of household members, indexed by i [, f], are bankers who run a domestic nancial intermediary. They obtain deposits b i,b,t from other household members and lend funds to wholesale producers and to the government, a i,x,t and a i,b,t respectively. Denoting by n i,t the net worth of nancial intermediary i and by W i,t the total value of its assets, the balance sheet of bank i is then given by: W i,t q x,t a i,x,t + q b,t a i,b,t = n i,t + b i,b,t (7) where q j,t is the relative price of claims a i,j,t. Depositors charge the real interest rate r h,t, whereas banks require a return of r x,t on the loans they make to rms. The interest rate on government bonds, r b,t, is assumed to equal the risk-free rate adjusted by a sovereign credit risk premium δ t+1 : r h,t = E t r b,t (1 δ t+1 ) (8) Rewriting (7), the evolution of bank i's net worth depends on the dierence between earnings on assets and interest payments on liabilities: n i,t = (r x,t 1 r h,t 1 ) q x,t 1 a i,x,t 1 + ((1 δ t ) r b,t 1 r h,t 1 ) q b,t 1 a i,b,t 1 +r h,t 1 n i,t 1 (9) Growth in equity above the risk-free return r h,t depends on the premium (r x,t r h,t ) earned on private lending as well as on the return on sovereign debt. The objective of bankers is to maximize their expected terminal net worth: N i,t = E (1 λ f ) λ s f βs+1 Λ t,t+1+s n i,t+1+s (1) s= To the extent that the expected discounted returns on their assets are higher than the risk-free rate, bankers will want to raise deposits and build their net worth indenitely. However, a moral hazard problem between depositors and bankers limits banks leverage. This occurs because, at any given period, bankers can divert a fraction ι of available assets. Having knowledge of this, depositors can force the bank into bankruptcy, but can only recover the remaining 1 ι of funds. Hence, depositors will only supply funds to the bank if the following incentive-compatibility constraint is satised: N i,t ιw i,t (11) that is, the value of carrying on doing business must be higher than the value of diverting funds. Due to this constraint on the ability of banks to raise external funds, the risk premium on loans to non-nancial rms may be positive. To solve the banker's problem, dene rst the leverage ratio of nancial intermediaries, φ i,t, as: W i,t = φ i,t n i,t (1) and banks funding conditions. Dedola et al. (13) extend the framework of Gertler and Karadi (11) to allow banks to take deposits from foreign households and to lend to foreign rms. 8

9 Guess then that N i,t = ν t W i,t +η t n i,t, where ν t is the marginal value of expanding assets, holding n i,t constant, and η t is the marginal value of the bank's net worth, holding its portfolio W i,t constant. After some algebra, the expressions for ν t and η t are given by: η t = E Ω t,t+1 r h,t (13) ν t = Ω t,t+1 ( (rx,t r h,t ) (r x,t r b,t (1 δ t+1 )) α W t ) (14) where αt W = q b,t a i,b,t /W i,t is the share of government debt in the bank's portfolio and Ω t,t+1, the banker's eective discount factor, is given by: 7 Ω t,t+1 = βλ t,t+1 {1 + θ [η t+1 + ν t+1 φ i,t+1 1]} (15) As shown in Gertler and Karadi (11), when (11) is binding, the leverage ratio becomes constant across to all bankers and equal to φ t = η t ι ν t (16) For positive values of net worth, the constraint binds only if < ν t < ι. With ν t >, it is protable to expand W i,t. However, if ν t > ι, the incentive constraint does not bind since the value from intermediation exceeds the gain from diverting funds. In the equilibria studied in this paper, the incentive-compatibility constraint always binds within a neighbourhood of the steady state. That is, the amount of funds banks can intermediate is limited by their net worth due to the borrowing constraint. Aggregate net worth is the sum of the net worth of existing banks plus the start-up funds of entering banks. Surviving banks carry their total net-worth into the next period, whereas new banks receive a fraction ɛ/ (1 λ f ) of the assets of exiting banks in order to start business. Hence, in aggregate: n t = λ f {[ (rx,t 1 r h,t 1 ) (r x,t 1 r b,t 1 (1 δ t )) α W t 1] φt 1 + r h,t 1 } nt 1 +ɛ {q x,t a x,i,t 1 + q b,t δ t a b,i,t 1 } (17).3 Production Capital producers: Perfectly competitive capital producers buy and repair undepreciated capital from wholesale rms and invest in new capital by purchasing and transforming domestic nal goods. The repaired and newly created capital is then sold to wholesalers as an input to production. The discounted real prot of capital producers, Π CP, is given by: Max z t E t s= β t+s Λ t,t+s {q x,t+s (k t+s (1 σ) k t 1+s ) z t+s } 7 The eective discount rate of bankers diers from that of the households due to the nancial friction. 9

10 where q x,t is the value of one unit of new capital and z t denotes the amount of nal goods invested to generate new capital. Capital producers are assumed to incur adjustment costs when investing in new capital. The law of motion of capital is thus given by: k t = [ 1 ψ ( ) ] zt 1 z t + (1 σ) k t 1 (18) z t 1 with ψ governing investment adjustment costs. Substituting (18) in the objective function of capital producers, the optimal level of investment is given by: 1 = q x,t ( 1 ψ ( zt ) ( zt 1 ψ 1 z t 1 z t 1 ) zt z t 1 ) ( ) zt+1 z +βλ t,t+1 q x,t+1 ψ 1 t+1 z t zt (19) Wholesale rms: Perfectly competitive wholesale rms use the composite labour input and capital in order to produce a homogeneous good. They purchase capital from capital producers at the real price q x,t, and nance their capital acquisition by borrowing from domestic banks. Banks thus need to issue claims a x,t equal to the number of units of capital acquired k t, pricing each claim at the price of a unit of capital. After production, wholesalers sell their capital to capital producers and pay the return r x,t over their loans. The homogeneous good is sold to domestic retailers at the real price p x,t. The production function of wholesale rms is given by: x t = ξ s t (k t 1 ) α (ξ u t l t ) 1 α () where ξ s t is the total factor productivity, ξ u t a drifting labour-augmenting technology common to both countries and α is the weight of capital in production. The demand curve for composite labour services is given by: w t = p x,t (1 α) x t l t (1) Perfect competition imposes zero prots and therefore the ex-post real return paid to banks is given by: r x,t 1 = p x,tαx t /k t 1 + q x,t (1 σ) q x,t 1 () Retail rms: A continuum of retail rms indexed by i [, n] purchase the homogeneous good produced by wholesalers at the price p x,t and dierentiate it into a continuum of retail goods that are sold to nal good rms at home and abroad. Hence, retailer i faces the following demand curve: y i,h,t = ( pi,h,t p h,t ) µp ( yh,t + yh,t ) (3) where y h,t and yh,t denote the aggregate demand for domestic retail goods by the Periphery and the Core, respectively, and where the law of one price is implicitly assumed to hold. Retail rms are 1

11 subject to Calvo price stickiness. Every period, a retailer is able to adjust prices with probability 1 λ p. When retail rms do not re-optimize prices, they simply update them to lagged ination. Retail prices follow: p i,h,t+s p i,h,t+s = p i,h,t (Πs k=1 π h,t+k 1) ϑ with prob. 1 λ p with prob. λ p (4) where indexation is governed by ϑ [, 1], a measure of the extent to which prices adjust to past ination. When allowed to adjust prices, retailer i maximizes the stream of real discounted prots, Π R (i), given by: Max p i,h,t E t s= {[ (βλ p ) s pi,h,t Λ t,t+s p ] x,t+s (yi,h,t+s + y ) } i,h,t+s p t+s p t+s subject to (3) and (4). The numeraire p t is the consumer price index. Solving for the optimal price of retailer i yields: p i,h,t p h,t = µ p E t s= (βλ p) s Λ t,t+s (y i,h,t+s + y i,h,t+s µ p 1 E t s= (βλ p) s Λ t,t+s (y i,h,t+s + yi,h,t+s ) ph,t+s ) px,t+s p t+s ( ph,t p h,t+s (Π s k=1 π h,t+k 1) ϑ) µ p ( ) 1 µp ph,t ( ) p h,t+s Π s ϑ(1 µp) k=1 π h,t+k 1 p t+s (5) Final good producers: Perfectly competitive rms produce a non-tradeable nal good by aggregating a continuum of domestic and foreign intermediate goods. The aggregation technology for the nal good is given by: y t = [(ϖ) 1 γ (y h,t ) γ 1 γ ] + (1 ϖ) 1 γ (τy f,t ) γ 1 γ γ 1 γ (6) where τ (1 n) /n normalizes the amount of imported goods into per capita terms. In the above CES aggregator, the home-bias parameter ϖ denotes the fraction of goods produced at home that is used in the production of the nal good. The elasticity of substitution between home-produced and imported intermediate goods is given by γ. Final good producers maximize prots p t y t p h,t y h,t p f,t τy f,t each period, subject to (6). The resulting optimal demand functions are given by: y h,t = ϖ ( ph,t p t ) γ y t (7) y f,t = (1 ϖ) τ ( pf,t p t ) γ y t (8) The consumer price index, p t, is obtained by plugging in (7) and (8) into (6): p t = [ϖ (p h,t ) 1 γ + (1 ϖ) (p f,t ) 1 γ] 1 1 γ (9) 11

12 .4 Government The government levies lump-sum taxes, T t, and issues sovereign bonds, d g,t, to nance exogenous government expenditure g. Government debt is held by domestic nancial intermediaries, which are assumed to provide the government with the amount of funds it requires. 8 Hence, in the aggregate, the number of claims held by banks must equal the total amount borrowed by the government, a b,t = d g,t. Lump-sum taxation targets the public debt-to-gdp ratio according to: T t = T (s t / s) κτ (3) where κ τ characterises the government's preferences between tax- and debt-nanced expenditure and s t d g,t /gdp t is the scal stance. Similarly to Chatterjee and Eyigungor (13) and Bocola (14), the government is assumed to issue long-term securities. Hence, each period government bonds mature with probability λ b, implying an average duration of bonds of 1/λ b periods. When bonds reach maturity, the government pays back the principal; otherwise investors receive the coupon µ b and retain the right to obtain the principal in the future. The government's ex post budget constraint is therefore given by: (λ b + (1 λ b ) µ b ) d g,t 1 + g t = T t + q b,t (d g,t (1 λ b ) d g,t 1 ) (31) where q b,t is the price of loans to the government. Conversely, the return on government bonds is given by: r b,t 1 = λ b + (1 λ b ) (µ b + q b,t ) q b,t 1 (3) Sovereign credit risk is modelled as in Schabert and Wijnbergen (11) and Corsetti et al. (1). The government's decision not to honour its debts depends on a scal limit above which the scal burden is deemed to be politically unacceptable. 9 Sovereign spreads are generated as the result of a preemptive game between the government and speculators, with the expected probability of default being a determining factor for the dynamics of sovereign bond prices and, consequently, of the net worth of banks. Every period the scal limit is drawn from a distribution with probability distribution function f (s t ). Agents only know f ( ) and form their expectations on that basis, with the probability of default being equal to the probability the scal stance s t exceeds the scal limit. Let (s t ) be a default indicator taking 1 when the draw is above the scal limit, and zero otherwise. As shown in Schabert and Wijnbergen (11) and Bonam and Lukkezen (13), the expectation over 8 The share of government bonds in the balance sheets of banks, α W t, is not an optimizing variable for bankers. Hence, banks do not necessarily build their portfolio optimally or engage in optimal pricing of sovereign bonds. Devereux and Sutherland (7) describe how to implement optimal portfolio choice in an open economy setting, while Dedola et al. (13) apply the same method to their model of banks with cross-border linkages. Kollmann et al. (13) assume instead that banks bear real costs on government and private bond holdings in order to pin down bank's portfolio composition. Regarding endogenous pricing of government bonds, Bocola (13) proposes a model where the government can actually default on its debt. The strategic default literature is growing rapidly after the seminal work by Eaton and Gersovitz (1981), and includes Aguiar and Gopinath (6), Arellano (8), Cuadra and Sapriza (8), among many others. Two recent papers that expand this literature by including a banking sector are Gennaioli et al. (13) and Sosa-Padilla (14). Because default can actually occur in these models, they are suited to characterize strategic default and its distributional consequences to economic agents. 9 Davig and Leeper (1) introduced the notion of scal limit used here. 1

13 the probability of default can be approximated by: ˆδ t = ( Θ/δ ) ŝ t + ε d t (33) where denotes a rst-order log-linear approximation, and where ε d t is an exogenous shock that captures the market's perception of sovereign credit risk. The parameters Θ denotes the elasticity of the probability of default with respect to changes in the scal stance, (s t ) / s t..5 Central Bank The single central bank in the monetary union is assumed to follow a targeting rule by which the nominal interest rate responds to the aggregate consumer price index and to the area-wide real GDP growth: i t = ( i ) 1 ρi ( i t 1 ) ρi ( ( πt π ) ( ) ρg ) 1 ρi ρπ gdp t ε gdp i t (34) t 1 where ρ i (, 1) is the smoothing parameter, and ρ π and ρ g are the usual response coecients. The aggregate variables in the Taylor rule, denoted with a, are the sum of the respective country variables weighted by their population size. The nominal interest rate is given by the Fisher equation: r t = i t π t+1.6 Market Clearing There are two types of markets for goods in each country that must clear in equilibrium. intermediate goods, production by the wholesale rms equals demand by domestic and foreign retailers: ( x t = Υ h,t yh,t + yh,t ) Note that, due to price dispersion, retailers incur real losses during price setting, which is given by Υ h,t. 1 On the other hand, the non-tradeable domestic nal good is sold to households, the government and to capital producers: For (35) y t = c t + z t + g + Ψ (e t b f,t ) (36) is dened as: Holdings of internationally traded nancial assets must also clear, b f,t +b f,t =. Real GDP gdp t = p h,t y h,t + e t p h,t y h,t (37) 1 Expression (35), and the denition of Υ h,t, are obtained from the aggregation of retail production x t = 1 y i,h,tdi. 13

14 with net exports being given by: nx t = e t p h,t y h,t p f,tτy f,t (38) where y h,t are exports of the home-produced retail goods and y f,t are imports of the foreign-produced goods..7 Distortionary Fiscal Policy Actual consolidation measures put forward during the sovereign debt crisis fall outside the category of lump sum taxation. Among the range of distortionary instruments used by European governments, this paper considers three: raising consumption taxes, cutting utility-enhancing public spending or productive public expenditure. As discussed below, the rst two instruments, by directly aecting households decisions over consumption, have the potential to match the response of consumption in the model to the recent experience in the Periphery of the Eurozone. On the other hand, the use of productive public expenditure to stabilise the scal stance is intended to emphasise the link between scal policy and real activity. Only one scal instrument is assumed to be available to the government at one time. The following changes are made to the baseline model to incorporate each new scal instrument: Consumption Tax: With consumption taxation, the government is assumed to tax household consumption at the rate τ c,t. The households budget constraint then writes: (1 + τ c,t ) c i,t + b i,b,t + e t r f,t 1 b i,f,t 1 w i,t l i,t + r h,t 1 b i,b,t 1 + e t b i,f,t Ψ (e t b i,f,t ) + V t T t and the rst-order condition () is replaced by: (39) ς t = 1 (1 + τ c t ) 1 c t ϱc t 1 (4) The government is assumed to hold lump sum taxation and government spending xed. It sets τ c,t in a similar fashion to (3), with κ c determining how quick the tax rate changes in order to stabilise the scal stance. Utility-Enhancing Public Expenditure: Under this scenario, the government uses public expenditure, g t, to consolidate or expand the scal budget in order to smooth out changes to the scal stance. Moreover, government spending consists of a public good that is provided to households. As such, the households instantaneous utility takes the form: u (c i,t, l i,t ) = log ( c i,t ϱ c t 1 ) ζ (l i,t) 1+ϕ 1 + ϕ 14

15 where c i,t is a CES aggregator of private consumption and the public good: c i,t = [ϖ c (c i,t ) γc + (1 ϖ c ) (g t ) γc ] 1 γc (41) with γ c <, so that private consumption and consumption of the public good are complements, while ϖ c accounts for the share of the private good in the consumption bundle. The rst-order condition () is then replaced by: ς t = ϖ c c t ϱ c t 1 ( ) 1 γc ct (4) c t The government follows a rule for g t in line with (3), with κ g calibrating the magnitude of the scal response to movements to the public debt-to-gdp ratio. The government consumes domestic nal goods to produce the public good, does not tax consumption, and holds lump sum taxes xed. Productive Public Expenditure: In this scenario, public spending is assumed to enter the private production of intermediate goods: x t = ξt s (k t 1 ) α (ξt u l t ) 1 α (g t ) χ (43) with χ governing the eect of government expenditure on private production: the higher the value of χ the stronger is the impact of scal policy on the productivity of wholesale rms. As before, government expenditure consumes domestic nal goods. The government sets g t following an equivalent rule to the one used with respect to the previous instrument, does not tax consumption, and holds lump sum taxes xed..8 Estimation Results The model is estimated for Portugal and the Eurozone using Bayesian techniques. In the spring of 11, Portugal became the third Eurozone member-state to request external nance assistance, after Greece and Ireland. At the time, the Portuguese government was facing an unprecedented increase in the costs of nancing public debt, while Portuguese banks were being cut o from market-based funding. When the assistance programme was signed in April, the 1-year yield on Portuguese government bonds was approaching 1%, public debt to GDP was around 11%, and the scal decit had reached 11.% the previous year. With the program, Portugal received 78 billion, or about 43% of GDP, under the conditionality of implementing sharp scal consolidation and pursuing structural reforms. 11 A full description of the estimation strategy and results can be found in the appendix. One period in the model equates to one quarter. During estimation, both governments are considered to only have access to lump sum taxation. Portugal's population represents around 3% of the total of the Eurozone, with the latter's GDP per capita around 1.7 times higher than Portugal's. The share 11 Figures and further discussion about the Portuguese adjustment program can be found in a report by the European Commission of

16 of imports to GDP represents about 3%. Estimation results show that prices are slightly slower to adjust in Portugal than in the Eurozone, taking more than 3 quarters on average. Indexation to past ination seems to be small in both regions, while wage stickiness appears to be signicantly higher in the Eurozone. Habits in consumption are similar in both countries, at around.5, whereas investment adjustment costs are estimated to be higher in Portugal. Although a range of 15 structural shocks were considered during estimation, in the following sections only a symmetric sovereign credit risk shock in each country will be considered. 3 Sovereign Spread Shocks and Fiscal Transfers This section starts by looking at the transmission of sovereign spread shocks in the model and discussing its consistency with the sovereign debt crisis in the Periphery of the Eurozone. The discussion is also focused on the impact dierent scal instruments have on the transmission of these shocks. The following subsection proposes two transfers schemes operated between governments and investigates the welfare and economic stability eects of their implementation. The last subsection extends the analysis of the transfer schemes to when governments use distortionary scal policy to stabilise the scal stance. 3.1 Inspecting the Mechanism Lump Sum Taxation: Figure 1 reports the impulse responses to a shock that raises the sovereign spread in the Periphery by 1% in annual terms, as seen in Portugal during 11. The solid blue line shows the baseline specication, where government debt to GDP equals 6% in the steady state, sovereign spreads do not respond to the scal stance, Θ =, and the government uses lump-sum taxation to manage oscillations of the public debt-to-gdp ratio. The increase in the probability that the government will not service its debt lowers the value of government bonds and, conversely, raises the premium investors require to hold these assets. As interest payments become heavier, the government incurs a budget decit, which raises the stock of public debt. With public debt increasing, taxes are automatically raised. Comparing to the actual decit of 7.4% in Portugal in 11, the jump in the budget decit predicted by the model, of around 1%, seems fairly small. Note however that between 1 and 13, taxes and social contributions fell by more than %, while unemployment benets, pensions, and other nancial liabilities all increased (European Commission, 14). Therefore, the baseline scenario serves as a lower bound in terms of the deteriorating eects of sovereign spread shocks on the government budget. As the price of government bonds plunges, banks, who hold these securities in their portfolios, see their total net worth contract. This triggers a persistent increase in banks' leverage ratios. In terms of magnitudes and recovery time, the model is consistent with actual events. Using the loan-to-deposits ratio as a measure of leverage, the gure for Portuguese banks at the beginning of 11 was equal to 157%. It took 15 quarters to reach 117%, a fall of about 5% and similar to Figure 1. Banks' equity also went through a slow recovery, with the average Core Tier 1 adjusting from 8.1% to 1% over the same period. 1 Due to leverage constraints, banks are forced to reduce 1 Figures taken from European Commission (14). 16

17 Figure 1: Responses to a Sovereign Spread Shock 1 5 r b r (annualized) r x r (annualized) Net Worth Leverage Public Debt to GDP Inflation (annualized) Policy Rate (annualized) Exchange Rate Consumption Investment Labour GDP Θ=.3 Debt/GDP=1% Θ=.3 and Debt/GDP=1% Baseline Impulse responses are expressed in terms of percent deviations from the steady state. lending and to raise the premium on loans to private rms in order to rebuild the value of their equity. In the baseline scenario, the pass-through of sovereign spreads to rm's borrowing costs is more than 1/3, with the increase by 1% in the former leading to a 3.5% increase in the latter. The drop in credit supplied by banks and the increase in borrowing costs induce a collapse in investment of more than 1% at the trough. As rms face higher costs of capital, labour demand also contracts and total employment falls. Consequently, real output falls, reaching a drop of more than % at the trough. The marked contraction in domestic demand due to the fall in investment induces prices to fall. However, given the small size of Portugal relative to the Eurozone, the nominal interest rate is cut by less than 5 basis points, a negligible policy loosening doing very little to buer the recession in Portugal. On the other hand, with lump-sum taxation and the fall in prices, and despite the fall in employment, households increase consumption. This result is at odds with the recent experiences in the Periphery of the Eurozone. In part, this result is due to the fact that households are net lenders in the model. Note, however, that other scal (and distortionary) consolidation measures were implemented during the sovereign debt crisis. These can account for a reversal in the response of consumption, as shown below. Figure 1 also shows three alternative scenarios to the baseline. The dashed dark-grey lines show the responses to the same shock when sovereign spreads respond to the evolution of the scal stance, i.e. for Θ =.3. Compared to the baseline, the responses under this scenario change very little. The solid light-grey lines show instead the case when spreads do not respond to the scal stance, but the steady state debt-to-gdp ratio equals 1% instead of 6%. The doubling 17

18 of this ratio clearly intensies the magnitude of the recession, leading to a fall in GDP more than double of that in the baseline. When domestic banks hold a larger stock of government securities in their balance sheets, a fall in the price of sovereign bonds produces a relatively higher loss in their portfolio. As a consequence, the pass-through to private lending rates reaches more than 3/4, with a 1% increase in the sovereign spread inducing a widening of the private risk premium of more than 7.5%. The resulting collapse in investment and the drop in labour are sizeable too and compare well with actual gures for Portugal: from 11 to 13, investment fell nearly 3%, while the unemployment rate went from 1.% to 17.3%. Finally, the dashed light-grey lines in Figure 1 report the worst scenario, when the public debt-to-gdp ratio equals 1% and sovereign spreads respond to the scal stance, Θ =.3. Unlike when the public debt represents 6% of GDP, having sovereign spreads responding to the scal stance under this scenario generates a bigger recession, with private lending rates jumping more than 8% and GDP falling.5% further. Hence, a high public debt-to-gdp ratio is not only a potential source of economic instability per se, it can also generate sizeable feed-back eects when sovereign spreads respond to the weakening of the scal stance. Moreover, this exercise assumes the standard response of sovereign spreads to be constant for both debt-to-gdp ratios (Θ =.3). However, it is possible that the elasticity of spreads is increasing with the debt-to-gdp ratio. If that is the case, the size of the feed-back eects reported in Figure 1 is rather biased downwards. Distortionary Fiscal Policy: Figure shows the responses of the Periphery to a sovereign spread shock when the government uses distortionary scal instruments. The values of the parameters governing scal policy, κ τ, κ c and κ g, are calibrated such that the increase in the scal stance is capped at 3% under each of the three distortionary instruments as well as under lump sum taxation. By doing so, the consolidation eort is normalized and the feed-back eects of scal policy to the economy are comparable. The remaining parameters are calibrated as follows. The steady state tax rate on consumption is set to %, in line with the case of Portugal before the crisis. productivity of the public good in private production, χ, is set to 1%. Finally, private consumption is assumed to represent ϖ c = 8% of total household consumption, and γ c, which governs the elasticity between private consumption and consumption of the public good, is set to.8 such that they are complements. The solid blue lines in Figure show the baseline, when the government uses lump sum taxation to stabilise the scal stance. The The dashed light-blue lines depict the scenario when the government uses consumption taxation to keep the scal stance to target. In this scenario, the government is led to collect more revenues than in the baseline. In order to reduce the public debt, it raises consumption taxes about 3 percentage points above steady state. This increase in taxes, however, generates a contraction in consumption, with households substituting consumption today for consumption in the future, when taxes are cut back. With the contraction in consumption adding to the contraction in investment, GDP falls further than in the baseline, pushing up on the public debt-to-gdp ration and explaining why revenues have to be raised higher than in the baseline. The solid light-grey lines present the case when the scal instrument used is a public good complementary to private consumption. To curb the increase in the scal stance, public spending has to be reduced, causing again GDP to fall more than in the baseline. Because private consumption 18