Public debt frontiers: The greek case

Public debt frontiers: The Greek case Gonzalo F. de-Córdobay Universidad de Málaga José L. Torres Universidad de Málaga Abstract Using a DGE model where the government is fully characterized, we compute the steady state relationship between the public debt/output ratio and the size of the government, measured as the total public expenditures/output ratio. We …nd the existence of a negative relationship between public debt long-run sustainable limit and government size. Calibration of the model for the Greek economy reveals that, for the period just before the current recession, i.e. 2002-2006, the steady state debt to GDP ratio (the long-run sustainability level) was 236.5%, whereas the observed …gure for the same period was around 100%. Nevertheless, the crisis starting in 2007 provokes fast growth in the total public expenditures to output ratio, driving the Greek economy to the long-run unsustainable-debt region. We conclude that an original …scal indiscipline did not cause the debt crisis and we have to look for alternative causes such as a credit crunch and/or gambling for redemption. We …nd that a gambling for redemption attitude towards the recent crisis triggered the Greek public …nancial disaster by crossing the debt frontier. JEL Classi…cation: H5; H6. Keywords: Fiscal policy, government expenditure, public debt sustainability, gambling for redemption, Dynamic General Equilibrium models. 1 Introduction One of the many derivations caused by the ongoing international …nancial crisis has focused the attention of economists and policy makers on the sovereign debt crisis, which is hitting some countries of the Euro Area with particular intensity. The severity of the debt crisis starting in 2008 and its disastrous potential consequences We thank J. Pérez, J. Rodríguez, D. Pontikakis, T. Kehoe and the participants at the 2011 S.A.E.T. meeting in Faro, (Portugal) for their helpful comments and suggestions. The authors acknowledge …nancial support from Proyecto de Excelencia Junta de Andalucia P07-SEJ-02479. yI want to thank Pedro Martín and the sta¤ of Bonsabor for helpful comments and …nancial support. 1 have fueled a debate where di¤erent measures have been proposed to prevent a similar crisis in the future and to provide stability to the European currency union. Those proposals can be summarized in two categories: economic reforms to provide long-term stability and zero budget de…cits, and automatic economic and political sanctions for de…cit sinners, to provide short-term stability. These proposals made by European leaders have been endorsed by the European Commission led by Barroso and the European Council led by Van Rompuy, and seem to be the most fundamental part of a comprehensive solution package to solve the European crisis. Other proposals such as the creation of a Eurobond or the increased involvement of the European Central Bank acting as a lender of last resort have also been discussed. However, such economic policies have important caveats: they would imply huge transfers of income from the North to the South, are legally dubious according to the Treaty and the statutes of the ECB and consequentially, these proposals have encountered enormous resistance from several Member States regarding their implementation. A reverse-engineering of the proposed solutions for the European debt crisis shows that the origins of this crisis can be found in i) A crisis of imbalances, caused by the weak competitiveness of peripheral Europe, and ii) A …scal crisis, due to either direct …scal indiscipline in the cases of Portugal and Greece, and irresponsible …nancial policies that triggered excessive …scal guarantees, as in the cases of Ireland and Spain. The question we want to study in this paper is whether the current European …scal crisis is a consequence of past …scal indiscipline (as implied by the austerity policies), or a bad response from political leaders pursuing generalized …scal stimulus as providing excessive …scal guarantees. In particular, we want to explore the Gambling for Redemption theory of Conesa and Kehoe (2011), where a …xed and exogenous probability of …scal revenues recovery invites for a gambling not even precluded by the possibility of a bailout. While at times this gambling works, sometimes the bet is lost triggering all aspects of an economic disaster. We test the Gambling for Redemption theory using a diagram where two key ratios of …scal data of a given country are plotted together with a line obtained from the collection of steady states from a general equilibrium model. To provide a clearer idea of the diagram we use, consider the budget equation of a government that cannot resort to money printing: Tt+ (Bt+1 Bt) = Gt+rBt Fiscal revenues plus newly issued debt must …nance current spending plus the service of existing debt at a given exogenous rate. The steady state equation is: Tss Gss =rBss 2 stating that an economy has to generate enough primary …scal surpluses to …nance the service of its debts to be sustainable long-term. If we divide the above equation by the steady state GDP, Yss;we obtain: Bss Yss = r1 r Gss Yss where is just the average steady state tax rate Tss=Yss:This equation, provides a mechanical relation between the two key ratios that we use to test the Gambling for Redemption hypothesis. However, the above equation is too simple. It does not take into consideration the various forms of taxation and expenditures that a government can use. The non-linearities that arise from government interventions in the economy are an important part of our test, and therefore our goal is to model a rich public sector that captures those non-linearities. To this end we construct a DGE model where the role of the government a¤ects a large variety of …scal policies on both sides of the government budget restriction: revenues and expenditures. In our model, total government spending is divided into several variables: public consumption of goods and services; public investment in physical capital; a public wage bill; transfer payments to households; and interest payments of public debt. As we will show in this paper, the amount of total debt is not independent from the spending policies, as di¤erent shares of total government spending have di¤erent e¤ects on …scal income: for example, spending in social transfers does not improve productivity of private factors, whereas increasing public investment does. Therefore, the amount of sustainable debt varies across policies. On the other hand, public revenues are raised by taxation and new debt issuance. We consider the existence of …ve taxes: consumption tax, labor income tax, capital income tax, social security tax and a corporate tax. Additionally, we include the …scal funding of the social security system of the economy as a pay-as-you-go system. As debt is modelled as if bond markets were in…nitely liquid, the term structure of the debt is irrelevant in our model. Any maturing bond can always be rolled over at the given rate in the steady state. This paper attempts to quantify the maximum amount of debt that a government can sustain by assuming that lenders always lend. We do not allow for self-ful…lling crises. These crises arise when lenders think that a government will not repay its debt. If lenders think a government will not repay, they do not lend. If a government cannot roll over the portion of its debt becoming due within a period, it may choose to default even though it would not default if the lenders do lend. This is the idea in Cole and Kehoe (1996, 2000). The maximum level of debt that can be sustained if lenders do not lend is much lower than the maximum that can be sustained if they do lend. Conesa and Kehoe (2011) show that governments with low debt can choose to run this debt up to levels where they risk crises if their country is unlucky enough to be in a recession period after period. 3 This is the idea of Gambling for Redemption. With this assumption of a perfect rolling over of debt, we compute the maximum level of sustainable debt, and provide a picture of the frontier dividing the sustainable region from the unsustainable region for any given level of public expenditure to GDP ratio. We …nd the existence of a steady state negative relationship between public debt/GDP ratio long-run sustainable limit and government size (measured as the total public expenditures/output ratio). We have chosen Greece for our study because it was the …rst country under the currency union to lose its triple A rating on government bonds, and the country has faced strong pressure to consolidate the budget. We carefully calibrate the model to reach the conclusion that Greece was well inside the sustainable debt to GDP ratio when the crisis hit. Then, the government decided not to respond with an immediate reduction in government spending. On the contrary, government spending smoothly kept increasing. The government consumption to GDP ratio increased as a consequence, rapidly driving the economy to the unsustainable region. In the meantime, the recovery didn’t happen. We conclude that a Gambling for Redemption attitude rather than …scal indiscipline is behind the Greek debt crisis drama. The structure of the rest of the paper is as follows: Section 2 presents the model, Section 3 discusses the calibration exercise, the main results from the calibrated model to the Greek economy are shown in Section 4, and …nally, Section 5 concludes. 2 The model We develop a general equilibrium model where the government a¤ects private decisions in a number of ways. We consider the role of taxes, public consumption of goods and services, public investment in public capital, public labor markets and public debt. We …rst describe the behavior of the government, then the …rms, and …nally the households. The government displays a high degree of disaggregation in both expenditures and …scal income sides. On the expenditure side, we distinguish four components: public consumption of goods and services; public investment in capital; public wage bill; and transfers. On the …scal income side, we consider four income taxes (consumption tax, labor income tax, capital income tax and corporate tax) plus revenues from the social security tax. Firms are represented by a CES production function nested within a standard Cobb-Douglas. The production of the …nal output requires four factors: labor services and capital, both private and public. Finally, consumers are modeled in a standard way, but including public goods in the utility function and splitting worked hours between the private and the public labor sectors. 4 2.1 The Government First, we describe the instruments at the government’s disposal with the elements present in the government budget constraint: Gt+RB tBt+ Dt=Tt+RD tDt+CBTt+ Bt(1) Equation (1) says that all cash outlays (including transfer payments to households) - for non-interest total government spending (Gt), interest payments of total government debt (RB ttimes Bt), and new purchases of …nancial assets (Dt) - must be funded by some combination of tax receipts (Tt), interest earnings on government assets (RD ttimes Dt), transfers from the central bank (CBTt), and new debt issuance (Bt). For Eurozone countries, transfers from the central bank are zero, and direct purchases of government bonds are precluded by the Treaty (i.e. CBTt= 0):If we denote by Btthe net position of the government, we can also set …nancial purchases to zero (i.e. Dt= 0): 2.1.1 Government spending Non-interest total government spending is de…ned as: Gt=Cg;t + (1 + ss t)Wg;tLg;t +Ig;t +Zt(2) where Cg;t is public consumption of goods and services, Ig;t is public investment, Wg;tLg;t is the wage bill for public employees and Ztare transfer payments to households, such as welfare, social security or unemployment bene…t payments. We assume that a certain level of public capital is necessary in the aggregate production function. Public investments accrue into the public structures stock. We assume the following accumulation process for the public capital: Kg;t = (1 Kg)Kg;t1+Ig;t (3) which is analogous to the private capital accumulation process. 2.1.2 Government decision rules We need to specify the government decision rules. These decision rules imply the election of i)a certain level of public spending and ii)its distribution among the di¤erent components. The level of government spending in the long run, given a certain amount of …scal revenues, depends on the target level for the public de…cit and public debt. While 5 the Maastricht Treaty1establishes limits together with sanctions for de…cit and debt sinners, these limits have only been respected to enter into the monetary union, but never after that date. Therefore, we do not consider the Maastricht criteria to be binding for these two variables. The distribution among the di¤erent components of public spending is as follows. Cg;t =1Gt Ig;t =2Gt (1 + ss t)Wg;tLg;t =3Gt Zt=4Gt where 1+2+3+4= 1. McGrattan et al. (1997) assume that public spending on goods and services is a stochastic process around a constant proportion of total output. We follow the same framework for the components of total government spending but in a deterministic environment. 2.1.3 Public labor market The public labor market is modeled following the work of Fernández de Córdoba, Pérez and Torres (2012). The purpose of the mechanism described in this section is to distort the labor market to prevent wages equalization between the private and the public sector. An analysis of the public labor market among OECD countries show that the public wage bill is a source of major di¤erences among these countries. Our analysis shows that government interventions in the wage setting of public wages can have a signi…cant e¤ect not only on the wage bill, but also in the growth path of the economy a¤ecting the income shares of private inputs, having therefore a long-term e¤ect on the debt frontier. We have chosen a mechanism where the government has preferences over the number of public workers and their pay. To provide an objective function for the government, we follow a standard text-book approach (for example see Oswald et al., 1The Treaty on European Union was signed on 7 February 1992 by the members of the European Community in Maastricht, Netherlands. The Treaty led to the creation of the euro, and stablished a set of rules imposing control over in‡ation, public debt and the public de…cit, exchange rate stability and the convergence of interest rates. With regard to public …nances it imposed an annual limit of 3% in the ratio of government de…cit to GDP, and a 60% of gross government debt prior to the entry in the European Monetary System 6 19842) and pose an objective function for the government as the solution of a game between a public sector union that cares about the wages of public-sector employees, Wg;t and a government that cares about the level of public employment, Lg;t given its budget constraint. Thus, the government wants to maximize the following objective function subject to a budget constraint: max !W g;t + (1 !)L g;t1= (4) where !is the weight given to wages and is a negative parameter indicating the curvature of the trade-o¤ between the elements present in the objective function of the government. If !is close to zero, then the main goal of the government is to maximize public employment (benevolent government preference), whereas if !is close to one, the main goal of the government is to maximize public wages (public sector union’s preferred option). Note that expression (4) encompasses the di¤erent approaches found in the literature. On the one hand, it takes into account the fact that public employment and wages are determined in an environment di¤erent to the private sector. The government itself can increase the number of public employees or can increase public wages subject to the budgetary constraint. On the other hand, it takes into account the fact that trade unions are more important in the public labor sector than in the private sector (see for instance Blanch‡ower, 1996). As de…ned previously, the government wage bill is de…ned as: 3Gt= (1 + ss t)Wg;tLg;t (5) Maximizing the government objective function subject to the government budget constraint is to …nd critical values for the auxiliary Lagrangian function: $g() = max !W g;t + (1 !)L g;t1= +(3Gt(1 + ss t)Wg;tLg;t) That provides, upon di¤erentiation, the …rst order necessary conditions: @$g() @Wg;t =!W g;t + (1 !)L g;t1=1!W1 g;t (1 + ss t)Lg;t = 0 @$g() @Lg;t =!W g;t + (1 !)L g;t1=1(1 !)L1 g;t (1 + ss t)Wg;t = 0 Dividing orderly: !W g;t = (1 !)L g;t (6) 2On related grounds Ardagna (2007) and Forni and Giordano (2003) consider the wage bill of the government, employment and wages, separately as arguments of the objective function of the government or the public sector union. 7 Combining this expression with equation (5) we obtain that public wages and employment are equal to: Wg;t =! 1!1=23Gt (1 + ss t)1=2 (7) Lg;t =! 1!1=23Gt (1 + ss t)1=2 ;if Wg;t > Wp;t (8) This distribution of the public resources depends on government preferences. However, private and public sectors are competing for the same labour input and as a consequence there is a relationship between public sector and private sector wages inducing a wage premium. The wage premium is implicit in equation (8) and it is part of the solution of the governments problem. This wage premium ensures the government that it’s demand for labor will be satis…ed. This relationship will become clearer once we present the household’s problem. 2.1.4 Tax revenues The government obtains resources from the economy by taxing consumption and income from labor, capital and pro…ts, whose e¤ective average tax rates are denoted by c t; l t; k t;  t, respectively. Additionally, we consider a pay-as-you-go social security system and thus we include the social security tax, ss t. The government budget in each period is given by, Tt=c tCp;t +l t(Wp;tLp;t +Wg;tLg;t) + k t(RtKp)Kp;t1 +k tRB tBt+ss t(Wp;tLp;t +Wg;tLg;t) +  tt where Cp;t is private consumption, Wp;t is private sector wages, Lp;t is private labor, Rtis the rental rate of private capital, Kpis the depreciation rate of private capital, Kp;t is private capital stock, and tare pro…ts to be de…ned later. 2.1.5 The government identity As we previously argued the government budget constraint can be written as: Gt+ (1 + RB t)Bt=Tt+Bt+1 With the meaning that non …nancial spending, plus servicing the existing government debt must be …nanced through taxes plus new debt. Putting together all the elements de…ned above, the government budget constraint can be written as: 8 Cg;t + (1 + ss t)Wg;tLg;t +Ig;t +Zt+ (1 + RB t)Bt =c tCp;t +l t(Wp;tLp;t +Wg;tLg;t) +k t(RtKp)Kp;t1+ss t(Wp;tLp;t +Wg;tLg;t) +  tt+Bt+1 (9) or, collecting uses and resources: Cg;t +Wg;tLg;t +Ig;t +Zt+ (1 + RB t)Bt =c tCp;t +l t(Wp;tLp;t +Wg;tLg;t) + k t(RtKp)Kp;t1 +ss tWp;tLp;t + tt+Bt+1 (10) 2.2 Firms The problem of the …rm is to …nd optimal values for the utilization of labor and capital given the presence of public inputs. The representative …rm operates a CES production function nested within a standard Cobb-Douglas production function, and thus this technology exhibits a constant return to private factors. The production of …nal output, Y, requires labor services, Land capital, K, both private and public. Goods and factors markets are assumed to be perfectly competitive. The …rm rents capital and hires labor to maximize period pro…ts, taking factor prices and public labor and capital as given. The technology is given by: Yt=AtKp p;t1Kg g;t1[L p;t + (1 )L g;t](1pg) (11) where Ytis aggregate output, Atis a measure of total-factor productivity, pand g are private and public capital share of output respectively, measures the weight of public employment relative to private employment and = 1=(1 )is a measure of the elasticity of substitution between public and private labor inputs. If we assume …nal output to be the unit of account, pro…ts are de…ned as: t=AtKp p;t1Kg g;t1[L p;t +(1)L g;t](1pg) (1+ss t)Wp;tLp;t RtKp;t1(12) Under the assumptions that private workers are paid their marginal productivity, we get: (1 + ss t)Wp;t =(1 pg)AtKp p;t1Kg g;t1[L p;t + (1 )L g;t](1pg) L1 p;t Rt=pAtKp1 p;t1Kg g;t1[L p;t + (1 )L g;t](1pg)  9 Table 2: The Greek economy model-calibrated parameters Parameter De…nition Value RBReal return of a Greek bond 0.0405 Discount factor 0.9673 RReal return to capital 0.1005 pPrivate capital income share 0.3184 gPublic capital technical parameter 0.0843 Public-Private employment elasticity of substitution 0.4326 Private employment weight 0.6008 Public wages/employment elasticity of substitution -1.0000 !Public wages weight 0.0765 3Ratio wage bill/total government spending 0.3280 4Ratio transfers/total government spending 0.4052 AFTP 1.4733 Consumption preferences 0.8437 4 The debt frontier Given the calibrated parameters and the key macroeconomic ratios for the period 2002-2006 for the Greek economy, we compute the steady state of the model economy. A key result from the model is the existence of a negative relationship between public debt long-run sustainable limit and government size measured as the total government spending to GDP ratio, given a particular menu of taxes, i.e., a particular level of …scal revenues and given an interest rate on public debt. A larger government size, given a constant level of public revenues, corresponds to a lower long-run sustainable level of public debt. The intuition behind this result is simple. In our model, public debt is modelled as if bond markets were in…nitely liquid and thus, any maturing bond can always be rolled over at the given rate in the steady state. In this context, the long term sustainable amount of debt depends on both public revenues and expenditures and on the public bond interest rate. The sustainable debt limit is increasing in public revenues and decreasing in public expenditure and bond interest rate. A negative shock to output will reduce both the public income/output ratio and the public expenditure/output ratio, driving the economy toward the long-run unsustainable debt area on one hand, and reducing the long-run sustainable amount of debt on the other hand. Our main result is better explained with Figure 4. The decreasing relationship between Public Expenditure to GDP ratio Gt=Yt;and total debt to GDP ratio, Bt=Ytin our notation, separates the space into two disjoint sub-spaces. Above the curve we have all pairs where given the ratio Gt=Yt;the amount of endogenous …scal 16 revenues are not enough to cover the services of total debt. Below the curve, we have all data pairs where …scal revenues su¢ ce to cover the given Gt=Ytratio and services the outstanding debt. [Insert here Figure 4] Two points are highlighted in the graph (blue circles). Both correspond to the observed ratio GSS=YSS = 0:4504 for Greece. The upper point is on the Debt to GDP curve, showing that the maximum level of sustainable debt as a percentage of GDP that Greece can a¤ord given the structure of public expenditures is 236:5467%. The lower point shows the actual level of Debt to GDP ratio at the steady state. As the reader can check, it belongs to the sustainable set. From this point, any reduction of total expenditure improves the credit position of Greece in the international debt markets. The vertical line drawn at Gt=Yt= 0:5423;shows the ratio of total expenditure to GDP that would force Greece to cancel all its outstanding debt. It is clear from the graph that this point is su¢ ciently far away from the actual steady state ratio previous to the crisis. Figure 4 also plots the actual values of both ratios for the period 2002-2011. These ratios, for the period 2002-2006 remain almost constant at a value of total public spending/GDP of 45% and a public debt/GDP of around 100%. We also highlight the "Gambling for Redemption" period, for the years 2007, 2008 and 2009. Whereas the …gures for 2007 are still well inside the long-run sustainable area, the …gures for 2008 are clearly in the unsustainable area. Moreover, the corresponding …gures for 2009 re‡ects an even worse situation, as the public expenditure to GDP ratio reaches a level for which no positive amount of public debt is sustainable. By that time, …nancial markets were clearly betting for a default. From this picture, we conclude that the current …nancial crisis a¤ecting Greece has to be explained by an approach not directly linked to the fundamentals of the economy, as a carefully calibrated standard neoclassical growth model shows. Prior to the crisis, the Greek economy was well inside the long-run sustainable debt area with a public budget carrying with it a constant level of public debt/GDP ratio. Nevertheless, the crisis rapidly deteriorated GDP and public revenues, driving the Greek economy to the long-run unsustainable area. One can argue that the initial value of public debt was too high (around 100% of GDP) and that a lower level of public debt would have increased the strength of the Greek economy to cope with the crisis and remain in the long-run sustainable area. However, looking to the evolution of the Greek economy from 2007, an initial lower level of public debt does not guarantee that it would have avoided the debt crisis, given the evolution of Public Expenditures to GDP. 17 From Figure 4 it is clear that small reductions in the Public Expenditure to GDP ratio induce large increases in the Debt to GDP ratio. The immediate implication is that reductions of expenditure above the expected decrease in GDP, together with an increase in …scal revenues from increased taxation should be enough to guarantee the solvency of the Greek State. Conversely, increases in the public expenditures to GDP ratio deteriorates the credit position very rapidly. The data shows that the swing to the right in the expenditures to GDP ratio from 2006 to 2009 was too large. 5 Conclusions This paper develops a DGE model in which the government is fully characterized in both income and spending sides. The model shows the existence of a negative relationship between public debt long-run sustainable limit and government size, given a particular menu of taxes. As the government size becomes larger, given a constant level of public revenues, the long-run sustainable level of public debt becomes lower. Therefore, the model can be used to quantify for a particular economy, the distance between the current level of public debt and the long-run sustainable level. Calibration of the model for the Greek economy reveals that, for the period just before the current recession, the steady state public debt/GDP ratio (the long-run sustainability level) was 236.5%, whereas the …gure in 2002-2006, the steady state reference, was around 100%. We …nd evidence that a Gambling for Redemption attitude towards the crisis, as in Conesa and Kehoe (2011) and Arellano, Conesa and Kehoe (2012) can explain quite well the path of the Greek economy from 2007. As Conesa and Kehoe (2011) point out, countries that are in deep recessions have the incentive to cut government spending very slowly and increase the public debt, gambling that a recovery in the economy will lead to larger …scal revenues. This argument is consistent with the recent experience of Greece during the period 20072009. Nevertheless, the debt-sustainability problem emerges when the recession is prolonged. In this case, government revenues never recover and the gamble for redemption cannot be maintained inde…nitely, forcing the default. The consequence we extract from this paper is that the government gambled for redemption and lost the bet. Period by period for three consecutive years, the global economy deteriorated, …scal revenues never recovered, and suddenly astronomical bond yields indicated that the game was over. The historically observed frequency of the cycle can entice governments to gamble for redemption with the hope that the next expected expansion will dissolve past …scal de…cits. This implies that the Gambling for Redemption attitude towards a crisis can be the product of our past statistical knowledge of the cycle. It is reasonable, as we argue, and also optimal as Conesa and Kehoe demonstrate, to gamble for redemption when purely statistically based policies are put in place. 18 Once the economic policy that emerges from a Gambling for Redemption strategy is proved incorrect by reality, some structural adjustments have to be put in place. The table in Appendix B shows that policies oriented to increase productivity, together with a …scal package that includes increases in VAT, labor taxes and corporate taxes, plus a re-structuring of public expenditures increasing public investment, at the expense of transfers, can be e¤ective to solve a debt crisis. The proposed combination of increasing by 10% the following vector of policy instruments (k; l; ; 3) would depress output by 3:04%;it would depress private consumption and public consumption by 2:73% and 3:03% respectively, and it would depress private investment by 4:03%;but it would rise the debt ceiling by 48:37%: 19 Appendix A.1: Walras’Law Take the budget constraint faced by the consumer: (1 + c t)Cp;t +Kp;t Kp;t1+Bt+1 Bt = (1 l t)[Wp;tLp;t +Wg;tLg;t] + (1 k t)(Rt)Kp;t1 +(1 k t)RB tBt+Zt+ t And substitute the value of Zt=GtCg;t (1 + ss t)Wg;tLg;t Ig;t to obtain: (1 + c t)Cp;t +Igt +Kp;t Kp;t1+Bt+1 Bt = (1 l t)[Wp;tLp;t +Wg;tLg;t] + (1 k t)(Rt)Kp;t1 +Gt+ (1 k t)RB tBtCg;t (1 + ss t)Wg;tLg;t + t Cpt +Cg;t +Igt +Ipt +Bt+1 Bt =c tCp;t + (1 l t)[Wp;tLp;t +Wg;tLg;t] + RtKp;t1k tRtKpKp;t1 +Gt+ (1 k t)RB tBt(1 + ss t)Wg;tLg;t + t But, the government identity establishes the following relation: (1 + RB t)BtBt+1 =TtGt Direct substitution yields Cpt +Cg;t +Igt +Ipt Tt =c tCp;t + (1 l t)[Wp;tLp;t +Wg;tLg;t] + RtKp;t1k tRtKpKp;t1 k tRB tBt(1 + ss t)Wg;tLg;t + t Government …scal income is given by: Tt=c tCp;t +l t(Wp;tLp;t +Wg;tLg;t) + k t(RtKp)Kp;t1 +k tRB tBt+ss t(Wp;tLp;t +Wg;tLg;t) Substitution and elimination drives to: 20 Cpt +Cg;t +Igt +Ipt =Wp;tLp;t +RtKp;t1+ t+ss tWp;tLp;t From the de…nition of pro…ts we …nd that, t=Yt(1 + ss t)Wp;tLp;t RtKp;t Substitution yields: Cpt +Cg;t +Igt +Ipt =Yt Therefore, Walras’Law is satis…ed at all times. Appendix A.2: Positive pro…ts In a private economy where the government supply capital and labor with market pricing, the …rm would have a pro…t function as:  t=Yt(1 + ss t)(Wp;tLp;t +Wg;tLg;t)Rt(Kp;t1+Kg;t1) Where Yt=AtKp p;t1Kg g;t1[L p;t + (1 )L g;t](1pg)  Under the assumptions that private factors are paid their marginal productivity, we get: (1+ss t)Wp;t =(1pg)AtKp p;t1Kg g;t1[L p;t +(1)L g;t](1pg) L1 p;t (29) (1+ss t)Wg;t = (1)(1pg)AtKp p;t1Kg g;t1[L p;t +(1)L g;t](1pg) L1 g;t (30) Rt=pAtKp1 p;t1Kg g;t1[L p;t + (1 )L g;t](1pg)  Rg;t =gAtKp p;t1Kg1 g;t1[L p;t + (1 )L g;t](1pg)  From the above equations we can obtain all income shares as: 21 (1 + ss t)Wp;tLp;t =(1 pg)AtKp p;t1Kg g;t1[L p;t + (1 )L g;t](1pg) L p;t (31) =(1 pg)L p;t L p;t + (1 )L g;t Yt(32) (1 + ss t)Wg;tLg;t = (1 )(1 pg)AtKp p;t1Kg g;t1[L p;t + (1 )L g;t](1pg) L g;t =(1 )(1 pg)L g;t L p;t + (1 )L g;t Yt RtKp;t1=pYt and Rg;tKg;t1=gYt Pro…ts are zero because of the homogeneity of the production function:  t=Yt(1 pg)L p;t L p;t + (1 )L g;t Yt(1 )(1 pg)L p;t L p;t + (1 )L g;t YpYtgYt;  t=Yt(1 (1 pg)pg) = 0 If, on the contrary, the government pays public factor through taxes, then there are positive pro…ts. Division of equation (29) by (30) yields equation (27) of section 3. Appendix A.3: Equilibrium conditions and de…nition The collection of the model’s …rst order conditions, market clearing and resource constraints are: 22 1 Cp;t +Cg;t t(1 + c t) = 0 (33) (1 )1 NtHLp;t Lg;t +t(1 l t)Wp;t = 0 (34) t+1 1 + (1 k t+1)(Rt+1 Kp)t= 0 (35) t1t(1 + (1 k t)RB t) = 0 (36) LtLp;t Lg;t = 0 (37) YtAtKp p;t1Kg g;t1[L p;t + (1 )L g;t](1pg) = 0 (38) RtpAtKp1 p;t1Kg g;t1[L p;t + (1 )L g;t](1pg) = 0 (39) (1 + ss t)Wp;t (1 pg)AtKp p;t1Kg g;t1[L p;t + (1 )L g;t](1pg) L1 p;t = 0 (40) tg+(1 )(1 pg)L g;t [L p;t + (1 )L g;t]Yt= 0 (41) Kp;t ((1 Kp)Kp;t1+Ip;t) = 0 (42) Kg;t (1 Kg)Kg;t1+Ig;t= 0 (43) Gt(Cg;t + (1 + ss t)Wg;tLg;t +Ig;t +Zt) = 0 (44) Cg;t 1Gt= 0 (45) 23 Ig;t 2Gt= 0 (46) (1 + ss t)Wg;tLg;t 3Gt= 0 (47) Zt4Gt= 0 (48) Wg;t ! 1!1=23Gt (1 + ss t)1=2 = 0 (49) Lg;t ! 1!1=23Gt (1 + ss t)1=2 = 0 (50) Ttc tCp;t +l t(Wp;tLp;t +Wg;tLg;t) + k t(RtKp)Kp;t1 +ss t(Wp;tLp;t +Wg;tLg;t) + k tRB tBt+ tt= 0 (51) Gt+ (1 + RB t)Bt(Tt+Bt+1) = 0 (52) This set of conditions fully characterizes a unique solution for any given policy vector. The complete set of equations of the model is completed with the budget constraint of the consumer and the following transversality conditions: lim t!1 ttKt+1 = 0 lim t!1 1 (1 + R)tBt= 0 De…nition of equilibrium: An equilibrium for this economy is a vector of prices (Wg; Wp; R), a vector of input quantities (Lg; Lp; Kg; Kp);and a vector of private consumption and investment (Cp; Ip)such that for a given …scal policy summarized by a collection of taxes (c; l; k; ss; )and expenditure proportions (1; 2; 3; 4); induce a vector of public consumption, investment, transfers, and debt services (Cg; Ip; Z; RB), such that the optimization problems of the household, the …rm, and the government are satis…ed in a way that the resources constraints are satis…ed and all markets clear. Appendix B: Sensitivity Analysis The results shown in the paper relate interest rates to the ratios Gt=Ytand Bt=Yt: We have seen during the crisis enormous variations in the yields that the Greek 24 bond had to pay to be attractive in the markets. In the calibration period 20022006, we observe a steady relation in the ratio G=Y '0:45;and B=Y '100%: The implication is that when the yield of the bond increases by a factor of four, the expenditure made by the government in any other area has to decrease by a similar amount, and we know how extremely di¢ cult this is. The result is that an enormous jump in the debt frontier has to take place. In this appendix we analyze the sensitivity of the model to changes in some key parameters. Table B.1 shows the percentage change in the relevant variables given an increase of 10% in the parameters of the …rst row. Several interesting results emerge from this sensitivity analysis. Overall, this exercise shows the robustness of the model. As expected, a rise in Total Factor Productivity increases output, consumption and investment in the same amount. Additionally, the sustainability debt level increases by 16.5%, showing that public debt sustainability is also very sensible to productivity shocks. An increase in taxes has a negative impact on all macroeconomic variables but on the sustainability debt level. From our model speci…cation, a higher level of public revenues, given a particular government size, allows to cover a higher amount of debt services. The higher impact came from the labor income tax and consumption tax. Also note that the public debt interest rate is a¤ected by the change in the capital income tax rate, increasing the cost of borrowing and partially compensating the positive e¤ect on the creditworthiness of the Greek debt. Also of interest is the reaction of our model economy to changes in total government spending composition. A rise in the proportion of public consumption (1) does not a¤ect output and investment, reducing private consumption and raising public consumption by the same amount. Nevertheless, this policy change reduces the long-run sustainability debt limit by around 2%. A rise in public investment (2) has a positive impact on all macroeconomic variables, raising the long-run sustainability debt limit by 0.75%. The positive impact of a rise in public wage bill (3) on output, consumption and investment is easily explained, as more public employment is added to the aggregate production function, in spite of a fall in private employment. At the same time, the residual parameter 4is reduced by the same amount. Therefore public accounts remain unchanged while more factors are placed into the production function. The table also shows that a change in the composition of wages and public employment has mild e¤ects on the economy. A reduction in civil servants’compensations increases the debt ceiling by just 1% at the cost of 0:67% decrease in output. Table B.1: Sensitivity Analysis 25