Public Debt Frontiers: The Greek Case

Public debt frontiers: The Greek case Abstract This paper attempts to quantify the maximum amount of debt that a government can sustain by itself, i.e., the limits to public indebtedness. Using a Dynamic General Equilibrium model where the government is fully characterized, we compute the steady state inverse relationship between the public debt to output ratio and the size of the government, measured as the total public expenditures to output ratio. This line is the budget constraint of a government in steady state. Calibration of the model for the Greek economy to …scal targets reveals that, for the period just before the current recession, i.e. 2002-2006, the debt to GDP ratio was very close to the calculate limits wich depends dramatically on the interest rates. However, short after de …- nancial crisis of 2008, sustained de…cits drove the Greek economy to a point where the Greek Government crossed the debt limit where the country could only meet its debt obligations only if international investors where willing to lend. We conclude that the hight initial level of debts previous the crisis together with the rise in interest rates were the causes of the posterior debt crisis. JEL Classi…cation: H5; H6. Keywords: Debt limit, …scal policy, government expenditure, public debt sustainability, Dynamic General Equilibrium models. We thank Javier Pérez, and Jesús Rodríguez. We bene…ted from the comments of Luis Puch, Antonia Díaz, Gustavo Marrero and the participants of the THUIT-2016 seminar held in U. Complutense de Madrid. We thank Pedro Cabrera who provided excellent research assistance. The authors acknowledge …nancial support from Proyecto de Excelencia Junta de Andalucia SEJ-1512 and Research Grant ECO2013-48884-C3-3. 1 1 Introduction One of the many debates caused by the recent international …nancial crisis has focused the attention of economists and policy makers on the sovereign debt sustainability. As a result, a controversy about the causes and the cures of debt crisis, which is still hitting some countries of the Euro Area with particular intensity, has emerged. Some of the proposed solutions for the European debt crisis shows that the perceived 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. However, in this paper we claim that Greece was before the crisis a country that could be compared to other eurozone member states in all …scal dimensions: Public spending over GDP, expenditure structure, average tax rates, number of public employees, etc., and therefore we argue that the current debt crisis hitting the Greek economy is not due to past …scal indiscipline or to initial inherently unsustainable debt levels but a consequence of government attitude towards the crisis, together with a spike in the interest rates faced by the Greek bond which …nally triggered the Greek public …nancial disaster. To support this claim, we attempt to quantify the maximum amount of debt that a government can sustain by itself, its sovereign debt limit. Beyond that limit the government risks the possibility of a self-ful…lling crisis. 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. We use a Dynamic General Equilibrium (DGE) model to compute those limits, to show that Greece was well below the critical thresholds. Conesa and Kehoe (2015) 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. This is the idea of gambling for redemption, where a …xed and exogenous probability of a recovery entices governments to gamble with the expenditure-debt policy, risking a default if period after period the recovery does not occur and a sunspot realization scares international lenders away. We compute the debt limits where the Cole-Conesa-Kehoe kind of arguments are more likely to explain what has occurred to Greece. We de…ne an equilibrium where the government roll over its debt and another equilibrium where it cannot do so, and calculate the welfare of the consumers at 2 each equilibrium. If debts levels are too large, it can be optimal for the government to decide to default on its debts, and this decision implicitly de…nes what it is a sustainable debt level. We show that using a diagram where two key ratios of …scal data (the debt/output and the government spending/output) are plotted together, is useful to asses how close an economy is from the default decision. For this diagram, 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. This line is called the government budget constraint . Along this line the economy has to generate enough primary …scal surpluses to …nance current government expenditures plus the interest service of its debts, rolling over the existing debt with zero de…cits. Therefore, the budbet constraint provides the maximum level of sustainable debt with rolling over. The debt frontier provides a picture dividing the long term sustainable region from the long term unsustainable region for any given level of public expenditure to GDP ratio. At the right of the debt frontier, all traders know that the economy cannot last for too long: Bad news and a recovery that never arrives con…gure a situation where rolling might not be possible, and where the government has to decide whether or not to default. In our model, if the government decides to default, it has to face a TFP penalty interpreted as an economic dislocation induced by the default. If on the contrary, the government decides not to default, then the economy has to generate enough …scal primary surpluses to pay back any maturing bond until the debt is canceled. These are the debt limits that we compute with the model. In this paper we compute the debt to GDP threshold where the government decides to default, and we show that above the computed limit, the government will choose to default with probability one if lenders decide not to lend. To this end, we construct a DGE model, calibrated for the Greek economy, 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 issued 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, and this is the ultimate reason why we construct a model with a very detailed public sector. On the other hand, public revenues are raised by taxation and new debt issuance, but taxable income varies across policies, and so will the debt needed to balance public accounts. We consider the existence of …ve taxes: consumption tax, labor income tax, capital income tax, corporate tax and a social security tax. Additionally, we include the …scal funding of the social 3 security system of the economy as a pay-as-you-go system. This rich public sector modeling is justi…ed because we want to show that Greece was not so di¤erent from the rest of euro area countries1and that we have to reject …scal indiscipline as the fundamental cause of the Greek default in favor of an alternative theory such as gambling for redemption. We have chosen Greece for our study because it was the …rst country under the Euro currency union to lose its triple A rating on government bonds, and the country has faced strong pressure to consolidate the budget, to …nally default. We carefully calibrate the model to …scal targets 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 beyond the line we draw and into the region where any additional bad news could scare investors away. In the meantime, the recovery didn’t happen, or the bad news arrived before the recovery, and the crisis unfolded. Imposing a reasonable default penalty to TFP, we …nd that the debt to GDP ratio of Greece by 2010 was such that the Greek government would have chosen to default if international lenders decide not to lend, provoking a self-ful…lling crisis. 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. Finally, 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 1Even taking into account the suspicion about some creative debt accounting carried out by the Greek Government in order to meet the Maastricht criteria to join the Euro Zone we …nd that the debt to GDP ratio limit was still well above given the expenditures to GDP ratio for the years before the crisis. The suspicious creative accounting was probably more important to act as a coordinating sunspot variable than the e¤ects on actual levels of debt. The Treaty on the European Union was signed on February 7, 1992 by the members of the European Community in Maastricht, Netherlands. The Treaty led to the creation of the Euro, and established 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 Union. 4 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. 2.1 The Government First, we describe 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 Euro zone 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, ss tis a social security tax, and Ztare transfer payments to households, such as welfare, social security or unemployment bene…t payments. Public investments accrue into the public structures stock, Kg;t. We assume the following accumulation process for the public capital: Kg;t = (1 Kg)Kg;t1+Ig;t (3) 5 which is analogous to the private capital accumulation process, and where Kgis the public physical capital depreciation rate. Next, we need to specify the government spending structure at the time of calibration. This spending structure implies the selection 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 levels for the public de…cit and public debt. While the Maastricht Treaty establishes 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 follows2 Cg;t =1Gt Ig;t =2Gt (1 + ss t)Wg;tLg;t =3Gt Zt=4Gt where 1+2+3+4= 1. We assume that public spending on goods and services are constant proportions of total output and these proportions are kept constant all along the exercise, that is, the government’s income and expenditure sides are fully parametrized. Appendix B reports the results of a sensitivity analysis where both public spending components and taxes rates are changed. 2.1.2 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 +ss t(Wp;tLp;t +Wg;tLg;t) +  tt 2This split of the government expenditures can be thought of as the result of maximization of preferences of the form Ug(Cg;t; Ig;t; Wg;tLg;t; Zt) = log Cg;t + log Ig;t + log Lg;t + log Zt, subjet to a budget contraint where the Government can spend Gt 6 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. 2.1.3 The government identity As we previously argued the government budget constraint can be written as: Gt+RB tBt=Tt+Bt+1 Bt 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: 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 (4) 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 (5) [Insert here Figure 1] 2.1.4 Default We have described up to this point a fully parametrized government. We say it is parametrized in the sense that all those decisions (tax code, expenditure proportions, public wages, wage premium, and public labor supply) were taken once and for all time. The only decision the government undertakes at any moment is whether to honor its debt obligations or, on the contrary, to default. This decision is registered by a binary variable z=f0;1gthat takes the value z= 0 if the government defaults in the current period or if it has ever defaulted in the past, and it takes the value z= 1 if the government decides to honor its debt obligations in the current period. The decision function used by the government to determine whether to pay or to default is the utility function of the consumers. In this way we assume that the Government is benevolent at the moment of taking a crucial decision for the entire economy. Since the value of za¤ects the value of other variables in equilibrium, we will postpone the de…nition of equilibrium until the model is completely speci…ed. 7 2.2 Trade unions 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 economies. 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 budget constraint and the debt limits we want to calculate. 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 de…ned over wages and employment, we follow a standard text-book approach (for example see Oswald, Grout and Ulph, 19843) 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 agrees with the public sector union to maximize the following objective function subject to a budget constraint: max !W g;t + (1 !)L g;t1= (6) 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 (6) 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 (7) 3On 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. 8 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 (8) Combining this expression with equation (7) we obtain that public wages and employment are equal to: Wg;t =! 1!1=23Gt (1 + ss t)1=2 (9) Lg;t =! 1!1=23Gt (1 + ss t)1=2 ;if Wg;t > Wp;t (10) This distribution of the public resources depends on government preferences. However, private and public sectors are competing for the same labor 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 (10) and it is part of the solution of the governments problem. This wage premium ensures the government that it’s demand for labor will always be satis…ed. This relationship will become clearer once we present the household’s problem. 2.3 Firms The problem of the …rm is to …nd optimal values for the utilization of labor and capital in 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 constant returns to scale. 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=At(z)Kp p;t1Kg g;t1[L p;t + (1 )L g;t](1pg) (11) 9 ratio yield the corresponding values for Lp;and Lg:The production function gets fully calibrated computing A(1) as a residual: A(1) = Y Kp pKg g[L p+ (1 )L g](1pg)  = 1:6135 Fix =1;in the government public sector objective function, and compute the value for !as !=1 1 + Wg Lg= 0:0794 Finally, we compute as: =Cp+Cg Cp+Cg+ (HLpLg)Wp1l 1+k = 0:8384 The public wage bill of Greece 3, is obtained as the public wage bill over total government expenditures 3= (1 + s)WgLg=G = 0:3213. Finally, putting together the di¤erent fractions of government expenditures we obtain as a residual the value of 4= 1 123= 0:1572 as total transfers to consumers. We collect the parameter values in two tables. The …rst table (Table 1) contains values taken from National Accounts, average e¤ective tax rates, depreciation rates And the wage premium. Table 2 shows the set of parameters that we calibrate using the equilibrium conditions from the model. [Insert here Figure 2] [Insert here Figure 3] Table 1: The Greek economy calibration targets Parameter De…nition Value RBNominal return of a Greek bond 0.041 YTotal GDP 100 G=Y Ratio total public spending/output 0.4504 I=Y Ratio total investment/output 0.2336 C=Y Ratio total consumption/output 0.7764 L=H Employment/labor endowment 0.5750 Lg=LpPublic labor/private labor 0.2399 Wg=WpPublic sector wage premium 1.4 16 Table 2: Government parameters Parameter De…nition Value Greece Germany 1Ratio public consumption/total government expenditure 0.4467 0.4024 2Ratio public investment/total government expenditure 0.0745 0.0432 3Ratio public wage bill/total government expenditure 0.3213 0.1712 4Ratio public transfers/total government expenditure 0.1575 0.3832 lLabor income tax rate 0.4100 0.3810 kCapital income tax rate 0.1640 0.1810 ss Social security contribution 0.3560 0.3390 Pro…t tax rate 0.2500 0.3870 cConsumption tax rate 0.1480 0.1240 B=Y Ratio public debt/output 1.0882 0.6560 NFraction of debt re…nanced every period 7 11 Table 3: Calibration of the economy Parameter De…nition Value Greece Germany Discount factor 0.9606 0.9606 Kp Private capital depreciation rate 0.0800 0.0800 Kg Public capital depreciation rate 0.0400 0.0400 Public-Private labor elasticity of substitution 0.4326 0.5762 Private employment weight 0.6008 0.6640 pPrivate capital income share 0.3066 0.2556 lLabor share 0.5852 0.6026 gPublic capital technical parameter 0.1082 0.1418 ATFP 1.6135 1.6422 Consumption-leisure preferences 0.8956 0.8792 Greek …gures for taxes, …scal revenues, total government spending and its distribution are not so di¤erent from the …gures for the rest of countries in the euro area. The tax menu is very similar to countries such as Germany. Fiscal revenues (including social security contributions) to GDP ratio for Greece is in the line of the rest euro area countries and even higher than countries like Ireland. Furthermore, government spending to GDP ratio was about 45% for Greece compared to the 47% for Germany or 53% for France, and public to private labor ratio is around 24% for Greece compared to about 32% for France. 17 4 Equilibrium, debt frontier and default Given the calibrated values for the parameters for the Greek economy, we compute the steady state of the model. In our framework, private agents decisions are not only a¤ected by the tax menu, but also by the composition of public spending. The composition of public spending is critical for output and, thus, also for …scal revenues. As a consequence, the amount of total debt is not independent of the spending policies, since 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. The e¤ects of these di¤erent policies imply that the amount of sustainable debt varies across policies. This is an important property of our theoretical framework. The questions that we want to respond is: Given a tax menu, given the government expenditure and its distribution and given a perpetual default penalty imposed on TFP if the government decides to default, What is the level of debt that leaves the government indi¤erent between honoring and defaulting the debt? Honoring the debt implies to pay large sums that could otherwise be used in providing goods to the consumer, investing in public capital, paying to public workers or transferring income to the poor. Defaulting implies the opposite, but in turn, the country faces a once and for all penalty for defaulting its debt. The answer to this question comes from the decision problem taken by a benevolent government that maximizes the utility of the consumer given by equation (15). This problem is: max U(Cp;t +Cg;t; Lt) + EtV(Bt+1; zt) s:t: Gt+zRB tBt=Tt+ Bt(28) z= 0 or z = 1; but z = 0 if z1= 0 With the model economy parametrized to replicate the size of the government for the period 2002-2006 we proceed to de…ne a steady state where the economy can roll over the existing debt as follows. De…nition of steady state with rolling over (z= 1): An equilibrium for this economy is a vector of prices (W g; W p; R p; R g; RB), a vector of input quantities (L g; L p; K g; K p), and a vector of private consumption and investment (C p; I p)such that for a given …scal policy summarized by a collection of taxes (c; l; k; ss; ) and expenditure proportions (1; 2; 3; 4);induces a vector of public consumption, investment, transfers, and debt services (C g; I g; Z; RBB), such that the optimization problems of the household, the …rm, and the government are satis…ed in a way 18 that the resources constraints are satis…ed and all markets clear with TFP given by A(1). This steady state induces a level of welfare for the consumer given by U=1 1U(C p; C g; L)(29) We can compute one steady state with rolling over for every ratio G=Y and build what we call the "debt frontier", de…ned as the sustainable debt limit for each level of public expenditure. Sustainable debt limit here stands for a level where …scal income is su¢ cient to cover current government expenditures and the service of debt. This notion of sustainable debt limit coincides formally with the steady state level of debt (with constant bond yields) for the model we have presented. [Insert here Figure 4] From the model we obtain a numerical representation of the trade-o¤ between public debt long-run sustainable limit and government size measured as the total government spending to GDP ratio. A larger government size, given a constant level of public revenues, corresponds to a lower long-run sustainable level of public debt. The debt frontier is the relationship between public expenditure to GDP ratio, G=Y; and total debt to GDP ratio, B=Y , implied by the government budget constraint. Above the curve, we have all pairs where given the ratio G=Y; the amount of endogenous …scal revenues are not enough to cover the services of total debt, RBB. Below the curve, we have all data pairs where …scal revenues su¢ ce to cover the given G=Y ratio and services the outstanding debt. Figure 4 above, shows that the ratios of public expenditures and total debt where very far from the debt limit, calculated with the real return of bonds set at 1% for the period 20022006. Figure 4 also plots the actual values of G=Y and B=Y ratios for the period 2002-2006. These ratios, remained almost constant for the period 2002-2006 at a value of total public spending/GDP of 45% and a public debt/GDP of around 100%. The intuition behind this result is simple. In our model, public debt is modeled 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 19 debt area on one hand, and reducing the long-run sustainable amount of debt on the other hand. The strong negative shock to output su¤ered by the Greek economy from 2007 onwards is re‡ected in Figure 5 as an increase in 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. Simple inspection of the …gures suggests that the Greek government decided to run large de…cits while waiting for a recovery to come. After 12 quarters running de…cits and piling debt, the yields of the Greek debt rose to a nominal yield of 12% in December 2010. In Figure 5 we plot two debt frontiers. The steeper one is the original computed frontier for a real return of bonds of 1%, consistent with the steady sate. The other is a debt frontier using a real return of 9%;but keeping constant the rest of parameters values consistent with the steady state (that is, without recalibrating our model economy). By 2009, Greek’s …scal ratios crossed the debt frontier. They where located in a place where …scal revenues would be insu¢ cient to service the existing debt at the new yields. [Insert here Figure 5] The debt level de…ned by the debt frontier becomes relevant when we consider the likelihood of a sun-spot variable capable to coordinate international investors scaring them away from buying bonds. The information obtained from a debt frontier crossing is that such situation has to be reverted. If no signals are produced, a self-fulling crisis can be started at any moment. Moreover, at any time this fully parametrized government can take the decision of defaulting on its debts, and thus a di¤erent steady state is induced by the decision of defaulting. The steady state for this economy after default is as follows. De…nition of steady state under default (z= 0): An equilibrium for this economy is a vector of prices (Wd g; Wd p; Rd p; Rd g), a vector of input quantities (Ld g; Ld p; Kd g; Kd p);and a vector of private consumption and investment (Cd p; Id p)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, and transfers (Cd g; Id g; Zd), 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 with TFP given by A(0), where A(0) = 0:95 A(1). In this case, the long term welfare level attained by the consumer is given by Ud=1 1U(Cd p; Cd g; Ld)(30) 20 Notice that the scenario with default introduces two modi…cations in the de…nition of equilibrium. First, the production function with government default is given by Yt=At(0)Kp p;t1Kg g;t1[L p;t + (1 )L g;t](1pg) (31) We choose a permanent default penalty of 5% as in Cole and Kehoe (1996) and Conesa and Kehoe (2015). Therefore TFP after a default is set to be 0.95 of the calibrated value for TFP in the scenario where the government honors its debt, and reported in Table 2. This results At(0) = 1:9234. The second modi…cation occurs in the government restriction which is simpli…ed to be Gt=Ttunder default. We can compute the equilibrium path for every possible value of (B=Y; G=Y )and to obtain the associated utility, denoted by Ud B0 Y0;G0 Y0. However, in our context, the level of sustainable debt indicated by the debt frontier is not the only relevant debt level. There is also a debt level where the government can honor its debt independently of what international investors and market yields do. For example, if international lenders do not lend, and yields rise, the government could decide not to roll over, but instead to pay back any maturing bond until all outstanding debt gets canceled. If the government decides to pay back all outstanding debt, then a constant fraction of the total debt has to be paid out every year until all bonds mature. We follow Chatterjee and Eyigungor (2012) considering that the fraction of debt that has to be repaid corresponds to the average maturity of debt. If in period kthe government decides to repay, and the average maturity of debt is , then the government budget constraint is Gk+1 Bk=Tk . . .=. . . Gk+1+1 Bk+1=Tk+1 Gk++j=Tk++j; j = 0;1;2: : : We use the value of = 4, which corresponds to the average maturity on the Greek debt in the year 2010 (see Figure 7), to calculate the equilibrium paths starting at any point as we did with the default path, to obtain the associated level of utility, denoted by Upb B0 Y0;G0 Y0. So for a given level of (G=Y ), we can vary the ratio (B=Y ), and compute the utility level associated to each pair. Comparing these two utility levels with that of an economy where it is always possible to roll over new debt, we construct Figure 6. In Figure 6, the ratio (G=Y )is …xed to the level where default occurred in 2010, and the debt to GDP ratio level varies from 0% to 350%. Two thresholds appear. 21 The debt to GDP that makes it preferable for the government to default if lenders decide not to lend, and the debt to GDP ratio where the government decides to default even if international lenders were ready to lend. At the point where the utility of paying back equates the utility of default we have a threshold of debt. We …nd that this threshold is consistent with the debt frontier we have calculated. For a level of around B=Y = 150% at the long-term unsustainable area de…ned by the debt frontier, we have that Greece would have preferred (as she did) to default if lenders decide not to lend (as it happened). The second threshold in Figure 6 is found near a point were B=Y = 300%. At this point, the government would choose to default even if international lenders are willing to lend and they do not expect a default. [Insert here Figure 6] From these pictures, 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 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 output and public revenues, driving the Greek economy to a situation where it was vulnerable to the realization of a sunspot capable of coordinating investors to require more yield to buy debt. Once yields rise, the frontier rapidly moves downwards to the left, leaving the Greek economy in a situation that cannot be sustained in the long-run. But increasing yields, and decreasing maturities forced a situation where a default was preferable than paying back, with the resulting default. 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 onwards, 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. From Figure 5 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. 22 5 Conclusions This paper develops a DGE model in which the government is fully characterized in both income and spending sides. Calibration of the model for the Greek economy provides evidence in favor of a gambling for redemption attitude towards the crisis, as in Conesa and Kehoe (2015) and Arellano, Conesa and Kehoe (2012). The gambling for redemption hypothesis can explain quite well the path of the Greek economy from 2007 onwards. As Conesa and Kehoe (2015) 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 2007-2009. Nevertheless, the debt-sustainability problem emerges when the recession is prolonged as indeed was the case. In this situation, government revenues never recover and the gamble for redemption cannot be maintained inde…nitely, forcing the default. The main consequence we extract from our analysis is that the Greek 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. When a recession is exceptionally long lasting, gambling for redemption is a bad choice. However, 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. 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 2:37%;it would depress private consumption and public consumption by 2:30% and 2:37% respectively, and it would depress total investment by 4:98%;but it would rise the debt ceiling by 24:47%: 23 Appendix A.1: Walras’Law Take the budget constraint faced by the consumer: (1 + c t)Cp;t +Kp;t Kp;t1 = (1 l t)[Wp;tLp;t +Wg;tLg;t] + (1 k t)(Rt)Kp;t1+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 = (1 l t)[Wp;tLp;t +Wg;tLg;t] + (1 k t)(Rp;t )Kp;t1 +GtCg;t (1 + ss t)Wg;tLg;t + t Or, Cpt +Cg;t +Igt +Ipt =c tCp;t + (1 l t)[Wp;tLp;t +Wg;tLg;t] + Rp;tKp;t1k tRp;t KpKp;t1 +Gt(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Bt+1 + (1 + RB t)Bt =c tCp;t + (1 l t)[Wp;tLp;t +Wg;tLg;t] + Rp;tKp;t1k tRtKpKp;t1 (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(Rp;t Kp)Kp;t1 +ss t(Wp;tLp;t +Wg;tLg;t) Substitution and elimination drives to: 24 Cpt +Cg;t +Igt +Ipt Bt+1 + (1 + RB t)Bt =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 Rp;tKp;t Substitution yields: Cpt +Cg;t +Igt +Ipt =Yt+Bt+1 (1 + RB t)Bt Which implies that all uses come from all available resources from an open economy. 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)Rp;t(Kp;t1+Kg;t1) where Yt=At(z)K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)At(z)Kp p;t1Kg g;t1[L p;t + (1 )L g;t](1pg) L1 p;t (A.2.1) (1+ss t)Wg;t = (1)(1pg)At(z)Kp p;t1Kg g;t1[L p;t+(1)L g;t](1pg) L1 g;t (A.2.2) Rp;t =pAt(z)Kp1 p;t1Kg g;t1[L p;t + (1 )L g;t](1pg)  Rg;t =gAt(z)Kp p;t1Kg1 g;t1[L p;t + (1 )L g;t](1pg)  25 [8] Fernández de Córdoba, G., Pérez, J. and Torres, J. L. (2012): Public and Private Sector Wages Interactions in a General Equilibrium Model. Public Choice. 150(1), 309-326 [9] Forni, L. and Giordano, R. (2003): Employment in the public sector, CESIFO Working Paper, n. 1085. [10] Mendoza, E., Razin, A. and Tesar, L. (1994): E¤ective tax rates in macroeconomics. Cross-country estimated of tax rates on factor incomes and consumption, Journal of Monetary Economics, 34, 297-323. [11] Oswald, A. J., Grout, P. A. and Ulph, D. T. (1984): Uncertainty, unions and the theory of public sector labor markets. Working Paper n. 176, Industrial Relations Section, Princeton University. [12] Chatterjee, S. and Eyigungor, B. (2012): Maturity, Indebtedness, and Default Risk. American Economic Review, 102(6), 2674-2699. 32 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 44 46 48 50 52 54 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 100 120 140 160 180 G/Y Left Scale B/Y Right Scale Figure 1: Public expenditures (G) and debt (B), as a proportion of GDP (Y). 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 0.1 0.15 0.2 0.25 0.3 0.35 Public labor / Private labor, Greece 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 1 1.5 2 2.5 Public Compensation per employee / Private compensation per employee, Greece Data Model Figure 2: Estimation of labor technological parameters 1970 1975 1980 1985 1990 1995 2000 2005 2010 0.16 0.18 0.2 0.22 0.24 0.26 Public labor / Private labor, Europe 1970 1975 1980 1985 1990 1995 2000 2005 2010 1.1 1.2 1.3 1.4 1.5 Public Compensation per employee / Private compensation per employee, Europe Data Model Figure 3: Same …t for Europe 0 50 100 150 200 250 40 42 44 46 48 50 52 54 Total debt to GDP ratio: Bt/Yt Public expenditure to GDP ratio: Gt/Yt 2003 2004 2005 2006 Figure 4: The debt frontier before the crisis 0 50 100 150 200 250 40 42 44 46 48 50 52 54 Total debt to GDP ratio: Bt/Yt Public expenditure to GDP ratio: Gt/Yt 2002 2003 2004 2005 2006 2007 2008 20092010 2011 Figure 5: The debt frontier after gambling 0 50 100 150 200 250 300 4.07 4.072 4.074 4.076 4.078 4.08 4.082 4.084 4.086 4.088 4.09 B/Y Utility Roll over Pay back at maturity Default Figure 6: Default thresholds in normal times 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 0 2 4 6 8 10 12 14 16 18 Average Maturity on the Greek Debt Years Figure 7: Public debt average maturity (Source: Greek Public Debt Management Agency) 40 42 44 46 48 50 52 54 56 0 50 100 150 200 250 Public expenditure to GDP ratio: Gt/Yt Total debt to GDP ratio: Bt/Yt Long term sustainable debt area [0.45,100%] Greece 2002−2006 Long term unsustainable debt area r = 0.04 r = 0.07 r = 0.05 35 Figure 8: Sensitivity Analysis