The “Mystery of the Printing Press” Monetary Policy and Self-ful…lling Debt Crises Giancarlo Corsetti Cambridge University and CEPR Luca Dedola European Central Bank and CEPR First Version December 2012. New revised version: October 2014
We thank, without implicating, an anonymous referee, Eric Van Wincoop, Guillermo Calvo, Robert Feenstra, Jordi Galí, Ricardo Reis, Pontus Rendhal, Hamid Sabourian, Pedro Teles, Oreste Tristani, Frank Smets and Gilles St. Paul, our discussants Pierpaolo Benigno, Alexander Guembel, Maren Froemel, Ramon Marimon, Gernot Mueller, Philippe Martin, Thepthida Sopraseuth as well as seminar participants at the Bank of England, Bank of Spain, UCDavis, Columbia University, European Central Bank, International Monetary Fund, Paris School of Economics, University of Amsterdam, the 2012 Conference on The Economics of Sovereign Debt and Default at the Banque de France, the 2012 workshop on Fiscal Policy and Sovereign Debt at the European University Institute, the 2012 conference on Macroeconomics after the Financial Flood in memory of Albert Ando at the Banca d’Italia, the T2M Conference in Lyon, the 2013 Banque de France and Bundesbank Macroeconomics and Finance Conference, the 2013 Barcelona Summer Forum: International Capital Flows and the 2014 conference on “The European Crisis — causes and consequence” in Bonn We thank Anil Ari for superb research assistance. Giancarlo Corsetti acknowledges the generous support of the Keynes Fellowship at Cambridge University,the Cambridge-Inet Institute at Cambridge and the Centre For Macroeconomics. The views expressed in this paper are our own, and do not re‡ect those of the European Central Bank or its Executive Board, or any institution to which we are a¢ liated.
Abstract
Sovereign debt crises may be driven by either self-ful…lling expectations of default or fundamental …scal stress. This paper studies the mechanisms by which either conventional or unconventional monetary policy can rule out the former. Conventional monetary policy is modeled as a standard choice of in‡ation, while unconventional policy as outright purchases in the debt market. By intervening in the sovereign debt market, the central bank e¤ectively swaps risky government paper for monetary liabilities only exposed to in‡ation risk and thus yielding a lower interest rate. We show that, provided …scal and monetary authorities share the same objective function, there is a minimum threshold for the size of interventions at which a backstop rules out self-ful…lling default without eliminating the possibility of fundamental default under …scal stress. Fundamental default risk does not generally undermine the credibility of a backstop, nor does it foreshadow runaway in‡ation, even when the central bank is held responsible for its own losses. JEL classi…cation: E58, E63, H63 Key words: Sovereign risk and default, Lender of last resort, Seigniorage, Debt monetization
“[T]he proposition [is] that countries without a printing press are subject to self-ful…lling crises in a way that nations that still have a currency of their own are not." Paul Krugman, “The Printing Press Mystery”, The conscience of a liberal, August 17, 2011. “Soaring rates in the European periphery had relatively little to do with solvency concerns, and were instead a case of market panic [...] [These countries] no longer had a lender of last resort, and were subject to potential liquidity crises.” Paul Krugman, “The Italian Miracle”, The conscience of a liberal, April 29, 2013. “Public debt is in aggregate not higher in the euro area than in the US or Japan. [T]he central bank in those countries could act and has acted as a backstop for government funding. This is an important reason why markets spared their …scal authorities the loss of con…dence that constrained many euro area governments’ market access.” Mario Draghi, Jackson Hole Speech, August 22, 2014.
1
Introduction
The recent sovereign debt crisis among some members of the euro area is commonly attributed to the inherent vulnerability to destabilizing speculation that follows from the loss of both monetary policy independence and the (government) ability to denominate debt in domestic currency. As exempli…ed by the Krugman’s quote at the beginning of this paper, a widely entertained hypothesis maintains that countries in control of the “printing press”can always eliminate the possibility of crises driven by self-validating expectations. This option would be precluded to countries without a currency of their own. The historical record, however, shows that outright default on public debt is far from rare, also in countries where debt is denominated in domestic currency and policymakers are in principle in control of the ‘printing press.’ In a long sample ending in 2005, Reinhart and Rogo¤ (2011) document 68 cases of overt domestic default (often coinciding with external 1
debt default).1 This evidence does not disprove the argument set forth in Krugman’s quote: in the data, it is di¢ cult to separate fundamental default from crises generated by self-ful…lling expectations. Eliminating the latter by no means implies that default cannot occur.2 Rather, the evidence emphasizes the need to identify the conditions under which disruptive speculation may emerge in the sovereign debt market, and the mechanisms and policies by which the central bank can stem it— a striking example of an effective backstop to government debt being recently the Outright Monetary Transactions (OMT) program launched by the European Central Bank in September 2012. In this paper, we develop a model of sovereign default driven by either self-ful…lling expectations, or weak fundamentals, and analyze the mechanisms by which either conventional or unconventional monetary policy can rule out the former. Benevolent …scal and monetary authorities choose the optimal rate of default under discretion, either imposing “haircuts”on debt holders (outright repudiation) or engineering surprise in‡ation, or both. We model conventional monetary policy as a standard choice of in‡ation, and unconventional policy as outright purchases in the debt market. We study whether either policy can provide a backstop for public debt as an equilibrium outcome, that is, feasible and welfare-improving from the vantage point of monetary policymakers. In the …rst part of the paper, we lay out in detail the main mechanism by which multiple equilibria emerge under lack of …scal commitment, building on Calvo (1988).3 Introducing fundamental and political risk, we 1 According to the data, domestic default (usually but not necessarily in conjunction with default on external debt) tends to occur under extreme macroeconomic duress — in terms of high in‡ation and negative growth. Reinhart and Rogo¤ (2011) shows that, in the year in which a crisis erupts, on average, output declines by 4 percent if the country defaults on domestic debt, against a decline of 1.2 percent, if the country defaults on external debt only. The corresponding average in‡ation rates are 170 percent (in cases of domestic debt default) against 33 percent (external debt default). 2 We should stress that the ability to prevent self-ful…lling crises does not rule out sovereign default altogether. Ex-post, defaults may be driven by weak fundamentals, and are typically associated with debt monetization and in‡ation — see the evidence in Reinhart and Rogo¤ (2009) and (2011) discussed above. As weak fundamentals may interact with self-ful…lling expectations of a crisis in determining sovereign risk, the case for central bank interventions remains strong. 3 See also Cohen and Villemort (2011) and Cole and Kehoe (2000) among others. In addition to fundamental default and political risk, our model also di¤ers from Calvo (1988) in several other dimensions. In the monetary version of the model, default is not restricted to debasing debt via in‡ation as in Calvo (1988). Finally, we model the balance sheet of the central bank allowing for interest-bearing liabilities.
2
di¤er from Calvo’s original contribution in two key dimensions. First, selfful…lling default obtains only for intermediate levels of public debt, even abstracting from …xed costs of default. Second, interest debt service is always increasing in the level of debt, so that the non-fundamental equilibrium is stable. We show that self-ful…lling debt crises can arise when the central bank is restricted to rely on conventional policies only. The ability to generate seigniorage revenue and debase debt with in‡ation cannot prevent self-ful…lling default — although it enlarge the range of debt for which the economy is not vulnerable to it, a point also stressed by Aguiar et al. (2013).4 In the second part of the paper, we show that welfare-decreasing equilibria driven by self-ful…lling expectations can instead be eliminated using unconventional monetary policies. When a modern central bank purchases government debt, it simultaneously issues monetary liabilities, mainly in the form of interest bearing reserves (see also Hall and Reis (2012), and Del Negro and Sims (2014)). In our analysis, the “printing press”argument comes into play by motivating the following key assumption. Monetary authorities stand ready to honour their own liabilities — not necessarily government debt — by redeeming them for cash (…at money) at their nominal value. Therefore, when purchasing government paper, the central bank e¤ectively swaps default-risky public debt for its own liabilities with a guaranteed face value, subject only to the risk of in‡ation.5 As a result, central bank interventions reduce uncertainty and the overall cost of debt service, altering the trade-o¤s faced by a discretionary …scal authority. We characterize a critical threshold of central bank interventions in the debt market beyond which, absent fundamental …scal stress, default is never the preferred policy option. This is because, with relatively sound fundamentals, interventions of the appropriate size keep the cost of debt low enough for the …scal authorities to optimally adjust the primary surplus. For interventions on a scale close to this critical threshold, default may still occur, but only in the presence of fundamental …scal stress. We also show that, to be credible, a backstop cannot have strongly adverse consequences on the future in‡ation choices by the central bank. This risk may be signi…cant when the central bank is held responsible for its own balance sheet losses, barring …scal transfers under any circumstances. The 4
In the monetary economy studied by Calvo (1988), outright default is ruled out by assumption: multiple equilibria then obtain only by virtue of a speci…c assumption on the costs of in‡ation. 5 See Gertler and Karadi (2012) for a similar notion of unconventional monetary policy applied to ouright purchases of private assets .
3
prospects of having to run high residual in‡ation to make good for these losses, i.e. the prospects of large deviations from the overall optimal policy, may ultimately make a backstop a dominated strategy, relative to the alternative of facing an equilibrium with belief-driven speculation. Nonetheless, we …nd that the conditions for a backstop to be credible/desirable under budget separation are not overly restrictive, if the …scal and monetary authorities share the same objectives. These …ndings are important in light of concerns that, on the one hand, the central bank may not have the ability to expand its balance sheet on a su¢ cient scale to e¤ectively backstop government debt. On the other hand, even if a backstop rules out belief-driven crises, large-scale purchases of government debt may foreshadow large losses on the central bank balance sheet, forcing monetary authorities to run suboptimal in‡ation policies. Our analysis shows that, to rule out belief-driven sovereign default, central bank purchases neither have to match the full scale of the government …nancing, nor have to guarantee the government in all circumstances, at the cost of high in‡ation. The gist of our argument is most easily understood referring to a situation in which the relevant (risk-free) nominal interest rate is at its lower bound. In this case, the central bank would be able to issue …at money at will to buy government paper, without any impact on current prices. To the extent that markets price the risk of non-fundamental default in sovereign rates, these purchases would arbitrarily reduce the cost of servicing the debt and thus eliminate any self-ful…lling equilibria (because …at money is subject only to in‡ation risk). However, to avoid undesirable in‡ation developments, appropriate …scal and monetary policy would be required in the future to deal with the increased monetary stock. Our model of unconventional monetary policy can be viewed as an extension to the case in which central bank liabilities are issued at the equilibrium interest rate — namely, at a rate consistent with expectations of future in‡ation. Also in this case, the central bank can expand its balance sheet, issuing interest-bearing monetary liabilities (that will always be convertible into cash/…at money at face value), with no immediate in‡ationary consequences. As discussed above, in doing so the monetary authority fully accounts for the implications of its purchases on the future optimal choice of primary surpluses and in‡ation. While our analytical framework is close to Calvo (1988), our model and results also build on a vast and consolidated literature on self-ful…lling debt crises, most notably Cole and Kehoe (2002) and more recently Lorenzoni and Werning (2014), as well as sovereign default and sovereign risk, see e.g. 4
Arellano (2008) and Uribe (2006) among others. A few recent papers and ours complement each other in the analysis of sovereign default and monetary policy. Jeanne (2011) and Roch and Uhlig (2011) analyze the role of an external lender of last resort where, in case of default, the government repudiates its entire stock of debt, while Reis (2013) discusses debt crises by modelling the central bank balance sheet in a similar way as ours. In a dynamic framework with no uncertainty, Aguiar, Amador, Farhi and Gopinath (2012) analyze a similar problem as in our paper focusing on in‡ation policies rather than balance sheet policies. Cooper (2012) and Tirole (2012) study debt guarantees and international bailouts in a currency union. By the same token, while we encompass trade-o¤s across di¤erent distortions in a reduced-form fashion, in doing so we draw on a vast literature, ranging from the analysis of the macroeconomic costs of in‡ation, in the Kydland-Prescott but especially in the new-Keynesian tradition (see e.g. Woodford 2003), to the analysis of the trade-o¤s inherent in in‡ationary …nancing (e.g. Barro 1983), or the role of debt in shaping discretionary monetary and …scal policy (e.g. Diaz et al. 2008 and Martin 2009), and, last but not least, the commitment versus discretion debate (e.g. Persson and Tabellini 1993). The text is organized as follows. Section 2 revisits the logic of selfful…lling sovereign debt crises in a non-monetary model. Section 3 shows that, in the absence of a monetary backstop, the same mechanism studied in the real economy of Section 2 is at work in economies with non-indexed debt. Section 4 analyze monetary backstop strategies. Section 5 concludes.
2
The logic of self-ful…lling sovereign debt crises
As in Calvo (1988), our main question concerns the determinants of the e at which a government can meet its …nancing need B market interest rate R by borrowing from private investors at a point in time, and the consequences e on the ex-post …scal choices by the of agents expectations (determining R) government. The model is solved under the maintained assumption that policymakers are unable to commit in a credible way to a …scal plan, detailing how public debt will be serviced and public spending …nanced in future periods, under di¤erent contingencies.6 Ex post, a discretionary government 6
In a speci…cation of the model with no output uncertainty, under commitment there are no self-ful…lling default crises, — as shown by Calvo (1988). For an analysis of default under commitment contingent on fundamental realization, see Adam and Grill (2011).
5
may choose to default, partially or fully, on its liabilities.7 Di¤erent from Calvo (1988), we explicitly allow for the possibility that default be driven by fundamental …scal and economic distress, in addition to self-ful…lling expectations. Most crucially, we also introduce political uncertainty about the type of government. With these extensions, we address two open issues with Calvo’s original contribution, concerning, …rst, the range of debt levels at which multiplicity can occur, and, second, the stability and comparative statics properties of equilibria— in turn shaping the relation of the interest bill with the stock of government liabilities. Since we are interested in the mechanism by which, given the government …nancing needs, default is precipitated by agents expectations (rather than, say, in the determinants of public debt accumulation), we develop our analysis in a two-period economy framework.8 Also, to explain this mechanism as clearly as possible, we initially abstract from the monetary dimension of the analysis: the central bank and a demand for its liabilities will be introduced from the next section on.
2.1
Model setup
Consider a two-period economy, populated by a continuum of risk-neutral agents who derive utility from consuming in period 2 only. The government is benevolent but, for reasons that will be detailed later in the text, we allow for political uncertainty about its type. Speci…cally, we assume that, in period 1, the government announces …scal plans that rule out default altogether. In period 2, with probability 1 the government will stick to its …scal plans and honor its liabilities entirely. With probability ; instead, the government will act under discretion and reoptimize: it will choose taxes and a default rate that maximize current agents’utility, taking market expectations and interest rates as given. The level of output in the 7
The set of equilibria in our model would be di¤erent if we assumed that the markets determined the present value of the government bond issuance, with the latter choosing the face value of repayments under non default (Chamon 2007, Lorenzoni and Werning 2014). In this case, multiplicity would require allowing for default on initial liabilities— if the funds obtained from the market fall short of the desired …nancing need by the government (see Cole and Kehoe 2000). 8 In our two-period economy, the …nancial need of the government in the …rst period coincides with the stock of public debt. In multiperiod models, there would be a fundamental distinction between the stock of debt B, on which the government may impose haircuts, and the short-term …nancial needs of the public sector, which determine the exposure of the government to a self-ful…lling crisis — including the primary de…cit, interest payments, as well as the rollover of outstanding bonds and bills coming to maturity during the period.
6
second period is also subject to uncertainty. Output may be High or Low with probability and (1 ), respectively. The timeline is as follows. In the …rst period, private agents can invest a given stock of …nancial wealth W either in domestic public debt B, at e or in a real asset K, with an in…nitely the gross market interest rate R, elastic supply, yielding an exogenously given “safe” real interest rate R. Consumers’ wealth in the …rst period is thus equal to W = B + K. The …scal authority announces tax plans consistent with no default, which will honor with probability 1 : With probability the …scal authority will instead reoptimize its choices under discretion. In the second period, uncertainty about output and the type of government is resolved. If the government does not reoptimize, it will adjust the primary surplus to the solvency requirement of the public sector. If the government instead acts under discretion and reoptimizes, as in Calvo (1988) it may impose a haircut on the owners of government debt at the rate 2 [0; 1], inducing distortions that a¤ect net output and aggravate the budget. The government has two instruments, primary surplus adjustment and default, both distortionary. Consistent with the literature on tax smoothing, we posit that taxation Ti results in a dead-weight loss of output indexed by z (Ti ; Yi ), where from now on a subscript i will refer to the output state i = L; H: Given the level of gross output Yi , the function z (:) is convex in T; satisfying standard regularity conditions. We realistically assume that, to raise a given level of tax revenue, dead-weight losses are larger, and grow faster in T , if the economy is in a recessionary state, that is: z (T ; YL ) > z(T ; YH ); 0
(1)
0
z (T ; YL ) > z (T ; YH ): Since what matters in our analysis is the size of the primary surplus, rather than the individual components of the budget, for simplicity we denote with G a constant, nondefaultable level of government spending, and use taxation or primary surplus interchangeably. Second, default entails costs that fall on the budget, proportional to the e 9 Upon defaulting, the government size of the ex-post haircut, that is i B R. incurs a …nancial outlay equal to a fraction 2 (0; 1) of the size of default.10 9
Our results would go through if the variable costs of default were in output, rather than in the budget. The main di¤erence would be that the perceived marginal bene…t of default for the …scal authority would be 1 instead of 1 ; the marginal cost would remain : 10 Sovereign default may entail di¤erent types of costs, including output and revenue
7
2.2
Buget constraints and utility
Under these assumptions, the budget constraint of the government in period 2 for i = L; H is Ti
G = (1
e+
e
i) BR
i B R;
;
i
2 [0; 1]
(2)
e is the market interest rate on public debt, set in period 1. The where R primary surplus — de…ned as the di¤erence between taxes T and government e but gross spending G — …nances debt repayment net of the haircut i B R, 11 e of the transaction costs of defaulting ( i B R). The utility of the country’s residents (equal to consumption under risk neutrality) is Ui = Ci = [Yi
z (Ti ; Yi )]
Ti + KR + (1
e
i) BR
(3)
Utility is equal to output, Y; net of losses from distortionary taxes, z (Ti ; Yi ), minus the tax bill, T , plus the revenue from portfolio investment. Consumers earn the safe (gross) interest rate R on their holdings of K; and the net (ex ei on their holding of public debt B. haircut) payo¤s (1 )R
2.3
Optimal choice between taxes and haircuts
In our model, with probability 1 the government sticks to its preannounced “no default policy” in period 2, and raises taxes as to satisfy the budget constraint in all states of nature Tei
e = Te G = BR
G;
i = L; H
(4)
where Tei denotes taxes in a no-default ( i = 0) equilibrium. It is worth stressing that, under mild conditions, this policy plan that we posit as a losses associated with a contraction of economic activity, as well as transaction costs in the repudiation of government liabilities. In the theoretical literature, some contributions (see e.g. Arellano 2008 and Cole and Kehoe 2000) posit that a default causes output to contract by a …xed amount; in other contributions (see e.g. Calvo 1988) the cost of default falls on the budget and is commensurate to the extent of the haircut imposed on investors. Calvo (1988) refers to legal and transaction fees associated to default. In a broader sense, one could include disruption of …nancial intermediaries (banks and pension funds) that may require government support. The relative weight of di¤erent default costs is ultimately an empirical matter — see e.g. Cruces and Trebesch 2012. 11 From an accounting perspective, the budget costs of default due to legal fees should be part of the the primary surplus. In what follows, we …nd it expositionally convenient to consider them as part of the debt service, hence we include them in the net interest bill of the government.
8
simplifying assumption will coincide with the optimal plan under commitment. This result can be derived by solving the problem of a benevolent government (with a probability 1 of being in charge in period 2) that e 12 internalizes the e¤ects of its decisions on expectations and thus on R: Default is instead a possibility if the government turns out to be discretionary — a case which occurs with probability . The optimal plan by the discretionary government is derived by maximizing agents’utility, Ci , subject to its budget constraint and the constraint on the default rate 2 [0; 1]; e as given.13 A key optimality condition is that, conditional on taking R default, taxation satis…es: z 0 Tbi ; Yi =
1
:
(5)
where from now on a hat above a variable, e.g., Tbi , denote an equilibrium with outright default. The government chooses the optimal tax level Tbi trading-o¤ the economic costs associated with raising revenue z (T ; Yi ) ; with the variable budget cost of default, indexed by the parameter . This tradeo¤ is independent of the interest rate and the size of debt. The primary surplus that the country …nds it optimal to generate conditional on default, Tbi G, in turn pins down net output Yi z Tbi ; Yi as well as the optimal haircut rate: 1 > bi =
e+G BR (1
Tbi > 0; e ) BR
i = L; H:
(6)
e as long as the country The optimal haircut is increasing in the interest rate R runs a primary surplus. Observe also that with a su¢ ciently low sovereign 12
The proof is available upon request. The economic logic of this result is as follows. As is well understood, a government acting under commitment could in principle make plans with contingent default (see Adams and Grill 2012). Yet, in our setting, this government e is already high, in anticipation of default by the discretionary will be aware that the rate R government in charge in period 2 with probability . With su¢ ciently high, the bene…ts from reducing the ex-ante market rates exceed the gains from committing to ex-post contingent default: it will be optimal to set = 0 in all states of nature, as to compensate for the adverse e¤ects on expectations of prospective default under discretion. In light of this result, our modelling assumption is a good approximation to the behavior of a government under commitment — which allows us to simplify considerably the algebra and the analysis in the main text. 13 A outside the range [0; 1] would be tantamount to assuming that the government is able to subsidize bond holders or tax them without incurring the output distortions associated to net taxes T .
9
e were the discretionary government to set its preferred tax rate Ti = rate R, b Ti ; the default rate i would be negative. But since haircuts can only be positive, the optimum is to repay obligations in full and set i = 0. Using (6) together with the constraint on admissible default rates 2 [0; 1], the optimal policy under discretion can be written compactly as follows: if bi < 0
i
if bi 2 (0; 1) if bi
i
1
i
e Ti = Tei = G + B R
=0 = bi
Ti = Tbi = z 0
=1
1
(7)
; Yi
(8)
e Ti = Tbi+ = G + B R
(9)
1
Note that, when the constraint i 1 is binding in equilibrium, the government optimally defaults on all its liabilities, but its current non-interest expenditure (including the variable budget costs of default evaluated at i = 1) may exceed Tbi — hence the notation Tbi+ . The above conditions are de…ned up to the size of the haircuts, to be determined jointly with equilibrium pricing by private markets, discussed below.
2.4
Debt pricing and equilibrium
The price of debt is pinned down by the interest parity condition, equating (under risk neutrality) the expected real returns on domestic bonds to the safe interest rate: e f(1 R
) + [ (1
H)
+ (1
) (1
L )]g
=R
(10)
Under rational expectations, agents anticipate the optimal discretionary e plan of the government conditional on the market interest rate R. A Bayesian perfect rational-expectation equilibrium (in pure strategies) is de…ned by the above condition (10), together with the conditionally optimal tax rates (5) or (9) and (4) and associated default rates, and the government budget constraint (2). We are interested in studying economies where, in equilibrium, fundamental default may be optimal for low realizations of output, but there is no fundamental reason for defaulting in the high-output state. Using the expression for the optimal haircuts in the two states (6) with 0 = bH < bL 1; it is easy to verify that in these economies the size of the initial B has to satisfy the following inequalities: 0<
TbL
G
< BR
(1 10
(1
)) TbH
G :
(11)
In words: the initial level of B is large enough that, in the low output state, the (positive) primary surplus under default TbL G will fall short of the interest bill of the government valued at the risk-free rate, BR. At the same time, B is small enough that, in the high output state, the (positive) primary surplus TbH G that would be optimally chosen under default can comfortably …nance the largest possible interest bill— corresponding to the case in which agents anticipate total repudiation in the low-output state, e = R= (1 setting R (1 )) :14 In the rest of this section, we will impose (11), together with the following: 1
>
> 0; 1
> 0:
(12)
As further discussed below, the condition 1 > ensures that multiple equilibria emerge only for relatively highly levels of B in the range (11). Moreover, imposing conveniently simpli…es our analysis by excluding corner solutions with L = 1 and H = 1. It is worth noting that, with the above restrictions in place, BR <
1
TbH
G ;
(13)
implying that the optimal rate of default in the high output state is always below 100 percent. These conditions are stricter than we need to prove our results, but allow us to formulate our main propositions in a tighter and therefore more accessible fashion.
2.5
Weak fundamentals and self-validating expectations as drivers of sovereign debt crises
Our …rst proposition establishes that, in our model, the equilibrium is generally not unique. With this proposition, we extend the main result by Calvo (1988) to a stochastic setting with fundamental and political risk, and derive a novel result relative to this author’s contribution. Namely, provided that the probability of a discretionary government in period 2 is not too high ( < 1 ), self-ful…lling crises are possible only when the government …nancing needs B are relatively high in the relevant range (11).15 14
Observe that a countercyclical G would increase ‘…scal stress’in the low output state, while raising …scal surplus in the good output state. Generalizing our model in this direction would aggravate notation, without producing additional insight. 15 In Calvo (1988), there are two equilibria for any level of B, no matter how small. The solution in Calvo (1988) is a special case of our analysis if we let ! 1 (output is non stochastic) and = 1. In the non-stochastic version of the model, the equilibrium may be unique for a special combination of parameters’values.
11
The proposition characterizes the threshold for B below which the economy only admits a fundamental equilibrium (denoted with the superscript F ). In this equilibrium, the interest rate charged on debt re‡ects anticipations of default in the low-output state of nature in period 2— based on the correct probability that the low-output state materializes ( ) and the discretionary government is in charge ( ). For B above such threshold, there is also a second, non-fundamental equilibrium (denoted with N ), in which market participants coordinate their expectations on default occurring in both the high and low output state — and thus charge a higher equilibrium interest rate than in F . Proposition 1 Holding conditions (11) and (12), there will be either one or two rational expectations equilibria which satisfy the pricing condition (10), together with the government optimizing conditions (7) through (9) and (2), depending on whether B is below or above the following threshold B7
(1
(1
)) TbH (1
G + (1 )R
) TbL
G :
(14)
When B is below the threshold (14), there will be a unique fundamental equilibrium in which default will occur only in the low output state of the world if the government is discretionary. When B is above the threshold (14), there will be a second equilibrium, driven by self-validating expectations, with deF N fault in both states under the discretionary government, with bL < bL and N N 0
L
Both haircuts and taxation vary across equilibria. In the fundamental equilibrium, the discretionary government only defaults in the low output state YL ; in the non-fundamental equilibrium, it imposes haircuts in both states of the world. The equilibrium interest rate will thus generally be higher than the safe rate R: In the F-equilibrium, the di¤erence is determined by rational expectations of default in the weak state. In the N-equilibrium, the di¤erence is driven by self-con…rming beliefs that the discretionary …scal authority will always default. Non-fundamental equilibria are welfare-dominated because the level of taxation is higher in each state of nature (whether or not the government defaults), and so are the overall tax-related distortions reducing output. The logic of belief-driven debt crises can be illustrated by writing the best-response default rate that satis…es the budget constraint and the optimality conditions of the discretionary government against the market 12
e together with the equilibrium R e charged by investors determined rate R, against the government-determined haircut rate. The discretionary government’s best-response is 8 8 99 e < < BR == Tbi Gi ;1 i -Government = M ax 0; M in e : : (1 ;; ) BR
Note that the best-response in state i does depends directly on the haircut e The inin the other states— it only depends on the market interest rate R: vestors’response, instead, varies across state, since it depends on the haircut rate anticipated to occur in the other state. For the High state, we can write e ( H ) as: the investor’s best response R H -Investors
=1
1
R e R
(1
)
(1
) (1
L)
e HowFor interior solutions in , both reaction functions are increasing in R. ever, the government best response is constrained to be non-negative. Multiplicity arises speci…cally because of this non-negativity constraint on .
2.6
The comparative statics of debt and notional interest bills: key di¤erences with Calvo 1988
An important question is whether countries that have a higher initial level of e This question liabilities B would also face higher notional interest bills B R: is relevant not only from a policy but also from a formal perspective, as a positive answer would imply that the equilibria are stable (see Lorenzoni and Werning 2014 for a discussion in the context of self-ful…lling default). The answer is far from obvious because the optimal default rate and thus the market interest rate are both endogenous in equilibrium, and may actually be falling in B. We …rst note that is a su¢ cient condition for the notional interest e bill B R in the fundamental interior equilibrium eF = BR
(1
) RB
[(1
(1
) (1
) TbL
)+ (
G
)]
(15)
to be unambiguously rising in B. However, the same condition is not sufe will also be rising in B in the non-fundamental …cient to ensure that B R 13
equilibrium: eN = BR
(1
) RB
TbH
(1
G + (1 )B
) TbL
G (16)
eN =@B crucially depends on the probability The sign of the derivative @B R of the government reneging on its …scal commitments. It is positive for <1 , that is, eN @B R >0 @B
()
<1
:
To gain intuition, let = 1 and = 1, as in the original contribution by Calvo (1988): there is no random variation in output, and Tb and G are invariant to B. This is equivalent to assuming that the primary surplus under default is invariant to B as well — implying that the expression eN is equal to a constant, see (2) evaluated at = 1. Since (1 (1 )) B R a higher B tends to reduce the endogenous default rate , with both B and eN must fall more than proportionally. The origi(1 (1 )) rising, R eN as well nal Calvo setup indeed predicts that the notional interest rate R eN generating a belief-driven debt crisis are as the notional interest bill B R lower, the higher the initial stock of debt B— a counterintuitive prediction implying that the non-fundamental equilibrium is also unstable. This admittedly unpalatable feature of Calvo (1988) follows from the modelling assumption restricting the primary surplus upon default to be independent of the amount of debt in the market. In our model, we remove this restriction, and allow for a weak dependence between primary surpluses and B by stipulating that, with some large enough probability, the government will not default in any state of the world. When 1 > , in our eN is rising with the level of initial debt, model the notional interest bill B R ensuring that the equilibrium is unique at relative low values of B.
2.7
Fixed vs variable costs of default
We conclude this section by noting that our results would go through qualitatively if the model featured also …xed costs of default (as is standard in the literature, see e.g. Cole and Kehoe 2000), in addition to variable costs. Introducing …xed costs in our setting would have two implications. First, the equilibrium would continue to be characterized by a threshold value for debt de…ning two regions of B; one in which the equilibrium is unique, the 14
other in which it is not — this threshold would obviously be di¤erent from the one characterized in our …rst proposition. Second, in the range of debt where equilibrium is unique, default may not occur at all, not even in the low-output state. Fixed costs may discourage debt repudiation even when the macroeconomic outcome turns out to produce …scal stress. In the literature, …xed costs are typically motivated with the observation that default is not frequent at low levels of debt. But (di¤erently from Calvo 1988) in our model self-ful…lling crises are already ruled out at low level of debt by virtue of variable costs of default only. Hence, because of the substantial algebraic complications that …xed costs would introduce in our analysis, we prefer to pursue expositional and analytical clarity by abstracting from them altogether — they would obviously be relevant from a quantitative perspective.
3
Sovereign default in a monetary model with nonindexed debt
In Section 2, we have analyzed the main mechanism by which discretionary …scal policy can make a country vulnerable to self-ful…lling sovereign debt crises in an economy with real debt. The question we address in the rest of the paper is whether the central bank quali…es as an institution that can rule out self-ful…lling sovereign debt crises under any circumstances. We will ask whether and under what conditions monetary policy— either conventional or unconventional— is able to shield countries with non-indexed public debt denominated in domestic currency from belief-driven crises. We refer to policies relying on the control of in‡ation as conventional. Via in‡ation, monetary authorities can raise seigniorage revenue, and exercise the option to debase public liabilities. By unconventional policies, we refer instead to the central bank purchases of government debt, matched by the simultaneous issuance of monetary liabilities— corresponding to an overall expansion of the central bank’s balance sheet. This section is devoted to the analysis of conventional monetary policy. As stressed by Calvo (1988), some degree of repudiation is a natural outcome in a monetary economy, because unexpected changes in in‡ation rates a¤ect the ex-post real returns on assets which are not indexed to the price level. Consistently, in our monetary model, repudiation in period 2 can take the form of a reduction in the real value of debt through in‡ationary surprises, in addition to outright default on debt holdings. So, there will be two instruments to reduce the ex-post value of public liabilities — haircuts or 15
surprise in‡ation — each with its own costs.16 The literature has long stressed that very large, unexpected in‡ation tends to be extremely disruptive. Accordingly, we posit the in‡ation has output deadweight costs, taking a convex form. As a result, in our model the cost of in‡ation and taxation as policy instruments are isomorphic: both are convex and impinge on output. We will show that, if the central bank is restricted to only pursue conventional in‡ation policy, the same nonuniqueness of equilibria analyzed in Section 2 also characterizes a monetary version of our economy with nominal, non-indexed public debt.
3.1
Model setup
Relative to the speci…cation in Section 2, the model set up changes as follows. First, to minimize the use of new notation from now on we rede…ne e in nominal, rather government liabilities B and the notional interest rate R than in real terms. Therefore, the real value of government payments in each state of the world in the second period is given by the net nominal e cash divided by the prevailing in‡ation rate, i.e., (1 i ) RB= (1 + i ) : Second, in addition to the …scal authority, we model a monetary authority that is benevolent— hence shares the same objective as the …scal one— but acts independently and subject to its own budget constraint.17 Note that, by narrowing the scope for con‡icting objectives, our analysis characterizes a reference allocation against which one can assess the consequences of alternative policy scenarios — revolving around political economy considerations or institutional settings that di¤erentiate the objectives and constraints of the monetary and …scal authorities. The monetary authority sets the period-2 in‡ation rate which, as in Calvo (1988), generates seignorage revenue at the rate Seigniorage =
i
1+
:
(17)
i
The cost of in‡ation C (:) is assumed to be convex, normalized such that C (0) = C 0 (0) = 0 — a standard instance being C ( ) =
2
2 :18
16 This is di¤erent from Calvo (1988), where default is implemented alternatively through outright repudiation (in the real version of the model), or in‡ation only (in the monetary version). 17 We should stress that a common objective function and budget constraint fundamentally narrow the scope for opportunistic behavior, even when the monetary and …scal authorities are operationally independent. It can be shown that, under discretion, the policy plan derived below will be the same under coordination. 18 We refer to the speci…cation in Calvo (1988), who restricts the demand for (non-
16
The timeline follows closely Section 2. In the …rst period, private agents can invest either in a real asset K, yielding an exogenously given safe real interest rate R, or in domestic nominal public debt B, at the gross nominal e As before, the …scal authority announces tax plans market interest rate R. consistent with no default, which will honor with probability 1 : In the second period, uncertainty about the type of government is resolved. If the government acts under discretion and reoptimizes (a circumstance which occurs with probability ), it may impose a haircut on the owners of government debt at the rate 2 [0; 1]. Whether or not the government re-optimizes, the central bank chooses the rate of in‡ation in period 2 under discretion, by maximizing agents’utility.
3.2
Budget constraints and utility
With any seigniorage revenue rebated to …scal authorities (in our model in‡ation rates will be positive in equilibrium), without loss of generality we can consolidate the budget constraints of the government and the central bank in period 2, and write: Ti
G = [1
i (1
)]
B 1+
i
i
e R
1+
; i
;
i
2 [0; 1]
(18)
Note that government spending can be …nanced at least in part through seigniorage, as well as via an in‡ationary debasement of outstanding (exdefault) public liabilities. The utility of the country residents is Ui = [Yi
z (Ti ; Yi )]
C ( i)
Ti
i
1+
+ KR + (1 i
i)
B 1+
i
e (19) R;
Utility falls with losses from raising distortionary taxes and in‡ation. Note i that residents are now subject to the in‡ation tax ; the real payo¤ 1+ i (1 i) e also falls with unexpected in‡ation. of public debt, B R, 1+ i
3.3
Optimal choice of in‡ation, taxation and default
Relative to the real economy studied in the previous section, the optimal discretionary plan is now de…ned over Ti ; i ; and i . A new condition states interest bearing) …at money to the case of a constant velocity, bypassing the need to impose a transversality condition. Note that our setup can be easily generalized to encompass an in‡ation La¤er curve, by positing that is a function of expected in‡ation.
17
that in‡ation is chosen by trading o¤ the output bene…ts from reducing distortionary income taxation net of the costs of default (if any), with the output cost of in‡ation: e+ z 0 (Ti ; Yi ) B R
e
iBR
z 0 (Ti ; Yi ) (1
) = (1 +
2 0 i) C ( i)
(20)
Observe that the in‡ation rate would not be equal to zero even if printing money generated no seigniorage revenue ( = 0). This is because a discretionary monetary authority will not resist the temptation to in‡ate nominal debt, if only moderately so according to the condition above.19 Positive costs of in‡ation indeed prevent policymakers from attempting to wipe away the debt with in…nite in‡ation. Conditional on default, however, the optimal rate of taxation is identical to the case of the economy with real debt (5), corresponding to the optimal default rate 2 3 (1 + ^ ) T^i G + ^ 1 bi = 41 5 (21) ~ 1 BR Using these expressions, we can then write the analogs of the conditions (7) through (9) together with the associated optimal in‡ation (as special cases of (20)), as follows: if bi < 0
if bi
e+ z 0 (Tei ; Yi ) B R
and
if bi 2 (0; 1) 1
i
and
= bi
1 i
and
Ti = Tei =
=0
i
=1
e+ BR
e BR 1+ei
= (1 + ei )2 C 0 (ei )
Ti = Tbi = z 0
1
1
= (1 + b)2 C 0 (b)
Ti = Tbi+ = G +
e+ z 0 (Tbi+ ; Yi ) B R
ei 1 + ei
+G
= (1 +
e BR 1+ i
2 0 i) C ( i)
(22) (23)
; Yi
(24) (25)
i
1+
i
(26) (27)
If no default ( i = 0), the revenue from taxation and seigniorage needs to …nance the government real expenditure and interest bill in full. The tax 19
Under commitment the monetary authority would choose a lower in‡ation rate. However, it would not be able to undo the multiplicity due to the lack of commitment by the …scal authority in choosing the size of the haircuts.
18
and the in‡ation rates are set according to (22) and (23). Both Tei and ei are always state-contingent in this case.20 Note that these choices are the same whether the …scal authority sticks to the plans announced in period 1 and does not reoptimize (occurring with probability 1 ) or the government turns out to be discretionary. Conditional on default ( i > 0), if the constraint i 1 is not binding, by the two conditions (24) and (25) the optimal in‡ation rate is identical across states of the world, i.e., bH = bL = b.21 If the constraint i 1 is binding in equilibrium, in‡ation rates are instead state dependent. When the optimal default rate is 100 percent, taxes and seigniorage will have to cover current non-interest expenditure, according to (26) and (27). Note that the optimal plan tends to minimize the joint distortions induced by taxation and default, on the one hand, and in‡ation, on the other hand. Hence it generally requires the simultaneous use of all available instruments— ruling out an uneven resort to extreme in‡ation as a substitute for outright default.
3.4
Debt pricing and equilibrium
Under risk neutrality, expected real returns are the same on government bonds and on the real asset: ~ (1 R
)
1 + eH
+
1 + 1 + eL
1 1+
H
+ (1
)
H
1 1+
L
= R:
L
(28) The interest parity condition pins down the price of government debt as a function of both expected default and expected in‡ation rates. A Bayesian perfect rational-expectation equilibrium (in pure strategies) is de…ned by these pricing conditions, together with the budget constraint (18), the optimal tax rates, either (24) or (26), or (22), and the optimal in‡ation, either (25) or (27). 20
To see this, rewrite the implicit conditon for in‡ation replacing Tei : e+G z 0 (B R
ei e+ ; Yi ) B R 1 + ei
= (1 + ei )2 C 0 (ei ) :
Since the function z 0 Tei ; Yi is state contingent, also the left-hand-side has to be state contingent. 21 This property of the optimal in‡ation rate depends on the simplifying assumption that the cost of in‡ation does not vary with the state of the world. It would be easy to relax this assumption, at the cost of cluttering the notation without much gain in terms of economic intuition.
19
As discussed in Section 2, we also assume conditions ensuring that an equilibrium with no default in the high-output state exists, and the set of F equilibria is increasing in B (with bH < 1). In this nominal economy, the analog of conditions (11) and (12) are: ! ! F F b b F L H BR > L 1 + bFL T^L G + > 0; T^H G + H 1 + bH 1 + bFH 1 + bFL (29) 1
where L
H
and
(1
) H
L
>
> 0; 1
> 0:
are de…ned as follows
1 1+eH
+ (1
(1
)
1 + ) 1+e L 1 1+eH
+ (1
1 1+~ F H
+ (1
1 + ) 1+e L
1 ) 1+b F
: (30)
L
1 : 1+~ F H
(31)
Interpreting the …rst set of inequalities: the level of debt is su¢ ciently high that, in the low state, the government revenue under fundamental default (including seigniorage) will fall short of the interest bill of the government valued at the nominal risk-free rate. Conversely, in the high-output state, there will be no fundamental reason for defaulting: we posit that the primary surplus net of the in‡ation tax revenue will be above the largest possible interest bill, corresponding to expectations of total repudiation in the lowoutput state. Moreover, we restrict (the probability of the good output state) and 1 (the probability of the …scal authority to honor commitments) to be higher than (the proportional budget cost of default).22
3.5
Self-validating expectations of sovereign default and macroeconomic resilience with non-indexed debt
We now show that, relative to the real economy studied in Section 2, debtmonetization and seigniorage obviously a¤ect the equilibrium policy tradeo¤s. But per se the option to print money does not rule out multiplicity. We start by establishing that that, under our assumptions, the in‡ation e as a function of rate is unique for any level of the nominal interest rate R the expected haircuts and in‡ation (in contrast with Calvo (1988)). 22
Once again these conditions are stricter than we need to prove our results. They nonetheless allow us to formulate our main propositions in a tighter and therefore more accessible fashion, ruling out corner solutions.
20
Lemma 2 With convex costs of in‡ation and the normalization C 0 (0) = 0, the conditions for optimal in‡ation determination under default (25) and under no default (23) yield a unique in‡ation rate, given bi , H = 0, and e agents expectations, as embedded in the market interest rate R. Consider (25) rewritten as
1
e+ BR 0 2 = C (b i ) : (1 + bi )
Clearly the left-hand side is decreasing in in‡ation, as the numerator is e at most a linear function of in‡ation through the nominal interest rate R: 0 Under convexity of in‡ation costs C ( ), the right-hand-side is instead nondecreasing in in‡ation. This results in a unique equilibrium in‡ation level. A similar argument applies for in‡ation determination in the case without default, as now on the left-hand side z0 ( ; Yi ) would be generally lower than =(1 ); and decreasing in in‡ation. Observe that, to ensure uniqueness, it would be enough that, for some _ > bi ; C 0 ( ) falls at a rate lower than the left-hand side (roughly given by (1 + ) 1 ). This is a quite more general condition than we assume in our model. Yet, it may not be satis…ed by some speci…cations of C ( ), for instance, if C ( ) is bounded for large but …nite values of the in‡ation rate (see Calvo 1988).23 In our model, C ( ) is speci…ed consistent with the notion that in‡ationary debasement tends to be extremely costly for society. Ensuring that the in‡ation rate conditional on a realized haircut rate is unique rules out the possibility of high interest rates and taxation in the presence of sound …scal fundamentals and no default. In other words, multiplicity only obtains in outright repudiation rates— as established by Proposition 3 below. Failing the above conditions, the model would admit an even larger set of equilibria. 23 Even in this case, however, it would be possible to obtain a unique equilibrium by assuming that seigniorage is not increasing in in‡ation, but instead obeys some kind of a La¤er curve. The assumption of Calvo (1988) provides an example of a monetary economy with multiple equilibria and self-ful…lling expectations of in‡ationary debasement of debt. Our results di¤er in two crucial dimensions. First, in the monetary version of our model the government may still choose to impose haircuts on the holders of public debt — a possibility that is instead ruled out by assumption in the monetary economy studied by Calvo. Second, as already explained, in‡ation costs are convex. In contrast, Calvo (1988) speci…es su¢ ciently non-convex costs C ( ), which together with an always increasing seiginorage, yield multiplicity in the rate of in‡ation itself. See also Obstfeld (1994) for a similar assumption.
21
In light of the above lemma, we can establish the main result of this section, namely, the existence of multiple (Bayesian perfect) equilibria when the level of government …nancing needs exceeds some (endogenously-characterized) threshold. Proposition 3 Holding the conditions (29), there will be either one or two rational expectations equilibria which satisfy the pricing condition (28), together with the government budget constraint (2) and its optimizing conditions for taxes (either (24) or (26), or (22)) and for in‡ation (either (25) or (27)), depending on whether B is below or above the following threshold h i F 1+bF 1+bF ( ) L ^H G + bL F ) 1+eH BR 7 (1 T + (1 ) 1+eLL 1 1+b L
(32)
+
(1 1
)
T^L
G+
bF L
1+bF L
:
For B below the threshold (32), there will be a unique fundamental equilibrium in which default occurs only in the low output state of the world, i.e., F bF H = 0 and 0 < L : For B above the threshold (32), there will be a second equilibrium, driven by self-validating expectations, where default rates are positive in both states. Multiplicity is actually of exactly the same kind as in the real economy, with partial repudiation via haircuts di¤ering across equilibria. As established by the above Lemma, under our assumptions there is no multiplicity in debt monetization, hence no equilibrium with high interest rates and taxation in the presence of sound …scal fundamentals and no default. An intriguing question is whether, everything else equal, the debt threshold for which the equilibrium is unique is higher in a monetary economy than in an economy without in‡ation-related bene…ts (seigniorage) and distortions. A positive answer would imply that, even if ine¤ective in ruling out self-ful…lling crises, in‡ationary …nance may nonetheless increase resilience to them. Comparing Propositions 1 and 3, the question boils down to identifying the conditions under which the following holds: " ! # ! F 1 + bFL 1 + bFL b L (1 ) (1 ) + (1 ) ( ) T^H G + + 1 + eH 1 + eL 1 + bFL ! F b L > + (1 ) T^L G + 1 + bFL [(1
) (1
)
(
)] T^H 22
G + (1
) T^L
G :
Su¢ cient conditions for this inequality to hold are either that bFL > eL ~N > R ~ F , or that > 0: Intuitively, exeH ; which is always satis…ed since R post in‡ation raises the debt threshold for which equilibrium is unique in the monetary economy, either by reducing the real value of outstanding public liabilities, or by producing additional revenue from the in‡ation tax. Note that a key reason for this sharp result is that, in the model, the maximum level of taxes under default, T^i , is independent of in‡ation. Similar to the Section 2, conditions (29) are su¢ cient for the notional e in nominal terms to be increasing in the initial level of interest bill B R nominal liabilities B, ensuring that all equilibria are stable. Namely, in the interior, fundamental equilibrium, given that ^ FL > ~ i (in‡ation in the state L under default is higher than in‡ation without default), is a su¢ cient ~ F to be increasing in B, where condition for B R (1
~F = BR (1
) (1
) BR )
(1 1+eH
+
) T^L (1 ) 1+eL
+
G+ h
^F L 1+^ F L
(1 ) 1+~ H
(1 ) 1+^ F L
i:
By the same token, in the interior non-fundamental equilibrium, 1 > ~ N to be increasing in B, where is a su¢ cient condition for B R h i ^N (1 ) BR T^H G + (1 ) T^L G + 1+^L N L ~N = BR : (1 ) (1 ) (1 ) (1 ) 1+eN + 1+eN N 1+^ H
3.6
L
L
Beyond conventional monetary policy: options to stem self-ful…lling crises
When multiple equilibria are possible, di¤erences in welfare across equilibria are driven by di¤erences in output and budget losses caused by taxation, in‡ation and default. Speci…cally, the increase in the interest rate due to self-ful…lling expectations causes unnecessary disruption not only in the lowoutput state, but also in the high-output state. The fact that equilibria with non-fundamental default are detrimental to social welfare raises the issue of what kind of policies can be deployed to prevent it. Calvo (1988), for instance, endorses the view that self-ful…lling debt crises can be prevented if in period 1 an institution could credibly set a ceiling R on the interest rate, at which it would stand ready to buy any amount of government debt.24 If the market interest rate cannot rise to the 24
Many policy analysts have recently made use of this argument, to advocate interven-
23
eN — the argument goes — the only possible equilibrium in which level R private agents hold any government debt at all, is one in which they optieF .25 The main idea is that a ceiling R < R eN would essentially mally bid R coordinate agents’expectations on the fundamental equilibrium.26 However, to be e¤ective, an intervention policy providing a backstop to government debt needs to be credible. This requirement is especially important in models attributing multiplicity of equilibria to discretionary policymaking. Under discretion, prospective interventions are a sustainable belief if they are (i) feasible and (ii) welfare-improving from the perspective of the intervening institution. Assuming that the intervening institution is benevolent, this means that welfare conditional on interventions must be higher than in the non-fundamental equilibrium in which markets charge eN , taking into account future discretionary policy choices. R
4
Monetary backstops
In Section 3 we have discussed the limits of conventional monetary policy (or in‡ationary debt …nancing). In this section we analyze unconventional policies whereby the central bank purchases government debt and expands its balance sheet by issuing its own liabilities. What makes this question particularly intriguing is that, from an aggregate perspective, any purchase of government debt by the monetary authorities is at best backed by their consolidated budget with the …scal authorities — i.e. there are no additional resources to complement tax revenues, including seigniorage. In light of the classic Wallace (1981) irrelevance result, a prerequisite for these policies to be successful is that central bank liabilities be di¤erent from government debt along some dimension. This prerequisite is already entertained in virtually all monetary models, where …at money, the core central bank liability, earns a lower interest rate than government debt, and is exposed to in‡ation risk, but not to overt default risk. Monetary models take for granted that central bank liabilities are a claim to cash, and there tions by the European Central Bank, likened to a "lender of last resort "; see e.g. De Grauwe (2011). 25 The introduction of this institution in the model a¤ects the set of possible equilibria. eN cannot occur, in the model there is another To wit: even if an equilibrium with R eF , and all public debt equilibrium in which agents refuse to buy government paper at R ends up being held by the intervening institution at the rate R. 26 In Corsetti and Dedola (2011), we show that, in contrast to a transfer implicit in an intervention rate below the fundamental rate, liquidity support does not discourage costly reforms that improve government budget (see also Corsetti et al 2005 and Morris and Shin 2006).
24
would be no discretionary attempts at tampering with the face value of the monetary base.27 Our analysis of monetary backstops emphasizes that it is by virtue of an interest rate di¤erential in issuing liabilities, re‡ecting di¤erent underlying risks, that monetary authorities may redress belief-driven runs in the public debt market. The gist of our argument is most easily understood referring to a situation in which the relevant, risk-free nominal interest rate is at its lower bound. In this case, the central bank would be able to issue …at money at will to buy government paper without any impact on current prices. If markets price in a risk of non-fundamental sovereign default, these purchases would arbitrarily reduce the costs of servicing the debt and eliminate self-ful…lling equilibria, because …at money is subject only to in‡ation risk. However, to avoid undesirable in‡ation developments, appropriate …scal and monetary policy would be required in the future to deal with the increased monetary stock. Our model of unconventional monetary policy can be viewed as an extension to the case in which monetary reserves are issued at an equilibrium interest rate — namely, at a rate re‡ecting expectations of future in‡ation. In our speci…cation, the central bank can expand its balance sheet, issuing interest-bearing monetary liabilities (that will always be convertible into cash/…at money at face value) with no immediate in‡ationary consequences. As discussed above, our analysis fully accounts for the implications of central bank purchases on the future optimal choice of primary surpluses and in‡ation.
4.1
Model setup
Hereafter, we extend our model allowing the central bank to purchase a share ! of government debt B at some pre-announced rate R in period 1. The central bank …nances its debt purchases by issuing monetary liabilities in the form of “reserves” H, remunerated at the default-free nominal rate (1 + i). The motivation for this speci…cation is twofold. From a modelling perspective, assuming that monetary reserves H are interest bearing allows us to introduce a demand for central bank liabilities (for a given price level) in the …rst period, consistent with the discretionary choice of in‡ation (the conventional monetary instrument) in the second period.28 From a policy 27
Nonetheless, there are historical examples to the contrary (see e.g. Velde 2007), raising interesting research questions. 28 In dynamic monetary models, buying government debt by increasing the money stock does not necessarily result in higher current in‡ation, as the latter mainly re‡ects future money growth (see e.g. Diaz et al. (2008) and Martin (2009), placing this consideration
25
perspective, our treatment of H re‡ects a key institutional feature of modern central bank liabilities. In practice, central banks have been able to expand their balance sheet without feeding in‡ationary pressures and expectations, even when operating away from the lower bound on riskless short term interest rates — by remunerating reserves in line with prevailing market rates. As discussed above, key to our analysis is that, while ex-post in‡ation surprises a¤ect the real value of all outstanding nominal liabilities (at the price of distortions induced by in‡ation), outright haircuts are applied to B only (at the price of default costs). The timeline is similar to the previous speci…cation, except that, in the …rst period, the central bank may intervene in the debt market, buying a share ! of B against issuance of reserves H. In addition to investing in the safe asset K, yielding R in real terms and in domestic nominal public e private agents can debt B, at the gross nominal market interest rate R, now also invest their …nancial wealth in ‘reserves’, yielding 1 + i, if any are supplied. As before, the …scal authority announces tax plans consistent with no default, which it will honor with probability 1 : In the second period, the central bank chooses the rate of in‡ation under discretion, and always repays its own liabilities in full.
4.2
Budget constraints and utility
Allowing for the possibility that the central bank buys and holds debt on its balance sheet raises two issues in the speci…cation of the government budget constraint. The …rst is whether a government that opts for default is able/willing to discriminate between private investors and monetary authorities, applying di¤erent haircuts. The second concerns the costs of defaulting on the central bank. For clarity of exposition, we …nd it analytically convenient to proceed under the following two assumptions: …rst, the government applies the same haircut i rate to all debt holder — corresponding to a ‘pari passu’clause in government paper; second, that the cost of defaulting is isomorphic for the central bank and private investors, i.e. it is a budget cost proportional to the haircut rate. We nonetheless allow for the two to di¤er, positing 1 > > CB 0: Under a ‘pari passu’ rule, the budget constraint of the central bank in at the heart of their analysis of time inconsistency in monetary policy).
26
the second period is: Ti = =
(1 (1 + i) i) !BR H= 1+ i 1+ i (1 (1 + i) i) + R !B: 1+ i 1+ i
i
1+
+ i
i
1+
i
(33)
where Ti denotes transfers from the central bank to the …scal authority in state i = L; H. Allowing for CB < , the government budget constraint in period 2 then reads: Ti
G = [1
i (1
)]
e R 1+
(1
!) B + [1
i (1
CB )]
i
R 1+
!B i
Ti
(34) e where R is the market interest rate at which agents are willing to buy the share of government debt (1 !) B not purchased by the central bank. Interactions between the …scal and monetary authorities are regulated by institutions and rules that, most often, hold central banks responsible for backing their own liabilities — constraining modalities and size of …scal transfers to the central bank — see e.g. Del Negro and Sims (2014). These constraints are not necessarily binding and may actually be relaxed in exceptional circumstances. In the actual conduct of monetary policy, indeed, there are instances in which the …scal authorities stand ready to provide targeted contingent transfers to the central bank, as backing to their market interventions. Yet, if the central bank intervenes in the sovereign debt market, it exposes its balance sheet to default risk and may su¤er large losses ex post. If this is the case, by (33), it is apparent that, in the absence of …scal transfers, the monetary authority would be forced to raise in‡ation and deviate from desired policies. In light of these considerations, we organize our analysis as follows. We initially state our main results in Proposition 4 below under the assumption that the constraint on …scal transfers to the central bank (if any) is not binding— this is equivalent to assuming a consolidated budget constraint. In a …nally subsection, we discuss the consequences for monetary backstops of a binding constraint. Consolidating the budget of the …scal and the monetary authorities yields the following key expression: Ti [1
i (1
)]
e R 1+
(1
G+
i
1+
!) B +
i
27
=
(35)
i i CB
R 1+
!B + i
(1 + i) !B 1+ i
Ultimately, for a given rate of in‡ation, the primary budget surplus (the di¤erence between taxation and …nal spending Ti G) augmented with seigniorage must be large enough to …nance both (i) the (gross) interest payments by the government to private investors (net of default but gross of the transaction costs associated to it); and (ii) the (gross) interest bill of the central bank— always paid in full under our assumptions. The utility of the representative agent is Ui = Yi
z (Ti ; Yi )
KR + (1
Ti
i ) (1
i
+ 1+ i B e (1 + i) H !) R+ 1+ i 1+ i
(36) C ( i) ;
Note that the net real asset payo¤s are determined by the realization of B e default and in‡ation. Namely, they are (1 R for public debt, i) 1+ i (1 + i) and for central bank liabilities. 1+ i
4.3
Optimal choice of in‡ation, taxation and default conditional on central bank interventions
As in Section 3, the discretionary policy plan is characterized under a policy scenario in which …scal and monetary authorities maximize the same objective function, taking as given the rates of return set in period 1, as well as each other instruments. The plan is also conditional on the intervention rate ! in period 1. b ) refer to an allocation conditional Let a bar above a variable (e.g., T i on positive debt purchases by the central bank, i.e., ! > 0. As before, in‡ation is chosen by trading o¤ the output bene…ts from reducing the need for distortionary income taxation and the costs of default (if any), with the output cost of in‡ation. So, if no default takes place, taxes satisfy the budget constraint (34) (or equivalently (35)) with = 0 : e =G T i
ei
1 + ei
+
e R (1 1 + ei
and the in‡ation rate is set according to: h e ; Y ) BR e+ z 0 (T i i
e R
!) B +
(1 + i) !B 1 + ei
i (1 + i) !B = 1 + ei 28
2
C 0 ei :
(37)
(38)
Conditional on a government default with an interior solution for taxes are set according to: b ;Y ) = z 0 (T i i
(1
so that the optimal default rate is: b = i
e +! !) R CB R e ! ) (1 !) R CB R
(1
e + ! (1 + i) B !) B R
(1
(1
) (1
1 + bi
e !) B R
b T i
(39)
G
CB !BR
and the optimal in‡ation rate satis…es: h i b ; Y ) BR e+ e (1 + i) !B = 1 + b z 0 (T R i i
2
i,
bi
C0 b :
(40)
(41)
Note that with a partial optimal default, by (39) and (41) the optimal in‡ation rate is identical across states of the world, i.e. bH = bL = b. Moreover, b ; Y ) = = (1 ); when CB = 0, (39) is identical to (5) In this case, z 0 (T i i as in the case without interventions. At a corner solution with complete default ( i = 1; bi 1), taxes adjust residually to satisfy the budget (including default costs): b T i
b+ = G + T i
e R (1 1 + bi
!) B +
CB
R !B 1 + bi
(42)
The optimal (unconstrained) in‡ation satis…es the analog of (41) evaluated b + . Observe that, for ! = 0; the above optimal plan is identical to the at T i
one derived in section 3.
4.4
Interest rate determination and equilibrium
As in section 3, the interest parity condition (28) pins down the price of government debt as a function of both expected default and expected in‡ation rates. When both B and H are held by the private sector, however, there is another equilibrium interest parity condition. In addition to (28), the interest rate on reserves 1 + i, free from outright default risk, must equal the real rate R; adjusted by expected in‡ation: (1 + i) (1
)
1 + eH
+
(1 ) 1 + eL 29
+
1+
+ H
(1 1+
)
= R:
L
(43)
Comparing this expression with (28), it is apparent that, in equilibrium, the interest rate on government debt must exceed the interest paid on central bank’s liabilities by the expected rate of default. The rational-expectation (Bayesian perfect) equilibrium (in pure strategies) is de…ned by these pricing conditions, together with the budget constraint (34), the optimal tax rates, either (39) or (42), or (37), and the b + : With the objecoptimal in‡ation, either (41) or its analog evaluated at T i
tive of focusing on economies with the properties described in Section 2, we again impose the conditions (29).
4.5
Equilibrium with credible backstops
It is apparent from the discretionary plan that the optimal haircut rate in period 2, and thus the sovereign debt service, depend on the level of period 1 interventions. Speci…cally, condition (40) (rewritten here for the case CB = 0) b = i
(1
e + ! (1 + i) B !) B R (1
) (1
1 + bi
e !) B R
b T i
G
bi
;
shows that, everything else equal, bi is decreasing on !: For a given sovereign e purchases of debt on a su¢ cient scale eventually bring the desired rate R; haircut bi to zero, ruling out default as an optimal policy outcome under discretion. Proposition 4 below establishes that, provided the central bank purchases enough government bonds, there is a unique fundamental equilibrium in which default occurs only in the low output state under discretion. When ! is large enough, the non-fundamental equilibrium characterized in Proposition 3 is ruled out. In writing this proposition, we …nd it useful to simplify the characterization of the equilibrium by positing CB = 0 — there are no budget costs implied by defaulting on the central bank.29 Proposition 4 If central bank purchases ! are above the following thresh29 The same equilibrium characterization in Proposition 3 is obtained for we posit that e : CB R = R
CB
> 0 if (44)
The intervention rate R is set proportionally to the market rate of debt, depending on the e ratio between the variable budget costs of default (under this assumption, R > R):
30
old: 2 6 6 6 4
1>! h (1
!= (1 ) (1
2 6 6 6 4
) BR N 1+b 1+~ H
)
BR
h
)
b ) T L
(1
N 1+b 1+~ L
+ (1
) h b ) T L
(1 N
+ (1
1+b 1+~ H
h
G+ (
G+ b
N
) 1+ 1+~ L
+ (1
b
N
1+ i hb
bN N 1+b i h
) i
N
b T H
i
b T H
G+
b
G+
N
1+b
N
i
bN bN 1+ 3
i
7 7 7; 5
3 7 7 7 5
a unique rational expectations equilibrium exists satisfying pricing conditions (28) and (43), where …scal and monetary authorities act independently pursuing the same objective function (36) subject to their consolidated budget constraint (35), and with the government optimally choosing taxes according to (39) in case of default. In this equilibrium default occurs only in the low output state of the world, with equilibrium haircuts given by FH = 0 and F 0 < b < 1: L
In the unique equilibrium with central bank purchases at the threshold ! = !; in‡ation rates in the High and Low output state satisfyby, respectively: F
e + z 0 (TeH ; YH ) B R F
e + BR
1
eF R
= (1 + eH )2 C 0 (eH ) (45) ;
(1 + i) !B
eF R
(1 + i) !B
=
implying the following equilibrium interest bill 2
eF = BR
0
6 61 4
B B @
! 1 3 (1 )(1 ) 1 + 1+~ + 1+~ F C 7 H L 1+~ H # C! 7BR ! " A 5 1 1 + 1+~ +(1 ) 1+~ + H L 1+ b F 1+~ F H
(1
!) (1
)
1+~ H
1 + 1+~
L
+
1+b
F
(1
)
1+~ F H
(1 1+
2
F C0 b ;
b T L G + )
bF
1+ b
F
bF
(46) F e eF ; and the optimal default rate in the low state is given by: where R > R bF = 0 L
B B1 @
BR (1 0 B B @
)
F 1+ b 1+~ H
bF
) 1+ 1+~
+(1
!
L
+
F 1+ b +1 1+~ F 1H 1
(1 )(1 ) 1 + 1+~ + 1+~ L C C H 1+~ F H ! " # C! CBR A A 1 1 + 1+~ +(1 ) 1+~ + H L 1+ b F 1+~ F H
31
b T L G +
(1
)
bF
1+ b
F
b T L G +
: bF
1+ b
F
(47)
;
The success of the backstop rests on the fact that debt purchases by the central bank a¤ect the trade-o¤s faced by the discretionary government in a favorable way. Raising the size of interventions progressively lowers the overall costs of servicing the public debt. A falling interest rate bill in turn progressively reduces the welfare-incentive to resort to a haircut rather N than adjusting the primary surplus — b falls in !. For large enough ini
N terventions, b
0 : default in the high state becomes a welfare-dominated H option. Compared with the non-fundamental equilibrium with default in both the high and the low output state characterized by Proposition 3, the unique fundamental equilibrium with positive interventions characterized by Proposition 4 features lower taxes in all states of the world without default, and also lower in‡ation (and thus related distortions) across the board, as a by-product of a lower interest rate bill. Because of the lower interest bill, it may even be possible for the unique equilibrium with positive interventions in Proposition 4 to be welfare-improving relative to the fundamental allocation characterized in Proposition 3.
4.6
Small vs large backstops
Proposition 4 establishes that the size of interventions required to rule out the adverse non-fundamental equilibrium does not need to cover the entire …nancing needs of the government. In particular, the minimum e¤ective backstop is not large enough to rule out default in a situation of …scal stress. However, following the same logic of Proposition 4, it is easy to show that, as the size of interventions grows above !, there is a higher threshold for !; ! >!, beyond which the monetary backstop ends up ruling out default in both the high and the low output state (e.g., for CB = 0, ! = 1). Intuitively, a near full backstop of public debt would eventually mean that the central bank essentially redresses the commitment problem at the root of the equilibrium multiplicity, with the interest bill falling below the fundamental level (without interventions): eF B (1 + i) B < R
Ruling out default under …scal stress crucially a¤ects the trade-o¤ in welfare levels across states of nature. In the high output state, a lower interest bill will imply that taxes and in‡ation be lower than in the fundamental equilibrium without interventions. Conversely, in the low output
32
state, no default means that taxes are bound to be higher, exacerbating distortions. In light of the properties of (1), the fundamental equilibrium with very large interventions will not necessarily be welfare improving, relative to a fundamental equilibrium with or without limited interventions.30
4.7
Central bank losses on sovereign debt holdings
Proposition 4 is derived for the case in which either (a) the two authorities e¤ectively consolidate their intertemporal budget constraints31 or (b) no …scal transfer to the central bank is required in equilibrium. In either case, central bank losses are irrelevant in determining the allocation. The following corollary states the condition under which a break-even constraint on the central bank is not binding, for the case of a partial backstop around the minimum threshold (! ' !). Corollary 5 The unique equilibrium characterized in Proposition 4 continues to exist under a central bank break-even constraint Ti 0; provided the following condition holds: 0 1 bF 1 F L b B (1 + i) C B C !B; 0 TL = + R (48) F F FA @ b b b 1+ 1+ 1+
The corollary suggests that high equilibrium seigniorage revenue may help in easing the central bank break-even constraint. Also, it shows that an appropriate intervention rate R can contain the risk of violation. Indeed, under the assumptions underlying Proposition 4 (that is, CB = 0, and no discrimination across creditors upon default), the central bank can always set R high enough to satisfy the above inequality in all circumstances.32 For any given anticipated default rate in the low output state, there is an intervention rate that is high enough to compensate for central bank losses if this state of the world materializes. 30
The problem is that the loss of one instrument — outright haircuts on public liabilities — would generally imply suboptimal adjustment in the other instruments (taxes and in‡ation). 31 In this case, any haircuts on the debt held by the central bank (if any) would be at best a wash, as they would generate the need for higher transfers to the central bank and possibly a tax adjustment to cover default costs. With these contingent transfers in place, monetary authorities can always set in‡ation according to the optimal condition (38). 32 In this case the intervention rate R does not impinge on any of the conditions de…ning the equilibrium.
33
The question is whether and when, under budget separation, a violation of the condition (48) can undermine the ability of a central bank to o¤er a monetary backstop. It is worth re-iterating that the problem at hand is compelling because, in practice, it is di¢ cult to exclude a positive probability of fundamental …scal stress. Even by intervening around the minimum threshold (! ' !), the central bank does expose its balance sheet to potential losses ex-post, because interventions on that scale do not necessarily rule out fundamental default. In case fundamental losses materialize, either taxes or seigniorage, or possibly both, must adjust, in line with the classical analysis by Sargent and Wallace (1981). With budget separation, losses are relevant to the extent they impinge on the optimal policy choice by the central bank. Speci…cally, a binding break-even constraint interferes with the monetary authorities’ability to set in‡ation rates that minimize distortions according to the optimality condition (38)— running counter the aforementioned fundamental principle that, in general, it is optimal to use all instruments (taxes, default and in‡ation) to minimize their combined distortions. With the social costs of this ine¢ ciency rising with in‡ation (and a large B), a heavy resort to the printing press may not entail an improvement over eN on public debt, the N-equilibrium.33 If markets coordinate on charging R the central bank may be reluctant to buy debt on a su¢ ciently large scale, on anticipation of large losses forcing highly ine¢ cient in‡ationary policies. The credibility of large-scale interventions is ultimately jeopardized. Yet, the mere violation of the condition (48) in the corollary above does not necessarily imply that the central bank is unwilling to implement the backstop. Consider an equilibrium with a small violation of (48). In the low output state, losses from interventions would force the monetary authorities to accept an ine¢ ciently high adjustment of in‡ation, deviating from the marginal conditions for optimal taxation and in‡ation (41). But with a contained suboptimal in‡ation adjustment, the equilibrium with interventions ruling out belief-driven debt runs will still be preferred over the non-fundamental equilibrium without interventions. A monetary backstop will be granted, as long as the deviation of in‡ation and taxation from their optimal rates is not too large. 33
Observe that, to the extent that the possibility of high in‡ation under …scal stress is anticipated by rational agents, prospective debt monetization drives up the interest on reserves 1 + i, exacerbating the central bank balance sheet problem.
34
5
Conclusions
This paper has reconsidered the question of whether and why the central bank can provide a backstop to the government, as to rule out self-ful…lling sovereign debt crises. Our main conclusions resonate with the widespread policy view that under appropriate conditions, a central bank has indeed the power to backstop the government debt, although for di¤erent reasons that many observers invoke. Our model highlights three crucial conditions. Firstly, a monetary backstop is successful to the extent that the central bank is able to issue liabilities at a lower interest rate than the government. In our analysis, successful intervention strategies rest on a swap of (default-) risky government debt with nominal liabilities which can always be redeemed against currency. Secondly, monetary policy making should not be itself a source of multiple equilibria in in‡ation and interest rates, possibly undermining any welfare gains from a monetary backstop. Namely, conditional on a realized haircut, in‡ation rates should be uniquely determined, ruling out the possibility of high interest rates and taxation in the presence of sound …scal fundamentals and no default. Lastly, a successful monetary backstop is greatly facilitated when the …scal and monetary authorities share the same objective function. Provided that …scal and monetary authorities are both benevolent (i.e. they both maximize social welfare), a monetary backstop is e¤ective under reasonably mild conditions, even when the central bank is held responsible for its own balance sheet losses, barring contingent …scal transfers. In this case. even if the two authorities act independently without consolidating their budget constraints, the optimal discretionary plan internalizes the e¤ects of own policy choices on overall distortions. Conversely, the credibility of a monetary backstop under budget separation may be called into question when political economy or distributional considerations cause the two authorities to trade-o¤ self-interested objectives with socially e¢ cient policies. Our results are at odds with views often voiced in the public debate, claiming that the central bank is ‘a lender of last resort to the government’ because it is not subject to a budget constraint. These views stress, alternatively, that a central bank can always consolidate its liabilities and force private banks to hold them inde…nitely, or debase them by a bout of unexpected in‡ation. In light of our analysis, both views have fundamental weaknesses. The view stressing the need for the central bank to impose …nancial repression over private banks by forcing them to hold reserves, de facto introduces the possibility of default on monetary liabilities, without 35
however working out its consequences. If the central bank is expected to tamper with its liabilities, it is easy to see that the arbitrage condition relating the rate on monetary liabilities and the risk free rate would have to include terms in the anticipated central bank’s haircut CB i : the optimal monetary policy would have to account for the optimal haircut on the holders of reserves. The logic of self-ful…lling beliefs would then apply to a discretionary central bank as well as to the government. The alternative, in‡ationary-debasement view downplays the social costs of running high in‡ation, historically conducive to …nancial and macro instability. If anything, our analysis suggests that the monetary authorities may not be willing to intervene at all in situations in which they may be forced to absorb balance sheet losses via signi…cant in‡ation. Exactly because high in‡ation is costly, in some circumstances the provision of a monetary backstop covering a large share of the government …nancing needs may be welfare dominated by the alternative of letting market coordinate on a nonfundamental equilibrium.34 Moreover, our analysis calls attention on the non-trivial fact that in‡ation rates are higher in an equilibrium with beliefdriven outright defaults: an e¤ective monetary backstop prevents high (let alone runaway) in‡ation, rather than creating price instability. Although our analysis is carried out in closed economy, it bears lessons for a currency union. As already mentioned, a common objective function among …scal and monetary authorities, and some …scal support to the central bank (if only limited to …nancial stress situations) greatly enhance the ability of a central bank to provide a monetary backstop. In a monetary union among essentially independent states, it may be possible that national governments pursue con‡icting, inward-looking objectives and/or be adverse to extending large-scale …scal backing to the common central bank. Our analysis, however, suggests that the conditions under which a common central bank has the ability to engineer a successful backstop to member states are fairly unrestrictive. This is especially true if, as is the case for the OMTs, governments can bene…t from the backstop only provided they agree to strict conditionality, ensuring stability of public …nances and possibly eliciting stricter cross-border cooperation. 34
The fact that, at the time of the writing, as a consequence of the current crisis in‡ation is at low or even negative rates and therefore its costs are low relative to the costs of unemployment, is irrelevant for the argument: what matters is an assessment of the cost of prospective in‡ation on a path of monetary debasement of debt.
36
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39
