Sovereign Defaults and Banking Crises

Episodes of sovereign default feature three key empirical regularities in connection with the banking systems of the countries where they occur: (i) sovereign defaults and banking crises tend to happen together, (ii) commercial banks have substantial holdings of government debt, and (iii) sovereign defaults result in major contractions in bank credit and production. This paper provides a rationale for these phenomena by extending the traditional sovereign default framework to incorporate bankers who lend to both the government and the corporate sector. When these bankers are highly exposed to government debt, a default triggers a banking crisis, which leads to a corporate credit collapse and subsequently to an output decline. When calibrated to the 2001-02 Argentine default episode, the model is able to produce default in equilibrium at observed frequencies, and when defaults occur credit contracts sharply, generating output drops of 7 percentage points, on average. Moreover, the model matches several moments of the data on macroeconomic aggregates, sovereign borrowing, and ﬁscal policy. The framework presented can also be useful for studying the optimality of fractional defaults. necessary improvements to regulatory policy for European banks and the ways in which they value their holdings of sovereign debt. Di↵erent proposals have been put forward aimed at lowering the fragility of the banking sector and its exposure to sovereign risk, like the implementation of Eurobonds (see. Favero and Missale, 2012), or the creation of European Safe Bonds (see Brunnermeier et al., 2011), among others. These proposals highlight how important it is for policy-making to have a better understanding of the dynamic relation between sovereign borrowing, bank fragility, and economic activity, and to have reliable quantiﬁcations of the impact of di↵erent government policies. Our paper provides builds on theory of the dynamics to provide a quantiﬁcation of the impact.


Introduction
1 Another related and current policy debate concerns the necessary improvements to regulatory policy for European banks and the ways in which they value their holdings of sovereign debt. Di↵erent proposals have been put forward aimed at lowering the fragility of the banking sector and its exposure to sovereign risk, like the implementation of Eurobonds (see. Favero and Missale, 2012), or the creation of European Safe Bonds (see Brunnermeier et al., 2011), among others. These proposals highlight how important it is for policy-making to have a better understanding of the dynamic relation between sovereign borrowing, bank fragility, and economic activity, and to have reliable quantifications of the impact of di↵erent government policies. Our paper provides builds on theory of the dynamics to provide a quantification of the impact. triggers a credit crunch, and this credit crunch generates output declines. Ours is the first 26 quantitative paper to endogenize the output cost of default as a function of the repudiated 27 debt. This makes our framework a natural starting point to study the optimality of fractional 28 defaults.

Related literature
This paper belongs to the quantitative literature on sovereign debt and default, following the 56 contributions of Eaton and Gersovitz (1981) and Arellano (2008). In particular, a related work 57 is by Mendoza and Yue (2012) who are the first to endogenize the cost of default: a sovereign 58 default forces the private sector to use less e cient resources. We propose an alternative and 59 complementary source for output costs: a disruption in domestic lending triggered by non-60 performing sovereign bonds in domestic banks' balance sheets. 61 In recent years there has been a surge in studies looking at the feedback loop between  Balloch (2016) studies an economy where domestic banks demand government debt for its 79 colateralizability properties (above and beyond its financial return). Domestic bank holdings 80 serve as an imperfect commitment device, and help the sovereign to raise funds from abroad 81 at lower rates. 2 Our analysis relates to these papers in that it also identifies the damage that 82 2 Another related study is Brutti (2011) who presents a sovereign debt model in which public debt is a source of liquidity and a default generates a liquidity crisis. financial institutions su↵er during defaults. We identify the reduced credit as the endogenous 83 mechanism generating output costs of defaults and also analyze the benefit side: how distor-84 tionary taxation can be reduced when defaults occur. Additionally, our dynamic stochastic 85 general equilibrium model allows us to quantify the importance of the "balance-sheet channel" 86 while also being able to account for various empirical regularities in emerging economies. The quantitative impact of sovereign defaults and banking crises depends on the specifics 138 of the transmission mechanism. This mechanism, in turn, depends on the modeling of the 139 financial sector, and so we devote this section to the bankers' problem describing the market 140 for loanable funds and discussing the main assumptions. The rest of the model economy, which 141 is standard in the quantitative literature of sovereign debt, is presented in the next section. Bankers are assumed to be risk-neutral agents. In each period, they participate in two 144 di↵erent credit markets: the loan market (between private non-financial firms and bankers) 145 and the sovereign bond market (between the domestic government and bankers). The working 146 assumption is that they participate in these markets sequentially. 7

147
The bankers lend to both firms and government from a pool of funds available to them 148 during each period. These bankers start the period with the following resources: A, s(k) and 149 b. A represents an exogenous endowment, which the bankers receive each period. 8 s(k) is 150 the return on a storage technology: the previous period the banker put k into this technology, 151 and today the return is s(k). b represents the level of sovereign debt owned by the bankers at 152 the beginning of the period (which was optimally chosen in the previous period). Hereinafter 153 d 2 {0, 1} will stand for the default policy, with d = 1 (0) meaning default (repayment).

154
Sequence of events for the bankers. Firstly, the banker receives the endowment, A, has access to 155 the stored funds from the previous period, s(k), and gets government debt repayment, b(1 d).

156
Secondly, with those funds in hand, the banker extends intraperiod loans to firms, l s . Finally,

Bankers problem
From the above timing we have that lending to the firms is limited by the funds obtained at 162 the beginning of the period: F ⌘ A + s(k) + b(1 d). This is captured in the following lending 163 constraint: l s  F. The problem of the bankers can be written in recursive form as: where W (·) is the banker's value function, E is the expectation operator, b 0 represents 165 government bonds demand, q is the price per sovereign bond, r is the interest rate on the 166 private loans, x is the end-of-period consumption of the banker (akin to dividends), stands 167 for the discount factor, and z is the aggregate productivity. We can rewrite (1) -(4) as follows: Assuming di↵erentiability of W (·), the first-order conditions are: 169 l s : r µ = 0 (5) Combining equations (5), (6), and the envelope condition with respect to k, we obtain: which defines the optimal choice of k 0 . Combining equation (7) with the envelope condition 170 with respect to b we obtain: (10) This expression shows that in the case of a default in the next period, (d 0 = 1) the lender 172 loses not only its original investment in sovereign bonds but also the future gains that those 173 bonds would have created had they been repaid. These gains are captured by r 0 . represents the lenders' opportunity cost of funds.

178
The loan supply function (l s ) is given by:

180
A central aim of this model is to highlight how a sovereign default generates a credit crunch, 181 which translates into an increase in borrowing costs for the corporate sector (firms) and a 182 subsequent economic slowdown. This mechanism puts the financial sector in the spotlight and 183 Figure 1 shows how the private credit market reacts to a sovereign default. The supply for 184 loans was just derived above, the demand for loans comes from the problem of firms (detailed 185 in the next section) and responds to standard working capital needs.

186
Given that the intraperiod working capital loan is always risk-free (because firms are as-187 sumed to never default on the loans), the bankers will supply inelastically the maximum amount 188 that they can. This inelastic supply curve is a↵ected by a default: when the government de-189 faults, bankers' holdings of government debt become non-performing and thus cannot be used 190 in the private credit market. This is graphed as a shift to left of the l s curve in Figure 1. This 191 ends up in firms facing higher borrowing costs (r ⇤ d=1 > r ⇤ d=0 ) and getting lower private credit in 192 equilibrium. The planner (whose problem is defined in section 3.4) takes into account how a 193 default will disrupt this market. Time is discrete and goes on forever. There are four players in this economy: households, 229 firms, bankers (whose problem was already outlined in Section 2), and the government. In  The bankers lend to both firms and government, and also have access to a storage technology.

235
Finally, the government is a benevolent one (i.e., it maximizes the households' utility). It faces 236 a stream of spending that must be financed and it has three instruments for this purpose:

251
(b) firms hire labor, produce and then distribute profits (⇧ F ) and repay principal 252 plus interest of the loan (l s (1 + r)).

253
(c) bankers choose how much to store for next period (k 0 ).

254
(d) labor and goods markets clear, and taxation (⌧ ) and consumption take place.

255
(e) at the end of period-t a re-access coin is tossed: with probability the govern-256 ment will re-access in the next period with a 'fresh start' (i.e., with b 0 = 0), and 257 with probability 1 the government will remain excluded in the next period. where U (c, n) is the period utility function, c t stands for consumption, n t denotes labor supply, w t is the wage rate, ⌧ t is the labor-income tax rate, and ⇧ F t represents the firms' profits.

275
Solving the problem we obtain: which is the usual intra-temporal optimality condition equating the marginal rate of substi-277 tution between leisure and consumption to the after-tax wage rate. Therefore, the optimality 278 conditions from the households' problem are equations (13) and (14).

279
Firms' problem. The firms demand labor to produce the consumption good. They face a 280 working capital constraint that requires them to pay up-front a certain fraction of the wage 281 bill, which they do with intra-period loans from bankers. Hence, the problem is: where z is aggregate productivity, F (N ) is the production function, l d t is the demand for 283 working capital loans, r t is the interest rate charged for these loans, and is the fraction of the 284 wage bill that must be paid up-front.

285
Equation (16) is the working capital constraint. This equation will always hold with equality 286 because firms do not need loans for anything else but paying w t N t ; thus any borrowing over 287 and above w t N t would be sub-optimal. Taking this into account we obtain the following 288 first-order condition: which equates the marginal product of labor to the marginal cost of hiring labor once the 290 financing cost is factored in. Therefore, the optimality conditions from the firms' problem are 291 represented by equation (17) and equation (16), evaluated with equality.

292
Government Budget Constraint. The government has access to labor income taxation and (in 293 case it is not excluded from credit markets) debt issuance in order to finance a stream of public 294 spending and (in case it has not defaulted) debt obligations. Its flow budget constraint is: where B t stands for debt (with positive values meaning higher indebtedness), g is an exoge-296 nous level of public spending, and ⌧ t w t n t is the labor-income tax revenue.
306 the aggregate resources constraint holds:

314
The government's optimization problem can be written recursively as: where V nd (V d ) is the value of repaying (defaulting). The value of no-default is: subject to: ( r e s o u r c e sc o n s t . ) The value of default is: subject to: (comp. eq. conditions)   The period utility function of the households is: where c controls the degree of risk aversion and ! governs the wage elasticity of the labor The bankers' storage technology is: The production function available to the firms is: The algorithm computes and iterates on two value functions: V nd and V d . Convergence in the equilibrium price function q is also assured.
12 Using GHH preferences, the marginal rate of substitution between consumption and labor does not depend on consumption, and thus the labor supply is not a↵ected by wealth e↵ects. For a study of how important GHH preferences are in generating output drops in the Sudden Stops literature, see Chakraborty (2009).
The only source of exogenous uncertainty in this economy is z t , total factor productivity 350 (TFP). The logarithm of TFP follows an AR(1) process: to the ratio of private credit to wage payments and the data show that for Argentina this ratio 361 was 52%. 13 We use TFP estimates from the ARKLEMS team in order to estimate ⇢ and " .

362
The discount factor for the bankers ( ) takes a usual value in RBC models with an annual  14 Accumulating k in this model is akin to hoarding cash (in a similar but nominal model). Hence, ↵ k < 1 implies a negative net real rate of return on k, a common occurrence for cash equivalent instruments in emerging economies.
countries. Here we take ! = 2.5 as the benchmark scenario, implying a Frisch wage elasticity of 0.67, a value in the middle range of the estimates. has defaulted on its domestic debt 5 times since its independence in 1816, implying a default 388 probability of 2.5%, which is our calibration target. As discussed above, the banking sector of 389 virtually every emerging economy is highly exposed to government debt. The average exposure   Overall, the benchmark calibration of the model is able to account for several salient facts 404 of the Argentine economy, as well as to approximate reasonably well the targeted moments. to keep in mind that the average output drop was not among the targeted moments in the 419 calibration strategy, which is why the mechanism presented in the paper is able to account for 420 53% of the observed output drop. 421 15 The exceptions are the default rate (which we compute using all simulation periods) and the credit and output drop surrounding a default (computed for a window of 11 years before and 4 years after a default). 16 We focus our quantitative analysis on the 2001-02 Argentine default. To do this, we choose a time window that is restricted to 11 years pre-default and 4 years post-default (i.e., 1991-2006 in the data), in order to be consistent with previous studies that report statistics for no-default periods and also to be consistent with This exercise gives a mean Domestic Debt to GDP ratio of 11.3% for the period 1991-2001.

430
As shown in Table 2, the benchmark calibration of the model features a debt-to-output ratio 431 of 11.5%, which is in line with its data counterpart.

432
The average level of storage chosen by the bankers is also in line with empirical evidence. The 433 benchmark calibration features an storage-to-assets ratio of 14.4% while the data counterpart 434 is 11.3%. 20

435
The level, cyclicality, and volatility of sovereign spreads were also not among the targeted 436 moments, and they are closely reproduced by the model. The same is true for the correlation 437 between the tax-rate and output: as in the data, the model exhibits a negative correlation. 21 438 This result has been dubbed "optimal procyclical fiscal policy" for emerging economies, in the 439 sense that the fiscal policy (in this case the tax rate) amplifies the cycle. Why is the tax rate 440 "procyclical" in our model? Because when output is high, it is cheaper to borrow and postpone 441 taxation, whereas when output is low, the reverse is true. Thus, we expect periods of high 442 output to be associated with lower tax rates and vice versa. Moreover, when the government 443 defaults it is left with only taxation in order to finance spending, which leads to even more 444 19 Both the real GDP per capita and the Private Credit per capita series are taken from WDI, and their respective trends are computed using annual data from 1991 to 2006. 20 Bank's assets in the model are loans, storage and debt. The data for the mean storage-to-asset ratio in Table 2 come from the Financial Structure Dataset (Beck et al., 2010), the WDI and the Argentine Central Bank, and it corresponds to bank holdings of money (and money-like instruments) as a fraction of total assets. 21 The data for ⇢(⌧, y) in Table 2  One contribution of this paper is to provide a framework able to deliver endogenous output 447 declines in default periods. Figure 2 shows the behavior of output around defaults: the model 23 Figure 2 is constructed from the model simulations as follows: first, we identify the simulation periods when defaults happen; secondly, we construct a time series of 11 years before and 4 years after each default and compute deviations from trend; thirdly, we compute relevant quantiles and construct a series for the median output deviations from trend around defaults; fourthly, we plot deviations from trend generated by the model and those observed in the data for the t 3 to t + 3 time window, with t denoting the default year.
24 See the Online Appendix for an analysis of the e↵ects of market re-access on output and credit recovery. 25 Figure 3 is constructed in the same way as Figure 2. See footnote 23.

Two properties of the output cost of defaults 468
Here we analyze two properties of the output costs of default: that they are increasing in 469 the level of TFP and that they are increasing also in the size of the default (i.e. the level of 470 outstanding debt that is repudiated).

471
Using the numerical solution of the model we are able to compute the e↵ect of defaults on 472 output. The left panel of Figure 4 shows the percent decline of output as a function of TFP. The shaded area in the left panel of Figure 4 represents the "default region," which are the levels of TFP shock at which the country decides to default when facing the mean debt-to-output level and the mean bank storage observed in the simulations.
27 Chatterjee and Eyigungor (2012) provide a detail discussion about the asymmetric nature of default costs. They use an ad hoc cost-of-default function (in an endowment-economy model) and their calibration implies the same asymmetry that our model delivers endogenously. 28 The shaded area in the right panel of Figure 4 represents the "default region," which (in this case) are debt-to-output levels for which the country decides to default when facing the mean TFP and the mean bank storage levels. 29 The liquidity role of government debt has been highlighted by Bolton and Jeanne (2011), Brutti (2011) and Sandleris (2016).

Benefit of defaults: reduced taxation 491
As argued in the introduction, the optimal default decision comes from balancing costs and 492 benefits of defaults. The costs of default were discussed above: output declines due to a credit 493 contraction. The benefits on the other hand come from reduced taxation. Figure 5 shows the 494 behavior of the labor income tax rate around defaults: we plot the equilibrium tax rate and also 495 the "counterfactual" tax rate that would have been necessary to levy if instead of defaulting 496 the government had repaid its debt.

497
The reduced taxation is precisely the di↵erence between the counterfactual tax rate and the 498 equilibrium tax rate: this di↵erence is of roughly 20 percentage points on average. This tax 499 decline represents a benefit of defaulting because households dislike increases in distortionary 500 taxes. In other words, a default allows the government to a↵ord a tax cut.

501
This subsection and the previous one show that the planner finds a strategic default to be the 502 optimal crisis resolution mechanism: due to worsening economic conditions, the sovereign finds 503 it optimal to default on its obligations (and assume the associated costs) instead of increasing 504 the tax revenues required for repayment. 30   The model also features a positive correlation between spreads and the debt-to-output ratio, 515 as seen in the data. From Figure 6 we can see that default incentives increase with the debt ratio, 516 hence bond prices are decreasing with the debt ratio (which results in the positive correlation 517 30 Adam and Grill (2017) study optimal sovereign defaults in a Ramsey setup with full commitment. They find that Ramsey optimal policies occasionally involve defaults, even when those defaults imply large costs. between spreads and debt ratios). 31 Next we turn to the behavior of spreads in the run-up to a default. Figure 7 shows that the 519 spreads generated by the model mimic the behavior of the Argentine spreads, in that they are 520 relatively flat until the year previous to a default, when they spike. The spreads dynamics in 521 the run-up to a default, as seen in the data, are well within the 99% confidence bands of the 522 model simulations.  using the entire Bankscope dataset (covering both advanced and developing countries). When 533 they focus only on defaulting countries, they find an exposure ratio that is roughly 15%. In this 534 subsection we re-calibrate our model to feature a lower exposure ratio close to this magnitude 535 and refer to this version as the "low-exposure" economy. 32 536 Table 3 shows selected moments of the data, the benchmark economy and the low-exposure 537 economy. We can see that the dynamics of the sovereign debt market remain mostly unchanged.

538
At a virtually identical default frequency (which was a targeted moment), the low-exposure 539 economy has a mean debt-to-output ratio of 6.39% (which represents 55% of the ratio obtained 540 in the benchmark economy and 56% of the observed ratio). The lenders understand that, 541 31 While it is true that higher debt makes the cost of default higher (see Section 5.3.1), it is also true that higher debt makes the benefit of defaulting higher: the counterfactual tax break that households enjoy during defaults is larger with larger debt stocks. Hence, what matters for the correlation between spreads and debt is the net e↵ect on default incentives. 32 The parameter values for the low-exposure calibration are the same as the benchmark calibration with the exception of the households' discount factor ( , which now is 0.99) and the level of bankers' endowment (A, which now takes the value of 0.2095). with a higher A (i.e. a higher bankers' endowment), debt is less important for the functioning of private credit markets and therefore the planner has a higher temptation to default on it, 543 therefore they reduce sovereign lending. They equilibrium spread is almost identical across the 544 two simulated economies, but more volatile for the low-exposure calibration. 33 545 As the theory predicts, an economy with a lower exposure ratio has a lower debt-to-output 546 ratio, should experience a smaller credit crunch and consequently exhibit milder output drops 547 at defaults. Along these lines, we see from Table 3 that the low-exposure calibration can explain 548 only 44% of the output decline at defaults (5.95% versus the observed 13.67%).

549
The main di↵erence between this low-exposure economy and the benchmark economy is  To quantify the e↵ect that movements in A may have we extend the benchmark model and 561 introduce the following functional form for banker's endowment, following Mallucci (2015): In this subsection we re-calibrate our model and refer to this version as the "stochastic-A" 563 economy. 34 The last column in Table 3 has the results for this version of the model. The 564 33 Other non-targeted business cycle moments (not reported in Table 3), like relative volatilities and correlations with output, are also in line with the data. 34 We calibrate parameters {a 0 , a 1 } to match the mean (26.5%) and the standard deviation (2%) of the exposure ratio. The calibrated values are a 0 = 0.16, and a 1 = 0.045. The stochastic-A version approximates well these two moments, featuring a mean exposure of 26.9% and a standard deviation of 2.4% (not reported in Table 3). All other parameters remain unchanged.
behavior of the sovereign debt market is very similar to the one in the benchmark calibration: spreads are large and volatile, and the mean debt level is also in line with the data. Both the 566 credit and the output drops are somewhat magnified, and so in that dimension the stochastic-A 567 economy is closer to the Argentine evidence explaining 55% of the output decline and 25% of 568 the credit crunch. Overall, the quantitative predictions of the model remain robust to this 569 extension.

571
The prevalence of defaults and banking crises is a defining feature of emerging economies.

572
Three facts are noteworthy about these episodes: (i) defaults and banking crises tend to happen 573 together, (ii) the banking sector is highly exposed to government debt, and (iii) crisis episodes 574 involve decreased output and credit.

575
In this paper, we have provided a rationale for these phenomena. Bankers who are exposed 576 to government debt su↵er from a sovereign default that reduces the value of their assets (i.e., 577 a banking crisis). This forces the bankers to decrease the credit they supply to the productive 578 private sector. This credit crunch translates into reduced and more costly financing for the 579 productive sector, which generates an endogenous output decline.    ) and (x), respectively. All variables are logged (except those that are ratios) and then de-trended using the Hodrick-Prescott filter, with a smoothing parameter of 6.25, as suggested by Ravn and Uhlig (2002). We report deviations from the trend. R s stands for bond spread. The data for sovereign spreads are taken from J.P. Morgan's EMBI, which represents the di↵erence in yields between an Argentine bond and a US bond of similar maturity. The spreads obtained in the simulations are computed as the di↵erence between the interest rate paid by the government and that paid by the private sector. Results are robust to using an ad hoc constant risk-free rate. Note: The mean and the standard deviation of a variable x are denoted by E(x) and (x), respectively. All variables are logged (except those that are ratios) and then de-trended using the Hodrick-Prescott filter, with a smoothing parameter of 6.25, as suggested by Ravn and Uhlig (2002). We report deviations from the trend. R s stands for bond spread. The data for sovereign spreads are taken from J.P. Morgan's EMBI, which represents the di↵erence in yields between an Argentine bond and a US bond of similar maturity. The spreads obtained in the simulations are computed as the di↵erence between the interest rate paid by the government and that paid by the private sector. Results are robust to using an ad hoc constant risk-free rate.    . The figure is constructed for the mean bank storage and mean debt-to-output (TFP) levels observed in the simulations. The solid line represents the percent output cost of a default, 1 y d=1 /y d=0 . The shaded area is the "default region": productivity (debt-to-output) levels for which default is optimal given that the banks storage and the debt-to-output (TFP) are at their mean levels.  Online Appendix for "Sovereign Defaults and Banking Crises" César Sosa-Padilla

University of Notre Dame
This Online Appendix presents the details of a number of analyses and robustness tests 1 that are referred to in the main paper. Section A presents a sensitivity analysis to assess 2 the robustness of the main quantitative results in the main paper. Section B discusses some 3 simplifying assumptions and how relaxing them may affect the main results.  Email address: csosapad@nd.edu (César Sosa-Padilla) 1 While columns 1 to 5 have self-explanatory headings, columns 6 and 7 warrant a minor clarification: they report output drops and credit drops around defaults (measured as peak-to-through using the de-trended series), respectively. of output and credit drops are considerable larger than in the benchmark calibration (precisely 22 because higher exposure ratios bring higher output and credit drops during defaults). These 23 dynamics imply a non-monotonic behavior of the default rate as we increase the value of γ.   Table 1 has the results for the sensitivity analysis regarding parameter φ.

31
When the government can re-access credit markets immediately after a default (φ = 1), the 32 overall costs of a default (exclusion from credit markets being among them) are reduced. A 33 lower default cost renders repudiation more attractive, so we see that for φ = 1 default is more 34 frequent. Consequently, the government has to pay higher spreads. If, on the other hand, we 35 lower φ (making re-access to credit markets less frequent), then the exclusion cost of default is 36 larger, default is chosen less frequently, and the government can obtain better debt prices (i.e., 37 it can pay lower spreads). 38 Figure 1 shows how a credit crunch looks in the model. The benchmark calibration of the 39 model features a collapse in the private sector credit (i.e., working capital loans to firms, in the 40 model). In the two panels of Figure 1 we can see the workings of a credit crunch: as firms are 41 in need of external financing, when loanable funds shrink, output shrinks along with them. 42 We can also see the effect of exclusion from financial markets: if the government remains 43 excluded, the private credit reduces (and remains low) and the output decline becomes more 44 protracted. On the other hand, an immediate re-access to the credit market implies a rapid 45 recovery in both credit and output. 2 46 2 As in Mendoza and Yue (2012), the v-shaped recovery of output after a default event is driven by two forces: TFP and re-access to credit. TFP is mean-reverting and thus very likely to recover after defaults. Also, when the sovereign regains access to credit markets, then the output recovery is even faster.
A.3. Relative weights in the social welfare function 47 The model in the main article makes the (common) assumption that the planner only 48 cares about the households utility. However, we can study the dynamics of the model under 49 different social welfare functions. In particular, we could study the default incentives and 50 the transmission mechanism from defaults to banking crises when the planner cares about a 51 weighted average of all residents utilities: households and bankers.