3.1 Households

Households are identical and risk-averse. Their instantaneous utility is given by the CRRA function over consumption:

(1) \begin{equation} u(c_t) =\frac {c_t^{1-\sigma }}{1-\sigma }. \end{equation}

Households save using domestically issued government bonds $b_d$ . They face a budget constraint, which is dependent on the government’s decision to default on their savings ( $\delta _d$ ).Footnote ⁶ When the government repays both debts, households’ budget constraint reads:

(2) \begin{equation} c^i=y^i-T(1+\tau )+(1-\delta _d)\left(b_d-q^i_d b_d'\right), \quad i \in \{r,fd,dd,td\} \end{equation}

where $b_d$ is the amount of domestic debt owed and repaid by the government to households, $b_d'$ is the new issuance of government domestic debt, $q^i_d$ is the domestic bond’s discount price, which depends on the government default decisions. Output $y^i$ and consumption $c^i$ also depend on the government repayment/default decision. $T$ is the amount of taxes raised by the government. Whenever taxes are negative, the household budget constraint is $c^r=y-T(1-\tau )+b_d-q_d^r b_d'$ , so that rebates or transfers are not distortionary. $\tau$ is an exogenous deadweight loss from taxation that drives a wedge between the benefit of taxation for the government and the cost of taxation for the agents. Here, we follow an idea from Chari et al. (Reference Chari, Kehoe and McGrattan2007), that many models are equivalent to a prototype model with time-varying wedges. In this case, many models with endogenous tax distortions can be mapped into our prototype specification with an exogenous tax wedge that resembles a time-varying labor tax wedge.Footnote ⁷

Output in this economy is an exogenous endowment that evolves according to an $AR(1)$ stochastic process in logs:

(3) \begin{equation} log(y_{t})=\rho _y log(y_{t-1})+u_t \qquad u_t \sim \mathcal{N}\big(0, \epsilon ^2_y\big). \end{equation}

The penalties that the government faces because of default are twofold. The government is excluded from the market and faces probabilities of returning to borrowing: $\theta _f$ to foreign and $\theta _d$ to the domestic market. In the default periods, the government also suffers an output cost, that is assumed to be asymmetric as in Arellano (Reference Arellano2008):

(4) \begin{equation} y^{i}_{t}=\min \{y_t, \gamma _i y\} \qquad i=\{\, fd,dd,td\}, \end{equation}

where $y^{i}$ is output in either domestic or foreign or total default, $y$ is the mean of the output process and $\gamma _i$ takes the separate values for domestic and foreign default and the multiple of two for total default. The cost function assumes the asymmetric default costs so that the default is more costly with high output realizations.

Similarly to output, the tax wedge evolves according to an $AR(1)$ in logs around the mean $\bar {\tau }$ :

(5) \begin{align} &\tau _t=\bar {\tau } \tilde {\tau }_t \end{align}

(6) \begin{align} &log(\tilde {\tau }_t)=\rho _{\tau }log(\tilde {\tau }_{t-1})+v_t \qquad v_t \sim \mathcal{N}\big(0, \epsilon ^2_{\tau }\big). \end{align}

3.2 Recursive equilibrium

We define a recursive equilibrium in which domestic households, foreign investors and the government act sequentially and the government acts with discretion. The aggregate state of the economy is given by two endogenous debts $(b_d,b_f)$ and two exogenous processes for income and the tax wedge $s=(y,\tau )$ . Every period, the government decides whether to repay its two outstanding debts, default on domestic debt, default on foreign debt or default on both:

(7) \begin{equation} V^0 \left(b_d,b_f,s\right)=max \big\{V^r \left(b_d,b_f,s\right),V^{dd} \left(b_f,s\right),V^{fd} \left(b_d,s\right),V^{td}(s)\big\} \end{equation}

The government’s default decisions are summarized by default indicators $\delta ^i_j$ assuming value 1 in the case of default, where subscript $j$ stands for the defaulted debt: foreign and domestic ( $j=f,d$ ) and superscript $i$ stands for the current state: repayment, foreign default and domestic default ( $i=r,fd,dd$ ). It is sufficient to define two default indicators for repayment periods: $\delta ^r_{f}, \delta ^r_{d}$ (repayment decision is taken with both equal to zero and total default decision is taken with both equal to one) and one for each of the two selective default periods: $\delta ^{fd}_{d}, \delta ^{dd}_{f}$ . The government’s choices are presented graphically in Figure 2, where tree branches correspond from the left to the right to repayment, total, selective foreign and selective domestic defaults.

Figure 2. Government decision tree.Notes: When both markets are open ( $V^0$ ), the government can decide to repay both debts ( $V^r$ ), default on both debts ( $V^{td}$ ), repay only domestic debt ( $V^{fd}$ ) or repay only foreign debt ( $V^{dd}$ ). Subsequent possible choices are depicted on the lower branches of the decision tree.

If the government decides to repay it solves the following problem:

(8) \begin{equation} V^r\left(b_d,b_f,s\right)=\underset {b_d',b_f'}{max} \Big \{ u(c^r) + \beta {\mathbb E}_{} \left [ V^0(b_d',b_f',s' \right ] \Big \} \end{equation}

subject to four constraints: the households’ budget constraint (2), the foreign bond price schedule, the domestic bond price schedule and the government budget constraint. The foreign bond price schedule is given by:

(9) \begin{equation} q^r_f \left(b'_d,b'_f,s\right)=\frac { {\mathbb E}_{} \left [ 1-\delta ^r_{f} \left(b'_d,b'_f,s' \right) \right ]}{1+r} \end{equation}

where $q^r_f$ is the discount price of a government bond issued with foreign investors $b'_f$ , who are risk-neutral, deep-pocket and have access to international risk-free rate $r$ , and $\delta ^r_{f}$ is the indicator of the government’s decision to default on foreign debt. A risk-free foreign investor assumption is employed by the vast majority of the literature. Unlike foreign, we assume that domestic investors are risk-averse.Footnote ⁸ The risk-averse price of domestic debt is dynamic and depends on six states: two exogenous shocks, two debts issued and two debts outstanding (as they all affect the marginal utility of consumption). Unlike in models facing risk-neutral marginal investors, the fluctuations in both current consumption and expected consumption affect debt discount prices. The domestic bond price schedule reads:

(10) \begin{align} &q^r_d \left(b_d,b_f,b'_d,b'_f,s\right)=\notag \\ &=\beta \frac {{\mathbb E}_{} \left [ \left(1-{\delta ^r_{f}}'\right) \big(1-{\delta ^r_{d}}'\big) u_c\big ({c^r}'\big ) +{\delta ^r_{f}}'(1-{\delta ^r_d}') u_c\big ({c^{fd}}'\big ) \right ] } {u_c\left (c^r\right )}, \end{align}

where future expected utility consists of two parts: one related to repayment ( $\delta ^r_{f}=\delta ^r_{d}=0$ ) and one to foreign default ( $\delta ^r_{f}=1$ ). Only then is domestic debt serviced so it is a valid savings vehicle that enables intertemporal consumption smoothing. In (10) state space notation for default indicators and consumption levels has been suppressed to facilitate legibility. The last constraint is the government budget constraint:

(11) \begin{equation} T+q^r_db'_d +q^r_f b'_f=g+b_d+b_f. \end{equation}

Second, if the government defaults on foreign debt (but services its domestic obligations) the economy suffers an output cost, with the probability $1-\theta _f$ is excluded from the foreign debt market (and remains only on domestic one) and the government can still decide to also default on domestic debt (yielding total default). The government’s problem is:

(12) \begin{equation} V^{fd}(b_d,s)=\underset {b_d'}{max} \Bigg \{ u(c^{fd}) + \beta {\mathbb E}_{} \left [ \theta _f V^0 \left(0,b_d',s'\right) +(1-\theta _f) max\big \{V^{fd}\left(b_d',s'\right),V^{td}(s')\big \} \right ] \Bigg \} \end{equation}

subject to households’ budget constraint (2), households’ first-order condition

(13) \begin{equation} q_d^{\, fd}\big(b_d,b'_d,s\big)=\beta \frac {{\mathbb E}_{} \left [ \theta _f \left (1-{{\delta _{d}^{r}}'}\left (.,0,.\right )\right ) u_c\left ({c^r}'\left (.,0,. \right ) \right ) +\left (1-\theta _f\right ) \left (1-{\delta _{d}^{fd}}'\right )u_c\left ({c^{fd}}'\right ) \right ] } {u_c\left (c^{fd}\right )}, \end{equation}

where expected future marginal utility consists of two parts: one related to readmission to foreign markets and one related to foreign default, where $\delta ^{fd}_{d}$ is the probability of government going from foreign into total default. In (13) some arguments have been suppressed to facilitate legibility. The last is the government budget constraint:

(14) \begin{equation} T+q^{\, fd}_d b'_d =g+b_d. \end{equation}

Third, if the government decides to default selectively on domestic debt it remains active on the foreign market, comes back to domestic borrowing with the probability $\theta _d$ , suffers the domestic output penalty and can still default on foreign debt:

(15) \begin{equation} V^{dd} \left(b_f,s\right)=\underset {b_f'}{max} \Bigg \{ u(c^{dd}) + \beta {\mathbb E}_{} \left [ \theta _d V^0\left(b'_f,0,s'\right) +(1-\theta _d) max\big \{V^{dd}\left(b_f',s'\right),V^{td}(s')\big \} \right ] \Bigg \} \end{equation}

subject to households’ budget constraint (2), the foreign bond price schedule

(16) \begin{equation} q^{dd}_f\left(b'_f,s\right)= \theta _d \frac { {\mathbb E}_{} \left [ 1-{\delta _{f}^{r}}\left(b'_f,0,s'\right) \right ] } {1+r}+(1-\theta _d)\frac { {\mathbb E}_{} \left [ 1-{\delta _{f}^{dd}}\left(b'_f,s'\right) \right ] } {1+r}, \end{equation}

which is a probabilities-weighted sum of the price of foreign debt in repayment and foreign debt in domestic default, with $\delta _{d}^{fd}$ being the probability of the government going from foreign default into total default. The last is the government budget constraint:

(17) \begin{equation} T+q^{dd}_fb'_f =g+b_f. \end{equation}

Fourth, if the government decides to pursue total default, the economy suffers the output penalties for both domestic and foreign default, and the government comes back to the international and domestic markets with probabilities $\theta _f$ and $\theta _d$ respectively. The government’s problem is summarized by:

(18) \begin{align} V^{td}(s)=u(c^{td})&+\beta {\mathbb E}_{} \left [ \theta _f\theta _d V^0(0,0,s) + \theta _f(1-\theta _d)V^{dd}(0,s')\right.\nonumber\\ &\left.+ (1-\theta _f)\theta _dV^{fd}(0,s')+(1-\theta _f)(1-\theta _d)V^{td}(s') \right ] \end{align}

subject to households’ budget constraint (2) and the government budget constraint

(19) \begin{equation} T=g. \end{equation}

Let $B=\{b_d,b_f\}$ define endogenous and $s=\{y,\tau \}$ define exogenous states in the economy.

Finally, the default schedules are derived from the government’s choice of value functions associated with repayment and defaults:

(20) \begin{align} &\text{Repayment: } &\delta ^r_f=0, \delta ^r_d=0 & \iff V^r \geq max\big \{ V^{fd}, V^{dd}, V^{td}\big \} \nonumber\\[-12pt]\end{align}

(21) \begin{align} &\text{Foreign default: }& \delta ^r_f=1, \delta ^r_d=0 & \iff V^{fd} \gt max\big \{ V^{r}, V^{dd}, V^{td} \big \} \nonumber\\[-12pt]\end{align}

(22) \begin{align} &\text{Domestic default: } & \delta ^r_f=0, \delta ^r_d=1 & \iff V^{dd} \gt max\big \{ V^{r}, V^{fd}, V^{td} \big \} \nonumber\\[-12pt]\end{align}

(23) \begin{align} &\text{Total default: } &\delta ^r_f=1, \delta ^r_d=1 & \iff V^{td} \gt max \big \{V^r, V^{fd}, V^{dd} \big \} \nonumber\\[-12pt]\end{align}

(24) \begin{align} &\text{Domestic repayment after FD:} &\delta ^{fd}_d=0 & \iff V^{fd} \geq V^{td} \nonumber\\[-12pt]\end{align}

(25) \begin{align} &\text{Domestic default after FD: }& \delta ^{fd}_d=1 & \iff V^{fd} \lt V^{td} \nonumber\\[-12pt]\end{align}

(26) \begin{align} &\text{Foreign default after DD: } & \delta ^{dd}_f=0 & \iff V^{dd} \geq V^{td} \nonumber\\[-12pt]\end{align}

(27) \begin{align} &\text{Foreign repayment after DD: } & \delta ^{dd}_f=1 & \iff V^{dd}\lt V^{td} \end{align}

4.1 Calibration

To solve the model numerically, we assume functional forms for the exogenous processes and assign parameter values. The data availability dictates the choice of a frequency for the model. As default frequencies and debt-to-GDP ratios, are best thought of at annual frequency we set up the model annually. There are two sets of parameters in the model. The first set, presented in Table 2, consists of values that are standard in the literature or that can be directly calculated from the data. The second set, presented in Table 3, consists of values calibrated so that the model replicates a selection of statistics presented in Stylized Facts. We set the risk aversion coefficient $\sigma$ equal to 2 and the risk-free interest rate $r$ to $1.7\%$ yearly, which are the standard values in the literature. The discount factor $\beta$ we set to 0.825, which is a yearly equivalent of the quarterly $\beta =0.953$ found in Arellano (Reference Arellano2008).

We calculate the level of government expenditure as spending on public consumption (government purchases of goods and services). We use a new dataset by Michaud and Rothert (Reference Michaud and Rothert2018) who calculate government expenditure for a sample of advanced and emerging economies with a detailed breakdown into different spending categories. The average spending on public consumption-to-GDP in emerging economies is 3.8%.

Table 3. Set parameters

We calculate persistence and standard deviation of output using our dataset introduced in Stylized Facts. Using the yearly output data series for the sample of 101 emerging economies, and de-trending using the HP filter, the mean of the estimates for $\rho _y$ is 0.69 and for $\epsilon _y$ is 0.094.

As there is no readily available measure of the tax wedge in the data, we identify the movements in the tax wedge via the movements in the TB. The two are inversely related.Footnote ⁹

Using the yearly data for the value-added taxes in 55 emerging economies (Prichard et al., Reference Prichard, Cobham and Goodall2014; World Tax Database, 2015) the estimate of $\rho _{\tau }$ is 0.71 and of $\epsilon _{\tau }$ is 0.11. For the mean tax wedge $\bar {\tau }$ we take a conservative stand and parametrize it at 0.025, which is the lowest estimate of the static deadweight loss from taxation that we have found in the literature (Harberger, Reference Harberger1964). We assume that the two processes are uncorrelated. This will allow the model to isolate the endogenous spillover effects from the exogenous interdependence and is consistent with the data (empirically, the correlation is equal to 0.0095).Footnote ¹⁰ Finally, we set the values of the exclusion probabilities $\theta _d, \theta _f$ to match the lengths of foreign and domestic defaults evidenced in Table 4, resulting in $\gamma _f=0.147$ and $\gamma _d=0.244$ . These are well within the range of parameters typically used in the literature.

Table 4. Calibrated parameters

Table 4 contains the values for the output penalties upon default $\gamma _d, \gamma _f$ , which we calibrate to match domestic and foreign default frequencies also evidenced in Table 4 of 3% on foreign, and 4.1% on domestic debt. This yields calibrated parameters of $\gamma _f=0.808$ and $\gamma _d=1.0175$ . In the next subsections, we study the quantitative properties of the model, but the calibration exercise already indicates that to match the quantitative behavior of foreign debt and default, the model requires a significant output penalty upon default: output drops to 0.808 whenever it would be above this level during a default episode. Conversely, on the domestic market, the exclusion from borrowing is a sufficient threat and almost no additional output penalties are required to sustain domestic debt and match the domestic default frequency. Output drops to 1.0175 (slightly above the average) whenever it would be above that level during a default episode. This means that additional production penalties on the domestic market are only operational when the government intends to default with a high output.Footnote ¹¹

We solve the model by discretizing the state space for income shocks and tax distortions using a variant of the Tauchen method to approximate a two-dimensional Markov process. Foreign and domestic bond asset positions are discretized using grids with 31 and 33 points, respectively. Income and tax distortion shocks are discretized using grids with 23 and 25 points, respectively. Value functions for repayment and selective defaults are computed iteratively through value function iterations combined with bond price updating, accounting for endogenous default decisions. We solve for equilibrium bond prices ensuring consistency with borrowers’ default incentives and lenders’ pricing through the Euler equation. The equilibrium policies and prices are obtained once the value and price functions converge within a prescribed tolerance. More details on the solution method, including grid construction, numerical acceleration techniques, and convergence criteria, are provided in the Online Appendix.

4.2 Policy functions

In this section we analyze default and debt issuance policies in the calibrated model. Throughout the analysis we find that the policies for foreign debt and default respond strongly to the changes in output and little (or not at all) to changes in the tax wedge. However, policies for domestic debt and default respond strongly to both output and the tax wedge. Even though markets are segmented, we also document spillovers from one market to the other.

Default sets. Figure 3 plots the default-repayment policies for foreign debt, and Figure 4 plots the default-repayment policies for domestic debt. The level of debt is plotted horizontally on each graph and the output (left panel) and the tax wedge (right panel) are plotted vertically.

Foreign default becomes more likely as the level of foreign debt goes up and as the output goes down. For high levels of output, any level of foreign debt is safe. There is almost no variability in the foreign default decision with respect to the tax wedge. The foreign default set is decreasing in output, therefore, the foreign interest rate is decreasing in output as well. Foreign default happens when the output suddenly drops.

Figure 3. Default sets for foreign debt in output (left) and tax wedge (right).Notes: The figure plots default sets on the foreign debt in the foreign assets-income space (left) and foreign assets-tax wedge space (right). The domestic debt level in both panels is set at 0, tax distortions, in the left panel, are set at 0.024, and income, in the right panel, is set at 0.86.

Figure 4. Default sets for domestic debt in output (left) and tax wedge (right).Notes: The figure plots default sets on the foreign debt in the foreign assets-income space (left) and foreign assets-tax wedge space (right). The foreign debt level in both panels is set at 0, tax distortions, in the left panel, are set at 0.024, and income, in the right panel, is set at 0.86.

Default on each debt becomes more likely when the output drops. Empirical work provides strong evidence that domestic and foreign defaults are associated with substantial and prolonged contractions in output (Reinhart and Rogoff, Reference Reinhart and Rogoff2011a; Schmitt-Grohé and Uribe, Reference Schmitt-Grohé and Uribe2017). Domestic default is not only driven by tax wedge, but (due to the specification of the default costs), it also depends on output fluctuations. Domestic default becomes more likely as the tax wedge increases. Domestic default happens only with low output. The medium and high output levels render the domestic debt virtually safe.

Debt issuance. Figure 5 plots the bond issuance policies, i.e. future assets as a function of today’s assets, in the left panel for foreign assets and in the right panel for domestic assets. Lines represent different output levels. In the Figure we also plot the 45-degree line, to show when the economy issues more debt (below) and less debt (above) than is currently outstanding. The economy accumulates foreign debt when output is high due to the countercyclicality of the interest rate. An economy with a default risk engages in procyclical foreign borrowing, it increases its debt position when the output is high, and reduces its debt position when the output is low. Similar results for foreign debt are found across quantitative models of sovereign default. For the low output, there is a well-defined debt limit, below which the currently outstanding debt will be defaulted. As such, the new debt issuance drops to zero, as the economy optimally chooses to default. For the high output, there is also a maximum level of debt sustainable in equilibrium: at some point, the issuance policy crosses the 45-degree line, which means that it is optimal for the economy to reduce its foreign debt position. Foreign debt issuance is almost exclusively driven by output fluctuations. Foreign default occurs in a recession when foreign debt is high.

Figure 5. Foreign (left) and domestic (right) debt issuance policies as functions of output.Notes: The figure plots future assets position, as functions of outstanding assets position on the foreign market (left panel) and domestic market (right panel), for low output (red line) and high output (blue line). The 45-degree line is included in both panels to indicate when the future asset position is equal to the current asset position. The level of domestic assets in the left panel is set to 0, and the level of foreign assets in the right panel is set to 0. The level of the tax wedge in both panels is set to 0.024. Low output ( $y_L$ ) is set to 0.86, and high output ( $y_H$ ) is set to 1.12, in both panels.

Domestic debt issuance is qualitatively different from foreign debt issuance. The assumed level of tax distortions is at the average. Irrespective of the output level, the government has incentives to save—both optimal issuance lines are above the 45-degree line. This suggests that tax distortions, and not output, are instrumental for debt build-up on domestic market, as we show in Figure 6. Interestingly, when domestic debt is low, and so it is safe, the incentives to save are stronger with higher output.

Figure 6. Foreign (left) and domestic (right) debt issuance policies as functions of tax wedge.Notes: The figure plots future assets position, as functions of outstanding assets position on the foreign market (left panel) and domestic market (right panel), for a low-tax wedge (red line) and high-tax wedge (blue line). The 45-degree line is included in both panels to indicate when the future asset position is equal to the current asset position. The low-tax wedge ( $\tau _L$ ) is set to 0.018, and the high-tax wedge ( $y_H$ ) is set to 0.035, in both panels. The level of output is set to 0.86, in both panels. The level of the asset outstanding on the other market is set to -0.18.

Conversely, in Figure 6 lines represent different levels of the tax wedge. The foreign debt policy is almost entirely driven by fluctuations in output and does not respond to changes in the tax wedge. Domestic debt strongly responds to the fluctuations in the tax wedge. When the tax wedge is low (red line), the government prefers to finance its expenditures via taxation, because raising taxes comes at the lowest cost for the economy. Therefore, debt issuance is low, regardless of the domestic debt outstanding. When the tax wedge goes up (blue line) the government employs a “gambling for redemption” policy. The government increases its domestic debt position—the issuance line is much below the 45-degree line. The government finds it optimal to pile up domestic debt in the hope that it will be repaid with taxes, sometime in the future, if the low-tax wedge day comes. If tax wedge remains high, the domestic debt is defaulted. Therefore, the tax wedge is thus instrumental to the build-up of domestic debt and to trigger domestic default.

Debt discount prices. Figure 7 plots the bond discount prices as functions of current assets, with the left panel showing foreign bond prices and the right panel showing domestic bond prices. Foreign bond prices reflect the perceived risk of default, and domestic bond prices reflect the perceived risk of default and the ratio of marginal utilities from consumption today and tomorrow.

Foreign bond prices decline as the economy accumulates more foreign debt, particularly when output is low. This reflects a higher default risk in recessions when the economy is already highly indebted. The price schedule becomes steeper in downturns, indicating increased sensitivity of foreign lenders to the risk of default. At very low levels of assets, bond prices drop sharply, as lenders demand very high returns or avoid lending altogether. This drives the endogenous borrowing constraints present in sovereign default models. In contrast, with high output and moderate debt levels, foreign bond prices reflect the risk-free rate, consistent with low risk and full repayment in equilibrium.

The behavior of domestic bond prices is qualitative similar but less quantitatively sensitive to the domestic debt level. When output is high and domestic debt is low and considered safe, domestic bond prices remain equal to the discount factor. However, as domestic debt increases especially when output is low, bond prices begin to fall, reflecting the increased risk perceived by domestic lenders. In particular, unlike foreign bonds, domestic bond prices do not fall to zero as the government internalizes the welfare of domestic creditors. The variation in domestic bond prices is procyclical, but less sensitive to domestic debt.

5.1 Stylized facts

We simulate the model by drawing Markov chains for the two exogenous shocks (productivity and tax distortion) across 100 model economies, which are identical ex-ante, each lasting for 10,000 periods. In each period, households and governments update their asset positions based on policy functions computed from the model solution, taking into account default decisions on foreign and domestic debt. Defaults occur endogenously whenever default values exceed repayment values. Post-default re-entry follows calibrated probabilities, and bond prices are updated accordingly. Tables 5 and 6 present average moments calculated across time, and averaged across the model economies. Figure 8 presents sample paths of the key model variables for randomly selected 200 periods in one randomly selected economy.

Table 5 presents a set of model-simulated equivalents of the empirical Stylized Facts presented in Section 2 in Tables 1 and 4, that is, debt-to-GDP ratios, default frequencies, and the debt correlation obtained from the data versus the respective numbers obtained from the model. The model reproduces all of the stylized facts laid out in the motivation for this paper. The most striking finding is that the model is easily capable of simultaneously delivering observed high debt-to-GDP ratios (1 and 2) and low default frequencies (4 and 5). The model explains 84% of the average foreign debt-to-GDP and 51% of the average domestic debt-to-GDP in emerging economies while matching low default frequencies almost perfectly. It is a well-documented fact that the standard model with only one-period foreign debt fails at this exercise (see discussion in Chatterjee and Eyigungor (Reference Chatterjee and Eyigungor2012)). This happens because of the shape of the default area in the debt-output space: high foreign debt goes hand in hand with a high foreign default frequency. Our model mitigates this strong interdependence by introducing the second instrument, domestic debt.

Including defaultable domestic debt breaks this strong interdependence. It changes the government decision problem by increasing the menu of options available to the government, thus making foreign default relatively less attractive. Instead of entirely relying on foreign debt as a source of income, the government can raise domestic debt. As foreign default is less attractive, higher levels of foreign debt can be sustained with a lower probability of foreign default, ceteris paribus. Thus, our relatively simple model with one-period domestic and foreign debt is able to explain two-thirds of the average foreign debt and almost half of the average domestic debt.

The correlation of domestic and foreign debt (3) in the model is close to zero, very close to what is observed in the data, where the correlation is not statistically significant. It is important to note, that debt-to-GDP rations and debt correlation are untargeted moments in the simulation exercise. These comparisons show that the model is a good fit for the data.

The model replicates well selective default frequencies observed in the data, both for foreign and domestic markets. At first glance, the model appears to substantially underestimate the total default frequency (6), which is 1.58% in the data, whereas in the model total defaults, defined as simultaneous defaults on both debts, never occur in the same period. This outcome stems directly from the assumption that the output penalty for total default equals the product of the penalties from selective defaults. As a result, a rational government in the model optimally defaults selectively on one debt first and waits to observe whether economic conditions improve; if they do not, it subsequently defaults on the other debt. We refer to this sequence as a total default by overlap, meaning that the economy reaches a state of total default in our simulation without a direct transition from total repayment. Instead, the economy moves from a state of selective default to total default. Importantly, when we calculate the frequency of total defaults by overlap, the model matches the data quite closely, slightly overestimating the empirical frequency.

Table 5. Stylized facts: model v data

Notes: Model moments are obtained from the calibrated model at an annual frequency. Corresponding data moments are repeated from Tables 1 and 4 and based on own calculations based on Panizza (Reference Panizza2008), Reinhart and Rogoff (Reference Reinhart and Rogoff2011b) and Borri and Shakhnov (Reference Borri and Shakhnov2017).

Figure 7. Foreign (left) and domestic (right) bond prices.Notes: The figure plots debt discount prices as functions of outstanding assets position on the foreign market (left panel) and domestic market (right panel), for low output (red line) and high output (blue line). Low output ( $y_L$ ) is set to 0.86, and high output ( $y_H$ ) is set to 1.12, in both panels. The level of the tax wedge in both panels is set to 0.024. The level of assets outstanding in the other market is set to -0.22 in both panels.

Table 6. Cyclical properties: model v data

Notes: Model moments are obtained from the calibrated model at an annual frequency. Corresponding data moments for GDP, Consumption and Net Exports are based on quarterly series 1991Q1–2024Q4, for 21 emerging economies, and are sourced from the OECD. GDP and Consumption are detrended using the Hodrik–Prescott filter. Data moment for primary balance is calculated using yearly data 2000–2024. Data sources are introduced and data transformations are explained in the Online Appendix.

5.2 Cyclical properties

Figure 8. Time series of key variables from the simulated model.Notes: The figure plots the time series of key variables from the simulated model: output, tac distortion, foreign default indicator, domestic default indicator, foreign bond, and domestic bond. The figure shows a randomly selected 200-period sample drawn from 100 simulations of 10,000 periods each. All variables are reported at the yearly frequency and are expressed in levels. The simulation assumes a sequence of output and tax distortion shocks calibrated to match observed volatilities.Source: Own calculation.

In the second step, we study the cyclical properties of the model. Figure 8 plots sample paths for the key model variables using a random 200-period subsample from the full simulated dataset. Table 6 presents the cyclical properties of the model, calculated as average moments over time and across economies. These model moments are compared with the moments calculated from the data and the moments obtained in the model without domestic debt.

Figure 8 shows the simulated time series of key macroeconomic variables. Output (GDP) exhibits considerable volatility, consistent with the empirical evidence for emerging market economies. Periods of depressed output following default episodes are clearly visible. The model generates seven foreign default events during the sample, each occurring when output is low and foreign debt levels are high. However, not all episodes of foreign debt accumulation end in default. Most foreign debt build-ups occur when output is high and do not culminate in default. Defaults on foreign debt typically follow a sequence where debt accumulation is associated with high output, but then a sudden and sharp decline in output triggers a default. Following foreign defaults the economy is excluded from borrowing in international markets, resulting in the zero-debt position, for a variable period.

The dynamics of domestic debt are more complex. Domestic debt is more volatile than foreign debt in the simulations, and its accumulation is primarily driven by fluctuations in tax distortions. When tax wedges are high, governments tend to issue more domestic debt. However, defaults on domestic debt are not solely tied to the level of debt or tax distortions. Instead, they often occur after a sharp drop in output, like foreign defaults. Thus, while tax distortions govern the build-up of domestic liabilities, output shocks play a central role in triggering domestic defaults.

The dynamics highlighted in the simulated time series lead to a set of aggregate moments commonly used to evaluate models of emerging markets. Table 6 presents a comparison between key moments from the data and those generated by the model, including consumption volatility, the cyclical properties of the trade balance and primary balance, and the behavior of sovereign spreads. We also evaluate the role of domestic debt by comparing the baseline model with an alternative specification that excludes domestic borrowing.

Excess consumption volatility is a well-known feature of emerging economies (1). In the model, consumption is not smoothed relative to output, because sovereign risk makes prices of debts volatile. This matches the observation that consumption is more volatile than output, both in the data and in the model.

The model reproduces the countercyclicality of the trade balance. The also captures higher correlation of primary balance with GDP compared to trade balance. In the standard model with only foreign debt, the trade balance and the primary balance are identical, but the introduction of domestic debt allows these two objects to differ. In recessions, governments face higher borrowing costs, leading to increased reliance on tax revenues, while in expansions they accumulate more debt when credit is cheaper. Accordingly, the trade balance is countercyclical, with a negative correlation with output (2), and the model matches this stylized fact.

Our model allows us to draw a clear distinction between the two. The change in the primary balance equals the sum of changes in both foreign and domestic debts. The model predicts strong procyclicality of the primary balance, and in the data the correlation between the primary balance and output (3) is also higher than that of trade balance (2), however, it is weakly positive. Yet, our model still improves over the model without foreign debt. The primary balance is less correlated with output than the trade balance because domestic debt issuance is less sensitive to output than foreign.

The model also replicates the countercyclicality of sovereign spreads on both foreign and domestic debt (8 and 9). As output falls, default risk increases, reducing bond prices and raising spreads. The correlations between spreads and output are close in magnitude and sign to those observed in the data.

Excess consumption volatility, countercyclical net exports, and countercyclical foreign spread are the standard data tests for small open economy models proposed by Neumeyer and Perri (Reference Neumeyer and Perri2005). Our model passes these tests, improving over earlier models by better capturing both the degree of countercyclicality of the trade balance and the procyclicality of the primary balance.

The novel features of our model, the tax wedge and domestic debt, allow us to look at the data in previously unexplored dimensions. We show the abilities and limitations of the model in matching these features with the data.

Domestic default frequency and domestic spread have not yet been looked at in either business cycle or sovereign default literature. In the simulated series, the domestic default frequency is very close to that observed in the data (Table 5), but the average domestic spread (6) and the standard deviation of domestic spread (7) are much higher than in the data. This is because domestic debt is priced the risk-averse domestic households.Footnote ¹²

On the other hand, the average foreign spread (4) is very close to that observed in the data. It is also less volatile than the domestic spread (5). These discrepancies follow from the assumptions of one-period bond and the difference in risk aversion between risk-neutral foreign investors and risk-averse domestic investors. In the domestic market, introducing a second, safe asset would bring down both the level and the volatility of the domestic spread (albeit at the expense of lower levels of domestic debt and lower probability of default). In the foreign market, Lizarazo (Reference Lizarazo2013) shows that introducing risk aversion on the side of foreign investors helps to bring foreign spreads to empirically observable levels. Alternatively, Chatterjee and Eyigungor (Reference Chatterjee and Eyigungor2012) shows that the model with long-term debt and non-linear default costs can match the level and volatility of the foreign spread.

Domestic spread is countercyclical (9), and the model reproduces this fact quantitatively well. The domestic spread in the model is driven mainly by changes in consumption, which are affected by output and foreign debt. As foreign debt is procyclical, both work in the same direction. This is why domestic spread is strongly countercyclical, much more so than in the data.

5.3 Default episodes

Using our model, we can study the behavior of key macroeconomic variables around different types of default episodes. Table 7 reports averages of output, tax wedge, consumption, debt-to-GDP ratios, and bond prices across all simulations, as well as conditional averages just prior to and at the time of a foreign or domestic default.

Table 7. Default episodes

Notes: The table reports average macroeconomic indicators and asset positions across all simulations (column 1), conditional averages before foreign default (column 2), at the onset of foreign default (column 3), before domestic default (column 4) and at the onset of domestic default (column 5). Debt-to-GDP ratios are computed using contemporaneous output. Discount prices reflect the average bond price prevailing in the respective period. Values are averages across all simulations and episodes.Source: Own calculations.

The results reveal several important patterns. First, output drops sharply at the time of a foreign default, with a larger and more sudden decline than at the time of a domestic default. This pattern partly reflects the model’s assumption that the output cost of a foreign default is higher. However, it is also an endogenous outcome: in the model, output remains above trend one year before a foreign default and falls precipitously when the default occurs. Both the table and the associated figure, Figure 9, highlight these differences. Prior to foreign defaults, output is typically higher, and the subsequent decline is deeper and more persistent than in the case of domestic defaults. Domestic defaults occur when output is already lower, and the resulting output drop is smaller and shorter-lived.

Figure 9 provides a more detailed comparison of these dynamics in the model and in the data. The top panel shows the average path of output deviations around foreign defaults, while the bottom panel focuses on domestic defaults. While the model broadly replicates the qualitative pattern seen in the data, it generates somewhat higher volatility around foreign defaults: output levels before foreign defaults are higher, and the drop is larger, compared to empirical observations. However, this behavior is an endogenous feature of the model, rather than a result of specific calibration targeting. Given that no explicit moment matching was done for these paths, the model’s ability to reproduce these patterns remains a notable success.

Second, the tax wedge surges before domestic default episodes, suggesting that tax distortions not only contribute to the accumulation of domestic debt, they also directly trigger default events. Third, the model predicts that consumption falls more sharply during foreign defaults than during domestic defaults, mirroring the larger output contraction. Fourth, both domestic and foreign debts tend to significantly above their respective averages just before default events, reflecting the model’s prediction that the riskiness of sovereign debt increases with its size, as shown in Figure 3.

Finally, despite the segmentation between domestic and foreign debt markets and the lack of correlation in the underlying shocks, the model generates important spillover effects between the two. The price of foreign debt declines before a domestic default and the price of domestic bonds falls after a foreign default. These spillovers arise because defaults in one market worsen the government’s repayment capacity in the other. For instance, following a domestic default, the government loses access to domestic borrowing and must rely more heavily on taxation to service foreign debt, increasing perceived default risk for foreign creditors. Similarly, after a foreign default, domestic savers, being risk-averse, demand a steep discount on domestic bonds as output collapses.

Overall, this section shows that the model, with two debt instruments and two distinct sources of risk, improves the ability to replicate the business cycle dynamics of emerging economies. Moreover, even in the presence of market segmentation, it generates realistic and endogenous cross-market spillovers, deepening our understanding of sovereign debt crises.

Figure 9. Average output path around foreign (top) and domestic default (bottom) in the data and in the model.Notes: The figure plots average output paths around default episodes. The top panel shows output around foreign defaults, and the bottom panel shows output around domestic defaults. Output deviations are measured relative to the trend, and all series are normalized to zero at the time of default. Model-generated paths are compared to empirical paths obtained from HP-filtered output series. Time is measured in years relative to the default event.Source: Own calculations.