metadata: authors: 0: author: Horn,Sebastian Andreas
1: author: Mihalyi,David
2: author: Nickol,Philipp
3: author: Sosa-Padilla,César
count: World
docna: 0: docna: Hidden Debt Revelations
docty: Policy Research Working Paper
abstracts: cdata!: How reliable are public debt statistics?
            This paper quantifies the magnitude, characteristics, and
            timing of hidden debt by tracking ex post data revisions
            across a comprehensive new database of more than 50 vintages
            of World Bank debt statistics. In a sample of debt data
            covering 146 countries and 53 years, the paper establishes
            three new stylized facts: (i) debt statistics are
            systematically under-reported; (ii) hidden debt accumulates
            in boom years and tends to be revealed in bad times, often
            during IMF programs and sovereign defaults; and (iii) in
            debt restructurings, higher hidden debt is associated with
            larger creditor losses. The novel data is used to
            numerically discipline a quantitative sovereign debt model
            with hidden debt accumulation and an endogenous monitoring
            decision that triggers revelations. Model simulations show
            that hidden debt has adverse effects on default risk,
            debt-carrying capacity and asset prices and is therefore
            welfare detrimental.
display_title: Hidden Debt Revelations
listing_relative_url: /research/2024/09/34391658/hidden-debt-revelations
topicv3: Economic Governance and Transparency
            m1326082 407,Debt Management m1327211 451,Debt Restructuring m1327213 454,Debt and Fiscal Sustainability m1327677 456
publishtoextweb_dt: 2024-09-16T00:00:00Z
dois: 10.1596/1813-9450-10907
origu: Off of Sr VP Dev Econ/Chief Econ (DECVP)
no_of_pages: 91
author_keys: 0: author_key: 2084381
1: author_key: 1965522
2: author_key: NA
3: author_key: NA
model_extractions: Policy Research Working Paper 10907

# Hidden Debt Revelations

_Sebastian Horn David Mihalyi Philipp Nickol César Sosa-Padilla_ Macroeconomics, Trade and Investment Global Practice September 2024
Policy Research Working Paper 10907

# **Abstract**

How reliable are public debt statistics? This paper quantifies the magnitude, characteristics, and timing of hidden debt by tracking ex post data revisions across a comprehensive new database of more than 50 vintages of World Bank debt statistics. In a sample of debt data covering 146 countries and 53 years, the paper establishes three new stylized facts: (i) debt statistics are systematically under-reported; (ii) hidden debt accumulates in boom years and tends to be revealed in bad times, often during IMF programs and sovereign defaults; and (iii) in debt restructurings, higher hidden debt is associated with larger creditor losses. The novel data is used to numerically discipline a quantitative sovereign debt model with hidden debt accumulation and an endogenous monitoring decision that triggers revelations. Model simulations show that hidden debt has adverse effects on default risk, debt-carrying capacity and asset prices and is therefore welfare detrimental.

This paper is a product of the Macroeconomics, Trade and Investment Global Practice. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://www.worldbank.org/prwp. The authors may be contacted at shorn1@worldbank.org; dmihalyi@worldbank.org; philipp.nickol@vwl.uni-due.de; and csosapad@nd.edu.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# **Hidden Debt Revelations**<sup>∗</sup>

Sebastian Horn David Mihalyi Philipp Nickol César Sosa-Padilla<sup>†</sup>

**Keywords:** _hidden debt, sovereign debt, default_ **JEL classification:** _F34, H63, G01_

> ∗We received valuable comments from Fernando Arce, Tamon Asonuma, Gadi Barlevy, Volker Clausen, Aitor Erce, Stelios Fourakis, Juan Carlos Hatchondo, Aart Kraay, Leonardo Martinez, Julian MartinezIriarte, Marti Mestieri, Ugo Panizza, Juan Passadore, Carmen Reinhart, Diego Rivetti, Juan Sanchez, Zachary Stangebye, and Christoph Trebesch as well as from seminar participants at the Kiel Institute, the Inter-American Development Bank, the University of Duisburg-Essen, the Ruhr Graduate School in Economics, the World Bank, the University of Rochester, the University of Michigan, Purdue University, the Chicago Fed, the Richmond Fed, the 2024 NBER IFM Spring Meeting, the 2023 SED Annual Meeting and the 2023 Annual Meeting of the Verein für Socialpolitik. We thank Evis Rucaj and the entire team of the World Bank Development Data Group for answering countless questions on the International Debt Statistics. Gregor Ilsinger and Robert Remy provided excellent research assistance. We thank the German Federal Ministry for Economic Affairs and Climate Action and the German Federal Ministry of Finance for their financial support. All views expressed in this paper are those of the authors. They do not necessarily represent the views of the World Bank.

> †Sebastian Horn: World Bank. Email: shorn1@worldbank.org; David Mihalyi: World Bank, Kiel Institute. Email: dmihalyi@worldbank.org; Philipp Nickol: UDE, RGS. Email: philipp.nickol@vwl.uni-due.de; César Sosa-Padilla: University of Notre Dame, NBER. Email: csosapad@nd.edu
# **1 Introduction**

Public debt statistics are a cornerstone of macroeconomic analysis. Investors, taxpayers, and academic researchers all have a keen interest in the level and composition of a country’s public debt. However, these statistics are subject to major limitations and incomplete reporting (World Bank, 2021; Horn et al., 2021). When Zambia and Chad sought debt restructurings in 2021, it took them more than six months to assemble comprehensive debt data and reconcile it with the records of their creditors (Estevão, 2021). Most famously perhaps, large revelations of previously unreported debts triggered major debt crises in Greece and Mozambique (Reinhart and Rogoff, 2011a,b; IMF, 2018). Despite the importance of hidden debt, there is little research that systematically measures its magnitude, characteristics, and effects.

We fill this gap by quantifying hidden debt by systematically tracking ex post revisions of debt figures across different editions (“vintages”) of the most widely used international debt statistics. The key idea is as follows: when previously unreported loans are reported, past debt statistics need to be revised. Tracking these revisions allows us to quantify the scale, characteristics, and timing of hidden debt accumulation and revelation. We apply this approach to a new and comprehensive dataset of the past 51 vintages of the World Bank’s International Debt Statistics that we digitize from archival sources all the way back to the 1970s. Our new approach and data allow us to systematically document the degree of under-reporting for more than 50 years of data and for up to 146 developing and emerging market countries.

Our empirical analysis makes three novel contributions to our understanding of hidden debt. First and foremost, we document that there is a pervasive under-reporting of public debts. We show that debt data revisions are systematically upward biased for almost all debtor regions and income groups. Across all countries and years, we identify USD 1 trillion in “hidden” sovereign borrowing that is added to debt statistics only in hindsight, more than twelve percent of total sovereign borrowing by all countries in our sample. This amount is a lower bound for the true magnitude of hidden debt since not all unreported debt is eventually revealed. In the cross-section of countries, hidden debt levels are highest in countries with weak institutions and low capacity, however, even the countries with the strongest institutions in our sample exhibit systematic downward bias in their debt reporting. Comparing across creditor groups, we document that non-bond private loans and bilateral loan instruments are the most prone to under-reporting.

Second, we show that hidden debt tends to accumulate when growth is strong and be revealed in economic downturns. For example, the COVID-19 recession was followed by the largest hidden debt revelation in 50 years.<sup>1</sup> We document that the procyclicality of hidden debt accumulation and revelation is mainly driven by time-varying monitoring efforts. In our

> 1Recent World Bank efforts to strengthen debt reporting are discussed in World Bank (2022a).

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data, hidden debt revelations are particularly sizeable during sovereign default episodes and IMF programs, when the sovereign’s books come under close scrutiny.<sup>2</sup> Third, we use our new data to shed light on the role of hidden debts during sovereign default episodes and the debt resolution process. One key concern among bondholders during sovereign restructurings is that hidden debt can dilute the recovery value of their own marketable claims. During recent debt restructuring episodes, for example in Zambia, such concerns amplified coordination issues and led to substantial delays in debt resolution, with potentially severe costs for debtors and creditors alike.<sup>3</sup> To systematically analyze the role of hidden debt in default episodes we combine our data on debt under-reporting with data on the outcomes of all sovereign restructurings with private creditors since 1970. We find that higher hidden debt at the onset of a restructuring is associated with both longer restructuring episodes and larger creditor losses, which suggests that high hidden debts do indeed dilute the recovery value of market investors.

Motivated by these findings, we develop a quantitative sovereign debt and default model (in the tradition of Eaton and Gersovitz, 1981, Arellano, 2008, and Aguiar and Gopinath, 2006) with hidden debt, asymmetric information and an endogenous information acquisition problem that generates hidden debt revelations. The sovereign debtor in the model faces an exogenous hidden debt accumulation process that is not observed by investors in the country’s market debt. Each period, however, the investors need to decide whether to monitor the sovereign’s books. In line with our empirical evidence, the model features a recovery rate for market debt that is diluted by undisclosed hidden debts of the sovereign. This aspect gives bond investors further incentives to monitor the sovereign, therefore triggering revelations of hidden debt, particularly during bad times when sovereign default risk is high, just as we observe in the data.

We calibrate this model with our new data and analyze the effects of both hidden debt and its revelation. We show that asymmetric information about the true level of indebtedness has sizeable effects on equilibrium outcomes: The existence of hidden debt increases default incentives and depresses sovereign bond prices. To compensate investors for the uncertainty about true debt levels, sovereign borrowers need to pay higher spreads for given levels of market debt. On the other hand, monitoring-induced revelations of hidden debt are uncertainty reducing and therefore decrease the sovereign’s borrowing costs for a given level of overall debt. If the revealed amount of hidden debt is large, however, the increase in overall debt leads to an increase in spreads that outweighs the spread compression from reduced uncertainty. Thus, our model predicts that the spread response to a revelation increases with the amount of hidden debt that is revealed. We corroborate this finding empirically by running panel regressions of bond price reactions on our new measures of hidden debt revelations.

> 2In contrast, we do not find evidence that governments strategically disclose hidden debts for political gains.

> 3Zambia’s bondholders rejected the government’s first debt relief request citing debt transparency concerns in 2020. The following year the government conceded that its debt had been under-reported. See Financial Times (2020, November 13) _“Zambia on brink of default after lenders reject debt relief request”_ and Financial Times (2020, September 30) _“Bondholders balk at Zambia’s plan to delay debt payments”_ .

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Overall, hidden debt is welfare detrimental because it worsens the borrowing opportunities of the debtor country. Eliminating the uncertainty associated with hidden debt (by making it public information) allows the economy to sustain higher debt at lower spreads, delivering large average welfare gains of 5.5 percent of permanent income. Our model also allows us to analyze the welfare effects of increased oversight in a world with asymmetric information and hidden debt. We find that only countries with strong fundamentals and low hidden debt levels benefit from increased transparency. In contrast, countries with high levels of hidden debt are likely to find exposure to greater scrutiny to be costly. This finding suggests that transparency policies are best implemented during good times to avoid the negative welfare effects of exposing hidden debts during times of crisis.

**Related literature.** Our findings and data shed new light on several well-documented empirical patterns in sovereign debt markets. One long-standing puzzle in the academic literature is why developing and emerging market countries have repeatedly entered default and debt distress at seemingly manageable levels of public debt, i.e., the widespread phenomenon of “debt intolerance” (Reinhart et al., 2003; Reinhart and Rogoff, 2009). The frequent and sizeable ex post upward revisions that we document here may help to rationalize the strong crisis susceptibility of debt-intolerant countries even at low levels of _reported_ debt. Relatedly, high uncertainty over the true value of developing country indebtedness may contribute to the high levels of consumption volatility in developing countries (Aguiar and Gopinath, 2007; Alvarez-Parra et al., 2013) and to the remarkably low cross-border capital inflows that these countries have been able to attract (Lucas, 1990; Alfaro et al., 2008; Greenwood et al., 2010). Our findings also add to a large and influential literature on the procyclicality of macroeconomic variables and policies in developing and emerging market countries (see, e.g., Kaminsky et al., 2004; Reinhart and Reinhart, 2008; Alesina et al., 2008; Bianchi et al., 2023; Azzimonti and Mitra, 2023). We show that the procyclical accumulation and revelation of hidden debt can amplify boom-bust patterns by increasing resources in good times and generating additional bad news during economic downturns. Finally, our finding that the instruments of different creditors differ systematically in their propensity to be under-reported contributes to a nascent literature on the importance of investor composition in sovereign debt and other asset markets (Fang et al., 2023; Coppola, 2024; Agarwal et al., 2024; Graf von Luckner and Horn, 2024).

Our paper also contributes to a large literature that studies the implications of asymmetric information and investor attention on asset prices and financial crises (for overviews see, e.g., Brunnermeier, 2001; Gorton and Ordonez, 2023; Veldkamp, 2023). In particular, our paper is closely related to a growing body of theoretical work that analyzes sovereign debt markets with asymmetric information and opaque borrowing (Kletzer, 1984; Alfaro and Kanczuk, 2022; Guler et al., 2022; Gamboa, 2023; Kondo et al., 2024; Gu and Stangebye, 2023), often with a focus on government reputation (D’Erasmo, 2011; Fourakis, 2021; Morelli and Moretti, 2023).<sup>4</sup> Our finding that hidden debt tends to be revealed during episodes of sovereign distress further informs and is consistent with theories that link financial crises to state-contingent information acquisition (Gorton and Ordonez, 2014; Cole et al., 2022, 2024;

> 4Related papers on unsecured consumer credit, default and asymmetric information include Chatterjee et al. (2023), Athreya et al. (2012), and Sanchez (2018).

3
Gu and Stangebye, 2023). We contribute to this literature by compiling rich new data and by integrating a simple information acquisition problem with a quantitative sovereign debt and default model that features asymmetric information about the sovereign’s true debt level.

Our findings have important implications for empirical research more broadly, as debt statistics are essential input variables for a large variety of research designs. Researchers should be wary of the fact that data downloads from different vintages of debt statistics can lead to significantly different results and can therefore complicate the replication and updating of empirical work (also see Aruoba, 2008; Christensen and Miguel, 2018; Goes, 2024). Empirical applications in macroeconomic forecasting or asset pricing, in particular, need to take into account that debt figures tend to get upward revised after their initial publication (Frankel, 2011; Beaudry and Willems, 2022; Akey et al., 2023; Estefania-Flores et al., 2023).

The rest of this paper is structured as follows: Section 2 motivates our approach by presenting two recent case studies. Section 3 introduces our new database of debt data revisions and our measure of hidden debt revelations. We explain in detail how our measure of hidden debt should be interpreted and point out important caveats. Section 4 presents the main statistical properties of debt data revisions, and it documents new stylized facts about the size, characteristics, and timing of hidden debt and its revelation. Section 5 presents our quantitative model of sovereign debt and default with hidden debt and an endogenous monitoring decision. Section 6 uses our new data to numerically discipline the model: we measure the impact of hidden debt on equilibrium default incentives, sovereign spreads, and welfare. Section 7 concludes.

# **2 Case studies**

In this section, we present two recent case studies to motivate our approach and to illustrate the main idea of using debt data revisions as a measure of hidden debt. First, Mozambique where the country’s Constitutional Council ruled that hidden debts were illegally contracted. Second, Zambia which faced continued concerns related to incomplete debt reporting.

## **2.1 Mozambique**

In 2016, Mozambique made international headlines when news reports revealed USD 1.2 billion in unreported sovereign debt liabilities. During the early 2010s, Mozambique was considered a development success story. The discovery of large natural gas deposits off the country’s northern coastline was followed by a surge in foreign direct investment and years of high real GDP growth. In 2013, at the height of the boom, the country issued sovereign bonds worth USD 850 million in international capital markets to fund investments in a tuna boat fleet. In the same year and the year after, state-owned enterprises used government 4
guarantees to borrow USD 1.2 billion from international banks Credit Suisse and VTB without disclosing these additional liabilities to bond investors and the public.<sup>5</sup> Two years later, in 2015, Mozambique first started to experience debt servicing difficulties. The tuna fleet, funded with the USD 850 million bond issuance, pulled in less than 5% of the tuna that it had expected, and the government approached bondholders with a plan to restructure the bond. After most bondholders had agreed to the restructuring in early 2016, rumors about large hidden debts started to emerge. In April 2016, the Wall Street Journal first reported about the additional and previously undisclosed bank loans that Mozambican state-owned enterprises had borrowed and the state guarantees that they carried.<sup>6</sup> The rumors about hidden debt led to a surge in Mozambique’s bond spreads (see Figure 1), with bond investors expressing concerns that the existence of undisclosed, additional liabilities would dilute the recovery value of their bonds in the event of a default, which ultimately happened in January 2017. Audits of Mozambique’s debt through the IMF and international accounting firms followed.<sup>7</sup> They confirmed the existence of USD 1.2 billion in hidden liabilities and the country’s Constitutional Council ruled that the loans were illegally contracted (Cortez et al., 2021). Ultimately, it took 4 years to settle renegotiations with bondholders and the country has not accessed international bond market ever since.

Mozambique’s hidden debts and their revelation can be quantified by comparing the country’s debt reports across different vintages of the World Bank’s International Debt Statistics. When initially reported, the 2014 debt figure for Mozambique was USD 7.1 billion (see Figure 2). This figure was strongly upward revised in subsequent vintages as the previously undisclosed loans became public knowledge. The latest debt figure for year 2014 is USD 8.5 billion, an increase of USD 1.4 billion or 8% of GDP).

# **2.2 Zambia**

Zambia increased external borrowing significantly during the 2010s. Supported by high commodity prices, the country contracted liabilities with numerous external creditors, including bondholders, bilateral creditors, commercial banks, export credit agencies and dozens of different suppliers. Debt issuance was carried out not only by the central government but also by a range of state-owned enterprises and special purpose vehicles that accumulated debt to finance infrastructure and energy projects (Brautigam, 2022). Whereas the country had contracted only five new loans in 2011, it contracted at least thirty new loans at the height of the boom in 2016 (Smith et al., 2017).

As the complexity of Zambia’s public debt portfolio increased, uncertainty over the true extent of the country’s indebtedness emerged. Zambia’s borrowing costs started to increase in April 2018, when the international press and major investors openly questioned the accu-

> 5See Financial Times (2017, June 25) _“State loans at heart of Mozambique debt scandal”_ .

> 6See Wall Street Journal (2016, April 3) _“Tuna and Gunships: How $850 Million in Bonds Went Bad in Mozambique”_ .

> 7See Reuters (2017, May 13) _“Mozambique receives Kroll audit into hidden debts”_ and Reuters (2017, July 11) _“IMF team visits Mozambique after damning debt audit”_ .

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**Figure 1:** Sovereign bond yields following Mozambique’s hidden borrowing

<!-- Start of picture text --> 2,800 Mozambique<br>Restructuring re-enters<br>of market debt debt distress<br>2,400<br>WSJ reports<br>on and IMF<br>confirms<br>2,000 existence<br>of hidden debt<br>1,600 Mozambique<br>signals intent<br>to restructure<br>market debt<br>1,200 Issuance<br>of market<br>and hidden<br>800 debt in 2013<br>400<br>0<br>Dec 2013 Apr 2014 Aug 2014 Dec 2014 Apr 2015 Aug 2015 Dec 2015 Apr 2016 Aug 2016 Nov 2016<br>(in basis points)<br>Sovereign bond yield spread<br><!-- End of picture text --> _Sources:_ Wall Street Journal (2016, April 3) _“Tuna and Gunships: How $850 Million in Bonds Went Bad in Mozambique”_ , Reuters (2016, April 23) _“IMF says Mozambique has over $1 bln of hidden debt”_ , J.P. Morgan (2024). _Notes:_ The figure plots the EMBI+ spread for Mozambique from December 2013 until December 2016. EMBI+ spread in basis points.

racy of the country’s debt statistics (see Figure 3).<sup>8</sup> At the beginning of 2020, the onset of COVID-19 and the accompanying capital outflows from emerging markets exacerbated the country’s debt challenges. In March 2020, Zambia’s ministry of finance sought advice from banks on the restructuring of USD 11.2 billion of foreign debt.<sup>9</sup> The news sent Zambia’s bond spread surging and ultimately pushed the country into default when the government missed a USD 42.5 million coupon payment on one of its Eurobonds in October 2020.

The uncertainty over the true scale of Zambia’s debt stock caused long delays in the ensuing debt resolution process. Creditor committees declined Zambian requests for a debt standstill and a restructuring proposal over concerns about the “lack of transparency regarding the country’s other external debts’’.<sup>10</sup> After several months of data reconciliation, Zambian authorities eventually published revised debt statistics that confirmed investor concerns and led Zambia’s new president to admit that the “hole is bigger than expected”.<sup>11</sup> Four years later, as of June 2024, the restructuring had not yet concluded.<sup>12</sup>

> 8See Africa Confidential (2018, April 6) _“Into the valley of debt”_ and Bloomberg (2018, April 8) _“Zambia’s bonds plummet on concern it’s pulling a Mozambique”._

> 9See Financial Times (2020, April 1) _“Zambia’s bonds drop on expected restructuring”._

> 10See Financial Times (2020, November 13) _“Zambia on brink of default after lenders reject debt relief request”_ and Financial Times (2020, September 30) _“Bondholders balk at Zambia’s plan to delay debt payments”_ .

> 11BBC (2021, September 1) _“Zambian President Hichilema inherits ‘empty treasury’”_ .

> 12Negotiations are still ongoing with non-bonded commercial creditors representing a quarter of the country’s external debt.

6
**Figure 2:** Mozambique’s hidden debt, 2006 – 2014

<!-- Start of picture text --> 8<br>Hidden debt (in 2014):<br>6<br>• USD 1.36bn<br>• 7.7% of GDP<br>4<br>2<br>0<br>2006 2007 2008 2009 2010 2011 2012 2013 2014<br>Initially reported external public debt<br>External public debt added through revisions<br>(USD billion)<br>Public external debt stock<br><!-- End of picture text --> _Notes:_ The figure shows the initially and most recently reported public and publicly guaranteed debt stocks for Mozambique between 2006 and 2014 in billion USD. The grey bars show the initially reported debt stocks. The red bars show additional debt stocks added through revisions in subsequent reporting. The data is from our new database (see Section 3 and Appendix A).

Our measurement approach allows to quantify Zambia’s hidden debts by comparing debt figures across different vintages of the World Bank International Debt Statistics (see Figure 4). The reported stock of Zambia’s external public and publicly guaranteed debt for 2021 amounted to USD 12.5 billion when it was initially published in the World Bank’s International Debt Report 2022. In the latest vintage, the same figure is given as USD 15.7 billion, indicating an upward revision of USD 3.2 billion or 14% of GDP.

# **3 Data, measurement and interpretation**

In this section, we introduce our new dataset of debt data revisions and explain how we quantify hidden debt and hidden debt revelations. Throughout this section, we focus on the main principles of data construction and measurement and refer interested readers to Appendix A for further details.

## **3.1 A new database of debt data revisions**

To systematically quantify hidden debt and its revelation, we construct a new and comprehensive database of all editions (i.e., “vintages”) of the World Bank’s International Debt 7
**Figure 3:** Sovereign bond yields during Zambia’s hidden debt saga

<!-- Start of picture text --> 10,000<br>Protracted default, data reconciliation<br>9,000 and<br>restructuring process<br>Creditors reject<br>8,000<br>restructuring over<br>transparency concerns<br>7,000<br>Zambia asks banks<br>6,000<br>for restructuring<br>advice on $11.2bn<br>5,000 of external debt<br>4,000<br>First rumors<br>about hidden debt<br>3,000<br>emerge<br>2,000<br>1,000<br>0<br>Jan 2018May 2018Aug 2018Dec 2018Apr 2019Aug 2019Dec 2019Apr 2020Aug 2020Dec 2020Apr 2021Aug 2021Dec 2021Apr 2022Aug 2022Dec 2022Apr 2023Aug 2023Dec 2023Mar 2024<br>(in basis points)<br>Sovereign bond yield spread<br><!-- End of picture text --> _Sources:_ Financial Times (2020, April 1) _“Zambia’s bonds drop on expected restructuring”_ , Financial Times (2020, September 30) _“Bondholders balk at Zambia’s plan to delay debt payments”_ , Financial Times (2021, November 10) _“Zambia’s new president tackles debt mountain and empty treasury”_ and J.P. Morgan (2024). _Notes:_ The figure plots the EMBI+ spread for Zambia from January 2018 until April 2024.

Statistics (IDS) and its predecessor publications. This subsection explains why we focus on the World Bank debt statistics and how we compile our new database.

**Why focus on the World Bank IDS?** The World Bank’s International Debt Statistics is uniquely suited for the purpose of our measurement approach. First, it is the most widely used source for developing and emerging market country external debt data and frequently cited by researchers, investors, rating agencies and market commentators. Reporting is mandatory for all countries with outstanding liabilities to the World Bank and debtor countries that violate their reporting obligations risk losing eligibility for financial support (World Bank, 2017). These conditions ensure high coverage across countries and time.

Second, the IDS has numerous desirable features that facilitate the interpretation of debt data revisions as a measure of hidden debt:

- The International Debt Statistics and its predecessor publications are based on direct debtor reporting. While the World Bank compiles the annual statistical report and performs consistency checks, all underlying data on debt instruments are reported by national debt management offices. Omissions and revisions of debt data can therefore be traced back to the reporting decisions of sovereign debtor countries.<sup>13</sup> An upward

> 13As explained in greater detail in Appendix Section A.2, the World Bank occasionally provides debt estimates if a reporting country does not fulfill its reporting obligations, but we exclude these estimates from our analysis.

8
**Figure 4:** Zambia’s opaque external debts, 2010 – 2021

<!-- Start of picture text --> 15<br>Hidden debt (in 2021):<br>12 • USD 3.18bn<br>• 14% of GDP<br>9<br>6<br>3<br>0<br>2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021<br>Initially reported external public debt<br>External public debt added through revisions<br>(USD billion)<br>Public external debt stock<br><!-- End of picture text --> _Notes:_ The figure shows the initially and most recently reported public and publicly guaranteed debt stocks for Zambia between 2010 and 2021 in billion USD. The gray bars show the initially reported debt stocks. The red bars show additional debt stocks added through revisions in subsequent reporting. The data is from our new database (see Section 3 and Appendix A).

revision implies that a sovereign debtor now reports a liability to the World Bank that it had not previously reported.

- All debt instruments enter the World Bank’s debt statistics with their nominal or face value. They are not adjusted for fluctuations in their market value. This implies that ex post data revisions do not reflect valuation changes; rather, they indicate changes in the underlying debt reporting.<sup>14</sup>

- Since the first publication of the World Debt Tables in 1973, the World Bank’s reporting guidelines have essentially remained unchanged. Section B.1 in the appendix provides a systematic comparison of the Debtor Reporting System (DRS) reporting manual over time and confirms that only minimal refinements have occurred over the past four decades.<sup>15</sup> This finding ensures that ex post data revisions do not reflect the evolution of reporting guidelines; rather, they can be traced back to changes in compliance with a stable set of rules over time.

**Sources and digitization:** Our new database combines more than 50 different editions (“vintages”) of the World Bank’s International Debt Statistics (2013–2023) and its prede-

> 14See Appendix Section B.2 below for a discussion of ex post foreign exchange rate revisions. We show that they are minuscule in size and cannot explain the revision patterns that we document.

> 15Appendix Section B.1 documents these minor refinements. Our results remain unchanged when eliminating vintages that introduced changes to the reporting guidelines.

9
cessor publications, the Global Development Finance reports (1997–2012) and the World Debt Tables (1973–1996). While the name of the publication has changed over the recent decades, all reports build on the same underlying data series from the World Bank’s DRS and on highly similar variable definitions (see Appendix B.1 for details).

The latest vintages of the debt statistics are readily available in machine-readable format on the World Bank’s website. For the majority of vintages, however, we need to digitize the data from PDFs or hard-copy reports. Specifically, we download all vintages of the International Debt Statistics (2013–2023) and eight vintages of the Global Development Finance reports (2005–2012) from the World Bank website. For all editions prior to 2005, we obtain PDFs or hard copies from different libraries and rely on a combination of optical character recognition (OCR) software and manual coding to render reports into machinereadable formats. Finally, we verify and reconcile the consistency of the data series and merge the data from all vintages into a single dataset (see Appendix A.2 for details).

**Scope of database:** Our new database covers debt statistics for an unbalanced sample of 146 developing and emerging market countries covering 53 years of data from 1970 to 2022. Appendix Table C6 provides a full list of all countries in our sample. For each country, the database combines the full reporting history with up to 51 different vintages so that each statistic can be compared across dozens of different debt reports.

**Table 1:** New database of debt data revisions: Scope and coverage

|Number of vintages|51|
|---|---|
|Number of variables|49|
|Number of countries|146|
|Time coverage|1970–2022|
|Number of observations|3,315,950|

_Notes:_ This table provides details on the scope and coverage of our new database on debt data revisions. See Appendix Table C6 for a full list of all countries in our sample.

**Key variables of interest:** Our dataset includes 49 debt-related indicators that the World Bank has published consistently over recent decades (see Appendix A.3 for details). In our core analysis presented in Section 4, we focus on the following key debt measures and concepts:<sup>16</sup>

- **Debt stocks:** Our key measure for the debt stock is the series on external, public and publicly guaranteed debt disbursed and outstanding (series code “DT.DOD.DPPG.CD” in the most recent vintage). It captures all external, long-term obligations of the general government and state-owned corporations and liabilities of private debtors that have been guaranteed by a public entity.

> 16Note that our analysis focuses on under-reporting of _external_ public debt only since no comparably systematic source exists for _domestic_ government debt. For a discussion of domestic debt as a source of hidden debt and rich historical case evidence, see Reinhart and Rogoff (2009) and Reinhart and Rogoff (2011b).

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- **Debt flows:** Our key measure for debt flows (or borrowing) is commitments to public and publicly guaranteed borrowers (series code “DT.COM.DPPG.CD” in the most recent vintage), where public and publicly guaranteed borrowers are defined as above and commitments refer to the total amount of long-term external loans for which contracts were signed in a given year.

# **3.2 Measurement and interpretation**

By comparing debt statistics across different vintages in our database, we can measure both the amount of unreported debt in any given year and the timing of discovery or revelation of previously unreported debt. More formally, we rely on the following two measures that we construct for both the debt stock and debt flow series.

where _Debt_ is either the debt stock or flow value, reported in vintages _V_ and _v_ 0, with _V_ being the most recent vintage and _v_ 0 being the first vintage with a value for country _i_ and year _t_ . In other words, the amount of unreported or hidden debt in a given year is defined as the difference between the debt value when first published and the debt value in the most recently published vintage.

We define hidden debt revelations as the amount of hidden debt uncovered in a given vintage and derive it as the difference in debt values in vintage _v_ and vintage _v −_ 1, summed across all past years for which both vintages report a value for _Debti,t_ .

where _Debti,t_ is defined as above, with _t_ 0 being the first year available in both vintages _v_ and _v −_ 1, and _T_ being the most recent year available in the same two vintages.<sup>17</sup> By definition, the total amount of hidden debt equals the total amount of hidden debt revelations for any particular country.

**Interpretation:** As explained above, the data from the World Bank International Debt Statistics that we analyze is exclusively based on debtor reporting. It is not subject to valuation changes and is compiled according to reporting rules that have been remarkably stable across 50 years. Therefore, revisions should be exclusively caused by changes in

> 17Note that equation (2) has a clearer interpretation for the flow measure than for the stock measure of debt. The reason is that an ex post addition of a single _loan_ leads to revisions of debt _stocks_ across all years until final repayment and therefore involves double-counting. The same issue does not exist for the flow measure.

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information about the underlying loans and bonds portfolio.<sup>18</sup> These properties of the World Bank’s debt statistics ensure that ex post upward revisions are associated with the debtor country reporting additional, previously unreported loans to the World Bank retrospectively. As the reporting guidelines are stable over time, any previously unreported loan should have been reported in the previous vintage and thus constitutes a violation of World Bank reporting guidelines. Our measure of hidden debt can therefore be summarized as initially under-reported debt in violation of prevailing reporting standards that is only revealed ex post.

Not all instances of hidden debt in our database are related to the deliberate hiding of liabilities. While such cases exist (see the case study on Mozambique in section 2 and the list of IMF reporting violations in appendix B.6), ex-post upward revisions can also be caused by a lack of statistical capacity in the reporting country. A debtor might for example lack the means to compile comprehensive debt statistics of its state-owned enterprises. As its capacity increases over time, new debtor entities are incorporated into the debt statistics and additional liabilities are identified and reported. Some of the upward revisions may be the results of accidental misreporting by the authorities, for example through typos when entering numerical values. But in such instances, we would expect cases of over-reporting and under-reporting to cancel each other out statistically.

**Distinction from contingent liability realizations:** The debt data revisions that we document are _not_ driven by contingent liability realizations, i.e., the government’s assumption of private sector liabilities. In contrast to hidden debt as defined here, contingent liability realizations do not require ex post revisions to previously published debt data; rather, they only lead to increases in subsequent annual public debt burden indicators (see Appendix Section B.3 for a detailed discussion and an empirical analysis of this proposition). Nevertheless, contingent liability realizations share several of the properties of hidden debt revelations that we document in this paper. The government’s assumption of private sector liabilities, most notably in the form of bailouts of domestic banks, tends to occur during times of distress and can lead to unanticipated jumps in the government’s debt burden (Diaz-Alejandro, 1983; Campos et al., 2006; Reinhart and Rogoff, 2011b; Bova et al., 2016; Hur et al., 2024). In this sense, our measure of under-reporting is a lower bound for the overall magnitude of “debt revelations” that bond investors endure in financial crises.

**Validation and robustness:** In Appendix Section B, we conduct several robustness and validation exercises to rule out the possibility that the debt data revisions that we observe are driven by alternative mechanisms. In particular, we verify that our revision patterns are not driven by changes in reporting rules (Section B.1), ex post revisions to exchange rates (Section B.2), contingent liability realizations (Section B.3), the reclassification of liabilities (Section C.1), by mere reporting lags (Section B.4) or revisions of dated debt figures (Section

> 18This stands in contrast with real GDP growth and other macro variables that are also subject to frequent revisions (see, e.g., Aruoba, 2008; Johnson et al., 2013; Goes, 2024). Since these variables need to be estimated or can be revised in response to methodological refinements or updated assumptions, the nature of revisions in these variables is different from that of revisions in debt data reporting that we document here.

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B.5), among others. We also verify that cases of reporting rule violations documented by the IMF Board align with the debt data revisions in our dataset (Section B.6).

**Limitations:** We emphasize two distinct limitations to our measure. First, loans that are initially missing from the IDS may have been reported in other debt databases. Such instances would still constitute a violation of World Bank reporting requirements but would imply less secrecy. Similarly, revelations within the IDS may follow revelations through other sources with a lag (see, e.g., the Mozambique case study in Section 2, where the hidden loans were added to the IDS after being revealed by an international audit). This issue warrants caution in regard to treating our debt data revisions as pure “news shocks” (Arezki et al., 2017).

Finally, our measure of hidden debt is a lower bound for the true level of unreported or hidden debt. Our revision-based measure of hidden debt captures only instances in which initially unreported debt is revealed at a later point in time. By definition, our measure does not capture the possibly large amount of unreported debt that remains unreported and that is never incorporated into debt statistics.

# **4 Main empirical findings**

In this section, we present the key statistical properties of debt data revisions and discuss the magnitude, characteristics and timing of hidden debt and its revelation. Our analysis reveals three key stylized facts about hidden debt.

- **Stylized fact 1: The size and characteristics of hidden debt** Hidden debt is large and common. Debt data revisions are systematically upward biased with a statistically significant mean revision of approximately 1% of GDP. Under-reporting of debt has occurred persistently across all decades, debtor regions and income groups, particularly in countries with weak institutions. On the creditor side, under-reporting is most severe for bilateral and non-bond commercial lending.

- **Stylized fact 2: The timing of hidden debt revelations** Hidden debt tends to be accumulated during boom years and is revealed during bad years, often in the context of IMF programs and external sovereign defaults.

- **Stylized fact 3: Hidden debt and sovereign defaults** During default episodes, hidden debt is associated with larger creditor losses (haircuts) and longer default spells.

The following subsections discuss in turn each of these findings.

## **4.1 Hidden debt is large and common**

Figure 5 shows the distribution of hidden debt, as measured by data revisions to external public and publicly guaranteed debt across all vintages, years, and countries in our database.

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Panel A focuses on debt stocks, while Panel B focuses on debt flows. Revisions are scaled by debtor country GDP, which is taken from the latest World Bank data release and not subject to revisions.

**Figure 5:** The distribution of debt stock and flow revisions

_Panel A:_ Revisions to debt stocks in percent of GDP <!-- Start of picture text --> 40%<br>30%<br>20%<br>10%<br>0%<br>-5% 0% 5% 10%<br>Ex-post PPG debt stock revision in % of GDP<br>median mean<br>Percent<br><!-- End of picture text --> _Panel B:_ Revisions to debt flows in percent of GDP <!-- Start of picture text --> 60%<br>50%<br>40%<br>30%<br>20%<br>10%<br>0%<br>-5% 0% 5% 10%<br>Ex-post PPG debt commitment revision in % of GDP<br>median mean<br>Percent<br><!-- End of picture text --> _Notes:_ The figure shows the percentage distribution of data revisions to debt stocks and debt flows (i.e. commitments) as defined in equation (1), in percent of GDP. Solid lines show the median, dashed lines show the mean. GDP data is taken from World Bank (2022) and not subject to revisions.

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**Table 2:** Summary statistics of debt data revisions

||N|Mean|Median|Std. Dev.|p-value|
|---|---|---|---|---|---|
|_As a percentage of GDP_||||||
|Debt stock (DOD)|5,702|1.06|0.09|5.76|0.000|
|Commitments (COM)|5,695|0.70|0.08|4.17|0.000|
|_In million USD_||||||
|Debt stock (DOD)|5,702|159.22|5.00|1,909.90|0.000|
|Commitments (COM)|5,695|148.60|6.00|1,169.82|0.000|

_Notes:_ The table reports summary statistics and p-values for data revisions to debt stocks and debt commitments as defined in equation (1), both in percent of GDP and in millions of nominal USD. GDP data is taken from World Bank (2022) and not subject to revisions. P- values are obtained from testing the null hypothesis that revisions have a mean of zero. We use Newey-West heteroskedasticity- and autocorrelation-consistent standard errors (Newey and West, 1987).

Two results stand out. First, Figure 5 reveals the large degree of uncertainty around the true level of indebtedness of developing and emerging market countries. Debt data revisions exhibit large dispersion, with frequent upward and downward revisions.<sup>19</sup> Approximately 70 percent of all debt stock statistics and 50 percent of all debt flow statistics published through the World Bank International Debt Statistics are revised at least once after their initial publication. This result is also reflected by the large standard deviation of 5.76 percent of GDP for stock revisions and 4.17 percent of GDP for flow revisions.

Second, the figure shows that debt data is systematically under-reported. If data revisions were the result of a well-behaved statistical process, one akin to noise or accidental misreporting, then we would expect the mean of the distribution to not be significantly different from zero (Aruoba, 2008). Figure 5 reveals that this is not the case. The distribution of both debt stock and debt flow revisions are heavily skewed to the right. While the median debt stock revision is close to zero, the average revision is positive and large at approximately 1 percent of GDP. Likewise, yearly undisclosed new borrowing has a mean of 0.7 percent of GDP. Table 2 combines the mean and median debt revisions with the standard deviation and shows that the mean revision as a percentage of GDP is positive and statistically different from zero at the 1% significance level. This result is incompatible with the notion of a purely noisy revision process and indicates systematic under-reporting of initial debt stocks and flows.<sup>20</sup> In Appendix Table C4 we show that this result is not driven by a specific subgroup but holds across all decades and almost all creditor types, debtor regions and income groups.

> 19For the flow measures, ex post upward revisions are four times as likely as downward revisions. For stock revisions, the same metric is not as insightful, since a single flow revision (e.g. a missing borrowing) may lead to persistent debt stock revisions until loans are repaid. Downward revisions can be caused by outright measurement error (e.g. typos) or by under-reporting of repayment flows (see Appendix Section C.3).

> 20Another way of assessing the magnitude of hidden debt and borrowing is to measure how much borrowing remained undisclosed in the initial reporting and was revealed only in subsequent vintages. Our data shows that 12.6 percent of all lending is only revealed retrospectively. Over the entire history of the World Bank’s debt report publications, USD 1 trillion in loans was initially unreported and revealed only in subsequent vintages.

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Our data also allows us to understand the determinants of under-reporting across debtors and creditors. To test for the role of debtor country institutions, Panel A of Figure 6 depicts the distribution of debt data revisions across country groups with different levels of institutional strength, as measured by their average score in the Polity V dataset. Figure 6 shows that reporting noise - as measured by the dispersion of the revision distribution - is substantially higher in countries with weak institutional strength, more limited checks and balances and low capacity. Notably, however, even the countries with the strongest institutions in our sample systematically under-report their debt, with a significant mean revision of 0.5 percent of GDP.

We next disaggregate debt data revisions by creditor group and find striking differences in the propensity of different instruments to be under-reported.<sup>21</sup> Panel B of Figure 6 reveals that the upward bias in revisions is largest in debt to bilateral and non-bond private creditors. However, for debt owed to the World Bank and for debt owed to private bondholders, the figure shows only very small revisions. This result is not surprising, given that data on (publicly traded) bonds is generally widely available and the World Bank can readily monitor its own lending activities and ensure that they are accurately reflected in borrower reporting. Lending by bilateral and other private creditors, on the other hand, is not traded in secondary markets and is often shielded from public scrutiny through non-disclosure clauses (Gelpern et al., 2023; Mosley and Rosendorff, 2023).

> 21Since the size of outstanding debt differs greatly across lender groups, we scale revisions by initial debt rather than GDP. See Appendix Table C3 for alternative scaling.

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**Figure 6:** Where is hidden debt the largest?

_Panel A:_ In borrower countries with weaker institutions <!-- Start of picture text --> 2.5%<br>2.0%<br>1.5%<br>1.0%<br>0.5%<br>0.0%<br>-0.5%<br>-1.0%<br>-1.5%<br>Lowest Second Third Highest<br>quartile quartile quartile quartile<br>Institutional strength<br>....<br>Panel B: In loans from bilateral and private creditors<br>25%<br>20%<br>15%<br>10%<br>5%<br>0%<br>-5%<br>-10%<br>-15%<br>Private of which: Bilateral Multilateral of which:<br>lending Bonds lending lending World Bank<br>Hidden debt<br>(in % of GDP)<br>Hidden debt<br>(in % of initially reported debt stock)<br><!-- End of picture text --> _Notes:_ This boxplot shows the distribution of hidden debt, as defined in equation (1), across debtor (Panel A) and creditor (Panel B) groups. Panel A splits the observations into quartiles of borrowing country institutional strength, as measured by average Polity V scores between 1970-2020 (Marshall and Gurr, 2020) . Panel B splits observations by creditor groups as defined by the World Bank. GDP data is taken from World Bank (2022) and is not subject to revisions.

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# **4.2 Hidden debt accumulates in boom years and is revealed during busts**

This section analyzes the cyclical patterns of hidden debt accumulation and revelation. We start by documenting that hidden debt tends to accumulate during boom years and be revealed during bust years. Figure 7 presents this key result in the form of binned scatter plots, following the optimal binning approach developed by Cattaneo et al. (2024).

Panel A shows the association between hidden debt and real GDP growth _in the year that is being revised_ . The figure shows that boom year data points are subject to higher upward revisions, implying that more unreported borrowing occurs during good times. Panel B shows the association between hidden debt _revelations_ and real GDP growth. That is, we focus on those years (vintages) in which hidden debt is revealed and added to the statistics. The negative association shows that previously unreported borrowing is more likely to be revealed during economic downturns. Hidden debt accumulation is markedly procyclical.

Table 3 sheds further light on the mechanisms that underlie hidden debt revelations in bad times. Specifically, in a fixed effects panel regression, we show that IMF programs and external sovereign defaults are associated with larger revelations of previously unreported debt, even when controlling for the business cycle, and for country and vintage fixed effects. While the variables explain only a small share of the overall variation in our noisy revision data, they are associated with economically sizeable effects. Both new IMF programs and sovereign default episodes are associated with an increase in hidden debt revelations of 12 percent of the standard deviation of hidden debt revelations. This result corresponds to approximately USD 200 million in newly revealed loans during the first year of the average IMF program or while a country is experiencing a sovereign default episode.

These findings confirm existing anecdotal evidence on the repeated discovery of hidden debts during crises and point to outside monitoring as a key driver of greater debt transparency.<sup>22</sup> Both IMF programs and external sovereign defaults are times of intense external scrutiny of a country’s debt statistics. In exchange for a lending program, the IMF requires detailed access to a country’s debt statistics to assess debt sustainability and calibrate program parameters and objectives. Similarly, during a sovereign default, a country’s creditors come together to reconcile their data with the debtor’s records as part of the debt restructuring process. In this context, the sovereign’s debt records are vetted by sovereign advisors and may be subject to additional checks by international audit firms working on behalf of creditors concerned about the dilution of their claims (see the Mozambique case study in Section 2 and the next subsection).

> 22An alternative hypothesis is that governments strategically reveal hidden debts for political gain, for example after coming to power or after elections. In Appendix Section C.2, we test whether domestic political factors can explain revelations of hidden debt. We do not find any evidence that governments strategically reveal previously unreported debt or that hidden debt revelations vary systematically across the political cycle.

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**Figure 7:** The procyclical nature of hidden debt

_Panel A:_ Which years are being revised?

<!-- Start of picture text --> .2<br>.1<br>0<br>-.1<br>p-value = 0.026<br>-.2<br>-10 -5 0 5 10 15<br>Real GDP growth in year which is revised<br>....<br>Panel B: When do revelations happen?<br>.2<br>.1<br>0<br>-.1<br>-.2 p-value = 0.001<br>-10 -5 0 5 10 15<br>Real GDP growth in year of revelation<br>Hidden debt - normalized<br>Hidden debt revelations - normalized<br><!-- End of picture text --> _Notes:_ Panel A shows the association between hidden debt and GDP growth in the year that is being revised. Panel B shows the association between hidden debt revelations and GDP growth in the vintage of the revision. The vertical axes show normalized hidden debt flows and their revelations, as defined in equations (1) and (2) respectively, standardized to account for outliers and to ease interpretation. Horizontal axes show detrended growth rates, winsorized at the 1<sup>st</sup> and 99<sup>th</sup> percentile. Trends were computed using the Hodrick-Prescott filter with a smoothing parameter of 100. Bins are constructed following the approach of Cattaneo et al. (2024). P-values and regression lines were obtained from panel regression in which we control for country fixed effects and the creditor composition of borrowing.

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**Table 3:** Drivers of hidden debt revelations

||Dep|. variable: Hid|den debt revelations, 1975-2020|
|---|---|---|---|
||(1)|(2)|(3)<br>(4)|
|Real GDP growth (WDI)|-0.03**<br>(0.01)||-0.03**<br>(0.01)|
|External sov. default||0.14***<br>(0.05)|0.12**<br>(0.05)|
|IMF program|||0.13***<br>0.12**<br>(0.04)<br>(0.05)|
|Observations|3,914|4,069|4,069<br>3,892|
|R-squared|0.049|0.047|0.048<br>0.053|
|Country FE|✓|✓|✓<br>✓|
|Vintage FE|✓|✓|✓<br>✓|

_Notes:_ This table shows regression results from a fixed effects panel regression of hidden debt revelations on real GDP growth, the occurrence of a sovereign default, and IMF programs. The dependent variable is the sum of all previously unreported loan commitments of a country as revealed by a new vintage (see Section 3.2 and equation (2) for details). Real GDP growth is detrended and winsorized at the 1<sup>st</sup> and 99<sup>th</sup> percentiles. Trends were computed using the Hodrick-Prescott filter with a smoothing parameter of 100. To account for outliers and to facilitate interpretation, real GDP growth and the dependent variable are standardized. IMF program measures the first year of a program and is from Horn et al. (2020). External sovereign defaults data is from Asonuma and Trebesch (2016) and refers to all years in which a country is in default. All regressions include country and vintage fixed effects. In regression (4) we additionally control for the creditor composition of external borrowing. Robust standard errors are shown in parentheses.

# **4.3 Hidden debt is associated with larger creditor losses and longer default spells**

The previous subsection showed that revelations of hidden debt are particularly common during external sovereign default episodes. In this context, international market creditors are often concerned about the existence of hidden debt that may dilute the recovery value of their claims. In several recent debt distress episodes, uncertainty over the true level of indebtedness has been a key obstacle to distress resolution that delayed the restructuring process and exacerbated the coordination issues among creditors (see Section 2 for anecdotal evidence).

Our newly collected data allows to empirically test, whether high hidden debts (as measured by subsequent upward revisions) are systematically correlated with longer and costlier debt restructuring processes. To test this hypothesis, we merge our hidden debt measures with the datasets on external sovereign defaults and restructurings compiled by Cruces and Trebesch (2013), Asonuma and Trebesch (2016) and Asonuma et al. (2023). Their combined data captures sovereign debt restructurings with external, private creditors between 1970 and 2020 and measures both net present value creditor losses (“haircuts”) and the length of each default episode (defined by the time between the initial missed payment and the resolution through a debt restructuring). This data allows to test whether high hidden debts at the onset of a default episode are associated with (i) larger haircuts and (ii) longer resolution processes.

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**Table 4:** Hidden debt and default spells

||Hair|cut|Duration|of spell|
|---|---|---|---|---|
||(1)|(2)|(3)|(4)|
|Hidden debt|1.23***|1.03**|2.04**|1.94**|
||(0.45)|(0.41)|(0.83)|(0.83)|
|Real GDP growth||-0.49<br>||-0.47<br>|
|||(0.37)||(0.74)|
|Debt to GDP ratio||0.25***||0.22**|
|||(0.05)||(0.10)|
|Real GDP p.c.||-0.76||-0.48|
|||(0.59)||(1.19)|
|Institutional strength||-0.55*||-0.99*|
|||(0.29)||(0.59)|
|Share of bond debt||-0.00||-0.24|
|||(0.18)||(0.36)|
|Share of debt to WB||0.41*||0.20|
|||(0.24)||(0.49)|
|Constant|33.78***|18.24***|36.83***|26.13*|
||(2.24)|(6.76)|(4.07)|(13.59)|
|Observations|148|140|148|140|
|R-squared|0.048|0.314|0.040|0.138|

_Notes:_ This table shows the results of OLS regressions of two outcome measures of sovereign defaults on our measure of hidden debt in a cross-section of external sovereign default episodes in 1970-2020. The dependent variable in columns (1) and (2) is the net present value loss suffered by creditors as a percentage (“haircut”). The dependent variable in columns (3) and (4) is the duration of the default spell in months, measured as the time between the default event and the restructuring. Data is from Cruces and Trebesch (2013), Asonuma and Trebesch (2016) and Asonuma et al. (2023). The hidden debt variable measures the share of unreported debt at the onset of the default episode as percentage of GDP and is constructed as defined by equation (1) in Section 3.2. Standard errors are reported in parentheses. See Appendix Section A.4 and text for details on and sources of the control variables included.

Table 4 shows the results from this exercise. Columns (1) and (2) show that higher unreported debts are indeed associated with higher creditor losses in statistically and economically meaningful ways. A one percentage point increase in the amount of unreported debt (as a percentage of GDP) is associated with an increase in the haircut of 1.23 percentage points. This correlation remains strongly significant and similar in size when we control for other common predictors of creditor losses and restructuring outcomes (Graf von Luckner et al., 2023; Bai and Zhang, 2012). Columns (3) and (4) repeat the exercise but focus on the duration of the default episode. We find a strong positive correlation between hidden debt and the length of the default spell in the cross-section of external sovereign debt crises since 1970. A one percentage point increase in the amount of unreported debt is associated with an increase in the default spell by approximately two months. Again, this result holds when controlling for other common determinants of restructuring outcomes.

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# **5 Model**

To quantify the effects of hidden debt and its revelation on default risk and asset prices and to explore the welfare implications of transparency policies, we develop a quantitative model that builds on the traditional framework of the sovereign debt and default literature (following Eaton and Gersovitz, 1981, Arellano, 2008, and Aguiar and Gopinath, 2006) with long-term debt and positive recovery rates (as in Hatchondo et al., 2016 and Hatchondo et al., 2021). Our main modifications to this framework are motivated by the insights derived from our new data, particularly the stylized facts presented in Section 4. Our model features a hidden debt accumulation process and allows for international lenders to monitor the country’s accounts, thereby triggering endogenous revelations of hidden debt. In the model, monitoring is costly, but investors have an incentive to monitor because hidden debt reduces their claims in the case of default through a diluting effect on their recovery rate. Our new data is used to inform the statistical properties of all of these model innovations.

To keep the framework tractable and to be able to make full use of our rich new dataset, our model abstracts from other potentially important features of hidden debt. Most notably, in the model, hidden debt accumulates exogenously and is not driven by a strategic borrower decision.<sup>23</sup> In this sense, our model economy is best understood as an economy in which the government has limited control over the borrowing decisions of the broader public sector, e.g. the country’s state-owned enterprises. Therefore, the model primarily reflects the case of countries with weak institutions and large uncertainty about the true level of indebtedness (see Figure 6).

Furthermore, our model features international lenders who form expectations about the level of hidden debt, and these expectations depend on the time that has passed since the last revelation. However, we abstract from investors learning from the country’s actions by assuming that investors arrive in overlapping generations. In addition to helping to keep the model tractable and allowing us to use the rich new data, the idea of having different generations of investors without learning is consistent with the “this time is different” narratives of past crisis episodes (Reinhart and Rogoff, 2009, 2011b). New generations of investors often repeat past mistakes by believing that financial crises are a phenomenon of the past.

## **5.1 Environment**

**Preferences and income process.** The representative agent in the borrowing economy has preferences given by

> 23For work on the strategic use of hidden debt, see Alfaro and Kanczuk (2022), Gamboa (2023) or Guler et al. (2022).

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where _E_ denotes the expectation operator of domestic agents, _β_ denotes the subjective discount factor, and _ct_ represents consumption. The utility function is strictly increasing and concave. The government cannot commit to future (default and borrowing) decisions.<sup>24</sup> The economy’s endowment of the single tradable good is denoted by _y ∈ Y ⊂_ R++. This endowment follows a Markov process.

**Market debt.** The small open economy borrows from a large pool of international investors by issuing long-duration bonds, _b_ . As in Hatchondo and Martinez (2009), a bond issued in period _t_ promises an infinite stream of coupons that decreases at a constant rate _δ_ .<sup>25</sup> In particular, a bond issued in period _t_ promises to pay _κ_ (1 _− δ_ )<sup>_j−_1</sup> units of the tradable good in period _t_ + _j_ , for all _j ≥_ 1. The advantage of this payment structure is that it enables us to condense all future payment obligations derived from past debt issuances into a one-dimensional state variable: the payment obligations that mature in the current period.

**Hidden debt.** We assume that in addition to market debt, the country also faces an exogenous process for hidden debt. Provided that there has not been a revelation in the previous period (more details on the revelation below), the country starts period _t_ with a level of hidden debt, _h_ , which has the same coupon structure as the market debt. Absent a default in period _t_ , the country needs to service the initial hidden debt (i.e., it pays the coupons due), and it draws a “hidden-debt issuance” realization _ε_ from a probability distribution _G_ ( _ε_ ). We assume that _ε_ is _iid_ and that _G_ ( _ε_ ) is common knowledge, and we will use our novel dataset to parameterize it. The hidden debt issuance shock _ε_ delivers new flows in period _t_ , and it is added to the stock of hidden debt.

**Monitoring.** While the probability distribution for _ε_ is common knowledge, we assume that the level of _h_ is not. Only the country knows its true level of hidden debt, and the lenders (who are risk averse) need to form expectations about this level. Every period, before deciding how many bonds to buy, lenders have an option to “monitor” the country’s statistics: they have to pay a monitoring fee _f_ to trigger a hidden debt revelation (i.e., they learn the true level of hidden debt). If they decide to not exercise this option, they can still buy government bonds but they need to take into account the additional uncertainty of not knowing the true indebtedness of the country. Throughout the paper, we maintain the assumption that this monitoring is the only way (apart from a default) in which lenders

> 24Thus, one may interpret this environment as a game in which the government making decisions in period _t_ is a player who takes as given the (default and borrowing) strategies of other players (governments) who will decide after _t_ .

> 25Arellano and Ramanarayanan (2012) and Hatchondo et al. (2016) allow the government to issue both short-term and long-term debt, and they study optimal maturity and the effects of debt dilution, respectively. Hatchondo et al. (2017) allow the government to issue both defaultable and non-defaultable debt. Roch and Roldán (2023) and Sosa-Padilla and Sturzenegger (2022) allow the government to issue debt with payments contingent on the level of income.

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can know the true level of hidden debt.<sup>26</sup> This assumption is consistent with our empirical results showing that revelations happen in times of high scrutiny (Table 3).

**Defaults and recovery rates.** When the government defaults, it does so on all (reported and hidden) current and future debt obligations. This is consistent with the observed behavior of defaulting governments, and it is a standard assumption in the literature.<sup>27</sup> Following the empirical evidence on hidden debt revelations (especially Table 3 above), we assume that a default triggers a hidden debt revelation.

A default event also triggers exclusion from the debt market for a stochastic number of periods. Furthermore, income is given by _y − φ_ ( _y_ ) in every period in which the government is excluded from debt markets. Starting the first period after the default period, with a constant probability _θ ∈_ [0 _,_ 1], the government may regain access to debt markets. We assume that to emerge from a default episode the country exchanges its defaulted bonds for new bonds. That is, the country reenters markets with a non-negative amount of debt. We call this amount, _bD_ and assume the following regarding _bD_ : where _h_<sup> ̃</sup> = max _{_ 0 _, h}_ and _α_ ( _y_ ) is a non-decreasing function of the income level realized upon reentry. These new bonds _bD_ are divided among holders of the previously issued market and hidden debt as follows. Holders of hidden debt (which was revealed at the default event) obtain _χh_<sup> ̃</sup> , with _χ ∈_ [0 _,_ 1].<sup>28</sup> Holders of the previously issued market debt obtain the remainder, _bD − χh_<sup> ̃</sup> . This implies the following recovery rate for market debt: From equation (5) it is clear how hidden debt can dilute the recovery rate for market lenders, which further justifies their potential decision to monitor the country’s accounts.

**Timing.** For a country that ended period _t −_ 1 in good financial standing, the timing of events within period _t_ is as follows:

0. The levels of market debt and of hidden debt _{b, h}_ are known to the government. Lenders know _b_ and how many periods have passed since the last hidden debt revelation, _τ_ .

> 26For example, one can think of uncertain and/or opaque items in the government’s budget constraint such that even after factoring in all the observables (coupon payments on market debt, issuances, consumption, etc.) lenders are still unable to perfectly infer the level of hidden debt. See Gamboa (2023) for empirical support in favor of this assumption.

> 27Sovereign debt contracts often contain an acceleration clause and a cross-default clause. The first clause allows creditors to call the full value of the debt that they hold in case the government defaults on a single payment. The cross-default clause states that a default on any government obligation constitutes a default on all the other contracts containing such a clause. As a result of these two clauses, after a default event, all future debt obligations become current.

> 28We assume that debt that is hidden at the time of default is excluded from the regular restructuring process. This hidden debt has an effective recovery rate of _χ_ .

24
1. _y_ and _ε_ are realized. All agents observe _y_ , but only the government observes _ε_ .

2. Lenders use their information to post (i) a monitoring rule, _m ∈{_ 0 _,_ 1 _}_ , and (ii) price schedules _q_ m and _q_ nm for the cases of monitoring and non-monitoring, respectively.

3. The government observes all states and lenders policy functions, and it makes a default decision: _d ∈{_ 0 _,_ 1 _}_

- If default ( _d_ = 1): no coupons are paid, all hidden debt is revealed, the country does not obtain any flows from _ε_ , and it suffers from income losses and exclusion while the default status persists.

- If repay ( _d_ = 0): the government can borrow again by choosing _b_<sup>_′_</sup> . When it evaluates possible values for _b_<sup>_′_</sup> it takes into account the fact that different borrowing levels imply different prices and different monitoring policies from lenders.

- If there is monitoring ( _m_ = 1), all discovered debt is added to _b_ , and the hidden debt going forward is zero ( _h_<sup>_′_</sup> = 0).

- If there is no monitoring ( _m_ = 0), hidden debt is _h_<sup>_′_</sup> = _h_ (1 _− δ_ ) + _ε_ .

4. Consumption and coupon payments (if relevant) take place.

For a country that ended period _t −_ 1 in financial exclusion, the first event that occurs is a realization of a reentry shock. With probability 1 _− θ_ the country remains excluded and has no decision in the period (it consumes its reduced income level). If reentry occurs (with probability _θ_ ), then the country receives a realization of _ε_ , its initial debt level gets reduced to _bD_ (according to equation 4), and its initial hidden debt is set to zero (since it had been revealed in the prior default event). The country then finds itself at step 2 above, and the timing of events continues as specified there.<sup>29</sup>

# **5.2 Foreign lenders**

We follow the modeling of lenders presented in Gu and Stangebye (2023); however, to use the full extent of our novel dataset of hidden debt revelations and to retain tractability, we simplify the information acquisition problem. We assume that foreign lenders are risk averse and that they arrive in overlapping generations, each with wealth _W_ . They have access to a risk-free asset that yields a net return of _r_ . When the sovereign starts the period in good standing and has not defaulted, the problem for a foreign lender is to decide whether to monitor the country’s debt: _m_ = 1 denotes monitoring, and _m_ = 0 denotes not monitoring. Monitoring is the only way in which lenders can acquire information about the true debt level of the country and it is costly: lenders have to pay a fee of _f_ .

When they make this decision they know _b_ , _y_ , and the number of periods since the last revelation ( _τ_ ), and they evaluate their value under monitoring or no monitoring for different candidate levels of _B_<sup>_′_</sup> . After this decision is made, hidden debt either continues to be

> 29Implicit in our timing is the assumption that when the government makes decisions ( _d_ and _b′_ ), lenders cannot change their monitoring policies or pricing schedules.

25
unknown to lenders or is fully revealed, and lenders then have to choose how many bonds to buy.<sup>30</sup> In the exposition of the lenders’ problem, we use _b_<sup>_′_</sup> to denote the borrowing choice of the government and _B_<sup>_′_</sup> to denote lenders’ investment in government bonds.<sup>31</sup> The lenders’ problem can be written as In turn, their value under monitoring is given by subject to where _τ_<sup>_′_</sup> = 1, _h_<sup>_′_</sup> = 0, _qD_ denotes the price of a bond in default, _b_<sup>_′′_</sup> =<sup>ˆ</sup> _b_ ( _b_<sup>_′_</sup> _, h_<sup>_′_</sup> _, y_<sup>_′_</sup> _, ε_<sup>_′_</sup> _, τ_<sup>_′_</sup> ), and _d_<sup>_′_</sup> = _d_<sup>ˆ</sup> ( _b_<sup>_′_</sup> _, h_<sup>_′_</sup> _, y_<sup>_′_</sup> _, ε_<sup>_′_</sup> _, τ_<sup>_′_</sup> ), with<sup>ˆ</sup> _b_ and _d_<sup>ˆ</sup> denoting the optimal borrowing and default policies that lenders expect the government to follow, respectively. _m_<sup>_∗_</sup> ( _b_<sup>_′′_</sup> _, y_<sup>_′_</sup> _, τ_<sup>_′_</sup> ) is the monitoring policy that current lenders expect the future generation of lenders will follow, and _E_<sup>_l_</sup> denotes the expectation operator of lenders in the case of monitoring.<sup>32</sup> The solution to this problem features a demand schedule for sovereign bonds given by The value of not monitoring is similar to that above, with two exceptions: (i) there is no monitoring fee ( _f_ ) to be paid, and (ii) there is no revelation of hidden debt, which implies that the information set in this case is different (and, hence, the subjective expectations are different). In this case, we use _Eτ_<sup>_l_todenotetheexpectationoperatoroflenders,wherethe</sup> sub-index _τ_ indicates that the lenders’ expectations about _h_<sup>_′_</sup> vary with the time since the last revelation. Therefore, the value under no monitoring can be written as follows:

> 30Note that in this framework, different from Gu and Stangebye (2023), the government has an informational advantage over lenders (it knows _h_ and _ε_ ), but we assume that it has no credible way of communicating the true level of hidden debt. This modeling approach is consistent with our finding that governments do not strategically reveal hidden debt for political gain (see C.2). Moreover, we assume that there is no communication between the different overlapping generations of lenders. These assumptions combined with the fact that the monitoring rule and pricing schedules cannot be changed after observing government actions imply that lenders do not learn from the country’s actions.

> 31In equilibrium, we will naturally have _b′_ = _B′_ .

> 32In the case of monitoring, _τ_ becomes zero (i.e. the last revelation of debt occurred in the current period), and lenders know for certain that _h_<sup>_′_</sup> = 0.

26
subject to where _R_<sup>_′_</sup> is given by equation (9) evaluated at _τ_<sup>_′_</sup> = _τ_ + 1. Lenders view _h_<sup>_′_</sup> as a random variable drawn from a distribution that depends on (i) _G_ ( _ε_ ) (the distribution of innovations to hidden debt, which is known) and (ii) the time since the last hidden debt revelation, _τ_ . The solution to lenders’ problem under no monitoring features a demand schedule for sovereign bonds given by where _Cl_<sup>_′_isgivenbyequation(12)and</sup><sup>_τ ′_=</sup><sup>_τ_+ 1.</sup> Finally, a foreign lender who arrives in a state in which the government is in default faces a similar problem but with a different set of returns. Debt is not serviced in default; however, in every period, there is a constant probability of reentry, in which case the government exchanges its defaulted bonds for new bonds, as specified above. This implies the following problem for foreign lenders in default: subject to where _θ ∈_ (0 _,_ 1) is the probability of reentry to financial markets, _h_<sup> ̃</sup> = max _{h,_ 0 _}_ and _τ_<sup>_′_</sup> = 1. As before, _d_<sup>ˆ</sup> represents the expected default policy, _b_<sup>_′′_</sup> =<sup>ˆ</sup> _b_ ( _bD,_ 0 _, y_<sup>_′_</sup> _, ε_<sup>_′_</sup> _, τ_<sup>_′_</sup> ) is the expected borrowing policy, and _m_<sup>_∗_</sup> ( _b_<sup>_′′_</sup> _, y_<sup>_′_</sup> _, τ_<sup>_′_</sup> ) is the expected monitoring policy. _bD_ and _ω_ ( _b, h, y_<sup>_′_</sup> ) are given by equations (4) and (5), respectively. Therefore, the price of a bond in default is given by 27
Note that in this case, the correct expectation operator is _E_<sup>_l_</sup> , the same as under monitoring. The reason is our assumption that a default triggers a revelation of hidden debt and therefore lowers uncertainty.<sup>33</sup>

# **5.3 The government’s problem**

A government that starts the period in good standing has the option to default on its debt. Therefore, As described above, a government default triggers (i) the revelation of all hidden debt and (ii) temporary market exclusion and income costs. We also assume there are no further additions to hidden debt during exclusion. Thus, the value under default is given by subject to where _h_<sup> ̃</sup> = max _{h,_ 0 _}_ , _h_<sup>_′_</sup> = 0, _τ_<sup>_′_</sup> = 1, and _bD_ ( _b, h, y_<sup>_′_</sup> ) is given by equation (4). The function _φ_ ( _y_ ) captures the income cost of defaults.

If the government decides to repay, then the problem is more involved, as it depends on the monitoring decision of lenders. The value of repayment is where _m_<sup>_∗_</sup> ( _b_<sup>_′_</sup> _, y, τ_ ) denotes the optimal monitoring policy, which the government takes as given (understanding how it depends on the level of _b_<sup>_′_</sup> ). In the case of monitoring ( _m_<sup>_∗_</sup> = 1), hidden debt is revealed and is added to the existing market debt, and the end-of-period level of hidden debt is zero ( _h_<sup>_′_</sup> = 0). In this case, the problem of the government is subject to

> 33This assumption is consistent with the evidence in our new dataset, in which we observe that revelations are high in default episodes. The uncertainty reduction effect of defaults has also been highlighted in recent work by Gutkowski (2022).

28
where _ι_ represents the issuance of new market debt and _q_ m( _b_<sup>_′_</sup> _, y_ ) is the per-bond price of this new debt. The last constraint is the “price-floor” constraint, which is typically used in models of sovereign default with long-term debt to avoid “infinite dilution” in the period prior to a default (see Hatchondo et al., 2016). To simplify the analysis, we treat _qh_ as a parameter.

In the case of no monitoring ( _m_<sup>_∗_</sup> = 0), hidden debt continues to be hidden to lenders, and its end-of-period level is _h_<sup>_′_</sup> = (1 _− δ_ ) _h_ + _ε_ . In this case, the problem of the government is subject to

## **5.4 Equilibrium definition**

A Markov perfect equilibrium is defined by value functions { _V_ ( _b, h, y, ε, τ_ ) _, V_ 0<sup>_M_(</sup><sup>_b, h, y, ε_)</sup><sup>_,_</sup> _V_ 0<sup>_NM_</sup> ( _b, h, y, ε, τ_ ) _, V_ 1( _b, h, y_ )}, policy functions { _d_ ˆ( _b, h, y, ε, τ_ ) _,_ ˆ _bM_ ( _b, h, y, ε_ ) _,_ ˆ _bNM_ ( _b, h, y, ε, τ_ )}, a monitoring rule _m_<sup>_∗_</sup> ( _b_<sup>_′_</sup> _, y, τ_ ), and bond price schedules _{q_ m( _b_<sup>_′_</sup> _, y_ ) _, q_ nm( _b_<sup>_′_</sup> _, y, τ_ ) _, qD_ ( _b, h, y_ ) _}_ such that: **(i)** given the bond price schedules and monitoring rule, government policies and value functions solve the dynamic programming problem defined by equations (18)–(22); **(ii)** given the bond price schedules and government policies, the monitoring rule solves the problem in equation (6); **(iii)** given government and lender policies, the price functions satisfy equations (10), (13), and (17); and **(iv)** the market for government debt clears.

# **6 Quantitative analysis**

In this section, we present the results from the quantitative model. First, we discuss the calibration strategy for our benchmark model and how the results fit the novel database described in Sections 3 and 4. Second, we examine the properties of the model regarding default incentives, monitoring policies, and borrowing terms for the government. Third, we study the relationship between revelations and equilibrium spreads, both in the model and in our novel database. Finally, we present the welfare implications of hidden debt by comparing the benchmark model results with an otherwise identical model where monitoring by creditors is cheaper and another model with full information on debt accumulation.

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# **6.1 Calibration**

**Functional forms and stochastic processes.** The utility function of the representative agent in a small open economy displays a constant coefficient of relative risk aversion, i.e.,

We assume that lenders have a utility function of the same form, with a coefficient of relative risk aversion given by _γl_ .

The endowment process for the borrowing country follows: where _|ρ| <_ 1 and _νt ∼ N_ (0 _, σν_<sup>2</sup> ). As in Chatterjee and Eyigungor (2012), we assume a quadratic loss function for income during a default episode _φ_ ( _y_ ) = max _{y_ [ _λ_ 0 + _λ_ 1[ _y −_ E( _y_ )]] _,_ 0 _}_ . The function controlling the minimum level of debt upon reentry is parametrized as _α_ ( _y_ ) = _<u>α</u>_ ~~.~~

We assume that innovations to (i.e., ‘issuances’ of) hidden debt _ε_ are _iid_ and follow a normal distribution with mean _με_ and variance _σε_<sup>2.Importantly, while lenders know the distribution</sup> of _ε_ , they can observe _ε_ and _h_ only upon a revelation. Knowing this distribution, how many periods have passed since the last revelation ( _τ_ ), and the law of motion for hidden debt conditional on no revelation (i.e. _h_<sup>_′_</sup> = (1 _− δ_ ) _h_ + _ε_ ), lenders understand that _h_<sup>_′_</sup> is distributed as follows:<sup>34</sup> Equation (23) makes it clear that as time passes since the last hidden debt revelation, lenders’ expectations of the future levels of hidden debt feature a higher mean and a higher variance.

**Parameter values.** Table 5 presents the benchmark values assigned to all parameters in the model. A period in the model refers to a year. The coefficient of relative risk aversion for the borrowing country, risk-free interest rate, and discount factor _β_ take standard values.

The parameters that govern the endowment process are estimated from our dataset. These values, _ρ_ = 0 _._ 6 and _σν_ = 3%, are close to those typically found in studies of emerging and low-income countries.<sup>35</sup> We assume an average duration of sovereign default events of three years ( _θ_ = 0 _._ 33), following Dias and Richmond (2007). We set _δ_ = 0 _._ 31; with this value, sovereign debt has an average risk-free duration of 5 years in the simulations, which is close to the average duration found in the previous literature.<sup>36</sup> The coupon is normalized to

> 34The distribution of _h′_ , conditional on _τ_ , is a straightforward consequence of the properties of the normal distribution. See Appendix D for more details.

> 35Note that the income autocorrelation is somewhat lower than the values estimated for countries with continuous market access (e.g. Mexico).

> 36We use the Macaulay definition of duration, which, with the coupon structure in this paper, is given by _D_ = (1 + _r_ ) _/_ ( _δ_ + _r_ ), where _r_ denotes the risk-free rate. Cruces et al. (2002), using a sample of 27 emerging

30
_κ_ = ( _r_ + _δ_ ) _/_ (1 + _r_ ), which ensures that a default-free bond (with the same coupon structure as our sovereign bonds) trades at a price of 1 _/_ (1 + _r_ ). The price floor _<u>q</u>_ is set to 70% of the risk-free price, which is never binding in the simulations.

**Table 5:** Benchmark parameter values.

|Borrower’s risk aversion|_γ_|2.0|Standard|
|---|---|---|---|
|Risk-free rate|_r_|0.04|Standard|
|Discount factor|_β_|0.90|Standard|
|Income autocorrelation coefcient|_ρ_|0.6|Estimated|
|Standard deviation of innovations|_σν_|0.03|Estimated|
|Probability exclusion ends|_θ_|0.33|Mean exclusion = 3 years|
|Debt duration|_δ_|0.31|Debt duration = 5 years|
|Bond coupon|_κ_|(_r_+_δ_)_/_(1 +_r_)|Risk-free bond price = 1_/_(1 +_r_)|
|Price foor|_q_|0_._7_/_(1 +_r_)|Never binding|
|Lender’s risk aversion|_γl_|2.0|Aguiar et al. (2016)|
|Lender’s wealth|_W_|2.5|Aguiar et al. (2016)|
|Hidden debt price|_qh_|1_/_(1 +_r_)|Normalization|
|Hidden debt recovery|_χ_|1.0|Normalization|
|Mean of _ε_|_με_|1%|Our dataset|
|Standard deviation of _ε_|_σε_|2%|Our dataset|
|Income cost of defaulting|_λ_0|0.07|Avg. market debt = 26%|
|Income cost of defaulting|_λ_1|1.75|Avg. spread = 3.0%|
|Monitoring fee|_f_|0.03%|Freq. of monitoring = 7.1%|
|Recovery rate parameter|_α_|0.15|Mean recovery rate = 55%|

_Notes:_ Mean and standard deviation of _ε_ and the monitoring fee are expressed in percent of GDP.

The second part of Table 5 details our parametrization of the lender’s side of the model and the properties of hidden debt. We follow Aguiar et al. (2016) in setting the risk aversion coefficient of lenders to the same value as that for the borrower ( _γl_ = _γ_ = 2). The lender’s wealth _W_ is set to 2.5 (i.e., 250% of the mean income in the borrowing country), which is in line with the parameter value used in Aguiar et al. (2016). The price of hidden debt _qh_ is normalized to the risk-free price and the effective recovery rate on hidden debt _χ_ is normalized to one. The mean and variance of innovations to hidden debt are set using the values found in our dataset.<sup>37</sup> The last part of Table 5 has the remaining parameters. We calibrate the default cost parameters ( _λ_ 0 and _λ_ 1), the monitoring fee ( _f_ ), and recovery rate parameter ( _<u>α</u>_ ~~)~~ to target four moments from the data: (i) an average debt-to-GDP ratio of 26%, (ii) a mean spread of 3.0%, (iii) a frequency of monitoring of 7.1%, and (iv) a recovery rate of 55%. The first three moments are computed directly from our dataset. The recovery rate is taken from Graf von Luckner et al. (2023) and corresponds to the mean recovery rate obtained by bondholders in the modern era of sovereign bond financing. We solve the model using value function iteration and interpolation (Hatchondo et al., 2010).

> economies, find an average duration of 4.77 years, with a standard deviation of 1.52 years. In a panel of 11 emerging economies, Bai et al. (2017) report an average debt duration of 6.7 years.

> 37We obtain _με_ of 1% and _σε_ of 2% after winsorizing our revelations data at the 1st and 99th percentiles.

31
**Model fit.** The moments reported in Table 6 are chosen to illustrate the ability of the model to replicate distinctive business cycle properties of economies with sovereign risk as well as the hidden debt revelation patterns that we observe in the data.

**Table 6:** Model fit

||Data|Model|
|---|---|---|
|**Targeted moments**|||
|Mean debt-to-GDP<br>|26|24|
|Mean spread (_rs_)|3.0|3.0|
|Mean recovery rate|55|56|
|Freq. of revelations|7.1|7.2|
|**Non-targeted moments**|||
|**a) Business cycle statistics**|||
|_σ_(_c_)_/σ_(_y_)|1.1|1.3|
|_ρ_(_c, y_)|0.9|0.8|
|_ρ_(_rs, y_)|-0.3|-0.4|
|_σ_(_rs_)|2.8|1.8|
|**b) Hidden debt revelation patterns**|||
|Mean Revelation/_y_|0.94|0.88|
|_ρ_(Revelation_/y, b/y_)|0.10|0.03|
|_ρ_(Revelation_/y, y_)<br>|-0.06|-0.18|
|_ρ_(Hidden debt_,_HC)|0.17|0.13|

_Notes:_ The standard deviation of _x_ is denoted by _σ_ ( _x_ ). The coefficient of correlation between _x_ and _z_ is denoted by _ρ_ ( _x, z_ ). HC is the debt haircut and is defined as one minus the recovery rate. Moments are computed using log-detrended series. Trends are computed using the Hodrick-Prescott filter with a smoothing parameter of 100. In the simulations, moments correspond to the mean value of each moment in 500 simulation samples, with each sample including 500 periods. To compute the frequency of monitoring in the data we condition on revelations outside of default years and on revelations that amount to at least 1% of GDP.

Table 6 shows that our model well approximates the moments used as targets and is broadly consistent with non-targeted moments in the data. In both the model and data, consumption is procyclical and more volatile than income and the sovereign spreads are volatile and countercyclical.

The model further produces hidden debt revelation patterns that closely match those observed in our novel dataset. Revelations are highly similar in (mean) size, and they are negatively correlated with income and positively correlated with the debt-to-income ratio. Finally, in the event of default, the stock of hidden debt is associated with higher net present value losses (haircuts) for market creditors, as observed in the data (see Section 4.3).

This ability of our model to replicate the revelations observed in the data also becomes evident when observing the full distribution of revelations in the data and the model output, presented in Figure 8. Both distributions exhibit a right skew, positive means and near-zero medians.

32
**Figure 8:** Hidden debt revelations in the data and model

<!-- Start of picture text --> Panel A: Data Panel B: Simulated model<br>70%<br>60%<br>50%<br>40%<br>30%<br>20%<br>10%<br>0%<br>-5% 0% 5% 10% -5% 0% 5% 10%<br>Revelations in % of GDP Revelations in % of GDP<br>median mean median mean<br>Percent<br><!-- End of picture text --> _Notes:_ The figure shows the percentage distribution of hidden debt revelations from our database and the simulated model. In the data, revelations are defined as in equation (2).

# **6.2 Default incentives, monitoring and borrowing opportunities**

**Default incentives.** Figure 9 uses an “income threshold” to illustrate the default incentives in our model. We define the income threshold _y_  ̃ as the value of income at which the government is indifferent between repaying and defaulting, for given values of the other state variables.<sup>38</sup> Figure 9 plots this income threshold over the initial debt stock and for two values of initial hidden debt. For _y < y_  ̃ the government defaults (and repays otherwise). As expected, the higher the initial debt is, the higher the income threshold, which implies that there is a larger portion of the income space for which the country prefers to default.  ̃ Likewise, higher hidden debt increases default incentives: _y_ increases with _h_ .

> 38Formally, _y_  ̃ is the income level that satisfies _V_ 0( _b, h,_  ̃ _yε, τ_ ) = _V_ 1( _b, hy_  ̃). We numerically verify that this threshold is unique.

33
**Figure 9:** Income thresholds, _y_  ̃

_Notes:_ Different colors represent different values of hidden debt _h_ in period _t_ . This figure assumes that _τ_ = 7 (the mean in the simulations) and _ε_ below its mean.

**Figure 10:** Repayment, monitoring and default regions.

_Notes:_ The figure shows equilibrium monitoring and default choices as a function of income and initial debt. The figure assumes that _τ_ = 7 (the mean in the simulations), _h_ at its mean and _ε_ below the mean.

**Monitoring and default in equilibrium.** Figure 10 illustrates how the equilibrium monitoring and default decisions depend on the initial level of market debt and income.<sup>39</sup> The default region (denoted in dark gray) has the properties discussed above (and given

> 39Recall that lenders’ monitoring policy cannot, by construction, depend on the hidden debt process.

34
our assumption that a default reveals previously hidden debt, there is no monitoring under default). The repayment region has both combinations of the state variables with and without monitoring. Equilibrium monitoring tends to occur when the initial debt and income are close to the default boundary: all other things being equal, higher initial debt and lower income increase the chances of observing monitoring in equilibrium.

**Borrowing opportunities.** Figure 11 shows the spread-debt menus from which the government can choose, conditional on the monitoring policy of lenders. As is usual in this class of models, higher borrowing comes at the cost of higher spreads. When the chosen borrowing is sufficiently high, the spread increase acts, in effect, as an endogenous borrowing limit.

**Figure 11:** Spread-debt menus

_Notes:_ The curves show combinations of next-period debt and spreads from which the country can choose in the current period, for both monitoring and no-monitoring cases. The thick portion of the curves indicates the levels of next-period debt, which, if selected by the government, prompt either monitoring or no monitoring. The plot assumes that _y_ is at its mean.

The spreads in Figure 11 are shown for the case in which the government has market access in period _t_ . Therefore, a debt revelation can occur in this situation only through monitoring. The thick part of the spread curves shows how higher borrowing can trigger monitoring and, hence, revelations. For the particular combination considered in Figure 11, if the country borrows beyond 28% of mean income, it triggers monitoring and pays higher spreads (approximately 150 bps higher).

# **6.3 Revelations and spreads**

In our model, revelations occur for two reasons: monitoring and default. Monitoring-induced revelations are associated with higher spreads (as suggested by Figure 11): on average, the 35
equilibrium spread on monitoring periods is higher than the mean in the simulations (4.6% vs 3.0%).<sup>40</sup> Upon default, the government cannot borrow; however, since bonds in default are still valuable (due to a positive recovery rate), we can compute the implied spread – this is also higher than the average spread in the simulations.<sup>41</sup>

**Figure 12:** The effect of _τ_ on spread menus

_Notes:_ The curves show combinations of next-period debt and spreads from which the country can choose in the current period when the country is facing a non-monitoring episode, for two values of _τ_ . The plot assumes that _y_ is at its mean.

Hidden debt revelations impact spreads over an extended period. Focusing on monitoringinduced revelations, we see that revelations in _t_ are related to spreads in _t_ + 1 in two ways. First, a revelation reduces the uncertainty about the hidden debt stock, which, all other things being equal, lowers the spreads offered to the country in the period after the revelation: Figure 12 shows the spread-debt menu curves that the country faces in period _t_ when a revelation took place in period _t−_ 1 (and, therefore, the time since the last revelation is _τ_ = 1) and when the last revelation was sufficiently back in time ( _τ_ = 15).<sup>42</sup> Having had a recent revelation, lenders understand that both the expected value and the variance of (new) hidden debt are low, which leads them to offer better prices for government bonds. Second, a revelation increases the stock of market debt that lenders know the country has, which, coupled with the more favorable borrowing terms, typically leads to more borrowing by the country and to higher spreads in equilibrium.<sup>43</sup> In our simulations, we see the

> 40These higher spreads are, in turn, due to the higher level of borrowing (which is what triggers the revelation) and compensate for the monitoring fee paid by lenders.

> 41This particular relationship between default-induced revelations and higher spreads is admittedly more mechanical. With an average recovery rate of 55% (a target in our calibration), the typical bond price in default and exclusion periods is substantially lower than that in non-exclusion periods. The implied spread in the default period is 36%, on average.

> 42Note that these two curves are the spread-debt menus for the no-monitoring case, as this is the only bond price that depends on _τ_ .

> 43A movement towards the right on the horizontal axis of Figure 12, along the _τ_ = 1 curve.

36
combined effect of these forces. All else equal, larger revelations and higher values of _τ_ (higher uncertainty) should lead to larger increases in spreads.

**Table 7:** Spread response to hidden debt revelations

||Model|Output|Data|base|
|---|---|---|---|---|
||(1)|(2)|(3)|(4)|
|Revelation size|1.29***|1.25***|0.22***|0.22***|
||(0.04)|(0.04)|(0.08)|(0.08)|
|Years since last revel. (_τ_)||0.03***||0.01|
|||(0.00)||(0.07)|
|Growth|-1.22***|-1.20***|-1.45***|-1.45***|
||(0.02)|(0.02)|(0.34)|(0.34)|
|Debt/GDP|1.76***|1.74***|0.79*|0.79*|
||(0.02)|(0.02)|(0.43)|(0.43)|
|Disclosed borrowing|4.32***|4.38***|-0.25|-0.25|
||(0.04)|(0.04)|(0.24)|(0.24)|
|Constant|4.49***|4.26***|4.73***|4.70***|
||(0.02)|(0.03)|(0.12)|(0.26)|
|Observations|594|594|594|594|
|Country fxed efects|||✓|✓|

_Notes:_ This table shows the results of OLS regressions of next-period sovereign spreads (measured in percentage points) on the size of hidden debt revelations, years since the last revelation ( _τ_ ), and additional control variables. Columns (1) and (2) use the data output from our calibrated benchmark model. We run 500 regressions in samples of 594 randomly drawn observations and report the mean coefficients across runs and their standard errors in parentheses. Columns (3) and (4) use our hidden debt database and spread data from JP Morgan’s EMBI+. We include country fixed effects to focus on within-country time variation. Robust standard errors are reported in parentheses.

We validate these spread response predictions in both the simulated data from our model and our new hidden debt database by using a fixed effect regression model.<sup>44</sup> In Table 7, we show that larger revelations are indeed associated with larger increases in spreads after controlling for growth, the initial debt stock and new (disclosed) borrowing. The effects in the benchmark model (column (1)) are much larger (129 bps increase in spread for a revelation of 1 SD) than those in the database (22 bps increase), which is likely explained by the low frequency of our hidden debt database (annual) and by the fact that the availability of data on spreads is limited to countries with typically higher statistical capacity.<sup>45</sup> We then introduce _τ_ into the regression framework to capture the duration of the hidden debt build-up.<sup>46</sup> As expected, in both the benchmark model (column (2)) and real-world data (column (4)), higher uncertainty as measured by higher values of _τ_ is associated with higher

> 44To make the two datasets comparable, we run regressions in 500 randomly drawn samples of identical length as in the real-world data, and we then report the mean coefficients and standard errors.

> 45The spread data is from the EMBI+ compiled by JP Morgan which calculates the average spread for sovereigns based on USD-denominated bond instruments that meet certain minimum liquidity, size, and time-to-maturity criteria.

> 46In our database, we do not measure _τ_ directly but can nonetheless approximate it as the time passed since the country experienced an above-mean revelation (measured in years).

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spreads, and the effects are of very similar magnitudes, although only the model coefficient is statistically significant. Regarding the control variables, the growth and debt stock measures have very similar coefficients.

# **6.4 The costs of hidden debt**

In this section, we use our model to study the welfare costs of hidden debt. To do so, we consider two distinct scenarios. First, we compare our model economy with hidden debt and limited information to a hypothetical full-information benchmark in which market investors readily observe the realizations of _ε_ and _h_ at the beginning of each period.<sup>47</sup> In a second comparison, we take the existence of asymmetric information as given and study the welfare implications of moving towards greater market transparency by enabling investors to exercise greater oversight over the sovereign’s books. More specifically, we simulate the model with different parameter values for the monitoring fee _f_ and analyze welfare gains (and losses) as monitoring becomes cheaper and more frequent.

**Welfare gains of observable** _h_ **and** _ε_ **.** To assess the welfare implications of hidden debt we measure the welfare gains of moving from our benchmark economy to an otherwise identical economy in which the process for hidden debt is still exogenous but perfectly observable to international lenders. Figure 13 shows these gains as a function of the income level, expressed as the constant proportional change in consumption that would leave a consumer indifferent between living in our benchmark model and moving to the “full information” economy.

Figure 13 holds _h_ at its mean and shows how welfare gains depend on the initial income level, for two levels of market debt (zero and the mean in the simulations). Welfare gains are uniformly positive and decrease in income. We also see that the country benefits more from moving to the full-information economy when its initial debt is larger. The average welfare gain of moving to the full-information economy (with initial debt equal to the mean level in the simulations) is equal to a 5.5% permanent increase in consumption. These welfare gains are approximately one order of magnitude larger than, for example, those coming from eliminating debt dilution (Hatchondo et al., 2016).

These large welfare gains occur mainly because the full-information economy has a much larger debt capacity than the benchmark economy (averaging 83% of GDP). This higher debt leads to a much higher level of average consumption obtained in the full-information economy than in the benchmark (approximately 45% larger).<sup>48</sup> The larger debt-carrying capacity of the full-information economy illustrates how hidden debt contributes to the “debt intolerance” phenomenon.

> 47See Appendix D.2 for the details on the full-information economy. We compute the equilibrium of this economy using the same parameter values reported in Table 5.

> 48Despite featuring more frequent defaults (24% vs 6%) and more volatile consumption (4.3 vs 1.3), the mean effect of higher consumption dominates and delivers substantial welfare gains.

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**Figure 13:** Welfare gains of making hidden debt observable

_Notes:_ The figure shows the welfare gains for two possible values of initial market debt (zero and the mean in the simulations, 26% of GDP), keeping initial _h_ at its mean. The figure assumes that _ε_ is at its mean.

**Welfare implications of greater oversight.** We next show how greater oversight, captured trough lower costs of monitoring, impacts welfare. In Figure 14, we see that moving from an economy with a high monitoring cost (and, hence, little to no monitoring in equilibrium) to another in which monitoring is less expensive (and monitoring-induced revelations are more frequent) can have differing results. At low levels of hidden debt, cheaper monitoring is welfare increasing (irrespective of market debt levels). However, at higher hidden debt levels, monitoring can be welfare detrimental, depending on the initial debt levels. When the level of initial _h_ is kept constant, higher market debt results in lower (and even negative) gains from greater oversight. The same holds true if we keep _b_ constant and increase the initial level of _h_ : higher debt is associated with welfare losses. These results suggest that only countries with strong fundamentals and low hidden debt levels benefit from increased transparency. Countries with high levels of hidden debt, on the other hand, face worse borrowing opportunities after being exposed to greater scrutiny and experience welfare losses. This finding implies that transparency policies are best implemented countercyclically to avoid the negative welfare effects of the exposure of hidden debts during times of crisis.<sup>49</sup>

> 49The average welfare gain of increased oversight is equivalent to a 0.02% permanent increase in consumption. This gain is similar in magnitude to that coming from eliminating the uncertainty in the world interest rate (Johri et al., 2022).

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**Figure 14:** Welfare gains from increased oversight

_Notes:_ The figure shows the mean welfare gains from increased oversight (by lowering the monitoring fee) as a function of initial debt and for different levels of hidden debt. These gains are unconditional averages over the _y_ and _ε_ states.

# **7 Conclusion**

This paper is the first to systematically measure the degree of public debt under-reporting in a large sample of developing and emerging market countries. We use our novel data to motivate and numerically discipline a state-of-the-art quantitative model of sovereign debt and default with hidden debt, endogenous recovery rates, and investor monitoring. Our results from the model indicate a sizeable effect of hidden debt revelations on equilibrium spreads, default incentives, and welfare. We find that eliminating the uncertainty associated with hidden debt and its dynamics delivers substantial welfare gains equivalent to a permanent increase of 5.5% in consumption.

Our results have important implications for both practitioners and academic researchers. Analysts in both asset pricing and country surveillance should take into account that debt statistics tend to increase after their initial publication. For researchers, our findings and data open exciting new avenues for studying information acquisition and expectation formation in sovereign debt markets with asymmetric information.

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