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 sovereign defaults; and (iii) in debt restructurings, higher the magnitude, characteristics, and timing of hidden debt hidden debt is associated with larger creditor losses. The by tracking ex post data revisions across a comprehensive novel data is used to numerically discipline a quantitative new database of more than 50 vintages of World Bank sovereign debt model with hidden debt accumulation and debt statistics. In a sample of debt data covering 146 coun- an endogenous monitoring decision that triggers revela- tries and 53 years, the paper establishes three new stylized tions. Model simulations show that hidden debt has adverse facts: (i) debt statistics are systematically under-reported; effects on default risk, debt-carrying capacity and asset (ii) hidden debt accumulates in boom years and tends to prices and is therefore welfare detrimental. be revealed in bad times, often during IMF programs and 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∗ Sebastian Horn David Mihalyi Philipp Nickol César Sosa-Padilla† 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 Martinez- Iriarte, 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 Insti- tute. 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 pub- lic 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 restructur- ings 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.1 We document that the procyclicality of hidden debt accumulation and revelation is mainly driven by time-varying monitoring efforts. In our 1 Recent World Bank efforts to strengthen debt reporting are discussed in World Bank (2022a). 1 data, hidden debt revelations are particularly sizeable during sovereign default episodes and IMF programs, when the sovereign’s books come under close scrutiny.2 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.3 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 coun- try’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. 2 In contrast, we do not find evidence that governments strategically disclose hidden debts for political gains. 3 Zambia’s bondholders rejected the government’s first debt relief request citing debt transparency con- cerns 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”. 2 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 phe- nomenon 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 rational- ize 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).4 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; 4 Related 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 statis- tics 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). Em- pirical 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 present- ing 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 hid- den 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.5 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.6 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.7 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 coun- try’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 Fig- ure 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 com- modity 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- 5 See Financial Times (2017, June 25)“State loans at heart of Mozambique debt scandal”. 6 See Wall Street Journal (2016, April 3) “Tuna and Gunships: How $850 Million in Bonds Went Bad in Mozambique”. 7 See Reuters (2017, May 13) “Mozambique receives Kroll audit into hidden debts” and Reuters (2017, July 11) “IMF team visits Mozambique after damning debt audit”. 5 Figure 1: Sovereign bond yields following Mozambique’s hidden borrowing 2,800 Mozambique Restructuring re-enters of market debt debt distress 2,400 WSJ reports on and IMF Sovereign bond yield spread confirms 2,000 existence of hidden debt (in basis points) 1,600 Mozambique signals intent to restructure market debt 1,200 Issuance of market and hidden debt in 2013 800 400 0 13 14 14 14 15 15 15 16 16 16 20 20 20 20 20 20 20 20 20 20 ec pr ug ec pr ug ec pr ug ov A A A D D D A A A N 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).8 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.9 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’’.10 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”.11 Four years later, as of June 2024, the restructuring had not yet concluded.12 8 See Africa Confidential (2018, April 6) “Into the valley of debt” and Bloomberg (2018, April 8) “Zam- bia’s bonds plummet on concern it’s pulling a Mozambique”. 9 See Financial Times (2020, April 1) “Zambia’s bonds drop on expected restructuring”. 10 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”. 11 BBC (2021, September 1) “Zambian President Hichilema inherits ‘empty treasury’”. 12 Negotiations 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 8 Hidden debt (in 2014): Public external debt stock 6 • USD 1.36bn • 7.7% of GDP (USD billion) 4 2 0 2006 2007 2008 2009 2010 2011 2012 2013 2014 Initially reported external public debt External public debt added through revisions 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 Interna- tional 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 compre- hensive 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 10,000 Protracted default, data reconciliation 9,000 and restructuring process 8,000 Creditors reject restructuring over transparency concerns Sovereign bond yield spread 7,000 (in basis points) 6,000 Zambia asks banks for restructuring advice on $11.2bn 5,000 of external debt 4,000 First rumors about hidden debt 3,000 emerge 2,000 1,000 0 ay 18 ug 8 ec 8 pr 8 ug 9 ec 9 pr 9 ug 0 ec 0 pr 0 ug 1 ec 1 pr 1 ug 2 ec 2 pr 2 ug 3 ec 3 ar 3 24 A 201 D 201 A 201 A 201 D 201 A 201 A 202 D 202 A 202 A 202 D 202 A 202 A 202 D 202 A 202 A 202 D 202 M 202 M 20 20 n Ja Sources: Financial Times (2020, April 1) “Zambia’s bonds drop on expected restructuring”, Fi- nancial 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 Statis- tics 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. Re- porting 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.13 An upward 13 As 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 15 Hidden debt (in 2021): 12 • USD 3.18bn Public external debt stock • 14% of GDP (USD billion) 9 6 3 0 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 Initially reported external public debt External public debt added through revisions 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.14 • Since the first publication of the World Debt Tables in 1973, the World Bank’s re- porting 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.15 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- 14 See 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. 15 Appendix Section B.1 documents these minor refinements. Our results remain unchanged when elimi- nating 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 machine- readable 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:16 • 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 gen- eral government and state-owned corporations and liabilities of private debtors that have been guaranteed by a public entity. 16 Note 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). 10 • 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. i,t − Debti,t v0 HiddenDebti,t = DebtV (1) where Debt is either the debt stock or flow value, reported in vintages V and v0 , with V being the most recent vintage and v0 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 . ∑ T ( ) v −1 HiddenDebtRevelationsv i = i,t − Debti,t Debtv (2) t=t0 where Debti,t is defined as above, with t0 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.17 By definition, the total amount of hidden debt equals the total amount of hidden debt revelations for any particular country. ∑ T ∑ V HiddenDebtt i = HiddenDebtRevelationsv i . (3) t=t0 v =v0 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 17 Note 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. 11 information about the underlying loans and bonds portfolio.18 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 assump- tion 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 18 This 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. 12 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. 13 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 40% median mean 30% Percent 20% 10% 0% -5% 0% 5% 10% Ex-post PPG debt stock revision in % of GDP .... Panel B: Revisions to debt flows in percent of GDP 60% median mean 50% 40% Percent 30% 20% 10% 0% -5% 0% 5% 10% Ex-post PPG debt commitment revision in % of GDP 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. 14 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.19 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 misre- porting, 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 approxi- mately 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 statis- tically 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.20 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. 19 For 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). 20 Another way of assessing the magnitude of hidden debt and borrowing is to measure how much bor- rowing 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. 15 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.21 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). 21 Since 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. 16 Figure 6: Where is hidden debt the largest? Panel A: In borrower countries with weaker institutions 2.5% 2.0% 1.5% 1.0% (in % of GDP) Hidden debt 0.5% 0.0% -0.5% -1.0% -1.5% Lowest Second Third Highest quartile quartile quartile quartile Institutional strength .... Panel B: In loans from bilateral and private creditors 25% 20% (in % of initially reported debt stock) 15% 10% Hidden debt 5% 0% -5% -10% -15% Private of which: Bilateral Multilateral of which: lending Bonds lending lending World Bank 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. 17 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.22 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). 22 An 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. 18 Figure 7: The procyclical nature of hidden debt Panel A: Which years are being revised? .2 .1 Hidden debt - normalized 0 -.1 p-value = 0.026 -.2 -10 -5 0 5 10 15 Real GDP growth in year which is revised .... Panel B: When do revelations happen? .2 Hidden debt revelations - normalized .1 0 -.1 -.2 p-value = 0.001 -10 -5 0 5 10 15 Real GDP growth in year of revelation 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 1st and 99th 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. 19 Table 3: Drivers of hidden debt revelations Dep. variable: Hidden debt revelations, 1975-2020 (1) (2) (3) (4) Real GDP growth (WDI) -0.03** -0.03** (0.01) (0.01) External sov. default 0.14*** 0.12** (0.05) (0.05) IMF program 0.13*** 0.12** (0.04) (0.05) Observations 3,914 4,069 4,069 3,892 R-squared 0.049 0.047 0.048 0.053 Country FE ✓ ✓ ✓ ✓ Vintage FE ✓ ✓ ✓ ✓ 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 1st and 99th 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. 20 Table 4: Hidden debt and default spells Haircut 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 -0.47 (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 unre- ported debts are indeed associated with higher creditor losses in statistically and economi- cally 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. 21 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.23 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 gener- ations 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 ∞ ∑ Et β j −t u ( c j ) , j =t 23 For work on the strategic use of hidden debt, see Alfaro and Kanczuk (2022), Gamboa (2023) or Guler et al. (2022). 22 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.24 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 in- vestors 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 .25 In particular, a bond issued in period t promises to pay κ (1 − δ )j −1 units of the trad- able 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 24 Thus, 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. 25 Arellano 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. 23 can know the true level of hidden debt.26 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 behav- ior of defaulting governments, and it is a standard assumption in the literature.27 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 : { } ˜ , bD (b, h, y ) = min α(y ), b + h (4) ˜ = max{0, h} and α(y ) is a non-decreasing function of the income level realized upon where h 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 ˜ , with χ ∈ [0, 1].28 Holders of the previously issued market debt obtain the event) obtain χh remainder, bD − χh ˜ . This implies the following recovery rate for market debt: ˜ bD (b, h, y ) − χh ω b (b, h, y ) = . (5) b 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 revela- tion, τ . 26 For 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. 27 Sovereign 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. 28 We 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 qm and qnm 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′ . When it eval- uates possible values for b′ 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′ = 0). – If there is no monitoring (m = 0), hidden debt is h′ = 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.29 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 ′ . After this decision is made, hidden debt either continues to be 29 Implicit 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.30 In the exposition of the lenders’ problem, we use b′ to denote the borrowing choice of the government and B ′ to denote lenders’ investment in government bonds.31 The lenders’ problem can be written as { } V ℓ (b′ , y, τ ) = max ℓ m VM (b′ , y ) + (1 − m) VN ℓ ′ M (b , y, τ ) . (6) m∈{0,1} In turn, their value under monitoring is given by ℓ VM (b′ , y ) = max ′ ′ E ℓ [ uℓ ( C ℓ )] (7) B subject to ′ Cℓ (B ′ , h′ , y ′ , ε′ , τ ′ ) = (W − f − qm B ′ )(1 + r) + B ′ R′ (8) [ ( R′ (b′ , h′ , y ′ , ε′ , τ ′ ) ≡ d′ qD (b′ , h′ , y ′ ) + (1 − d′ ) × κ + (1 − δ ) m∗ (b′′ , y ′ , τ ′ ) qm (b′′ , y ′ ) )] ∗ ′′ ′ ′ ′′ ′ ′ + (1 − m (b , y , τ )) qnm (b , y , τ ) (9) where τ ′ = 1, h′ = 0, qD denotes the price of a bond in default, b′′ = ˆ b(b′ , h′ , y ′ , ε′ , τ ′ ), and ˆ(b′ , h′ , y ′ , ε′ , τ ′ ), with ˆ d′ = d ˆ denoting the optimal borrowing and default policies that b and d lenders expect the government to follow, respectively. m∗ (b′′ , y ′ , τ ′ ) is the monitoring policy that current lenders expect the future generation of lenders will follow, and E ℓ denotes the expectation operator of lenders in the case of monitoring.32 The solution to this problem features a demand schedule for sovereign bonds given by E ℓ {u′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ℓ (Cℓ (B , h , y , ε , τ )) × R (b , h , y , ε , τ )} q m ( b′ , y ) = ′ ′ . (10) E ℓ [uℓ (Cℓ (B ′ , h′ , y ′ , ε′ , τ ′ )) (1 + r)] 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 ℓ different). In this case, we use Eτ to denote the expectation operator of lenders, where the sub-index τ indicates that the lenders’ expectations about h′ vary with the time since the last revelation. Therefore, the value under no monitoring can be written as follows: ℓ ′ ℓ ′ VN M (b , y, τ ) = max ′ Eτ [ uℓ ( C ℓ )] (11) B 30 Note that in this framework, different from Gu and Stangebye (2023), the government has an informa- tional 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 com- munication 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. 31 In equilibrium, we will naturally have b′ = B ′ . 32 In 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′ = 0. 26 subject to ′ Cℓ (B ′ , h′ , y ′ , ε′ , τ ′ ) =(W − qnm B ′ )(1 + r) + B ′ R′ (12) where R′ is given by equation (9) evaluated at τ ′ = τ + 1. Lenders view h′ 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 ℓ Eτ {u′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ℓ (Cℓ (B , h , y , ε , τ )) × R (b , h , y , ε , τ )} qnm (b′ , y, τ ) = ℓ [u′ (C ′ (B ′ , h′ , y ′ , ε′ , τ ′ )) (1 + r )] , (13) Eτ ℓ ℓ ′ where Cℓ is given by equation (12) and τ ′ = τ + 1. 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: ℓ ′ VD (b, h, y ) = max E ℓ [uℓ (Cℓ )] (14) B subject to ′ Cℓ ˜ y ′ )B )(1 + r) + B R′ , (B, h, y ′ , ε′ , τ ′ ) = (W − qD (b, h, D (15) [ ˜ y ′ ) + θ ω (b, h, y ′ ) d R′ (b, h, y ′ , ε′ , τ ′ ) = (1 − θ)qD (b, h, D ˆ(bD , 0, y ′ , ε′ , τ ′ ) qD (bD , 0, y ′ ) + [ ( ˆ(bD , 0, y ′ , ε′ , τ ′ )) κ + (1 − δ ) m∗ (b′′ , y ′ , τ ′ )qm (b′′ , y ′ )+ (1 − d (16) ] )] ∗ ′′ ′ ′ ′′ ′ ′ (1 − m (b , y , τ )) qnm (b , y , τ ) where θ ∈ (0, 1) is the probability of reentry to financial markets, h˜ = max{h, 0} and τ ′ = 1. ˆ represents the expected default policy, b′′ = ˆ As before, d b(bD , 0, y ′ , ε′ , τ ′ ) is the expected borrowing policy, and m∗ (b′′ , y ′ , τ ′ ) is the expected monitoring policy. bD and ω (b, h, y ′ ) are given by equations (4) and (5), respectively. Therefore, the price of a bond in default is given by E ℓ {u′ ′ ′ ′ ′ ′ ℓ (Cℓ ) × RD (b, h, y , ε , τ )} qD (b, h, y ) = ℓ ′ ′ . (17) E [uℓ (Cℓ )(1 + r)] 27 Note that in this case, the correct expectation operator is E ℓ , the same as under monitoring. The reason is our assumption that a default triggers a revelation of hidden debt and therefore lowers uncertainty.33 5.3 The government’s problem A government that starts the period in good standing has the option to default on its debt. Therefore, { } V (b, h, y, ε, τ ) = max d V1 (b, h, y ) + (1 − d) V0 (b, h, y, ε, τ ) (18) d∈{0,1} 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 [ ] V1 (b, h, y ) = ˜ y ′ ) + θ V ( bD , h ′ , y ′ , ε ′ , τ ′ ) u(cD ) + βEy′ ,ε′ |y (1 − θ) V1 (b, h, (19) subject to ( ) cD = y − ϕ(y ) + h˜−h (20) ˜ = max{h, 0}, h′ = 0, τ ′ = 1, and bD (b, h, y ′ ) is given by equation (4). The function where h 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 V0 (b, h, y, ε, τ ) = m∗ V0M (b, h, y, ε) + (1 − m∗ ) V0N M (b, h, y, ε, τ ) where m∗ (b′ , y, τ ) denotes the optimal monitoring policy, which the government takes as given (understanding how it depends on the level of b′ ). In the case of monitoring (m∗ = 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′ = 0). In this case, the problem of the government is { ′ ′ ′ ′ ′ } V0M (b, h, y, ε) = max ′ u ( c ) + βE y ′ ,ε′ |y V (b , h , y , ε , τ ) (21) b subject to c = y − κ ( b + h) + q m ( b ′ , y ) ι + q h ε ι = b′ − [(1 − δ )b + (1 − δ )h + ε] h′ = 0, τ ′ = 1, ι > 0, only if qm (b′ , y ) > q, 33 This 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 qm (b′ , 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∗ = 0), hidden debt continues to be hidden to lenders, and its end-of-period level is h′ = (1 − δ )h + ε. In this case, the problem of the government is { } V0N M (b, y, h, ε; τ ) = max ′ u(c) + βEy′ ,ε′ |y V (b′ , y ′ , h′ , ε′ , τ ′ ) (22) b subject to c = y − κ(b + h) + qnm (b′ , y, τ )ι + qh ε ι = b′ − (1 − δ )b h′ = (1 − δ )h + ε ′ τ = τ +1 ι > 0 only if qnm (b′ , y, τ ) > q . 5.4 Equilibrium definition { A Markov perfect equilibrium is defined by value { functions V (b, h, y, ε, τ ), V0M (b, h, y, ε), } } V0N M (b, h, y, ε, τ ), V1 (b, h, y ) , policy functions d bM (b, h, y, ε), ˆ ˆ(b, h, y, ε, τ ), ˆ bN M (b, h, y, ε, τ ) , a monitoring rule m∗ (b′ , y, τ ), and bond price schedules {qm (b′ , y ), qnm (b′ , 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. 29 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., c 1− γ u ( c) = , with γ ̸= 1 . 1−γ 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: log(yt ) = (1 − ρ)µ + ρ log(yt−1 ) + νt , ( ) where |ρ| < 1 and νt ∼ N 0, σν 2 . As in Chatterjee and Eyigungor (2012), we assume a quadratic loss function for income during a default episode ϕ (y ) = max {y [λ0 + λ1 [y − E(y )]] , 0}. The function controlling the minimum level of debt upon reentry is parametrized as α(y ) = α. We assume that innovations to (i.e., ‘issuances’ of) hidden debt ε are iid and follow a normal 2 distribution with mean µε and variance σε . Importantly, while lenders know the distribution 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′ = (1 − δ )h + ε), lenders understand that h′ is distributed as follows:34 ( ) 1 − (1 − δ )τ 2 1 − (1 − δ )τ h′ ∼ N µε , σε . (23) δ δ 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.35 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.36 The coupon is normalized to 34 The distribution of h′ , conditional on τ , is a straightforward consequence of the properties of the normal distribution. See Appendix D for more details. 35 Note that the income autocorrelation is somewhat lower than the values estimated for countries with continuous market access (e.g. Mexico). 36 We 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 q 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 coefficient 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 floor 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 λ0 0.07 Avg. market debt = 26% Income cost of defaulting λ1 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.37 The last part of Table 5 has the remaining parameters. We calibrate the default cost parameters (λ0 and λ1 ), the monitoring fee (f ), and recovery rate parameter (α) 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. 37 We 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 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 ) -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 ob- served 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 Panel A: Data Panel B: Simulated model 70% median mean median mean 60% 50% Percent 40% 30% 20% 10% 0% -5% 0% 5% 10% -5% 0% 5% 10% Revelations in % of GDP Revelations in % of GDP 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 incen- ˜ as the value of income at which the tives in our model. We define the income threshold y government is indifferent between repaying and defaulting, for given values of the other state variables.38 Figure 9 plots this income threshold over the initial debt stock and for ˜ the government defaults (and repays otherwise). two values of initial hidden debt. For y < y 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. ˜ increases with h. Likewise, higher hidden debt increases default incentives: y 38 Formally, y ˜ is the income level that satisfies V0 (b, h, y ˜). We numerically verify that this ˜ε, τ ) = V1 (b, hy 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.39 The default region (denoted in dark gray) has the properties discussed above (and given 39 Recall 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 gov- ernment 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%).40 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.41 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 monitoring- induced 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).42 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.43 In our simulations, we see the 40 These 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. 41 This 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. 42 Note 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 . 43 A 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 Database (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 fixed effects ✓ ✓ Notes: This table shows the results of OLS regressions of next-period sovereign spreads (measured in per- centage 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.44 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.45 We then introduce τ into the regression framework to capture the duration of the hidden debt build-up.46 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 44 To 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. 45 The 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. 46 In 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). 37 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 47 readily observe the realizations of ε and h at the beginning of each period. 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 iden- tical 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, ex- pressed 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).48 The larger debt-carrying capacity of the full-information economy illustrates how hidden debt contributes to the “debt intolerance” phenomenon. 47 See 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. 48 Despite 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. 38 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, cap- tured 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 equilib- rium) 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 monitor- ing 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 bor- rowing 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.49 49 The average welfare gain of increased oversight is equivalent to a 0.02% permanent increase in con- sumption. This gain is similar in magnitude to that coming from eliminating the uncertainty in the world interest rate (Johri et al., 2022). 39 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 mo- tivate 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 for- mation in sovereign debt markets with asymmetric information. 40 References Agarwal, I., D. Jaume, E. 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A-7 A.3 Data coverage, descriptive statistics and key variables of interest . . . A-9 A.4 Data sources for control variables . . . . . . . . . . . . . . . . . . . . A-11 B Data validation B.1 Changes in reporting rules . . . . . . . . . . . . . . . . . . . . . . . . A-12 B.2 FX data revisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-15 B.3 Treatment and impact of contingent liability realization . . . . . . . . A-15 B.4 Accounting for the possibility of reporting lags . . . . . . . . . . . . . A-17 B.5 Revisions to the latest debt statistics . . . . . . . . . . . . . . . . . . . A-19 B.6 Comparison with IMF reporting violations . . . . . . . . . . . . . . . A-21 C Additional results and figures C.1 Debt data revisions to total external debt stocks . . . . . . . . . . . . A-22 C.2 Hidden debt revelations and political cycles . . . . . . . . . . . . . . A-24 C.3 Additional descriptive statistics . . . . . . . . . . . . . . . . . . . . . A-28 D Model Appendix D.1 Details about the lender’s expectations . . . . . . . . . . . . . . . . . A-38 D.2 Details about the full-information economy . . . . . . . . . . . . . . . A-39 References for Online Appendix . . . . . . . . . . . . . . . . . . . . . . A-41 A-1 A Constructing the new database of debt data revisions This appendix chapter gives a detailed description of how we construct our new database of debt data revisions. We describe all underlying sources, the data digitization and cleaning process and present key descriptive characteristics of the final dataset. We also present a variety of additional empirical exercises that we have carried out to minimize measurement error and to validate the interpretation of our hidden debt measure. A.1 Data sources and digitization Our new database of debt data revisions draws on the debt statistics published by the World Bank since the 1970s. More specifically, our database centers around the International Debt Statistics (2012–2023) and its predecessor formats, the Global Development Finance Reports (1997–2012) and the World Debt Tables (1973–1996). Table A1 provides a detailed list of all vintages that enter our final database. All these vintages build on the World Bank’s Debtor Reporting System (DRS), which was established in 1951. Sovereign debtors that borrow or guarantee loans extended by the World Bank Group need to agree to report detailed data on their long-term public and publicly guaranteed debt through the DRS. The World Bank compiles this loan-level data and publishes it annually through its flagship debt report. Table A1 gives an overview of all 51 vintages that we have compiled. Digitization: The data from the most recent debt reports is readily available in a machine- readable format on the World Bank’s website. 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’s website.50 For all reports prior to 2005, we are required to digitize the original reports and extract the data into a machine-readable format. Original reports were either downloaded from the World Bank website in PDF form or were scanned from the original hard copies that we obtain from different libraries. The third column of Table A1 provides an overview on which vintages were downloaded and which were scanned.51 The digitization of the PDF reports and hard copies itself relies heavily on the use of Optical Character Recognition (OCR) Software and manual coding. Section A.2 discusses various steps that we undertake to ensure the accuracy of our data. 50 See /https://www.worldbank.org/en/programs/debt-statistics/idr/products 51 PDFs of vintages back until 1991–1992 can be found here: /https://www.worldbank.org/en/programs/ debt-statistics/publications. PDFs of earlier vintages (1973–1991) can be found via the World Bank’s Documents & Reports page here: /https://documents.worldbank.org/en/publication/documents- reports. A-2 Table A1: Overview of WDT, GDF, IDS and IDR vintages Title Short form Availability Version used World Debt Tables WDT1973 PDF only World Debt Tables: External Public Debt WDT1974 Hard copy of LDCs World Debt Tables Volume II: External WDT1975 PDF only Public Debt of LDCs World Debt Tables. External Public Debt WDT1976 Hard copy of LDCs World Debt Tables. External Public Debt WDT1977 Hard copy of Developing Countries World Debt Tables. External Public Debt WDT1978 Hard copy of Developing Countries World Debt Tables Volume II: External WDT1979 PDF only Public Debt of 96 Developing Countries World Debt Tables Volume II: External WDT1980 Hard copy Public Debt of 99 Developing Countries World Debt Tables: External Public Debt WDT1981 PDF only of Developing Countries and Territories World Debt Tables: External Debt of De- WDT1982-83 PDF only veloping Countries – 1982-83 Edition World Debt Tables: External Debt of De- WDT1983-84 Hard copy veloping Countries – 1983-84 Edition World Debt Tables: External Debt of De- WDT1984-85 PDF only veloping Countries – 1984-85 Edition World Debt Tables: External Debt of De- WDT1985-86 Hard copy veloping Countries – 1985-86 Edition World Debt Tables: External Debt of De- WDT1986-87 Hard copy veloping Countries – 1986-87 Edition World Debt Tables: External Debt of De- WDT1987-88 Hard copy veloping Countries – 1987-88 Edition World Debt Tables: External Debt of De- WDT1988-89 PDF only veloping Countries – Volume II. Country Tables – 1988-89 Edition World Debt Tables 1989-90 External Debt WDT1989-90 PDF only of Developing Countries – Volume 2. Country Tables World Debt Tables 1990-91 External Debt WDT1990-91 Hard copy of Developing Countries – Volume 2. Country Tables A-3 World Debt Tables 1991-92 External Debt WDT1991-92 PDF only of Developing Countries – Volume 2. Country Tables World Debt Tables 1992-93 External Fi- WDT1992-93 PDF only nance for Developing Countries – Volume 2. Country Tables World Debt Tables 1993-94 External Fi- WDT1993-94 PDF only nance for Developing Countries – Volume 2. Country Tables World Debt Tables 1994-95 External Fi- WDT1994-95 PDF only nance for Developing Countries – Volume 2. Country Tables World Debt Tables 1996 External Finance WDT1996 PDF only for Developing Countries – Volume 2. Country Tables Global Development Finance 1997 – Vol- GDF1997 PDF only ume 2 Country Tables Global Development Finance 1998 – Coun- GDF1998 PDF only try Tables Global Development Finance - Country GDF1999 PDF only Tables 1999 Global Development Finance - Country GDF2000 PDF only Tables 2000 Global Development Finance: Building GDF2001 PDF only Coalitions for Effective Development Fi- nance – Country Tables 2001 Global Development Finance: Financing GDF2002 PDF only the Poorest Countries – Country Tables 2002 Global Development Finance: Striving for GDF2003 PDF only Stability in Development Finance – II: Summary and Country Tables 2003 Global Development Finance: Harnessing GDF2004 PDF only Cyclical Gains for Development – II: Sum- mary and Country Tables 2004 Global Development Finance: Mobilizing GDF2005 Online Apr. 2005 Finance and Managing Vulnerability – II: Summary and Country Tables 2005 Global Development Finance: The Devel- GDF2006 Online Nov. 2005 opment Potential of Surging Capital Flows – II: Summary and Country Tables 2006 A-4 Global Development Finance: The Global- GDF2007 Online Dec. 2006 ization of Corporate Finance in Developing Countries – II: Summary and Country Ta- bles 2007 Global Development Finance: The Role of GDF2008 Online Nov. 2007 International Banking – II: Summary and Country Tables 2008 Global Development Finance: Charting a GDF2009 Online Dec. 2008 Global Recovery – II: Summary and Coun- try Tables 2009 Global Development Finance External GDF2010 Online Feb. 2010 Debt of Developing Countries 2010 Global Development Finance External GDF2011 Online Dec. 2010 Debt of Developing Countries 2011 Global Development Finance External GDF2012 Online Dec. 2011 Debt of Developing Countries 2012 International Debt Statistics 2013 IDS2013 Online Dec. 2012 International Debt Statistics 2014 IDS2014 Online International Debt Statistics 2015 IDS2015 Online International Debt Statistics 2016 IDS2016 Online International Debt Statistics 2017 IDS2017 Online International Debt Statistics 2017 IDS2017 Online International Debt Statistics 2018 IDS2018 Online International Debt Statistics 2019 IDS2019 Online International Debt Statistics 2020 IDS2020 Online International Debt Statistics 2021 IDS2021 Online International Debt Statistics 2022 IDS2022 Online International Debt Report 2022 IDR2022 Online International Debt Report 2023 IDR2023 Online Notes: The table shows all vintages that enter our final database. Vintages with availability “online” and “PDF only” are available from the World Bank’s websites. Vintages labeled “hard copy” are vintages which we obtain from different libraries and scan ourselves. For vintages 2005–2011 there is more than one version per vintage available, column “Version used” indicates the ones that enter our database. See text for further details. Merging data from different vintages: After all 51 vintages have been digitized and brought into machine-readable formats, we merge the data into a single dataset. While the underlying debt data definitions and concepts have remained remarkably stable over time (see B.1 for a detailed examination), some of the variable names and codes have been changed across the history of the World Bank’s debt statistics. To merge data across vintages, we create a mapping of the modern series codes into the vintage-specific variable names and codes. Table A2 provides details on each of the key variables that we use in our analysis. A-5 Table A2: Mapping series codes and variable names across vintages Modern seriescode 1973-1974 1975-1976 1977-1980 1981-1988 1989-1993 1994-2004 Description (2005 onwards) Panel A: Public and publicly guaranteed (DPPG) Debt outstanding and TOTAL ALL Debt TOTAL EXTERNAL PUBLIC disbursed Debt Outstanding beginning of LENDERS: Outstanding & DEBT: OUTSTANDING DEBT OUTSTANDING (LDOD) DT.DOD.DPPG.CD period: Disbursed only OUTSTANDING Disbursed (DISBURSED ONLY) (DISBURSED ONLY) (DOD) Commitments TOTAL ALL Transactions during period: TOTAL EXTERNAL PUBLIC Memorandum Items: LENDERS: Commitments DT.COM.DPPG.CD Commitments DEBT: COMMITMENTS Commitments COMMITMENTS Disbursements TOTAL ALL Transactions during period: TOTAL EXTERNAL PUBLIC LENDERS: Disbursements DT.DIS.DPPG.CD Disbursements DEBT: DISBURSEMENTS DISBURSEMENTS Principal repayments TOTAL ALL TOTAL EXTERNAL PUBLIC Transactions during period: Service LENDERS: DEBT: PRINCIPAL Principal Repayments DT.AMT.DPPG.CD Payments: Principal PRINCIPAL PAYMENTS REPAYMENTS Panel B: Creditor categories Official creditors TOTAL OFFICIAL Official Creditors DT.DOD.OFFT.CD A-6 LENDERS Multilateral Loans from International INTERNATIONAL ORGANIZATIONS Multilateral DT.DOD.MLAT.CD Organizations of which: IBRD IBRD DT.DOD.MIBR.CD of which: IDA IDA DT.DOD.MIDA.CD Bilateral Loans from DAC Governments DAC GOVERNMENTS GOVERNMENT Loans from East Bloc Governments EAST BLOC GOVERNMENTS Bilateral DT.DOD.BLAT.CD LENDERS Loans from Other Governments OTHER GOVERNMENTS Private creditors TOTAL PRIVATE Private Creditors DT.DOD.PRVT.CD LENDERS of which: Bonds Bonds DT.DOD.PBND.CD of which: Commercial banks Credits from Private Banks PRIVATE BANKS Commercial banks DT.DOD.PCBK.CD of which: Other private creditors OTHER PRIVATE Credits from Other Private Creditors OTHER PRIVATE CREDITORS Other private DT.DOD.PROP.CD LENDERS Notes: The table shows the mapping of the modern series codes into variable names and codes in vintages 1973–2004. Panel A provides the series code mapping for the most important stock and flow measures, while Panel B provides the mapping for the different creditor categories. Grey shaded areas indicate that the variable is not available in a vintage. A.2 Data cleaning To ensure the quality of our digitized data and to minimize measurement error from the application of the OCR software, we use two algorithmic procedures to detect potential coding errors and to check the consistency of our digitized data across and within vintages. Across-vintage consistency checks: In this consistency check, we make use of the fact that each debt figure appears in multiple vintages. For each data point, we check whether the reported value is different from the one published in the previous and the subsequent vintage. A potential measurement error is flagged if the difference between the value in the lead and the lag vintage is zero, but the value itself is unequal to the value in the lag vintage. We resolve these cases by revisiting the original sources. Within-vintage consistency checks: We further identify potential measurement error by tracking deviations of several accounting identities that need to hold within each vintage. First, it must hold that the following aggregates can be derived as the sum of their sub- components, DP P Gv v v i,t = OF F Ti,t + P RV Ti,t (24) v v v OF F Ti,t = BLATi,t + M LATi,t (25) v v v v P RV Ti,t = P BN Di,t + P CBKi,t + P ROPi,t (26) where the total public and publicly guaranteed debt stock (DP P G) of country i in year t from vintage v is equal to the sum of the debt stock owed to official (OF F T ) and private (P RV T ) creditors. These in turn have to be equal to the sum of the debt stocks owed to bilateral (BLAT ) and multilateral creditors (M LAT ), and equal to the sum of debt stocks owed to bondholders (P BN D), commercial banks (P CBK ), and other private creditors (P ROP ), respectively. The decomposition of debt to private creditors shown in Equation (26) is only available from vintage 1990 onwards. These identities cannot only be derived for debt stocks (DP P G), but also for all flow vari- ables, including disbursements (DIS ) and principal repayments (AM T ). For commitments (COM ), only equation (24) and equation (25) can be checked, since commitment data is not available for all sub-components, as we discuss in greater detail below (see Section A.3 and Table A4). We derive all these identities from each of the newly digitized vintages. Whenever one of the identities does not hold in our digitized dataset, we return to the original PDFs and make sure that all components of the identity were digitized correctly and that inconsistencies were not introduced by our digitization effort. The procedure ensures with very high probability that our digitized data is an exact replication of the underlying World Bank debt reports. Elimination of estimates and preliminary data points: If a developing or emerging market country does not fulfil its reporting obligations towards the World Bank’s Debtor Reporting System (DRS), the World Bank may choose to provide estimates or other non- reported values. Such cases are clearly labeled in the World Bank debt reports. More A-7 precisely, every debtor country is assigned one of the following debtor reporting statuses in each of the vintages:52 (A) “actual”/“as reported”. Indicates that the country was fully current in its reporting and that World Bank staff are satisfied that the reported data give an adequate and fair representation of the country’s total public debt. (E) “estimate”. Indicates that the country was not current in their reporting and that a significant element of staff estimation has been necessary in producing the data tables. (P) “preliminary”. Based on reported or collected information but, because of incom- pleteness or other reasons, includes an element of staff estimation. To avoid diluting our hidden debt revelation measure, our analysis only considers country- vintage observations that are classified as “actual” or “as reported” and discards all data points which are classified as either “preliminary” or as “estimates”.53 All revisions that we identify are therefore revisions to data points that World Bank staff considered an “adequate and fair representation of the country’s total public debt” at the time of the first data release. Minor data transformations: To ensure consistency of the data across vintages, we further undertake the following minor data transformations: • We transform all the data into millions of nominal USD and round all entries to full integers without decimal points. • Data for the Democratic Republic of the Congo and for Zaire are subsumed under ISO code “COD”. Data for Yugoslavia, Serbia and Montenegro, and Serbia are subsumed under ISO code “SRB”. • In WDT1973 and WDT1974, debt stocks are reported as beginning-of-period values, wheres in all following vintages they are reported as end-of-period values. Hence we adjust the 1973 and 1974 values to match the reporting format of all following vintages. • In IDS2013 and IDS2014, zeros are reported for all values in 1970 and 1971, although non-zero entries are available in vintages prior to 2013 and after 2014. We replace zero entries with the values reported in IDS2015. In some cases, vintages from IDS2018 until IDR2023 report zeros where previous vintages reported missing values. We replace these zeros with missing values. Lastly, IDS2017, IDS2021, IDS2022, IDR2022 and IDR2023 report several values as missing despite the fact that in previous vintages 52 In the first editions of the World Debt Tables, for vintages from 1973 to 1978, no explicit reporting status is provided. The forewords of these vintages, however, emphasize that only the statistics of those countries are released that World Bank staff considers sufficiently complete to give a fair representation of the country’s debt. As a result the number of included countries varies from year to year. We take this as evidence that all data points from these vintages can be considered as “actual” reporting and not as preliminary or estimated figures. The empirical results presented in this paper are robust to dropping all observations from vintages 1973 to 1978. 53 In a few rare instances, the reporting status is contradicted in the “country notes” section in the appendix of the debt report. For example, the IDS 2021 reporting status for Guinea is classified as “actual”, but the country notes state that the long-term PPG debt for 2016 is a World Bank staff estimate. In such cases, we overrule the classification and drop the observation. A-8 these were reported as zeros. We replace these missing values with zeros. We undertake both these steps to ensure that “non-revisions” are neither under-represented (in case of previously missing values) nor overrepresented (in case of previously reported zeros) in our database as a result of inconsistent coding of zero values. • Lastly, we discard countries from our database for which we have less than five vin- tages available. These countries are the Czech Republic, Russia, Taiwan (classified as “actual” in only one vintage), Slovenia, Timor-Leste (classified as “actual” in only three vintages), the Bahamas, Israel and South Africa (classified as “actual” in only four vintages). A.3 Data coverage, descriptive statistics and key variables of inter- est Table A3 summarizes the coverage of our final database. Our data comes from 51 vintages, spans years 1970 to 2022, covers 146 different countries and includes 49 different variables. While our final database includes information on 49 different variables, our main analytical interest centers on a few key concepts that we introduce here. Table A3: 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. 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). It captures all external, long-term obligations “of public debtors, including the national govern- ment, Public Corporations, State Owned Enterprises, Development Banks and Other Mixed Enterprises, political subdivisions (or an agency of either), autonomous public bodies, and external obligations of private debtors that are guaranteed for repayment by a public entity”. Long-term external debt is defined as debt that has an original or extended maturity of more than one year and that is owed to nonresidents by residents of an economy and repayable in currency, goods, or services. The series is available in all vintages and for all countries and years. Debt flows / commitments: Our key measure for borrowing and lending (i.e. for debt flows) are commitments to public and publicly guaranteed borrowers (series code DT.COM.DPPG.CD). Commitments are the total amount of long-term loans which are contracted in a given year. As before, long-term external debt is defined as debt that has an original or extended maturity of more than one year and that is owed to nonresidents A-9 by residents of an economy and repayable in currency, goods, or services. This series is available in all vintages and for all countries and years. Subcomponents by creditor type: For various parts of the analysis and in particular when measuring creditor characteristics of hidden debt, we are interested in breakdowns of outstanding debts and flows by creditor type. The World Bank’s debt statistics offer differ- ent decompositions to do this. Unfortunately, not all of these break-downs are consistently available across the past 51 vintages. Total commitments and total debt stocks can be divided into debt to private and debt to official creditors. Data for the group of official cred- itors can further be decomposed into series for bilateral and multilateral creditors. These series are available in our database for vintages 1977–2023. Since vintage 1989, a decom- position of the data for private creditors is available and includes bondholders, commercial banks and other private creditors.54 Table A4 summarizes the availability of all these series. Table A4: Available components by vintage Panel A: Debt outstanding and disbursed/Disbursements/Repayments Creditor category Vintage Official creditors Multilateral 1977 - 2023 Bilateral 1977 - 2023 Private creditors Bondholders 1989-90 - 2023 Commercial Banks 1989-90 - 2023 Other private creditors 1979 - 1980, 1989-90 - 2023 Panel B: Commitments Creditor category Vintage Official creditors Multilateral 1977 - 1992-93, 2020 - 2023 Bilateral 1977 - 1992-93, 2020 - 2023 Private creditors Bondholders n/a Commercial Banks n/a Other private creditors 1979 - 1980 Notes: The table shows the availability of different creditor categories for debt stocks and commitments over all vintages included in our database. Categories “official” and “private” are available for vintages 1977 - 2023, both for stocks and commitments. 54 In earlier vintages, the private creditor decomposition consisted of categories “financial markets” and “suppliers”. However, as these categories were not reported in full, consistency checks as described in A.2 are not possible for these vintages. Hence, we do not take them into account, neither here nor in our analyses. A-10 A.4 Data sources for control variables Table A5: Data sources for control variables Variable Mnemonic Description Source (from source) Nominal GDP NY.GDP.MKTP.CD GDP (current US$) World Bank GDP (current US$) Fouquin and Hugot (2016) Real GDP NY.GDP.MKTP.KN GDP (constant LCU) World Bank Real GDP p.c. GDP at constant national Feenstra et al. (2015) prices divided by popula- tion Consumption NE.CON.TOTL.KN Final consumption expen- World Bank diture (constant LCU) Income groups Classifications based on World Bank GNI EMBI+ spreads J.P. Morgan Emerging J.P. Morgan (2024) Markets Bond Spread IMF programs Dummy variable for first Horn et al. (2020) year in IMF program Sovereign default Dummy for years in default Asonuma and Trebesch (2016) Institutional strength Average score on the Polity Marshall and Gurr (2020) V dataset Haircuts Net present value loss suf- Cruces and Trebesch fered by creditors (in per- (2013), Asonuma and cent) Trebesch (2016) and Ason- uma et al. (2023) Duration Time between the default Cruces and Trebesch event and the debt restruc- (2013), Asonuma and turing (in months) Trebesch (2016) and Ason- uma et al. (2023) A-11 B Data validation To validate our hidden debt measure and its interpretation, we engage in a series of empiri- cal tests and validation exercises. We begin this part by systematically comparing reporting guidelines of the World Bank’s debt statistics over time and confirm that only minor refine- ments have occurred across the 51 vintages that we analyze. We also rule out that data revisions are driven by ex post revisions of exchange rates, by contingent liability realiza- tions or reporting lags, and confirm that the systematic upward bias in debt data revisions is also present when only focusing on revisions to the most recent debt data. Finally, we compare our measure of hidden debt revelations to a series of prominent data manipulation cases that were discussed by the IMF board. B.1 Changes in reporting rules To what extent are ex post data revisions driven by changes in reporting rules over time? To answer this question, we search for changes in the reporting guidelines of the World Bank’s Debtor Reporting Manual. Over the course of the International Debt Statistics’ history, the World Bank has published four different Reporting Manuals: In 1962, 1980, 1989 and in 2000. The Debtor Reporting Manual from 2000 is still in effect today and can be downloaded from the World Bank’s website. Its three predecessor publications were obtained from the IMF library. We systematically go through all four reporting manuals and confirm that the manuals define reporting obligations and the perimeter of debt statistics in a highly similar way. Table B1 summarizes our comparison with respect to the definition of external debt, the definition of the public sector and the definition of long-run debt. The only minor change we detect is that the 1980 reporting manual refines the definition of what constitutes an external debt instrument.55 55 Re-running our main analyses over a truncated sample that excludes all vintages prior to 1980 does not lead to any changes in our results. A-12 Figure B1: World Bank Debt Reporting Manuals: 1962 - 2020 Notes: World Bank Debtor Reporting System Reporting Manuals from 1962, 1980, 1989 and 2000. A-13 Table B1: Debtor Reporting System Manuals’ Definitions over Time 1962 1980 1989 2000 Definition of Debt owed to foreign- Debt owed by residents of the reporting country to non-residents thereof. The external debt: ers and, in the case of term non-residents includes, besides non-resident individuals, all foreign publicly-issued loan cap- public bodies, foreign corporations (except branches thereof in the reporting ital, all bonds issued in country), and international organizations; in short, any individual or foreign markets, includ- organization that is not physically located in the reporting country. ing bonds later repatri- ated. All such debts should be treated as ex- ternal debt, whether the medium of payment is for- eign currency, local cur- rency goods or services. A-14 Definition of Long-term debt for purposes of DRS reporting is that with an original contractual or extended maturity long-term of more than one year, measured from the date of signing the loan agreement (commitment date) to the debt: date on which the last payment is due. Definition of Public and publicly guaranteed debt constists of all debt of the public sector together with debt of the public and private sector with a public-sector guarantee in the borrowing. For purposes of the DRS, the public publicly guar- sector consists of the following types of institutions: anteed debt: (a) Central governments and their departments; (b) Political subdivisions such as states, province and municipalities; (c) Central banks; (d) Autonomous institutions, such as financial and non-financial corporations,commercial and de- velopment banks, railways, utilities, etc., where: (i) The budget of the institution is subject to the approval of the government of the reporting country; or (ii) The government owns more than 50% of the voting stock or more than half of the members of the board of directors are government representatives; or (iii) In case of default, the state would become liable for the debt of the institution. Sources: IBRD (1962) and World Bank (1980, 1989, 2000). B.2 FX data revisions Debtor countries with large amounts of non-USD debt are exposed to valuation changes in their reported debt stock, even when debt reporting centers entirely on nominal or face values. For such countries, ex post revision to USD exchange rates could lead to ex post revisions in the outstanding debt stock that are inconsistent with our interpretation of ex post upward revisions as cases of hidden debt revelations. To rule out this possibility, we quantify ex post revisions to exchange rate data in the IMF’s International Financial Statistics, the data source that underlies exchange rate calculations in the World Bank’s IDS. Due to the limited availability of archived IMF IFS data, we only calculate year-on-year revisions to the yearly average and end of period exchange rate data between 2019 and 2021. The average ex post revision of the period average exchange rate ranges between -0.00044 percent and 0.00158 percent, the average ex post revision of the end of period exchange rate ranges between -0.00396 percent and 0.00130 percent in the underlying period. Revisions to exchange rates are therefore far too low to explain the sizeable magnitude of debt stock revisions we document in this paper. B.3 Treatment and impact of contingent liability realization An alternative explanation for the documented debt data revisions could come from the realization of contingent liabilities. During downturns, a sovereign might be forced to bail- out private sector entities (e.g. banks or private-public partnerships) and assume their liabilities (see, e.g., Bova et al., 2016). This might mechanically generate the cyclical revision patterns that we observe, without implying any under-reporting of debt. We addressed this competing interpretation of the data in two ways. First, we consulted the World Bank debt data team to understand how debt assumptions are treated in the data. We were informed that debt assumptions do not require ex post revision of the debt data, since they do not change the pre-debt assumption debt stocks. Debt assumptions should therefore just lead to a discrete increase in the debt series (within the same vintage). We empirically confirm this information by merging our data on debt data revisions with the dataset of implicit and explicit contingent liability realizations compiled by Bova et al. (2016). Their data captures 111 instances of contingent liability realizations in low and middle-income countries between 1990 and 2014 and allow us to test whether contingent liability realizations are associated with increased debt data upward revisions. We begin our analysis by testing whether years with contingent liability realizations have higher mean debt revelations than years without contingent liability realizations. Panel A of Figure B2 shows that this is not the case. Years in which contingent liability realizations occurred, on average, had lower mean revelations and the difference between the means is not statistically significant. These results are confirmed in an event study regression (Panel B of Figure B2). Years following the realization of contingent liabilities are not associated with significantly higher hidden debt revelations. A-15 Figure B2: Contingent liability realizations and hidden debt revelations Panel A: Mean comparison 1% 0.8% Mean hidden debt revelation (in % of GDP) 0.6% 0.4% 0.2% 0% Years without contingent Years with contingent liability realizations liability realizations .... Panel B: Hidden debt revelations before and after contingent liability realizations 1 .5 Impact on debt revelations 0 -.5 -1 -5 -4 -3 -2 -1 0 1 2 3 4 5 Years before and after contingent liability realization Point estimate 90% confidence interval Notes: Panel A compares the mean hidden debt revelation in percent of GDP for years with and without contingent liability realizations between 1990 and 2014. Panel B shows point estimates and 90 percent confidence intervals obtained from regressing standardized hidden debt revelations on a set of year and country fixed effects and lags and leads for contingent liability realization events. Data on contingent liability realizations is from Bova et al. (2016), hidden debt revelations are defined as in equation (2). A-16 B.4 Accounting for the possibility of reporting lags This subsection tests whether the under-reporting bias could simply be driven by reporting lags. For this purpose, Figure B3 plots the cumulative frequency distribution of the number of years between an unreported borrowing and its revelation. Figure B3: CFD of the time between unreported borrowing and revelation 100% Cumulative frequency distribution 80% Time to revelation: 60 % Mean: 7.61 years Median: 4 years 40% 20% 0% 0 5 10 15 20 25 30 35 40 45 50 Years between unreported borrowing and revelation Unweighted Weighted by revision size Notes: This figure plots the cumulative frequency distribution of the time between an unreported borrowing and its revelation. The red line takes into account the revision size by weighting the years since accumulation by the revision in percent of GDP, while the grey line does not. The median revelation takes place four years after the unreported borrowing. On average, it takes 7.61 years for hidden borrowing to be revealed. The difference between median and mean is driven by around 10 percent of unreported loans that only get revealed more than 15 years after their commitment date. Around 20 percent of unreported loans get revealed at the first possible instance, that is two years after the (unreported) borrowing. This short time span could be consistent with a pure reporting lag, for example if state- owned enterprises of a country follow fiscal years that differ from the World Bank reporting calendar. Table B2 shows that our main finding of systematic under-reporting bias is robust to drop- ping unreported loans that get revealed in the first two vintages. This confirms that the systematic bias that we document is not merely the result of reporting lags. A-17 Table B2: Summary statistics of hidden debt revisions, excluding up to the first two vintages after initial reporting N Mean Median Std. Dev. p-value Panel A: Debt stocks In percent of GDP 5702 1.06 0.09 5.76 0.000 excl. first year 5550 0.88 0.05 5.32 0.000 excl. first two years 5515 0.76 0.02 5.52 0.000 In mn. USD amounts 5702 159.22 5.00 1,909.90 0.000 excl. first year 5550 121.82 3.00 1,635.39 0.001 excl. first two years 5515 97.61 1.00 1,434.19 0.001 Panel B: Commitments In percent of GDP 5695 0.70 0.08 4.17 0.000 excl. first year 5542 0.48 0.01 5.45 0.000 excl. first two years 5508 0.39 0.00 2.93 0.000 In mn. USD amounts 5695 148.60 6.00 1,169.82 0.000 excl. first year 5542 91.54 1.00 965.71 0.000 excl. first two years 5508 64.81 0.00 838.86 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. While rows one, four, seven, and ten repeat the results of Table 2, the remainder of the table repeats the same exercise after excluding the first and the first two vintages after initial publication of a debt stock. GDP data is taken from World Bank (2022) and not subject to revisions. We use Newey-West heteroskedasticity- and autocorrelation- consistent standard errors (Newey and West, 1987) when calculating p-values. A-18 B.5 Revisions to the latest debt statistics This subsection tests whether the systematic upward bias in debt data revisions is also present when we focus only on revisions that change the latest available year in a debt data series. Figure B3 shows that it can take more than 30 years for initially unreported debt to be fully revealed. Arguably, revelations that occur after such a long time period are of little relevance to a country’s creditors. We therefore derive summary statistics for only those revelations in each vintage that change the latest available debt data point, e.g. a revelation in 2021 which updates the 2019 debt stock value compared to its initially published value in 2020. Table B3 and Figure B4 show that these revelations exhibit the same systematic upward bias as the full sample. Table B3: Summary statistics of revisions to the latest available data N Mean Median Std. Dev. p-value In percent of GDP Debt stock (DOD) 3,128 0.30 0.00 3.55 0.000 Commitments (COM) 3,111 0.42 0.00 6.98 0.001 In mn. USD amounts Debt stock (DOD) 3,128 71.87 0.00 1,578.36 0.007 Commitments (COM) 3,111 108.49 0.00 1,448.00 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, only for revisions to the values initially reported in the respective prior year. GDP data is taken from World Bank (2022) and not subject to revisions. We use Newey-West heteroskedasticity- and autocorrelation-consistent standard errors (Newey and West, 1987) when calculating p-values. A-19 Figure B4: The distribution of recent debt stock and flow revisions Panel A: Latest revisions to debt stocks in percent of GDP 70% median mean 60% 50% Percent 40% 30% 20% 10% 0% -5% 0% 5% 10% Ex-post PPG debt stock revision in % of GDP .... Panel B: Latest revisions to debt flows in percent of GDP 80% median mean 70% 60% 50% Percent 40% 30% 20% 10% 0% -5% 0% 5% 10% Ex-post PPG commitment revision in % of GDP 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, only for revisions to the values initially reported in the respective prior year. The solid lines show the median, which is 0% of GDP for debt stocks in Panel A and 0% of GDP for debt flows in Panel B. Dashed lines visualize the mean, which is 0.30% of GDP in Panel A and 0.41% of GDP in Panel B. GDP data is taken from World Bank (2022) and not subject to revisions. A-20 B.6 Comparison with IMF reporting violations Member countries of the IMF that misreport information to the Fund face sanctions under Article VIII of the IMF’s Articles of Agreement, unless misreporting is solely due to a lack of capacity. If the IMF’s Executive Board concludes that a member country has misreported information for other reasons than lack of capacity, it can establish a breach of obligation on the part of the member country and decide on the application of sanctions. All Board decisions with respect to a breach of obligations will be publicly announced. By going through IMF reports and policy documents, we are able to identify 50 instances in which IMF member countries were sanctioned for intentionally misreporting data. 16 of these cases, all but one of which are also listed in a related report by the IMF (2006), are both closely related to the publication of statistics on debt and fiscal policy and affect countries and years that are covered by our new database. Table B4 lists these cases, the dates on which they were discussed by the IMF board, and the size of the revelation we observe in the subsequent vintage. In all but four cases we are able to indeed observe revelations, ranging from USD 4 million to USD 1.3 billion. Table B4: IMF reporting violations and hidden debt revelations Country Date discussed Revelation Vintage (mln. USD) Argentina September 17, 2004 57 GDF 2006 Burkina Faso February 2, 2005 12 GDF 2006 Chad June 23, 2003 4 GDF 2005 Djibouti December 20, 2002 0 GDF 2004 Dominica April 8, 2004 0 GDF 2006 Dominica July 3, 2005 12 GDF 2007 Ghana June 28, 2001 115 GDF 2003 Hungary February 21, 1990 1,226 WDT 1991–92 Nepal January 18, 2006 127 GDF 2007 Pakistan March 4, 2021 800 IDS 2022 Tajikistan February 7, 1999 0 GDF 2000 Tajikistan February 13, 2002 23 GDF 2003 Tajikistan November 12, 2002 78 GDF 2004 Turkey April 26, 2005 1,270 GDF 2007 Uganda July 30, 2004 0 GDF 2006 Ukraine December 13, 1995 49 GDF 1997 Notes: The table lists 16 instances in which IMF member countries were sanc- tioned for misreporting data, the dates on which these cases were discussed by the IMF board (IMF, 2021; IMF, 2006), and the size of the revelation we observe in the subsequent debt statistics vintage. A-21 C Additional results and figures C.1 Debt data revisions to total external debt stocks In addition to public and publicly guaranteed (ppg) external debt, the IDS also publishes series on private non-guaranteed external debt and on total external debt, which is the sum of ppg and private non-guaranteed debt. In contrast to our preferred series of ppg debt, the data on private non-guaranteed debt that the IDS publishes is not based on debtor reported loan-level data but is reported to the World Bank in aggregate by national authorities. It can therefore not be ascertained that this data series exhibits the same desirable properties that facilitate the interpretation of debt data revision for ppg debt and that we discuss in Section 3.2. Still, our collection of historic IDS vintages allows to study revision patterns to private non-guaranteed and total external debt and we discuss these patterns in this appendix section. Figure C1 plots the distribution of revisions to total external debt (Panel A) and to private non-guaranteed external debt (Panel B). Both revision distributions are highly similar to the distribution for public and publicly guaranteed debt presented in Figure 5 in the main text. The average debt stocks revisions are 2.08 % of GDP and 1.23 % of GDP respectively, while the medians are close to zero, and the distributions exhibit a visible right skew. Table C1 confirms these properties by showing that the means of both distributions are significantly different from zero both in percent of GDP and in USD terms. Table C1: Revisions to total external and private non-guaranteed debt stocks N Mean Median Std. Dev. p-value In percent of GDP Total long-term debt (DOD) 5,597 2.20 0.09 12.17 0.000 Private nonguaranteed debt (DOD) 5,605 1.30 0.00 10.94 0.000 In mn. USD amounts Total long-term debt (DOD) 5,597 837.01 5.00 6,268.27 0.000 Private nonguaranteed debt (DOD) 5,605 682.57 0.00 5,862.85 0.000 Notes: The table reports summary statistics and p-values for revisions of total external and private non- guaranteed external debt stocks, defined analogously to 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. We use Newey-West heteroskedasticity- and autocorrelation-consistent standard errors (Newey and West, 1987) when calculating p-values. In addition to being interesting and policy relevant findings in their own right, the confirmed upward bias in revisions to private non-guaranteed debt also rules out the possibility that the under-reporting bias in ppg debt is purely driven by changes in the composition of total external debt (i.e. by the ex post reclassification of private non-guaranteed debt into ppg debt). A-22 Figure C1: The distribution of total and private non-guaranteed debt stock revisions Panel A: Total external debt stocks in percent of GDP median mean 40% 30% Percent 20% 10% 0% -5% 0% 5% 10% Ex-post long term debt stock revision in % of GDP .... Panel B: Private non-guaranteed debt stocks in percent of GDP median mean 100% 90% 80% 70% 60% Percent 50% 40% 30% 20% 10% 0% -5% 0% 5% 10% Ex-post private debt stock revision in % of GDP Notes: The figure shows the percentage distribution of data revisions to the total external debt stocks and to the private non-guaranteed debt stocks, defined analogously to equation (1), in percent of GDP. The solid lines show the median, dashed lines show the mean. GDP data is taken from World Bank (2022) and not subject to revisions. A-23 C.2 Hidden debt revelations and political cycles In section 4.2, we show that hidden debt revelations are more likely to occur during bad times, in particular during episodes of high outside scrutiny. An alternative hypothesis is that governments strategically reveal hidden debts for political gain, for example after coming to power or after elections. This hypothesis is motivated by a large political economy literature that studies institutional and political drivers of government reporting practices (see, e.g., Martinez, 2022). Against this backdrop, this section presents additional regressions results that test whether domestic political factors can explain revelations of hidden debt. We do not find any evidence that governments strategically reveal previously unreported debt for political gains or that hidden debt revelations vary systematically across the political cycle. More specifically, we consider the following variables as potential political drivers of hidden debt revelations: • Elections: We use data from the Database of Political Institutions to measure the incidence of both legislative and presidential elections (Cruz et al., 2021). In our sample of IDS reporting countries, we identify 687 parliamentary and 408 presidential elections. As in the literature on political business cycles, one might conjecture that hidden debt revelations are less likely before an election but more likely after an election (Nordhaus, 1975). • Changes in political leaderships: We use data from the Archigos dataset of polit- ical leaders to measure the incidence of changes in the political leadership of a country (Goemans et al., 2009). Specifically, we use a dummy variable to indicate all years in which a new leader enters office and a dummy variable to indicate all years in which a leader entered office in an irregular manner, e.g., through a coup or through direct imposition by another state. Incoming leaders might have particularly high incentives to reveal unreported debts at the beginning of their tenure. In our dataset of IDS re- porting countries, we identify 433 regular changes and 61 irregular changes in political leadership. We begin our analysis by including these measures in the fixed effects regression presented in section 4.2. Table C2 shows that none of the included political economy variables enters the regression with a statistically significant coefficient. A possible explanation for these null results might be that political events impact hidden debt revelations with a significant time lag or lead, i.e., a change in political leadership could affect debt reporting practices only after a number of years. To test for dynamic effects, we run panel event study regressions as in Schmidheiny and Siegloch (2023) or Clarke and Tapia Schythe (2020). More specifically, we estimate the following model: ˆ ∑ j HDRit = α + βj xj it + σi + θt + ϵit j =j A-24 Table C2: Political drivers of hidden debt revelations Dep. variable: Hidden debt revelations, 1975-2020 (1) (2) (3) (4) (5) Executive election 0.03 0.04 (0.06) (0.06) Legislative election 0.01 0.00 (0.05) (0.05) Regular change in leadership -0.01 -0.03 (0.04) (0.05) Irregular change in leadership -0.05 -0.05 (0.10) (0.12) Real GDP growth (WDI) -0.04** (0.02) IMF program 0.11** (0.05) External sov. default 0.10* (0.06) Observations 3,511 3,510 3,924 3,924 3,411 R-squared 0.054 0.057 0.044 0.044 0.063 Country FE ✓ ✓ ✓ ✓ ✓ Vintage FE ✓ ✓ ✓ ✓ ✓ Notes: This table shows regression results from a fixed effects panel regression of hidden debt revelations on various political economy variables (see text for details and sources). The dependent variable is the sum of all previously unreported loan commitments of a country as revealed by a new vintage (as defined in equation (2)). To account for outliers and to ease interpretation, the dependent variable is standardized. All regressions include country and vintage fixed effects and robust standard errors clustered at the country level. In column (5) we additionally control for the creditor composition of external borrowing. where HDRit are revelations of previously hidden debt as defined in section 3.2 above, σi and θt are country and vintage fixed effects and ϵit is an unobserved error term. The leads and lags of xit capture the years before and after a political event of interest and are defined as follows:    [t ≤ Eventss + j ] if j = j   xit = [t = Eventss + j ] j if j < j < ˆ j    [t ≥ Events + j ] s if j = ˆ j Figures C2 and C3 show the results of the panel event study regressions and confirm the results from the static regression model. Hidden debt revelations show no statistically sig- nificant co-movement with the political cycle. A-25 Figure C2: Hidden debt revelations and the political cycle: event study panel regressions Panel A: Election of executive leader 1 .5 Impact on debt revelations 0 -.5 -1 -5 -4 -3 -2 -1 0 1 2 3 4 5 Years before and after election of executive leader Point estimate 90% confidence interval .... Panel B: Election of legislative branch 1 .5 Impact on debt revelations 0 -.5 -1 -5 -4 -3 -2 -1 0 1 2 3 4 5 Years before and after election of legislative branch Point estimate 90% confidence interval Notes: This figure shows point estimates and 90 percent confidence intervals obtained from regressing standardized hidden debt revelations as defined in equation (2) on a set of lags and leads for elections of the executive (Panel A) and legislative branch of government (Panel B). A-26 Figure C3: Hidden debt revelations and changes in political leadership: event study panel regressions Panel A: Change in political leadership 1 .5 Impact on debt revelations 0 -.5 -1 -5 -4 -3 -2 -1 0 1 2 3 4 5 Years before and after change in political leadership Point estimate 90% confidence interval .... Panel B: Irregular change in political leadership 1 .5 Impact on debt revelations 0 -.5 -1 -5 -4 -3 -2 -1 0 1 2 3 4 5 Years before and after political coup Point estimate 90% confidence interval Notes: This figure shows point estimates and 90 percent confidence intervals obtained from regressing standardized hidden debt revelations as defined in equation (2) on a set of lags and leads for regular (Panel A) and unregular changes in political leadership (Panel B). A-27 C.3 Additional descriptive statistics Table C3: Debtor and creditor characteristics: debt commitment revelations (% of GDP) N Mean Median Std. Dev. p-value Panel A: Debtor characteristics Regions Europe 238 0.45 0.14 1.12 0.000 Asia 854 0.59 0.00 18.45 0.081 Middle-East and North Africa 428 0.90 0.15 4.09 0.000 Sub-Saharan Africa 1,152 0.84 0.11 7.84 0.000 Latin America 951 0.70 0.08 3.21 0.000 Income groups Low income 557 0.73 0.11 3.04 0.000 Lower middle income 1,325 0.74 0.09 16.27 0.008 Upper middle income 1,229 0.65 0.04 3.45 0.000 High income 59 0.41 0.15 0.89 0.001 Decades 1970s 458 0.59 0.11 2.67 0.000 1980s 558 0.99 0.24 8.79 0.003 1990s 743 0.92 0.09 3.23 0.000 2000s 885 0.53 0.01 4.83 0.000 2010s 1,028 0.54 0.06 17.20 0.074 Bond market access Non-market access countries 2,010 0.82 0.06 5.91 0.000 Market access countries 1,668 0.57 0.09 13.61 0.003 Panel B: Creditor characteristics Official creditors 3,482 0.45 0.03 9.64 0.000 Multilateral 962 0.10 0.00 1.62 0.045 World Bank 2,011 0.01 0.00 0.30 0.056 Bilateral 964 0.36 0.01 1.81 0.000 Private creditors 3,456 0.25 0.00 3.75 0.000 Notes: The table reports summary statistics and p-values for debt commitment revelations as defined in equation (2) in percent of GDP, broken down by debtor regions, income groups, decades of reporting and bond market access in Panel A, and creditor groups in Panel B. For commitments, only the official and private creditor breakdown is available for all vintages, which is reflected in the number of observations presented. See Section A.3 and Table A4 for details. We use Newey-West heteroskedasticity- and autocorrelation-consistent standard errors (Newey and West, 1987) when calculating p-values. Table C4 repeats the exercise for debt stock revisions. A-28 Table C4: Debtor and creditor characteristics: debt stock revisions in % of GDP N Mean Median Std. Dev. p-value Panel A: Debtor characteristics Regions Europe 315 -0.23 0.01 2.53 0.232 Asia 1,246 0.65 0.00 4.59 0.001 Middle-East and North Africa 689 0.01 0.04 4.15 0.962 Sub-Saharan Africa 1,874 1.63 0.10 7.73 0.000 Latin America 1,358 1.69 0.48 4.76 0.000 Income groups Low income 1,471 1.43 0.01 8.80 0.000 Lower middle income 1,519 0.59 0.11 3.24 0.000 Upper middle income 957 0.55 0.03 2.48 0.000 High income 17 0.41 0.00 1.27 0.203 Decades 1970s 892 1.51 0.59 4.56 0.000 1980s 1,030 1.88 0.15 8.57 0.000 1990s 1,216 1.40 0.13 7.73 0.000 2000s 1,279 0.24 0.01 3.10 0.061 2010s 1,172 0.56 0.05 2.41 0.000 Bond market access Non-market access countries 3,174 1.15 0.03 6.91 0.000 Market access countries 2,351 1.01 0.17 3.91 0.000 Panel B: Creditor characteristics Official creditors 5,702 0.58 0.03 5.04 0.000 Multilateral 5,697 0.20 0.00 1.77 0.000 World Bank 5,659 -0.01 0.00 0.50 0.376 Bilateral 5,699 0.38 0.00 4.73 0.000 Private creditors 5,690 0.38 0.00 5.13 0.000 Bonds 5,525 0.09 0.00 1.27 0.002 Banks and other private 5,681 0.29 0.00 3.17 0.000 Notes: The table reports summary statistics and p-values for data revisions of debt stocks as defined in equation (1) in percent of GDP, broken down by debtor regions, income groups, decades of reporting, bond market access and creditor groups. GDP data is taken from World Bank (2022) and not subject to revisions. We use Newey-West heteroskedasticity- and autocorrelation- consistent standard errors (Newey and West, 1987) when calculating p-values. A-29 Table C5: Creditor characteristics: debt stock revisions in % of initially reported debt N Mean Median Std. Dev. p-value Total PPG debt 6,157 26.66 0.28 584.38 0.051 Official creditors 6,143 26.79 0.14 585.66 0.051 Multilateral 6,053 3.15 0.00 23.81 0.000 World Bank 5,702 -0.01 0.00 12.39 0.966 Bilateral 6,091 9.81 0.00 84.30 0.000 Private creditors 5,378 59.71 0.00 989.33 0.010 Bonds 2,432 7.47 0.00 235.18 0.150 Banks and other private 5,176 77.02 0.00 1,673.78 0.016 Notes: The table reports summary statistics and p-values for debt stock revisions as defined in equation (1) in percent of initially reported debt, broken down by creditors. GDP data is taken from World Bank (2022) and not subject to revisions. We use Newey-West heteroskedasticity- and autocorrelation-consistent standard errors (Newey and West, 1987) when calculating p-values. A-30 Table C6: Summary statistics of debt stock revisions in % of GDP by country N Mean Median Std. Err. p-value Afghanistan 24 0.11 0.04 0.56 0.503 Albania 32 -0.95 -0.01 3.79 0.311 Algeria 51 0.94 0.91 1.78 0.017 Angola 35 2.64 0.38 7.24 0.151 Argentina 51 0.03 0.21 1.01 0.869 Armenia 29 -0.30 0.03 1.00 0.124 Azerbaijan 28 0.68 0.38 0.95 0.004 Bangladesh 50 -0.42 -0.22 1.22 0.122 Barbados 25 0.36 0.21 1.36 0.383 Belarus 29 0.45 0.16 0.94 0.083 Belize 51 0.87 0.00 3.33 0.106 Benin 51 -0.45 0.02 6.02 0.760 Bhutan 41 1.85 0.00 3.58 0.027 Bolivia 51 2.57 1.40 5.60 0.009 Bosnia and Herzegovina 22 -0.91 -0.01 2.10 0.240 Botswana 51 0.89 0.26 2.82 0.119 Brazil 51 0.35 0.03 0.86 0.094 Bulgaria 40 0.04 0.06 2.54 0.942 Burkina Faso 51 -0.21 0.10 1.18 0.483 Burundi 51 -0.51 0.03 1.72 0.196 Cambodia 29 0.12 0.04 0.45 0.083 Cameroon 51 1.10 0.00 3.32 0.137 Cape Verde 41 -0.09 -0.22 1.71 0.786 Central African Republic 51 -0.89 0.11 2.83 0.160 Chad 14 0.90 0.01 1.91 0.195 Chile 42 0.34 0.04 0.84 0.106 Colombia 51 4.46 0.59 9.66 0.050 Comoros 51 0.69 0.52 0.72 0.000 Congo 51 0.78 0.42 1.20 0.000 Costa Rica 41 0.18 0.00 1.50 0.512 Cote d’Ivoire 18 -0.01 0.00 0.01 0.106 Croatia 16 -0.01 0.00 0.10 0.484 Cyprus 51 1.61 0.71 2.95 0.007 Democratic Republic of Congo 51 3.89 1.32 5.06 0.005 Djibouti 17 0.19 0.00 0.54 0.132 Dominica 35 0.98 0.00 5.17 0.280 Dominican Republic 40 3.86 3.49 4.04 0.000 Ecuador 51 1.05 0.22 1.53 0.006 Egypt 51 3.92 0.76 5.08 0.004 El Salvador 51 0.32 0.18 2.87 0.565 A-31 N Mean Median Std. Dev. p-value Equatorial Guinea 51 -0.06 0.00 3.60 0.940 Eritrea 51 -2.37 0.00 4.98 0.052 Estonia 17 0.07 0.00 0.91 0.738 Ethiopia 9 0.02 0.00 0.06 0.356 Fiji 11 -0.07 0.00 0.18 0.250 Gabon 40 15.59 0.19 22.11 0.019 Gambia 51 1.32 1.18 2.22 0.009 Georgia 51 0.92 0.54 1.46 0.000 Ghana 51 1.04 0.48 2.98 0.049 Greece 51 11.15 1.45 18.96 0.022 Grenada 15 -7.61 -1.13 13.35 0.116 Guatemala 19 0.27 0.17 0.38 0.025 Guinea 29 0.81 0.38 2.63 0.048 Guinea-Bissau 34 -1.22 -1.21 3.94 0.248 Guyana 44 1.04 1.84 3.22 0.181 Haiti 51 2.99 2.02 3.02 0.000 Honduras 51 7.27 2.41 17.04 0.075 Hong Kong 51 0.20 0.12 1.85 0.665 Hungary 13 -0.28 0.07 2.14 0.618 India 16 0.32 0.19 0.77 0.074 Indonesia 51 2.44 1.25 3.29 0.006 Iran 51 0.71 0.26 1.42 0.015 Jamaica 51 -0.35 -0.14 1.59 0.346 Jordan 49 -1.82 0.00 5.10 0.146 Kazakhstan 13 0.28 0.01 1.00 0.413 Kenya 51 2.57 2.21 3.13 0.001 Kosovo 45 2.25 0.42 2.87 0.007 Kyrgyz Republic 51 0.42 -0.24 5.10 0.727 Laos 28 -2.54 -4.63 12.18 0.347 Latvia 51 0.23 0.19 1.42 0.341 Lebanon 24 2.05 1.57 3.35 0.023 Lesotho 21 -0.37 0.00 0.88 0.195 Liberia 22 0.34 0.00 1.30 0.492 Lithuania 40 0.20 0.00 1.06 0.345 Macedonia 51 3.78 0.21 10.68 0.144 Madagascar 17 -0.43 0.00 0.70 0.109 Malawi 30 1.01 -0.20 4.95 0.392 Malaysia 51 -0.28 -0.12 3.92 0.744 Maldives 51 3.00 2.95 2.97 0.000 Mali 41 -0.18 0.00 1.66 0.541 Malta 51 0.55 0.21 1.11 0.024 Mauritania 21 -0.17 0.00 2.46 0.806 A-32 N Mean Median Std. Dev. p-value Mauritius 29 1.13 0.04 2.38 0.045 Mexico 26 0.08 0.06 0.40 0.180 Moldova 17 0.64 0.05 1.32 0.106 Mongolia 32 -0.31 0.00 0.66 0.136 Montenegro 51 0.10 0.00 2.95 0.821 Morocco 51 0.54 0.49 1.81 0.207 Mozambique 51 7.27 3.05 10.46 0.006 Myanmar 28 -0.81 0.07 5.65 0.543 Nepal 51 -0.93 -0.56 2.59 0.073 Nicaragua 34 -0.39 0.00 2.99 0.649 Niger 45 0.00 0.03 0.73 0.989 Nigeria 51 0.50 0.00 1.79 0.203 Oman 51 -0.41 0.01 1.60 0.263 Pakistan 51 3.86 2.32 8.49 0.039 Panama 51 -0.07 0.00 0.43 0.428 Papua New Guinea 51 0.10 0.00 1.74 0.757 Paraguay 51 0.01 0.24 1.20 0.973 Peru 36 -0.01 0.00 1.14 0.982 Philippines 51 0.51 0.32 0.93 0.019 Poland 51 0.60 0.42 1.12 0.024 Romania 51 -0.15 0.00 1.23 0.488 Rwanda 19 -0.21 -0.13 0.44 0.143 Saint Kitts and Nevis 51 0.20 0.12 2.26 0.696 Saint Lucia 37 7.37 1.71 15.14 0.025 Saint Vincent and the Grenadines 51 -0.64 -0.07 2.53 0.106 Samoa 51 1.16 0.38 2.07 0.012 Sao Tome and Principe 51 14.31 7.15 20.30 0.007 Senegal 51 1.86 0.33 2.74 0.010 Serbia 44 0.62 0.00 1.85 0.189 Seychelles 26 -0.54 -0.17 1.43 0.180 Sierra Leone 43 0.81 0.00 2.58 0.208 Singapore 34 -0.02 0.00 0.79 0.912 Slovak Republic 51 2.19 2.12 2.41 0.000 Solomon Islands 51 0.02 0.00 0.63 0.895 Somalia 17 0.43 0.13 0.61 0.062 South Korea 29 0.06 0.07 0.52 0.540 Sri Lanka 33 1.39 0.48 1.84 0.012 Sudan 14 1.94 1.17 2.11 0.031 Swaziland 29 -6.47 -2.72 8.68 0.008 Syria 20 -2.11 -0.62 4.44 0.214 Tajikistan 41 1.18 0.00 3.49 0.120 Tanzania 36 -0.82 0.00 2.32 0.140 A-33 N Mean Median Std. Dev. p-value Thailand 39 2.69 0.00 7.90 0.074 Togo 51 1.09 0.71 2.17 0.009 Tonga 51 1.07 0.00 4.70 0.326 Trinidad and Tobago 51 -0.07 -0.01 0.80 0.565 Tunisia 29 0.75 -0.09 3.87 0.330 Turkey 27 0.31 0.00 1.39 0.225 Turkmenistan 50 1.04 0.46 3.35 0.166 Uganda 36 0.11 0.00 1.57 0.797 Ukraine 51 -0.06 0.04 1.37 0.803 Uruguay 51 0.43 0.26 0.72 0.004 Uzbekistan 33 0.34 0.17 4.84 0.746 Vanuatu 29 0.21 0.10 1.10 0.451 Venezuela 29 0.91 0.07 2.26 0.165 Vietnam 42 0.67 0.29 2.43 0.110 Yemen 36 1.39 0.21 3.29 0.106 Zambia 41 -0.10 0.00 0.60 0.515 Zimbabwe 39 -1.20 0.00 2.15 0.021 Notes: The table reports summary statistics and p-values for data revisions to debt stocks as defined in equation (1) in percent of GDP for each country in our sample. N pertains to the number of available years in our dataset. GDP data is taken from World Bank (2022) and not subject to revisions. We use Newey-West heteroskedasticity- and autocorrelation-consistent standard errors (Newey and West, 1987) when calculating p-values. A-34 Figure C4: Debt stock revisions Figure C5: Debt commitment revisions 40% 50% 40% 30% 30% Percent Percent 20% 20% 10% 10% 0% 0% -5% 0% 5% 10% -5% 0% 5% 10% Ex-post debt stock revision Ex-post debt commitment revision in % of GDP in % of GDP Figure C6: Disbursement revisions Figure C7: Principal repayments revisions 60% 70% 60% 50% 50% 40% 40% Percent Percent 30% 30% 20% 20% 10% 10% 0% 0% -5% 0% 5% 10% -5% 0% 5% 10% Ex-post disbursement revision Ex-post principal repayment revision in % of GDP in % of GDP Figure C8: Debt stock revisions vis-a-vis Figure C9: Debt stock revisions vis-a-vis private creditors bondholders 80% 80% 70% 70% 60% 60% 50% 50% Percent Percent 40% 40% 30% 30% 20% 20% 10% 10% 0% 0% -5% 0% 5% 10% -5% 0% 5% 10% Ex-post debt stock revision Ex-post debt stock revision vis-à-vis private creditors in % of GDP vis-à-vis bondholders in % of GDP A-35 Figure C10: Debt stock revisions vis-a-vis Figure C11: Debt stock revisions vis-a-vis bilateral creditors multilateral creditors 80% 80% 70% 70% 60% 60% 50% 50% Percent Percent 40% 40% 30% 30% 20% 20% 10% 10% 0% 0% -5% 0% 5% 10% -5% 0% 5% 10% Ex-post debt stock revision Ex-post debt stock revision vis-à-vis bilateral creditors in % of GDP vis-à-vis multilateral creditors in % of GDP Figure C12: Debt stock revisions vis-a-vis the World Bank 100% 90% 80% 70% 60% Percent 50% 40% 30% 20% 10% 0% -5% 0% 5% 10% Ex-post debt stock revision vis-à-vis the World Bank in % of GDP Figure C13: Debt commitment revisions Figure C14: Debt commitment revisions vis-a-vis official creditors vis-a-vis private creditors 80% 80% 70% 70% 60% 60% 50% 50% Percent Percent 40% 40% 30% 30% 20% 20% 10% 10% 0% 0% -5% 0% 5% 10% -5% 0% 5% 10% Ex-post debt commitment revision Ex-post debt commitment revision vis-à-vis official creditors in % of GDP vis-à-vis private creditors in % of GDP A-36 Figure C15: Debt commitment revisions Figure C16: Debt commitment revisions vis-a-vis multilateral creditors vis-a-vis bilateral creditors 80% 80% 70% 70% 60% 60% 50% 50% Percent Percent 40% 40% 30% 30% 20% 20% 10% 10% 0% 0% -5% 0% 5% 10% -5% 0% 5% 10% Ex-post debt commitment revision Ex-post debt commitment revision vis-à-vis multilateral creditors in % of GDP vis-à-vis bilateral creditors in % of GDP Notes: The histograms in Figures C4 - C16 exclude observations above +10% and below -5% of GDP. The solid red line visualises the respective subsample median, the dashed red line the respective subsample mean. A-37 D Model Appendix D.1 Details about the lender’s expectations Here we explain how lenders form their expectation over h′ , conditional on no-revelations for τ periods. 1. In the period of a hidden debt revelation, they observe h and ε both of which get added to the stock of debt. The variable τ gets reset to zero. 2. Standing on that period, they know: h′ = 0 and τ ′ = 1, but they need to take expectations over ε′ . We have already assumed that ε ∼ N (µε , σε 2 ) 3. In the next period (assuming no revelation), they know that τ = 1 and that h = 0, but they still need to form expectations over h′ and ε′ . They also know h′ = (1 − δ )h + ε, but they did not observe ε. So h′ ∼ N (µ, σ 2 ). 4. In the next period, τ = 2. They understand that h′ = (1 − δ )h + ε but this time both terms are random variables. The first one is a normal multiplied by (1 − δ ) and the second is a normal. That sum is distributed N ((1 − δ )µ + µ, (1 − δ )σ 2 + σ 2 ) 5. In the following period, τ = 3. The lender understands h′ = (1 − δ )h3 + ε3 where h3 is the h′ in the previous period (when τ was 2). So, now (1 − δ )h3 is itself a ( ) random variable that is distributed N µ((1 − δ ) + (1 − δ )2 ), σ 2 ((1 − δ ) + (1 − δ )2 ) , and ε3 is still distributed N (µ, σ 2 ). So, h′ (the sum of the two) is: ( ) h′ ∼ N µ((1 − δ ) + (1 − δ )2 ) + µ, σ 2 ((1 − δ ) + (1 − δ )2 ) + σ 2 which can be rewritten as: ( ) h′ ∼ N µ(1 + (1 − δ ) + (1 − δ )2 ), σ 2 (1 + (1 − δ ) + (1 − δ )2 ) 6. Finally, for a generic period with τ ≥ 1 we have   ∑ τ ∑ τ h′ ∼ N µ (1 − δ )j −1 , σ 2 (1 − δ )j −1  , j =1 j =1 and using the formula for the geometric sum we obtain ( ) 1 − (1 − δ )τ 2 1 − (1 − δ )τ h′ ∼ N µ ,σ , δ δ which is the expression used in section 6.1. A-38 D.2 Details about the full-information economy We model the full-information economy as one in which the lenders perfectly observe h, know how it evolves, and also see the realization of ε. Therefore, there is no concept of monitoring anymore. Given this assumption, τ is no longer a state variable. Therefore, since h is not hidden anymore, all agents in the model treat h and b in the same way. The only remaining difference between them is that b is chosen by the government but h is still governed by the random variable ε. Below we outline the equations of the model that are changed to capture this full-information economy. Recovery rate. Recalled we used bD to denote the non-negative amount of debt with which the country reenters after a default episode. This level is now given by bD (b, h, y ) = min {α(y ), b + h} , (27) where α(y ) is still a non-decreasing function of the income level realized upon reentry. As before, these new bonds bD get divided among holders of the previously issued debt (both market b and hidden h). This implies the following recovery rate (for all types of debt): bD (b, h, y ) ω b (b, h, y ) = . b+h Foreign lenders. We keep the assumption that foreign lenders arrive in overlapping gen- erations, each with wealth W . They have access to a risk-free asset that yields a net return of r. The lender’s problem is specified below. V ℓ (b′ ; y, h′ ) = max ′ ′ Ey′ ,ε′ |y [uℓ (Cℓ )] (28) B subject to ′ Cℓ (B ′ , h′ , y ′ , ε′ ) =(W − q (b′ , h′ , y )B ′ )(1 + r) + B ′ R′ with R′ (b′ , h′ , y ′ , ε′ ) ≡ d′ (b′ , h′ , y ′ , ε′ ) qD (b′ , h′ , y ′ )+ [ ] (1 − d′ (b′ , h′ , y ′ , ε′ )) × κ + (1 − δ ) q (b′′ , h′ , y ′ ) , where qD denotes the price of a bond in default, b′′ = B (b′ , h′ , y ′ , ε′ ), with B denoting the optimal borrowing policy that lenders expect the government to follow, and the lender understands the law of motion for hidden debt: h′ = h(1 − δ ) + ε. The solution to this problem features a demand schedule for sovereign bonds given by56 Ey′ ,ε′ |y {u′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ℓ (Cℓ (B , h , y , ε )) × R (b , h , y , ε )} q (b′ , y, h) = . (29) Ey′ ,ε′ |y [u′ ′ ′ ′ ′ ′ ℓ (Cℓ (B , h , y , ε )) (1 + r )] 56 The lenders observe ε. However, the fact that ε is iid, implies that its period-t realization does not affect the bond price and hence it is not an argument in q (b′ , y, h). A-39 A foreign lender that arrives in a state in which the government is in default faces a similar problem, but with a different set of returns. Namely, ℓ ′ VD (b, h, s) = max ′ E ℓ [ uℓ ( C ℓ )] (30) B subject to ′ Cℓ (B ′ , h, y ′ , ε′ ) = (W − qD (b, h, y )B ′ )(1 + r) + B ′ R′D [ R′ ′ ′ ′ ′ ′ ′ ′ D (b, h, y , ε ) = (1 − θ ) qD (b, h, y ) + θ ω (b, h, y ) d(bD , 0, y , ε )qD (bD , 0, y ) + ] [ ] ′ ′ ′′ ′ (1 − d(bD , 0, y , ε )) κ + (1 − δ )q (b , 0, y )] The solution to this problem implies the following demand schedule for defaulted bonds: E ℓ {u′ ′ ′ ′ ′ ℓ (Cℓ ) RD (B, h, y , ε )} qD (b, h, y ) = ℓ ′ ′ . (31) E [uℓ (Cℓ )(1 + r)] Government’s problem. A government that starts the period in good standing has the option to default on its debt. Therefore, { } V (b, h, y, ε) = max d V1 (b, h, y ) + (1 − d) V0 (b, h, y, ε) d∈{0,1} As in the benchmark model, a government default triggers (i) the “revelation” of all the “hidden” debt (that is to say, h is added to b and h′ = 0) and (ii) temporary market exclusion and income losses. The value under default is therefore given by: [ ] V1 (b, h, y ) = u (y − ϕ(y )) + βEy′ ,ε′ |y (1 − θ) V1 (b, h, y ′ ) + θ V (bD , 0, y ′ , ε′ ) (32) where bD (b, h, y ′ ) is given by (27). The function ϕ(y ) captures the income cost of defaults. Finally, the government’s value under repayment is as follows. { } V0 (b, y, h, ε) = max ′ u(c) + βEy′ ,ε′ |y V (b′ , y ′ , h′ , ε′ ) (33) b subject to c = y − κ ( b + h ) + q ( b′ , h ′ , y ) ι + q h ε ι = b′ − (1 − δ )b h′ = (1 − δ )h + ε ι > 0 only if q (b′ , h, y ) > q . Calibration. The results in section 6.4 are obtained by solving the full-information econ- omy using the same calibration as in the benchmark economy (Table 5). A-40 References for Online Appendix Asonuma, T., D. Niepelt, and R. Ranciere (2023). Sovereign bond prices, haircuts and maturity. Journal of International Economics 140, 103689. Asonuma, T. and C. Trebesch (2016). Sovereign debt restructurings: Preemptive or post- default. 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