metadata: authors: 0: author: Samano Penaloza,Agustin
count: Mexico
docna: 0: docna: International Reserves and Central Bank Independence
docty: Policy Research Working Paper
subtopic: Financial Structures,Inflation,Services & Transfers to Poor,Economic Assistance,Disability,Access of Poor to Social Services,International Trade and Trade Rules,Public Financial Management,Public Sector Economics,Public Finance Decentralization and
            Poverty Reduction
teratopic: Finance and Financial Sector Development,Macroeconomics and Economic Growth,Social Protections and Labor,Poverty Reduction,International Economics and Trade,Public Sector Development
abstracts: cdata!: This paper proposes a novel theory of
            reserve accumulation that emphasizes the role of an
            independent central bank. Motivated by a positive
            correlation between reserve accumulation and central bank
            independence in Latin America, the paper develops a
            quantitative sovereign default model with an independent
            central bank that can accumulate a risk-free foreign asset.
            The findings show that if the central bank is more patient
            than the government and as patient as households are, in
            equilibrium, the government issues more debt than what is
            socially optimal, and the central bank accumulates reserves
            to undo government over-borrowing. A key insight is that the
            government can issue more debt for any level of reserves but
            chooses not to because doing so would increase sovereign
            spreads, making it more costly to borrow. Quantitatively,
            the analysis finds that the central bank independence
            channel accounts for 75 percent of the average reserve
            levels observed in Mexico from 1994 to 2017. Finally, the
            paper shows that accumulating reserves improves social
            welfare. Welfare gains come from reducing the costs of
            front-loading public spending.
geo_reg_key: 119228,517191
repnme: repnme: International Reserves and Central Bank Independence
display_title: International Reserves and Central
            Bank Independence
listing_relative_url: /research/2021/11/33571526/international-reserves-central-bank-independence
topicv3: Public Finance Management m1326316 716,Inflation m1326709 0870F4727ACED1CF8525815C00471347,Trade m1326924 698,Social Assistance m1327201 1466,Central Banks m1327453 1235
publishtoextweb_dt: 2021-11-02T00:00:00Z
dois: 10.1596/1813-9450-9832
historic_topic: Finance and Financial Sector Development,Macroeconomics and Economic Growth,Social Protections and Labor,Poverty Reduction,International Economics and Trade,Public Sector Development
origu: DECRG: Macroeconomics & Growth (DECMG)
no_of_pages: 48
author_keys: 0: author_key: 2046387
model_extractions: Policy Research Working Paper 9832 International Reserves and Central Bank Independence _Agustin Samano_ Development Economics Development Research Group November 2021
Policy Research Working Paper 9832

# **Abstract**

This paper proposes a novel theory of reserve accumulation that emphasizes the role of an independent central bank. Motivated by a positive correlation between reserve accumulation and central bank independence in Latin America, the paper develops a quantitative sovereign default model with an independent central bank that can accumulate a risk-free foreign asset. The findings show that if the central bank is more patient than the government and as patient as households are, in equilibrium, the government issues more debt than what is socially optimal, and the central bank accumulates reserves to undo government over-borrowing. A key insight is that the government can issue more debt for any level of reserves but chooses not to because doing so would increase sovereign spreads, making it more costly to borrow. Quantitatively, the analysis finds that the central bank independence channel accounts for 75 percent of the average reserve levels observed in Mexico from 1994 to 2017. Finally, the paper shows that accumulating reserves improves social welfare. Welfare gains come from reducing the costs of front-loading public spending.

This paper is a product of the Development Research Group, Development Economics. 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 author may be contacted at asamanopenaloza@worldbank.org.

_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
# International Reserves and Central Bank Independence<sup>*</sup>

Agustin Samano<sup>†</sup>

**JEL Codes:** E58, F32, F34, F41

**Keywords:** International Reserves, Central Bank Independence, Sovereign Debt

> *The ideas presented here are based on the first chapter of my dissertation at the University of Minnesota. I am particularly grateful to Manuel Amador, Javier Bianchi, and Tim Kehoe for all of their advice and guidance. For helpful comments, I thank Roman Acosta, Cristian Aguilera, Marco Bassetto, Carlos Esquivel, Eugenia Gonzalez-Aguado, Daniel Samano, Juan Sanchez, Ana Maria Santacreu, and the participants of the Minnesota Trade Workshop, the Minnesota-Wisconsin International/Macro Workshop, the XXIV Workshop on Dynamic Macroeconomics at Vigo, the Federal Reserve Bank of St. Louis PhD Students Workshop 2020, the 15th Economics Graduate Student Conference at Washington University in St. Louis, and the SED 2021 Annual Meeting. I am grateful to Lars Peter Hansen and the Macro Finance Research Program for supporting this research project. The generous financial support from donor, Edward R. Allen, is greatly acknowledged. I am grateful to the Center for Latin American Monetary Studies (CEMLA), the Federal Reserve Bank of Boston, and the Federal Reserve Bank of Minneapolis for their hospitality. The findings, interpretations, and conclusions expressed in this paper are entirely those of the author. They do not necessarily represent the views of the World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent. All errors are my own.

> †The World Bank Research Department; Email: asamanopenaloza@worldbank.org
# **1 Introduction**

The accumulation of international reserves and public debt in emerging economies is puzzling because economies facing default risk pay high interest rates on their liabilities and receive low interest rates on their reserves.<sup>1</sup> Why, then, do economies paying significant sovereign spreads prefer to accumulate international reserves instead of paying back public debt? Moreover, what is the social welfare effect of reserve accumulation? Even though a large and growing literature addresses these questions, all previous studies have ignored the interaction between the central bank and the government by assuming a consolidated entity that simultaneously chooses reserves and debt.<sup>2</sup> In practice, the central bank often manages international reserves, the government issues public debt, and policymakers may have different incentives driving their choices. This is particularly possible if the central bank is independent from the government. Furthermore, Figure 1 illustrates a positive association between the accumulation of reserves and the widespread adoption of central bank independence (CBI) legislation in Latin America. To the best of my knowledge, this is the first study to explore the role of CBI in the accumulation of international reserves.

<!-- Start of picture text --> 20 1<br>15 0.75<br>10 0.5<br>5 0.25<br>Reserves (Avg Latin America)<br>Independence (Avg Latin America)<br>0 0<br>1970197519801985199019952000200520102015<br>CBI Index<br>Reserves (% GDP)<br><!-- End of picture text --> Figure 1: International Reserves and Central Bank Independence _Notes:_ The figure presents the average levels of international reserves and central bank independence for 11 Latin American countries: Argentina, Bolivia, Brazil, Chile, Colombia, Ecuador, Mexico, Paraguay, Peru, Uruguay, and Venezuela. The left y axis presents the reserves-to-GDP ratio using data from the IMF and the right y axis reports a _de jure_ central bank independence index based on the Cukierman, Webb, and Neyapti index.

> 1Rodrik (2006) estimates that emerging economies incur an annual average GDP loss of 1% by maintaining high levels of reserves and debt.

2The assumption of a consolidated entity choosing reserves and debt implies perfect coordination between policymakers. Subsection 2.3 presents evidence on the lack of perfect coordination between the central bank and government.

1
I use a sovereign default model—Eaton and Gersovitz (1981); Aguiar and Gopinath (2006); Arellano (2008)—enhanced to incorporate an independent central bank that can save in a riskfree foreign asset (i.e. international reserves). As is common in sovereign default models, the government can issue defaultable one-period debt with foreign lenders. I also follow the literature by modelling political pressures as giving the government a low discount factor relative to the foreign lenders.<sup>3</sup> In contrast, I assume that the central bank is more patient than the government is and as patient as households are (i.e. benevolent central bank) to capture the idea that independent central banks operate within institutional frameworks that isolate them from political pressures and that align the central bank’s incentives with those of the households.<sup>4</sup> This assumption, which is the main departure from the literature, leads to a disagreement among policymakers about households’ intertemporal consumption. I show that, in equilibrium, the lack of perfect coordination between the central bank and government rationalizes simultaneously positive levels of reserves and debt.<sup>5</sup> On one hand, an impatient government would like to increase its current spending and therefore will issue more debt than what is socially optimal. On the other hand, a benevolent central bank would like to undo government borrowing by accumulating reserves.<sup>6</sup> Because the government could also undo the effects of reserve accumulation by issuing more debt for any level of reserves, why, then, would the central bank choose to accumulate reserves? Consider a portfolio in which the economy is holding zero reserves. For any reserve asset bought by the central bank, the government could issue one bond to undo the effect of the central bank’s purchases on the net debt position. However, the government’s cost of undoing purchases is increasing in the level of reserves because portfolios having higher levels of reserves and debt implies higher sovereign spreads. Therefore, the government understands that it could undo the effect of reserve accumulation on the net debt position but chooses not to because having higher spreads reduces the amount of consumption that can be front-loaded. Thus, by accumulating international reserves, the central bank has the ability to shift resources toward the future in a way that an impatient government cannot undo.

> 3A well-established political economy literature has provided several models that generate impatient governments. See for example, Alesina and Tabellini (1990) and Persson and Svensson (1989) for closed economies, and Aguiar and Amador (2011) and Cuadra and Sapriza (2008) for environments with external sovereign debt. 4See for example, Grilli, Masciandaro, and Tabellini (1991) and Walsh (2003).

> 5In an important early work, Alfaro and Kanczuk (2009) found that canonical sovereign default models with oneperiod debt cannot rationalize simultaneously positive levels of reserves and debt in equilibrium.

> 6Aguiar, Amador, and Fourakis (2020) identify and quantify the cost of front-loading public spending that arises when an impatient government over-borrows.

2
It is essential for the mechanism of the model to assume that when a government defaults, international lenders cannot seize the international reserves held by the central bank. Otherwise, the relevant statistic would be the foreign net position, as in Arellano (2008). To illustrate this point, suppose that after a default, a central bank cannot maintain control of its reserves. Therefore, accumulating reserves would increase the repayment value but not the default value. Thus, buying one reserve asset would decrease the probability of default to the same magnitude as increasing debt by one bond, but in the opposite direction. Subsection 2.3 describes the case of Argentina in 2015, which is consistent with this assumption and guarantees that vulture funds will not be allowed to seize the reserves held by an independent central bank.<sup>7</sup> The model is solved numerically to evaluate its quantitative predictions regarding the levels of international reserves, public debt, and sovereign spreads. I calibrate the model using data for Mexico, a typical emerging economy with an independent central bank, which is a common reference for studies on reserve accumulation. The central bank’s discount factor is disciplined by matching the money market interest rate, and the government’s discount factor is calibrated internally by targeting public debt.<sup>8</sup> I find that, under the benchmark calibration, model simulations account for 75% of the average level of reserves observed in Mexico from 1994 to 2017. Moreover, I also find that in periods of high income and low spreads, the government increases borrowing and the central bank accumulates more reserves, which accounts for a high and positive correlation between reserves and debt that is consistent with the pattern observed in the data.

Finally, I contrast the baseline model with an economy in which the central bank is as impatient as the government is (i.e. consolidated government). I show that, in accordance with Alfaro and Kanczuk (2009), a sovereign default model with a consolidated government cannot rationalize simultaneously positive levels of debt and reserves. By comparing these two economies, I quantify the welfare gains of having an independent central bank that can accumulate reserves. I find that accumulating reserves by 6 _._ 5% of GDP reduces the net debt position by 3 _._ 0% of GDP and increases social welfare by 0 _._ 1%. Welfare gains come from reducing the costs of front-loading public spending and mitigating the distortion in households’ intertemporal consumption.

> 7Any other government agency that is granted independence, such as a sovereign wealth fund, does not have access to the special status that central bank reserves receive in international law.

> 8By following this calibration strategy, the model can match high levels of debt without implying an outrageous domestic interest rate as standard default models do when assuming a low discount factor.

3
**Related literature.** —This paper mainly contributes to the literature on reserve accumulation, in particular the one using sovereign default models to study the joint dynamics of international reserves, public debt, and sovereign spreads. For example, Alfaro and Kanczuk (2009); Bianchi, Hatchondo, and Martinez (2018); Tavares (2018); and Bianchi and Sosa-Padilla (2020).

Alfaro and Kanczuk (2009), which is closely related to this paper, enhances a sovereign default model to incorporate the possibility that the government accumulates international reserves. They show that, in this framework, the precautionary motive for reserve accumulation does not play a quantitatively important role to account for positive reserve levels because the insurance works by transferring resources to default. Moreover, the model cannot rationalize positive levels of reserves and debt because accumulating reserves is costly and a consolidated government, which is in charge of reserves and debt management, can always get the same net position by reducing debt instead of accumulating reserves. In contrast to Alfaro and Kanczuk (2009), I depart from the assumption of a consolidating government. Instead, I introduce a central bank that is more patient than the government and can accumulate reserves. I show that, by introducing an independent central bank, it is possible to rationalize positive levels of reserves and debt in equilibrium.

Bianchi, Hatchondo, and Martinez (2018) rationalize positive levels of international reserves and public debt in a canonical sovereign default model with long-term debt. They show that when debt maturity exceeds one period, the benefit of accumulating reserves is to provide a hedge against rollover risk. In their model, the consolidated government transfers resources from good times to bad times by accumulating reserves and long-term debt simultaneously. Tavares (2018) explores the role of reserves in sovereign debt restructuring. In his model, accumulating reserves improves lenders recovery rates after default, which implies a drop in sovereign spreads. Bianchi and SosaPadilla (2020) study the accumulation of reserves using a sovereign default model with nominal rigidities under a fixed exchange rate. In their model, issuing debt to accumulate reserves allows the government to reduce the average and the volatility of future unemployment. Thus, accumulating reserves provides macroeconomic stability. In contrast to these papers, I depart from the assumption of a consolidated government. Therefore, I contribute to the literature by providing a tractable model of sovereign default and reserve accumulation without assuming perfect coordination between the central bank and the government.<sup>9</sup>

> 9An interesting avenue for future research is to study all of the reserve accumulation motives presented above

4
Other papers seeking to explain the demand for international reserves have studied the precautionary motive for reserve accumulation. Aizenman and Lee (2007) study the accumulation of reserves in an open-economy version of Diamond and Dybvig (1983), generating endogenous sudden stops. Caballero and Panageas (2008) show that significant gains arise from having financial instruments that provide insurance against sudden stops. Durdu, Mendoza, and Terrones (2009) also model reserve accumulation as insurance against a sudden stop resulting from domestic shocks. Jeanne and Ranciere (2011) model reserves as an Arrow-Debreu security that pays off in a sudden stop, and they provide a simple analytical formula to quantify the optimal amount of reserves. Calvo, Izquierdo, and Loo-Kung (2012) address the optimal level of international reserves in a statistical model by balancing the expected cost of a sudden stop against the opportunity cost of holding reserves. They find that Latin America is closest to model-based optimal levels, while reserves in Eastern Europe lay below optimal levels, and those in Asia lay above. Hur and Kondo (2016) shed light on the upward trend in the reserves-to-debt ratio by studying the accumulation of reserves in a multi-country model with endogenous sudden stops. Jeanne and Sandri (2020) study reserve accumulation using a model in which the private sector can also accumulate a risk-free foreign asset. They show that, even though both private and central bank assets serve as insurance against a sudden stop, only the central bank internalizes the insurance role of reserves and, thus, accumulates international reserves. Cespedes and Chang (2020) study the interaction between optimal reserve accumulation and central bank liquidity provision in a small open economy under financial stress. In their model, accumulating reserves provides liquidity when financial frictions are binding. Arce, Bengui, and Bianchi (2019) propose a macroprudential theory of reserve accumulation by showing that the government accumulates reserves to reduce its exposure to sudden stops due to over-borrowing by the private sector. Their study is closely related to this paper in the sense that the central bank accumulates reserves to mitigate the costs of over-borrowing, but they focus on private over-borrowing instead of on government over-borrowing. In contrast to this strand of the literature, this paper not only endogenizes sudden stops but also the choice of public debt, which is key to understanding the puzzling behavior of the joint dynamics among reserves and public debt observed in emerging economies.

through the lens of my two-policymakers-approach; and determine how these motives for reserve accumulation are affected by the lack of perfect coordination between policymakers.

5
A different strand of the literature analyzes the role of reserves in implementing exchange rate policies. Obstfeld, Shambaugh, and Taylor (2009) document that countries with a higher level of reserves in 2007 had less exchange rate depreciation during the 2008 crisis. Ghosh, Ostry, and Qureshi (2017) show that central banks in emerging markets engage in foreign exchange interventions to smooth fluctuations in the real exchange rate, selling foreign reserves to prevent depreciation and buying reserves to prevent appreciation. Fratzscher et al. (2019) use daily data on sterilized foreign exchange intervention to test if intervention has the desired effect on the exchange rate; they found that it does. Fanelli and Straub (2018) develop a theory of foreign exchange interventions in a small open economy with limited capital mobility. They show that, in order to avoid excessive currency appreciation, central banks accumulate reserves to lean against the wind of global capital flows. Cavallino (2019) studies foreign exchange interventions as an additional tool to stabilize the economy in the presence of portfolio shocks. Amador et al. (2020) study foreign exchange intervention as a policy when the nominal interest rate is at the zero lower bound. Then, they use the model to show that a violation in interest rate parity generates a capital inflow, which the central bank must absorb by accumulating reserves. Davis, Devereux, and Yu (2020) study how foreign exchange interventions can be used to prevent sudden stops in a small open economy that faces exogenous shocks in its borrowing costs. In contrast to this strand of the literature, my paper abstracts from exchange rate considerations and studies the accumulation of reserves in a real model with a single tradable good. However, I study reserve accumulation in an environment with a lack of perfect coordination between policymakers. One could think, for instance, that this lack of coordination could come from a disagreement between committing to a specific exchange rate policy versus boosting the government’s fiscal capacity.<sup>10</sup> Overall, this paper contributes to the literature by providing a novel theory of reserve accumulation that highlights the role of an independent central bank.

**Layout.** —Section 2 documents that central banks with more independence tend to accumulate more international reserves. Section 3 presents the model. Section 4 illustrates the mechanism for reserve accumulation in a deterministic version of the model. Section 5 describes the model’s calibration and presents the quantitative results. Section 6 concludes the paper.

> 10Even though this subject is outside the scope of this paper, the microfoundations of the disagreement between central banks and governments could be an interesting avenue for future research.

6
# **2 Facts on Reserves and Central Bank Independence**

This section presents empirical evidence on the interaction between reserves and central bank independence. Subsection 2.1 describes the data sources used. Subsection 2.2 documents that central banks with more independence tend to accumulate more reserves. Finally, subsection 2.3 provides anecdotal evidence to support a key assumption of the model.

## **2.1 Data**

I use annual data from 1970 to 2017 for 11 Latin American countries.<sup>11</sup> As is common in the literature, I exclude data for default episodes, following Catao and Mano (2017).

For central bank independence, I use a _de jure_ CBI index from Garriga (2016). Following Cukierman, Webb, and Neyapti (1992), the index is based on 16 criteria coded on a scale from 0 to 1 (lowest and highest independence, respectively) and reflects the central banks’ political, financial, and policy independence from the government. For international reserves, I use data from the International Financial Statistics. As defined by the IMF (2001), reserves are "official public sector foreign assets that are readily available". This definition includes foreign currencies and foreign-currency deposits and securities, special drawing rights (SDRs), and the reserves position at the IMF. Following the standard convention, I exclude gold. For public debt, I use data from the IMF Historical Public Debt Database for the 1970-2012 period, and from the IMF World Economic Outlook Database for the 2012-2017 period. In line with my motivation, I consider all forms of defaultable public debt. This includes all maturities, and debt denominated in domestic and foreign currency as well as issued domestically or externally. For GDP, I use data from the World Development Indicators Database. For spreads, I use the Emerging Market Bond Index Plus (EMBI+) for the 1994-2017 period. For inflation rates, I use data from the International Financial Statistics.

> 11I focus on this region because, in the early 1990s, most countries in the region approved central bank independence reforms at the same time. The full sample consider for this study includes Argentina, Bolivia, Brazil, Chile, Colombia, Ecuador, Mexico, Paraguay, Peru, Uruguay, and Venezuela.

7
# **2.2 International Reserves and Central Bank Independence**

Motivated by a history of dealing with high inflation rates, in the early 1990s, most Latin American countries approved central bank independence reforms to insulate central banks from short-term political pressures and mitigate the inflation bias that may arise under discretionary policy.<sup>12</sup> While the negative correlation between CBI and inflation is a well-established fact,<sup>13</sup> the effect of CBI on the accumulation of foreign assets held by central banks has not been studied.

Because the positive association between CBI and reserves, as presented in Figure 1, could be driven by other confounding factors, I estimate the following panel fixed-effect regression: where _αi_ represents time-invariant country-fixed effects and _γt_ denotes time-fixed effects. The term ( _A/y_ ) _i,t_ denotes the level of reserves, normalized by GDP for country _i_ at time _t_ . All of the explanatory variables are lagged one period to control for endogeneity. In addition, ( _CBI_ ) _i,t_ denotes the CBI index for country _i_ at period _t_ , ( _y_ ˆ) _i,t_ is the cyclical component of GDP for country _i_ at period _t_ , and ( _B/y_ ) _i,t_ denotes the level of public debt normalized by GDP for country _i_ at period _t_ . The term _εi,t_ denotes the regression residuals. In the baseline specification, I include as regressors, all of the variables considered in the theoretical model except for sovereign spreads.<sup>14</sup> Table 1 shows that, other things equal, the positive correlation between reserve accumulation and central bank independence is robust to various controls and specifications. The regression estimate _β_ 1 can be interpreted as indicating that a one-point increase in _de jure_ CBI is associated with a _β_ 1 percent increase in reserves. Specifications (2), (3), and (4) control for other variables commonly used to explain the accumulation of reserves, such as inflation rates, exchange rate regime, and sovereign spreads. The coefficient associated with the inflation rate is negative and significant, which suggests that reserve accumulation is related to inflation rates even after controlling for central bank independence.<sup>15</sup> To control for exchange rate regime, I introduce a dummy variable that

> 12See Rogoff (1985), Waller (1992), Walsh (1995), Svensson (1997), and Walsh (2003).

> 13See Alesina and Summers (1993), Walsh (2008) and Waller (2011). Although the correlation is a well-established fact, the evidence on causality is mixed.

> 14The data available for sovereign spreads starts in 1994, which implies that by considering this variable in the baseline regression, I lose most of the observations from the pre-independence period.

> 15Even though this fact is outside the scope of this paper, an interesting avenue for future research may be to provide

8
assigns the value "0" to flexible exchange rate regimes and "1" to fixed exchange rate regimes.<sup>16</sup> The coefficient associated with the exchange rate regime implies that countries with fixed exchange rates accumulate more reserves, which is consistent with Bianchi and Sosa-Padilla (2020). Finally, the coefficient associated with sovereign spreads suggests a negative correlation between reserves and spreads, which is inconsistent with the model.<sup>17</sup> Overall, and to the best of my knowledge, this is the first paper that documents a positive correlation between reserve accumulation and central bank independence.

Table 1: Panel Regressions

|||Dependent vari|able: _log_(_A/y_)||
|---|---|---|---|---|
||(1)|(2)|(3)|(4)|
|**CBI**|**2**_._**36**<sup>_∗∗_</sup>|**2**_._**38**<sup>_∗∗_</sup>|**2**_._**37**<sup>_∗∗_</sup>|**3**_._**45**<sup>_∗∗_</sup>|
||(**0**_._**96**)|(**0**_._**92**)|(**0**_._**90**)|(**0**_._**94**)|
|_log_(ˆ_y_)|_−_0_._95|_−_1_._41<sup>_∗∗_</sup>|_−_1_._42<sup>_∗∗_</sup>|_−_0_._65<sup>_∗∗_</sup>|
||(0_._64)|(0_._59)|(0_._58)|(0_._23)|
|_log_(_B/y_)|_−_0_._24|_−_0_._18|_−_0_._17|0_._21|
||(0_._30)|(0_._28)|(0_._27)|(0_._17)|
|infation||_−_0_._20<sup>_∗∗_</sup>|_−_0_._20<sup>_∗∗_</sup>|_−_0_._13<sup>_∗∗_</sup>|
|||(0_._08)|(0_._09)|(0_._05)|
|fx regime|||0_._05|0_._35<sup>_∗_</sup>|
||||(0_._15)|(0_._19)|
|spreads||||_−_0_._47<sup>_∗∗_</sup>|
|||||(0_._16)|
|Number of countries|11|11|11|9|
|Observations|359|359|359|148|
|_R_<sup>2</sup>|0_._47|0_._51|0_._51|0_._61|

_∗ ∗∗ ∗∗∗ p <_ 0 _._ 1; _p <_ 0 _._ 05; _p <_ 0 _._ 01 a monetary framework that rationalizes the negative correlation between reserve accumulation and inflation rates. 16I use the fine classification codes from Ilzetzki, Reinhart, and Rogoff (2017).

17Subsection 5.2 discusses the main reason for this discrepancy between the model and the data.

9
## **2.3 Supportive Anecdotal Evidence**

This subsection provides anecdotal evidence that supports a key assumption of the model: the central bank’s capability to retain its reserves when the government defaults.

**International Reserves after Default.** —In August 2015, the Argentinian central bank won the reversal of a U.S. court ruling that had allowed bondholders to try to hold the central bank responsible for the debt that had been defaulted in 2002. According to _Reuters_ , "The 2nd U.S. Circuit Court of Appeals in New York overturned a 2013 ruling denying a bid by Banco Central de la Republica Argentina (BCRA) to dismiss claims by U.S. investment firms holding $2 _._ 4 billion in judgments against the South American country. U.S. District Judge Thomas Griesa had previously held that the central bank had waived its sovereign immunity, and that as a result, the hedge funds could move forward with a lawsuit targeting the central bank’s assets."<sup>18</sup> This case set an international precedent and guarantees that vulture funds would not be allowed to seize the international reserves held by the central bank when the government defaults on its foreign liabilities. Moreover, the case of Argentina in 2015 illustrates that central bank’s reserves receive a special status in international law that is not received by any other government agency that is granted independence, such as a sovereign wealth fund.

# **3 Model**

This section presents a dynamic small-open economy model in which households receive a stochastic endowment, the government issues non-state-contingent defaultable debt, and the central bank buys a reserve asset that pays a risk-free interest rate. The model extends the seminal work of Eaton and Gersovitz (1981) by adding an independent central bank, and is similar to Alfaro and Kanczuk (2009) except for the assumption that the government behaves as a consolidated entity.

> 18U.S. Appeals Court says bondholders cannot seize Argentina’s reserves, _Reuters_ , August 31, 2015.

10
# **3.1 Environment**

**Endowments.** —Time is discrete and indexed by _t ∈{_ 0 _,_ 1 _,...}._ The economy’s endowment of the single tradable good is denoted by _y ∈_ R++. The endowment process is given by

where _|ρ| <_ 1 and _εt ∼ N_ (0 _, η_<sup>2</sup> ).

**Households.** —The representative household has preferences given by

where E denotes the expectation operator conditional on information at time 0, _β_ is the households’ discount factor, and _c_ is private consumption. The utility function _u_ : R+ _→_ R is strictly increasing and strictly concave. The households’ budget constraint is given by where _Tt ∈_ R denotes lump-sum transfers from the government and _τ_<sup>_π_</sup> _∈_ R++ is an exogenous inflation tax collected by the central bank. I assume that the inflation tax is constant over time and sufficiently large to finance the accumulation of reserves.<sup>19</sup>

**Two Policymakers.** —The economy is populated by a government and a central bank. Both policymakers maximize the same utility function as households but they differ in their discount factors. Therefore, the objective function of policymaker _j ∈{F, M}_ is given by

where _β_<sup>_F_</sup> and _β_<sup>_M_</sup> denote the discount factors of the government and the central bank, respectively. In particular, I assume that the government is more impatient relative to the central bank and house-

> 19In the absence of money, the central bank does not have any endogenous income to finance the accumulation of reserves. By allowing an exogenous inflation tax, I introduce a source of income for the central bank in the simplest way. Alternatively, I can assume fiscal support as most of the related literature implicitly does. However, in any case the resource constraint of the economy is the same and the results do not change substantially.

11
holds, i.e., _β_<sup>_F_</sup> _< β_<sup>_M_</sup> = _β_ . This assumption, which is key for most results in this paper, is meant to capture the idea that an independent central bank may be more patient than the government about the use of reserves to finance a public deficit.<sup>20</sup> Previous studies assume a consolidated government, with a high degree of impatience, which chooses simultaneously reserve and debt levels. In contrast, I introduce a government that issues public debt and a central bank that accumulates reserves. While the assumption of a high degree of impatience is reasonable for the government given the insight of Alesina and Tabellini (1990) and Persson and Svensson (1989), which show that political turnover generates in effect a low discount factor for the government; this assumption may not be accurate for an independent central bank, which operates in an institutional framework that isolates it from short-term political pressures and that align the central bank’ incentives with those of the households.<sup>21</sup>

**Central Bank’s Budget Constraint.** —The central bank can use seigniorage, _τ_<sup>_π_</sup> _y_ , to buy a risk-free foreign asset, _A ∈_ R+, that pays one unit of consumption good in the next period and is traded at a constant price _q_<sup>_∗_</sup> . I assume that _τ_<sup>_π_</sup> is sufficiently large to finance the accumulation of international reserves, and the central bank can also transfer resources to the government, Ω _∈_ R++.<sup>22</sup> Therefore, the central bank’s budget constraint is given by

where _At_ denotes the central bank’s reserves holdings at the beginning of period _t_ and _At_ +1 represents the level of reserves chosen by the central bank during period _t_ .

**Government’s Budget Constraint.** —The government can issue non-state contingent oneperiod debt _B ∈_ R+ at price _q_ , which in equilibrium depends on the amount of debt issued, the new stock of reserves, and the exogenous shocks. As in canonical sovereign default models, the government lacks commitment and it can choose to default at any time. Finally, the government

> 20For instance, in December 2010, Argentina President Cristina Fernandez de Kirchner announced a plan to use reserves to pay back debt and the central bank president, Martin Redrado, refused to support her plan. This case illustrates the potential disagreement that may arise when policymakers have different incentives driving their choices about the adequate use of reserves.

> 21On these two arguments see Grilli, Masciandaro, and Tabellini (1991), and Walsh (2003).

> 22In practice, central banks transfer their surplus annually to the government (In the case of Banco de Mexico, these funds are called "Remanente de Operaciones"). However, most central banks can also transfer resources indirectly by buying government bonds. In the model, I abstract from this distinction and consider any form of transfer from the central bank to the government.

12
also receives transfers from the central bank that can be used either to transfer resources to the households or to pay previous liabilities. Therefore, the government’s budget constraint is given by where _Bt_ denotes liabilities at the beginning of period _t_ and _Bt_ +1 represents the amount of bonds issued in period _t_ .

**Resource Constraint.** —By consolidating the budget constraints of the households, central bank, and government—eq. (2), (3), and (4)—we obtain a standard expression for the resource constraint

**Default.** —When the government defaults, I assume exclusion from financial markets with reentry probability _θ ∈_ (0 _,_ 1), an exogenous default cost, and zero recovery rate (i.e. fraction of the loan that lenders recover after a default).<sup>23</sup> I follow Arellano (2008) and Chatterjee and Eyingungor (2012) by capturing default costs (e.g. reputation costs, sanctions, and misallocation of resources) as an income loss _φ_ ( _y_ ), which is increasing in income.

As discussed in subsection 2.3, I assume that if the government defaults on its foreign liabilities then the lenders cannot seize the central bank’s reserves and the central bank still has access to financial markets. Even though this is a standard assumption in the literature and is consistent with observed default episodes, it is important to mention that this is key for my results. Otherwise, the central bank cannot offset government borrowing by accumulating reserves and the relevant statistic would be the net debt as in Arellano (2008).

Therefore, the resource constraint during default is given by

**Foreign Lenders and Risk Premium.** —There is a continuum of identical foreign lenders of measure one. They have perfect information regarding the endowment process of the economy and can observe the level of income, debt, and reserves every period. We assume that foreign lenders

23All these assumptions are common in the literature.

13
price bond’s payoffs using a stochastic discount factor, _m_ , given by where _ε_ and _η_ are the parameters governing the income process, _r_<sup>_∗_</sup> denotes the discount rate, and _κt ≥_ 0 represents risk premium shocks. This specification of the lenders’ discount factor delivers a time-varying endogenous risk premium on sovereign bonds that captures disturbances to financial markets that are exogenous to local conditions.<sup>24</sup> The risk premium shock follows a two-state Markov process with values _κL_ = 0 and _κH >_ 0, and transition probabilities _πL_ and _πH_ . In normal times, _κt_ = _κL_ = 0, lenders are risk neutral as in Arellano (2008). Otherwise, _κt_ = _κH >_ 0, lenders become risk averse and require a higher expected return to buy government bonds.<sup>25</sup> This shock plays an important role matching the distribution of spreads that we observe in the data, but it is not crucial for the core mechanism of reserve accumulation presented in this paper.<sup>26</sup>

**Disagreement Between Policymakers.** —In the model, the accumulation of reserves is driven by the assumption of two policymakers with different discount factors. This assumption leads to a disagreement among policymakers about households’ intertemporal consumption. On one hand, the impatient government would like to increase current spending and therefore issues more debt than what is socially optimal. On the other hand, the benevolent central bank (i.e. patient central bank) would like to transfer resources toward the future and therefore improves the net position of the economy as a whole. Since policymakers have different policy instruments to affect the net debt position of the economy, defined as _N ≡ B − A_ , the disagreement among policymakers could be illustrated by rewriting the resource constraint—eq. (5)—as follows

where the third term of the RHS, _qtBt_ +1, illustrates that government can front-load consumption by

> 24This specification of the lenders’ discount factor is a special case of the discrete-time version of the Vasicek (1977) one-factor model of the term structure, and it has been used in other sovereign default models such as Arellano and Ramanarayanan (2012), and Bianchi, Hatchondo, and Martinez (2018).

> 25A higher value of _κH_ can be seen as capturing the correlation between the small open economy’s GDP and the lenders’ income process, or alternatively, the degree of diversification of foreign lenders.

> 26The appendix presents an alternative calibration where I abstract from the risk-premium shock to emphasize the conflict of interest among government entities as the main force for reserve accumulation.

14
issuing debt, and the fourth term of the RHS, _q_<sup>_∗_</sup> _At_ +1, illustrates that by accumulating reserves the central bank can reduce consumption today to transfer resources toward the future. Furthermore, equation (8) illustrates that the bond prices play a key role for the mechanism of the model. While the price of international bonds _q_<sup>_∗_</sup> is constant, the domestic bond price schedule _qt_ is a function of the policymakers’ choices due to the endogenous probability of default. As in Arellano (2008), the bond price schedule is decreasing in debt because the new level of debt only affects negatively tomorrow’s repayment value but not tomorrow’s default value, which increases the probability of default and decreases the bond price schedule. In contrast, the new level of reserves affects both the repayment and default values. Subsection 5.3 shows that the central bank’s ability to shift resources toward the future in a way that cannot be undone by the government depends on the dynamics of the bond price schedule and reserves.

**Timing.** —The timing of actions within each period is as follows:

1. Shocks, _st_ = ( _yt, κt_ ) are realized, and the aggregate state of the economy is given by ( _st, Bt, At_ ).

2. The government chooses whether or not to default, _Dt_ = _{_ 0 _,_ 1 _}_ .

- (a) If default occurs, _Dt_ = 1, the government is excluded from financial markets and the central bank chooses the new level of reserves, _At_ +1.

- (b) Otherwise, _Dt_ = 0, policymakers move simultaneously: the government issues new debt, _Bt_ +1, taking as given the bond price schedule, _qt_ ( _st, Bt_ +1 _, At_ +1), and the central bank chooses the new level of reserves, _At_ +1.

3. Households consume, _ct_ .

# **3.2 Recursive Problems**

I focus on Markov perfect equilibria, where policymakers’ strategies depend only on payoffrelevant-state variables. Since households simply consume their endowment after transfers, and lenders provide the amount of debt demanded by the government, as long as the expected return on domestic bonds equals the return on the risk-free foreign asset,<sup><u>1</u></sup> _q_<sup>_<u>∗</u>_, the only two strategic agents</sup> in the model are the policymakers. Therefore, we can interpret this environment as a simultaneous game in which the government makes default and debt choices in period _t_ taking as given the 15
central bank’s strategy, and vice versa, the central bank chooses the new level of reserves at period _t_ taking as given the government’s strategy. We now drop time subscripts and move to the recursive formulation where _x_ and _x_<sup>_′_</sup> , respectively, indicate current and future values of variable _x_ .

**Government.** —Let _V_<sup>_F_</sup> ( _s, B, A_ ) be the value function of the government that faces the state ( _s, B, A_ ) and has the option to default. Given a bond price schedule _q_ , the function _V_<sup>_F_</sup> satisfies the following functional equation:

where _Vr_<sup>_F_denotes the government’s repayment value given by</sup> subject to and _Vd_<sup>_F_represents the government’s default value given by</sup> subject to where _A_<sup>ˆ</sup> _r_ ( _s, B, A_ ) and _A_<sup>ˆ</sup> _d_ ( _s, A_ ) denote the central bank’s decision rules for reserves accumulation in repayment and default states, respectively.

The solution to equation (9) yields decision rules for default, _D_<sup>ˆ</sup> ( _s, B, A_ ), and debt issuance, _B_ ˆ( _s, B, A_ ). The default rule is equal to 1 if the government defaults and is equal to 0 otherwise. In 16
the recursive equilibrium, lenders use these decision rules, as well as the decision rules for reserves, to price debt contracts. The decision rules for reserves solve the central bank’s recursive problems described below.

**Central Bank.** —The central bank’s choice of reserves accumulation depends on whether the government has access to financial markets. In repayment states, the central bank’s value function _Vr_<sup>_M_</sup> is given by

subject to where _B_<sup>ˆ</sup> ( _s, B, A_ ) denotes today’s debt choice, _D_<sup>ˆ</sup> ( _s_<sup>_′_</sup> _, B_<sup>_′_</sup> _, A_<sup>_′_</sup> ) represents tomorrow’s default choice, and _Vd_<sup>_M_is the central bank’s value function in default states given by</sup> subject to Solution to equation (10) yields a decision rule for reserve accumulation in repayment, _A_<sup>ˆ</sup> _r_ ( _s, B, A_ ). The third and fourth lines of this equation illustrate that if the government has access to financial markets, the central bank takes as given the government’s strategy. Consequently, households’ consumption is determined by the policymakers’ interaction. In contrast, equation (11) illustrates that if the government is excluded from financial markets, households’ consumption is exclusively determined by the central bank through its decision rule for reserve in default, _A_<sup>ˆ</sup> _d_ ( _s, A_ ).

17
**Bond Price Schedule.** —Bond prices compensate lenders for their risk-adjusted opportunity cost:

where bond prices depend not only on the debt issued but also on the new stock of reserves. Subsection 5.3 shows that the portfolio composition is relevant to determine the bond prices, and not only the net debt position of the economy. Finally, we use lenders’ stochastic discount factor and their portfolio condition—eq. (7) and (12)—to get an expression for the risk-free foreign bond price, given by

# **3.3 Recursive Equilibrium**

A Markov perfect equilibrium for this economy is defined by (i) a set of value functions _V_<sup>_F_</sup> , _Vr_<sup>_M_,and</sup><sup>_V_</sup> _d_<sup>_M_;(ii)decisionrulesfordefault</sup><sup>_D_ˆ,borrowing</sup><sup>_B_ˆ,reservesindefault</sup><sup>_A_ˆ</sup><sup>_d_,reservesin</sup> repayment _A_<sup>ˆ</sup> _r_ , and consumption _c_ ˆ; and (iii) a bond price function _q_ such that:

1. Given q, policy functions _{D_<sup>ˆ</sup> _, B_<sup>ˆ</sup> _}_ solve the government’s problem—eq. (9).

2. Given q, policy function _A_<sup>ˆ</sup> _r_ solves the central bank’s problem in repayment—eq. (10).

3. _A_<sup>ˆ</sup> _d_ policy function solves the central bank’s problem in default —eq. (11).

4. Given policymakers’ policies, policy function _c_ ˆ satisfies the resource constraint.

5. Given policymakers’ policies, _q_ satisfies the lender’s no arbitrage condition—eq. (12).

18
# **4 Deterministic Case**

To illustrate that the disagreement between policymakers can rationalize positive levels of international reserves and public debt, I begin by considering a deterministic version of the model in which endowments are known at period 0, _yt_ = 1 for all _t_ , and there is no risk-premium shock, _κt_ = 0 for all _t_ . I also assume that the reentry probability is zero, _θ_ = 0, and the exogenous default cost is given by _φ_ ( _y_ ) = _γ_ , where 0 _< γ <_ 1. Therefore, the endowment after default is given by _y_<sup>_de f_</sup> = (1 _− γ_ ).

In this environment, there is no default in equilibrium. Instead, there is an endogenous borrowing limit that represents the maximum level of debt such that the government is willing to repay. Lenders know that for any level of debt above the borrowing limit, the government’s optimal choice is to default on its liabilities. Therefore, they will not lend more than this amount. In this section, I show that in debt-constrained economies in which the government issues more debt than what is socially optimal, an independent central bank has the ability to discipline the net debt position of the economy by accumulating reserves.<sup>27</sup> Proposition 1 characterizes the endogenous borrowing limit. Proposition 2 characterizes the equilibrium for an economy in which the central bank is as impatient as the government (i.e. consolidated government), which is equivalent to the deterministic version of Alfaro and Kanczuk (2009). Proposition 3 characterizes the equilibrium for an economy populated by a social planner (i.e. as patient as households) choosing the optimal allocations of debt and reserves. Proposition 4 shows that the baseline model rationalizes positive levels of reserves and debt. Corollary 1 shows that, in the baseline model, the central bank can implement the optimal net debt position of the economy by accumulating reserves.

**Proposition 1** _(Characterization of the borrowing limit). Let B denotes the borrowing limit._<sup> ̄</sup> _If β_<sup>_M_</sup> = _β_ = _q_<sup>_∗_</sup> _then B_<sup> ̄</sup> = 1 _−γq∗_<sup>_._</sup> _Proof. See appendix._

Proposition 1 tell us that, under some assumptions, the borrowing limit does not depend on the level of reserves. This result follows from assuming that the central bank discounts the future at

> 27This section also shows that the mechanism for reserve accumulation presented in this paper does not depend on the precautionary motive, which is common in the literature.

19
the same rate as households and the rest of the world. This assumption enables me to analytically characterize the borrowing limit and illustrate in a simple way the main mechanism of the model.

**Proposition 2** _(Consolidated Government Equilibria) Let Bt_<sup>_al f_</sup> _and At_<sup>_al f_</sup> _denote, respectively, debt and reserves levels in equilibrium. For any initial level of debt and reserves, B_ 0 _and A_ 0 _, ∃ t_  ̄ _such that if β_<sup>_F_</sup> = _β_<sup>_M_</sup> _< β_ = _q_<sup>_∗_</sup> _then Bt_<sup>_al f_</sup> = _B and A_<sup> ̄</sup> _t_<sup>_al f_</sup> = 0 _for all t >_  ̄ _t. Proof. See appendix._

Proposition 2 tell us that a consolidated government does not accumulate reserves. This result, consistent with Alfaro and Kanczuk (2009), is driven by the impatience of the government relative to the rest of the world. Since a consolidated government can get the same net debt position through different combinations of reserves and debt, when the borrowing constraint is binding an impatient government has no incentives to hold positive levels of reserves. Otherwise, the portfolio of reserves and debt is undetermined. Figure 2 illustrates that, in this specific example, the government consumes its reserves in the first period and borrows up to the borrowing limit in the next four periods. Even though it is possible to observe positive levels of reserves in the first four periods, a consolidated government would eventually deplete the reserves and borrow up to the borrowing limit due to its relative impatience.

**Proposition 3** _(Social Planner Equilibria) Let Bt_<sup>_SP_</sup> _and At_<sup>_SP_</sup> _denote, respectively, debt and reserves levels in equilibrium. For any initial levels of debt and reserves, B_ 0 _and A_ 0 _, if β_<sup>_F_</sup> = _β_<sup>_M_</sup> = _β_ = _q_<sup>_∗_</sup> _then ∀ Bt ∈_ [ _B_ 0 _, B_<sup> ̄</sup> ] _∃ At ≥_ 0 _such that:_

_Proof. See appendix._ Proposition 3 illustrates that in an economy populated by a benevolent social planner (i.e. consolidated government as patient as households), there are multiple combinations of reserves and debt that can constitute an equilibrium as long as the net debt position is the same. Therefore, the optimal net debt position is unique and equal to the initial net debt level.

20
**Proposition 4** _(Independent Central Bank Equilibria) Let Bt_<sup>_∗and A_</sup> _t_<sup>_∗denote, respectively, debt and_</sup> _reserves levels in equilibrium. For any initial level of debt and reserves, B_ 0 _and A_ 0 _, if β_<sup>_F_</sup> _< β_<sup>_M_</sup> = _β_ = _q_<sup>_∗_</sup> _then Bt_<sup>_∗_=</sup><sup>_B and A_ ̄</sup> _t_<sup>_∗>_0</sup><sup>_for all t >_0</sup><sup>_._</sup> _Proof. See appendix._

**Corollary 1** _(Optimal Net Debt) Let Bt_<sup>_∗andA_</sup> _t_<sup>_∗denote,respectively,debtandreserveslevelsin_</sup> _the independent central bank equilibria. For any initial levels of debt and reserves,B_ 0 _and A_ 0 _, the net debt position is given by Nt_<sup>_∗_=</sup><sup>_B_</sup> _t_<sup>_∗−A_</sup> _t_<sup>_∗_=</sup><sup>_N_</sup> _t_<sup>_SP._</sup>

Proposition 4 tell us that, if the central bank is more patient than the government, in equilibrium, the economy holds positive levels of reserves and debt. This result follows from the assumption of different discount factors, which leads to a disagreement between policymakers. On one hand, the impatient government prefers to front-load consumption and therefore issues more debt than what is socially optimal. On the other hand, the central bank prefers to smooth consumption and accumulates reserves to shift resources toward the future. Since policymakers have different policy tools to affect the net debt position of the economy, the equilibrium is such that the government borrows up to the borrowing limit and the central bank accumulates reserves to offset government over-borrowing. Figure 3 illustrates that the central bank accumulates reserves as long as the impatient government issues debt. Thus, the net debt position of the economy remains constant.

The disagreement between policymakers, as well as the different policy tools that policymakers have to affect the net debt position, leads to a simultaneous game where the government uses debt markets to front-load consumption and the central bank accumulates international reserves to smooth consumption. Figure 4 illustrates policymakers’ best responses for a given initial levels of debt and reserves. While the central bank’s best response is increasing in debt, the government’s best response is increasing in reserves. Therefore, in equilibrium the central bank accumulates reserves to push the government to the borrowing limit and discipline the net debt position of the economy. Thus, the central bank’s ability to discipline the net debt position depends on the fact that the government is debt-constrained. Otherwise, the government can undo the effect or reserve accumulation on the net debt position by issuing more debt for any level of reserves.

While in the deterministic model the existence of an endogenous borrowing limit is guaranteed by assuming that the government lacks commitment and debt is defaultable, in the stochastic model 21
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# **5 Quantitative Analysis**

In this section, I present the quantitative analysis of the model. Subsection 5.1 presents the benchmark calibration. Subsection 5.2 presents key statistics in the data and model simulations. Subsection 5.3 inspects the mechanism of the model. Subsection 5.4 explores the social welfare implications of having an independent central bank that can accumulate international reserves.

## **5.1 Calibration**

**Functional Forms.** —The utility function with constant relative risk aversion is given by

with _σ_ = 1, and I follow Chatterjee and Eyingungor (2012) by adopting the functional form for default costs given by

**Parameter Values.** —The model is solved numerically to evaluate its quantitative predictions regarding the level of international reserves, public debt, and sovereign spreads. The appendix describes the computation of the model. I calibrate the model using data for Mexico from 1994 to 2017, a typical emerging economy with an independent central bank used commonly as a reference for studies on reserves accumulation.<sup>28</sup> A period in the model refers to a year. I choose a subset of parameter values (summarized in table 2) that can be directly pinned down from the data, and then I choose a second subset of parameter values (summarized in table 3) such that model simulations match key aspects of the data.

The risk aversion parameter value ( _σ_ = 2) is standard in quantitative business cycle and sovereign default studies. The international risk-free interest rate is set to match the average real interest rate for US Treasury Bills from 1980 to 2017, which is set to 1 _._ 1% ( _r_<sup>_∗_</sup> = 0 _._ 011). I use spreads from the EMBI+ to parameterize the lenders’ stochastic discount factor. I assume that a period with high risk aversion is one in which the global EMBI+ is one standard deviation above the median over the sample period. With this procedure, I obtain 6 episodes of high risk premium every 20 28The time period starts in 1994 because the Mexican central bank independence reform was approved in 1993.

24
years with an average duration equal to 0.7 years, which implies _πLH_ = 0 _._ 3 and _πHL_ = 0 _._ 8.<sup>29</sup> The parameter values that govern the endowment process are chosen to mimic the behavior of logged and linearly detrended GDP. The estimation of the stochastic process for the cyclical component of GDP yields _ρ_ = 0 _._ 66 and _η_ = 0 _._ 034. I set the reentry probability to match an average duration in financial exclusion of 9 years, which corresponds to the time period in which Mexico was excluded from financial markets in its last default episode (1982-190). This yields _θ_ = 0 _._ 11. Finally, the central bank’s discount factor is disciplined by the average money market interest rate observed in Mexico during the period that the central bank has been independent. This is a real interest rate of 3 _._ 5%, which implies _β_<sup>_M_</sup> = 0 _._ 966.

Table 2: Parameters Calibrated from the Data

|Parameter|Description|Value|Source / Target|
|---|---|---|---|
|_σ_|Risk aversion|2|Alfaro and Kanczuk|
|_r_<sup>_∗_</sup>|International risk-free interest rate|0_._011|US Treasury bills rate = 1_._1%|
|_πLH_|Probability of transiting to high risk premium|0_._30|Global EMBI +|
|_πHL_|Probability of transiting to low risk premium|0_._80|Global EMBI +|
|_ρ_|Auto-correlation of_y_|0_._66|Mexico’s GDP|
|_η_|Variance of_y_|0_._034|Mexico’s GDP|
|_θ_|Reentry probability|0_._11|9 years in default (1982-1990)|
|_β _<sup>_M_</sup>|Central Bank’s discount factor|0_._966|MX money market rate = 3_._5%|

Table 3: Parameters Calibrated by Simulation

|Parameter|Description|Value|Target|
|---|---|---|---|
|_β _<sup>_F_</sup>|Government’s discount factor|0_._939|Debt to GDP = 44_._4%|
|_d_0|Default cost parameter|_−_0_._809|Average spread = 267 bp|
|_d_1|Default cost parameter|0_._902|Increase in spread = 296 bp|
|_κH_|Pricing kernel parameter|0_._27|Default probability = 2%|

> 29On average, the global EMBI+ was 2 percentage point higher in those episodes than in normal periods.

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There are four parameters calibrated by simulation: the government’s discount factor _β_<sup>_F_</sup> , the parameters associated with the exogenous default cost _d_ 0 and _d_ 1, and the pricing kernel parameter _κH_ . I choose these four parameters to match four targets in the data: (i) an average public debt of 44 _._ 4% of GDP, (ii) an average level of spreads of 267 basis points, (iii) an increase in the spread during high risk premium periods of 296 basis points, which is the average increase in the sovereign spread observed in Mexico during the three high risk premium episodes identified in the data, and (iv) a historical probability of default equal to 2%, which is a rough estimate based on the 2 default episodes observed in Mexico in the last 100 years according to Catao and Mano (2017). The government’s discount factor mainly determine the average debt level, the values of the default cost mainly determine the behavior of spreads, and the pricing kernel parameter is mainly disciplined by the probability of default.

I use total public debt data from IMF datasets. While this data includes domestically held and long-term debt, in the model all domestic bonds mature in one period and are held by foreigners.<sup>30</sup> Since the model is not rich enough to consider many debt instruments, there is a trade-off when choosing the debt instrument that disciplines the model.<sup>31</sup> While there is no perfect way to solve this trade-off, I choose to target total public debt because it is the most general instrument that approximates the impatient behavior of the government. In the appendix, I present an alternative calibration in which the government’s discount factor is calibrated to match debt service.

# **5.2 Key Statistics: Model vs Data**

Now, I report long-run moments in the data and in the model simulations.<sup>32</sup> Table 4 shows that model simulations match the calibration targets. Table 5 shows that the model also does a good job in mimicking the behavior of reserves and debt. In particular, model simulations rationalize a reserves to GDP ratio of 6 _._ 5%, which corresponds to 75% of the average level of reserves observed in Mexico from 1994 to 2017 (8 _._ 7% of GDP). Moreover, the model matches a high and positive

> 30Total public debt data also includes debt denominated in domestic and foreign currency, while the model implicitly assumes that the real exchange is equal to one so there is no distinction between domestic and foreign currency. 31In a work in progress, I am enhancing the baseline model by adding long-term debt as in Bianchi, Hatchondo, and Martinez (2018).

> 32Moments in the model are computed by generating 1,000 simulations samples of 500 periods each and taking the last 50 observations of samples in which the last default was observed at least 25 periods before the beginning of the sample.

26
correlation between reserves and debt observed in the data, as well as the pro-cyclical behavior of reserves. Most of these results are consistent with Bianchi, Hatchondo, and Martinez (2018).<sup>33</sup> The model also generates volatile spreads and a high correlation between consumption and income, which is consistent with previous studies that do not consider reserve accumulation such as Aguiar and Gopinath (2006) and Arellano (2008). The model generates a spread volatility that is higher than the observed in Mexico, but it is close to the median for emerging market economies documented by Bianchi, Hatchondo, and Martinez (2018). The model does a good job matching the correlation of sovereign spreads with debt and output shocks but it delivers a positive correlation between spreads and reserves that is not consistent with the data. This is explained by the fact that, in the model, reserve holdings make default episodes less painful and increases the incentives to default. However, the model abstracts from other benefits of having reserves that could explain the negative correlation between spreads and reserves observed in the data.<sup>34</sup> To emphasize my contribution to the literature, I contrast the workings of the baseline model with an economy in which the central bank is as impatient as the government, this is _β_<sup>_M_</sup> = _β_<sup>_F_</sup> = 0 _._ 939. The rest of the parameter values are the same as in the benchmark calibration. By doing so, I can replicate the results by Alfaro and Kanczuk (2009), in the sense that a canonical sovereign debt model with one-period bonds cannot simultaneously rationalize high levels of reserves and debt. Table 6 not only illustrates this fact but also shows that the probability of default is higher in the baseline model than in the consolidated government economy. In the economy populated by an independent central bank, the probability of default is 1 _._ 8%, while in the consolidated government economy the probability of default is only 0 _._ 5%. Even though the consolidated government economy is not re-calibrated, because this would change the degree of impatience of the government and these two economies would not be comparable, the fact that the probability of default increases when the central bank is independent from the government is somehow counter-intuitive. As I mentioned above, reserve holdings help to mitigate default costs and increase the incentives to default. Alternatively, we could interpret this result as a commitment device that is costly due to the lack of perfect coordination between the government and the central bank.

> 33In contrast with their model, I do not consider long-term debt. By considering only one-period bonds, I abstract from the hedging motive against rollover risk and explore the central bank independence channel as a mechanism for reserve accumulation.

> 34For example, Tavares (2018) studies the role of reserves in debt restructuring and shows that having reserves increases lenders recovery rates after default, which implies a drop in sovereign spreads ex-ante.

27
Table 4: Targeted Moments

||Data|Model|
|---|---|---|
|mean_B/y_(%)|44_._4|44_._4|
|mean_rs_(%)|2_._7|2_._7|
|∆(_rs_)for_κ_ =_κH_ (%)|3_._0|4_._0|
|default prob(%)|2_._0|1_._8|

Table 5: Non-targeted Moments

||Data|Model|
|---|---|---|
|**mean**(**A**_/_**y**)**(%)**|**8**_._**7**|**6**_._**5**|
|corr(_A/y,B/y_)|0_._6|0_._8|
|corr(_A/y,y_)|0_._7|0_._4|
|corr(_c,y_)|0_._8|0_._8|
|std(_rs_) (%)|1_._3|4_._0|
|corr(_rs,y_)|0_._0|0_._0|
|corr(_rs,B/y_)|0_._1|0_._1|
|corr(_rs,A/y_)|_−_0_._4|0_._1|

Table 6: Independent Central Bank vs Consolidated Government

|||Baseline|Consolidated|
|---|---|---|---|
||Data|Model|Government|
|**mean**(**A**_/_**y**)**(%)**|**8**_._**7**|**6**_._**5**|**0**_._**3**|
|mean_B/y_(%)|44_._4|44_._4|41_._1|
|mean_rs_(%)|2_._7|2_._7|2_._6|
|∆(_rs_)for_κ_ =_κH_ (%)|3_._0|4_._0|4_._3|
|default prob(%)|2_._0|1_._8|0_._5|
|corr(_A/y,B/y_)|0_._6|0_._8|0_._0|
|corr(_A/y,y_)|0_._7|0_._4|0_._0|

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# **5.3 Central Bank Independence Channel**

The accumulation of international reserves in the model is driven by the assumption of different discount factors, which leads to a disagreement between the central bank and government about household’s intertemporal consumption. This disagreement can be illustrated by considering two economies where reserves and debt are chosen by the same policymaker. Let _A_<sup> ̄</sup><sup>_F_</sup> ( _s, B, A_ ) and _B_ ̄<sup>_F_</sup> ( _s, B, A_ ) denote policy functions for reserves and debt in an economy that is only populated by the government (i.e. _β_<sup>_F_</sup> = _β_<sup>_M_</sup> _< β_ ), also called consolidated government economy. For a given aggregate state, the households’ consumption can be expressed by rewriting the resource constraint (eq. 5), where _B_<sup>_′_</sup> = _B_<sup> ̄</sup><sup>_F_</sup> ( _s, B, A_ ) and _A_<sup>_′_</sup> = _A_<sup> ̄</sup><sup>_F_</sup> ( _s, B, A_ ).

Now, I consider an economy where the benevolent central bank chooses reserves and debt ( _β_<sup>_F_</sup> = _β_<sup>_M_</sup> = _β_ ). Let _A_<sup> ̄</sup><sup>_M_</sup> ( _s, B, A_ ) and _B_<sup> ̄</sup><sup>_M_</sup> ( _s, B, A_ ) denote policy functions for reserves and debt in such an economy, also called the social planner economy. Analogously, households’ consumption can be expressed as where _B_<sup>_′_</sup> = _B_<sup> ̄</sup><sup>_M_</sup> ( _s, B, A_ ) and _A_<sup>_′_</sup> = _A_<sup> ̄</sup><sup>_M_</sup> ( _s, B, A_ ).

Figure 6 illustrates the disagreement between policymakers by plotting policy functions for consumption for the consolidated economy and the social planner economy, _c_ ̄<sup>_F_</sup> ( _s, B, A_ ) and _c_ ̄<sup>_M_</sup> ( _s, B, A_ ) respectively. Panel (a) shows that, given the aggregate state, the impatient government would choose to deliver higher consumption today to the households than what the benevolent central bank would choose. This disagreement is represented by the difference in consumption. Panel (b) illustrates that the disagreement about intertemporal consumption implies a discrepancy about the desirable net debt position of the economy, where the government would choose to issue more debt than what is socially optimal.

In the baseline model, policymakers not only disagree about intertemporal consumption but also have different policy tools to affect the net debt position of the economy as a whole. In particular, the impatient government would like to front-load consumption by issuing debt and the central bank would like to transfer resources toward the future by accumulating reserves. There29
fore, the benefit of accumulating international reserves in the model depends on the central bank’s ability to reduce the net debt position of the economy and affect the equilibrium consumption. To illustrate this point, it is convenient to see how consumption decreases when the central bank accumulates reserves where the first term, _−q_<sup>_∗_</sup> , illustrates that the central bank has to pay _q_<sup>_∗_</sup> units of consumption today to buy one risk-free asset, and the second term represents that accumulating reserves also affects the units of consumption delivered to the households when the government is issuing _B_<sup>_′_</sup> bonds. However, for any level of reserves, the government can undo the effect of the accumulation of reserves by issuing more debt. This is where the first term, _q_ ( _s, B_<sup>_′_</sup> _, A_<sup>_′_</sup> ), illustrates that by issuing debt the government can deliver _q_ ( _s, B_<sup>_′_</sup> _, A_<sup>_′_</sup> _,_ ) units of consumption to the households plus the marginal effect of issuing one more bond on the price schedule, which is denoted by the second term.

Equations 16 and 17 illustrate that the interaction between the bond price schedule and the level of reserves and debt is crucial to understand the mechanism of the model. Figure 7a shows that the bond price schedule is decreasing in debt as in standard sovereign default models, but it is almost constant on the accumulation of international reserves. This result holds because, in contrast to debt levels, the reserves level affects both the default value and the repayment value for the government. Therefore, a change in the level of international reserves does not substantially change the incentives to default for the government, thus the bond price schedule is almost flat on the accumulation of reserves. Figure 7b shows that both default and repayment values increase on the level of reserves, almost at the same rate, without changing the default incentives for the government.

To show that sovereign risk is crucial for the central bank’s ability to offset over-borrowing by the government, suppose that there is no default risk. Therefore, the price of domestic bonds is equal to the price of foreign bonds for any aggregate state, _q_ ( _s, B_<sup>_′_</sup> _, A_<sup>_′_</sup> ) = _q_<sup>_∗_</sup> , and neither reserves 30
nor debt affect the bond prices. This is which implies that by issuing one more bond the government delivers _q_<sup>_∗_</sup> units of consumption and, vice versa, the central bank transfers one unit of consumption from today to tomorrow by buying one bond at price _q_<sup>_∗_</sup> . This is, Therefore, the spread on interest rates, _rs_ =<sup><u>1</u></sup> _q_<sup>_−_</sup> _q_<sup><u>1</u></sup><sup>_<u>∗</u>_, is key to undo government borrowing because</sup> it increases the cost of holding portfolios with high levels of reserves and debt.

Figure 8 shows portfolios of reserves and debt that would deliver the same consumption as in equilibrium. Solid dots represent choices of reserves and debt in equilibrium, ( _A_<sup>ˆ</sup> _r_ ( _s, B, A_ ) _, B_<sup>ˆ</sup> ( _s, B, A_ )), given the aggregate state ( _s, B, A_ ). Panel (a) illustrates that for any level of international reserves, the government can issue more debt to undo the effect of the central bank’s choice on the net debt position, and vice versa, the central bank can accumulate reserves to undo government borrowing. This figure also illustrates that the government issues more debt in periods of high income than in low income periods, and the central bank accumulates more reserves in high income periods than in low income periods. While the pro-cyclical behavior of debt is a common feature of sovereign default models, the pro-cyclical behavior of reserves follows from the fact that the central bank accumulates more reserves when the government over-borrows more. Panel (b) shows that the sovereign spread is increasing in portfolios with higher levels of reserves and debt, which increases the cost of reversing the effect of the central bank’s choice on the equilibrium consumption.

In a nutshell, by accumulating international reserves, the central bank has the ability to shift resources toward the future in a way that cannot be undone by the government due to the sovereign spreads faced by the economy.

31
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# **5.4 Welfare Analysis**

Now, I explore the question of whether accumulating reserves is welfare improving. On one hand, the central bank accumulates international reserves to undo government over-borrowing. On the other hand, this is costly because using reserves to pay back debt reduces spreads. To quantify the welfare gains of accumulating reserves, I contrast the baseline model with the consolidated government economy (i.e. _β_<sup>_M_</sup> = _β_<sup>_F_</sup> = 0 _._ 939). Table 7 shows that, by accumulating international reserves, an independent central bank can transfer resources towards the future in a way that cannot be undone by an impatient government, reducing the net debt position of the whole economy.

Table 7: Welfare Gains

||Independent|Consolidated|
|---|---|---|
||Central Bank|Government|
|mean B/y(%)|44_._4|41_._1|
|mean A/y(%)|6_._5|0_._3|
|net debt position(%)|37_._9|40_._8|
|**change in welfare**(%)|**0**_._**1**|**0**_._**0**|

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# **6 Conclusion**

This paper proposes a novel theory of reserve accumulation that emphasizes the role of an independent central bank in three key aspects: (i) independence allows central banks to manage their reserves without interference from the government, (ii) an independent central bank may be more patient than the government and more prudent about the use of reserves to finance a public deficit, and (iii) even if the government defaults on its foreign liabilities, the central bank’s reserves cannot be appropriate by disgruntled creditors. I show that these three elements together can account for a rise in international reserves that coincides with the widespread adoption of central bank independence legislation in Latin America.

I use a quantitative sovereign default model enhanced to incorporate an independent central bank to assess whether it can quantitatively account for the fact that countries facing significant sovereign spreads hold simultaneously large levels of international reserves and public debt. The main contribution of this paper is to provide a new channel for reserve accumulation. I find that, by accumulating reserves, an independent central bank is able to shift resources toward the future in a way that cannot be undone by an impatient government. Quantitatively, my central bank independence channel accounts for 75% of the average level of reserves observed in Mexico from 1994 to 2017, a period during which the Mexican central bank has been independent.

Overall, this paper provides a tractable framework to study the joint dynamics of international reserves, public debt, and sovereign spreads without assuming perfect coordination between the central bank and the government. I believe an interesting avenue for future research may be to study other reserve accumulation motives through the lens of my two-policymakers-approach; and determine how these motives are affected by the lack of perfect coordination among policymakers.

35