SOVEREIGN DEBT, DEFAULT AND INTERNATIONAL LIQUIDITYLIQUIDITY

Jointly with Hernán D. Seoane (UC3M)

3.1. Introduction

Since the Great Financial Crisis in 2008, followed by the European Debt Crisis and the COVID-19 crisis years later, the largest central banks around the world expanded their balance sheets while as soon as the nominal interest rates policies met the zero lower bound (ZLB), which drove other interest rates down, i.e. the risk free rates. This expansion in the balance sheets of central banks, i.e. their liabilities, increased the degree of liquidity worldwide as the central bank liability is money. This translated into cheap funding to the financial private sector. The size of the expansion for three of the largest Central Banks around the world (the USA FED, the Banks of Japan and the ECB) can be seen in Figure 3.1. As interest rates of risk free assets were low, and financial intermediaries had large liquidity, the newly created money, flew to risky assets.

In this paper, we explore the impact that increases in the world liquidity have on the dynamics of debt, spreads and default incentives in Emerging Economies. Excess liquidity drive down risk free rates and has two opposing effects on the dynamics of debt and spreads. On the one hand, a lower risk free rate decreases the average return that emerging economies need to pay on their debt. The cost of debt, hence decreases. On the other hand, the increase in liquidity increases the search for yields of international investors, making capital more abundant to emerging economies which may increase the level of debt and, consequently make these economies vulnerable to capital flow reversals, i.e.

Sudden Stops.

To address this question, we develop a variant of the standard small open economy model with incomplete markets and no-commitment in the tradition of Eaton and Gerso- vitz [1981b], with endogenous output following closely the environment of Mendoza and Yue [2012] and extend it to include international lenders that may be risk averse and have limited funds to allocate between risk-less and risky assets, similarly to Lizarazo [2013], with wealth shocks and a positively sloped supply of risk-less assets. We calibrate this model to match Argentina. This stylized model is able to generate a complex dynamic:

an increase in investor’s wealth, that may proxy an expansion of Quantitative Easing (QE) operations, (1) increases the demand of safe assets (savings’ glut), (2) decreases the risk free rate and (3) triggers a search for yield response, i.e. investors diversify portfolio and

Figure 3.1: Assets of the Central Banks

Note: Assets of the Central Banks. For the USA: Total Assets (Less Eliminations from Consolidation), Millions of U.S. Dollars, Quarterly, Not Seasonally Adjusted.

For the Bank of Japan: Total Assets for Japan, 100 Million Yen, Quarterly, Not Sea- sonally Adjusted. For the ECB: Central Bank Assets for Euro Area (11-19 Coun- tries), Millions of Euros, Quarterly, Not Seasonally Adjusted. Source: St. Louis FRED.

increase their demand of risky assets. These events resemble some recent dynamics in fixed income markets.

In this environment we can study the impact on Emerging Economies of reducing world liquidity, which will occur when large central banks reduce the size of their balance sheets. We find that reducing the average size of international investors wealth triggers a short run response consistent with a Sudden Stop episode. In the long run, the reduction of liquidity reduces consumption, output, imports and debt to output ratios permanently, and increase interest rates, spreads and default probability.

The importance of the risk free rate level and volatility has been widely studied as a key factor to understand the business cycle in emerging countries. Diaz-Alejandro [1984] studies the importance of US interest rate in the regional default in Latin Amer- ican countries at the beginning of the 1980s decade. This has become one of the most accepted hypothesis behind those defaults. The sudden unexpected increase in the risk free rate increased the borrowing cost of Latin American countries, triggering a regional

default. Neumeyer and Perri [2005] and Uribe and Yue [2006] studied the business cycle of Emerging countries with interest rates shocks focusing on a similar underlying question and exploiting different variants of working capital constraints. This literature has concluded that increases in the world interest rate have a negative impact on the business cycle of emerging countries: as these economies are usually net debtors, high rates im- poverishes these economies and makes future consumption cheaper pushing consumption down due to both channels. In the presence of default risk, this also tends to increase the borrowing costs.

Our objective is to complement this theory. We want to study whether is it possible that liquidity expansions in the world may increase the vulnerability of emerging countries? Our answer is yes, and the channel that may translate a low interest rate into a higher default risk is determined by the behavior of international investors. In this paper we show that this channel exists, induces plausible dynamics and can be quantitatively relevant.

Our paper fits contributes to the literature on international macro and finance. Empiri- cally, the relationship between monetary policy and risk taking behavior has been studied by Buch et al. [2014] who provide evidence on the link between monetary policy and search for yield by banks in the period before the Global Financial Crisis using survey data of the Federal Reserve Bank. The authors identify a risk-taking channel of monetary policy: an expansive monetary policy increases the risk exposure of small domestic banks.

This paper is related also to the low interest rate environment, drivers and conse- quences. Depending on the underlying model, the low interest rate environment may be considered more or less long lasting (i.e. the secular stagnation hypothesis suggests the current levels of interest rates may be long lasting). In our stylized model we introduce a reduced form relationship between the risk free rate the supply of risk-less assets. We do not take, at this point, a position on the source of the relationship or a clear cut definition of the risk-free asset. This assumption is motivated by the empirical relationship observed after the 2007 Financial Crisis and the 2012 European Debt Crisis when aggressive expansions of the Balance Sheets of Central banks drove down the market interest rates. The channel, even though important from an economic perspective, is irrelevant for the purpose of the stylized model. Clearly, several alternative hypothesis would fit the reduced form assumed in the simple version of the model (from Alan Greenspan’s conundrum, to the savings glut hypothesis of Ben Bernanke or the secular stagnation hypothesis).

Related to this last point, we are studying one source of North-South crisis contagion that has not been studied by the literature yet, i.e. coming from liquidity expansions. With our model we can study the sources of vulnerability and contagion in emerging economies

from world financial crisis.

The remainder of the paper goes as follows. In section 3.4 we introduce our baseline model, an extension of the baseline model in the strategic default literature. Section 4.1 we describe our strategy to take the model to the data. Section 3.6 studies the implications of the standard Arellano [2008b] and Section 3.7 studies the model implications and its quantitative results. In Section 3.8 we use our model to study the impact on debt, defaults and spreads after the Quantitative Tightening (QT) of major central banks. Finally, Sec- tion 4.6 discuss our findings.

3.2. Empirical analysis

We collect data on global liquidity, international borrowing, spreads and default risk for several emerging and developed economies since early 2000s. This section presents evidence based on contemporaneous and dynamic correlations. We build a DSGE model in the next section to provide a structural analysis to the data and quantify the role of different drivers.

Figure 3.2: Average contemporaneous correlation between global liquidity and endogenous variables.

Note: Quarterly correlation between the cyclical component of liquidity, GDP, debt, spread and default probability. Details about definitions of these data is in the Data appendix.

Figure 3.4 shows the contemporaneous correlation between a measure of global liq-

uidity and endogenous variables, on average for all, developed and emerging economies.

We present the variables as deviations in logs from a HP filtered trend. Since global liquidity is an unobservable variable, we use as a proxy the total assets of the main central banks: FED, ECB and the Bank of Japan. Similarly, the default probability on the general government debt is also directly unobservable. We use as a proxy the implicit default probability extracted from the spreads of the Credit Default Swaps (CDS) issued to insure against a default event on 5-year government bonds of the considered economies. We work with this maturity because it tends to be the most liquid one and, therefore, the one for which more data is available.

This instrument in exchange of a market premium,sp, promises to cover the losses in case of a default event. When this event happens for every monetary unit of face value insured the holder of a CDS will receive an amount equal to that monetary unit minus the recovered amount, (1−rec). This will happen with a probability equal to the default probability,d p. Following the common practice in finance, we assume that spreads adjust to meet the no arbitrage condition, resulting in the equation: sp = (1−rec)d p. Solving for the default probability we get that the implicit default probability in the 5 year period is considered to be:

d p= sp

1−rec (3.1)

The picture reveals a strong negative correlation between liquidity and GDP across all regions, particularly evident during the 2008, 2012, and 2020 crises. This correlation can be explained by the fact that liquidity increases serve as a policy response to major crises and heightened uncertainty. In other words, liquidity functions as a policy instrument.

This negative correlation holds true for emerging economies as well, as their output is impacted by crises in the developed world⁴Another notable feature depicted in the figure is the positive contemporaneous correlation among liquidity, spreads, debt, and default probability. This co-movement of variables aligns with the hypothesis presented earlier.

Figure 3.10 displays the dynamic correlations at lags of 1 to 4. As observed, increases in liquidity exhibit a positive correlation with output two quarters ahead. Debt has substantially increased over time, while spreads and default probability have decreased.

Particularly noteworthy is the significantly higher growth of debt in emerging economies compared to developed economies. This pattern is accompanied by a lower correlation of spreads and a relatively more pronounced decrease in default probabilities.

However, these pictures do not provide a clear understanding of how the high world liquidity environment impacts debt, default incentives, and debt pricing in emerging economies.

Several challenges arise in addressing this issue. Firstly, the standard issue of endogene-

4This result remains robust even when considering different data treatments, as demonstrated in the appendix using growth rate data.

(a) GDP (b) Debt

Figure 3.3: Dynamic correlations at 0 to 4 lags between global liquidity and endogenous variables.

Note: Correlation between lagged cyclical component of liquidity, GDP, debt, spread and default probability. Details about definitions of these data is in the Data appendix.

ity needs to be addressed. Additionally, the analysis must consider the distinct dynamics resulting from the crisis impact and the global response of liquidity. To address both channels, we present a structural model of endogenous default incorporating production and a global supply of liquidity.

3.3. LSAP shocks and Emerging markets

This section studies the impact of US Large Scale Asset Purchases (LSAP) shocks in Emerging markets financial access, particularly its impact on Sovereign debt issuance, GDP, Sovereign Spreads, the CDS, and the Current Account. While the previous section primarily presented some initial correlations to examine the data, this section employs an impulse response analysis using data from Argentina.

A LSAP policy operates at the heart of the financial system using the Fed’s balance

sheet. In particular, the Fed buys long-term treasuries or mortgage backed securities (MBS) from financial intermediaries using reserves. That is, the LSAP improves the balance sheet of financial intermediaries and provides them with liquidity. Moreover, it also (in the context of low interest rates) introduce an incentive to invest in high yield assets.

Figure 3.4: US Large Scale Asset Purchases shock.

Note: IRF for a LSAP shock of 1 standard deviation in %. The grey area indicates 10% confidence bands. A period is one quarter. The LSAP shock is identified by Swanson [2021]. Data is for Argentina in nominal terms.

These empirical findings highlight several significant aspects. Firstly, it becomes evident that the monetary expansion following the US financial crisis has facilitated emerging markets’ ability to accumulate debt under more relaxed financial conditions, which is crucial for our analysis. Secondly, there is a negative correlation between overall world liquidity and GDP, reflecting the policy measures implemented in response to the global crisis. Importantly, these effects occur without any clear increase in default probability or decline in spreads.

3.4. Model

We study an infinite horizon small open economy with a representative consumer, a representative firm that produces a final good, intermediate input producers and the government. The rest of the world is populated by a representative potentially risk averse international investor and a supplier of risk-free assets. The assumptions regarding the small open economy are borrowed from the environment of Mendoza and Yue [2012] and for convenience, we keep their notation. We combine this environment with potentially risk averse lenders similar to those in Aguiar et al. [2016]. In the remainder of this section we present each agent in detail and compute the private sector equilibrium conditions.

3.4.1. Households

The representative household supply labor and demand consumption goods. The household owns the domestic firms and receive lump sum government transfers. As standard in the literature, the household does not save or borrow, all international asset trades are done by the government as we will specify later. Hence, the household problem is given by,

maxc_t,Lt

∞

∑︂

t=0

β^tu(ct−g(Lt)), subject to

ct =wtLt+π_t^f +π^m_t +Tt.

Here, ct is the consumption of the final good and Lt represents labor supply. π_t^f are the profits of the final producer,π^m_t denotes the profits of intermediate input producer andTt

are the transfers from the government. We assume that the utility function is GHH with a Frisch elasticity of 1/(ω−1).

3.4.2. Final good producer

There is only one final good in the economy that is used for domestic consumption or for international trade. The firm that produces the final good hires labor,L_t^f, and buys an intermediate inputM(m^d_t,m^∗_t), we assume the stock of capital is fixedk. The production technology for the final good is Cobb-Douglas

yt = zt

(︂M(m^d_t,m^∗_t))︂α_M (︂

L_t^f)︂α_L

k^α^k,

whereztis the TFP shock that follows an autoregressive process in logs and M(m^d_t,m^∗_t) is an intermediate input in production. The intermediate good combines both domestically produced and imported inputs:

M(m^d_t,m^∗_t)= [︂

λ(︂

m^d_t)︂µ

+(1−λ)(︁

m^∗_t)︁µ]︂^1/µ

with

m^∗_t = [︄∫︂

j∈[0,1](m^∗_jt)^νd j ]︄1/ν

In this models, the key parameters are:µ, that defines the elasticity between imported and domestic inputs andν, that defines the elasticity of substitution between imported varieties. Imported inputs are traded internationally at a price for each jvariety, p^∗_j, that is exogenously determined, while the endogenous relative price of domestic inputs is p^m_t . The financial friction of the private sector is a working capital constraint over a subsetΘ of imported inputs on the interval [0, θ] that needs to be paid in advance. The setup is the one of Fuerst (1992) where we denote the working capital loans byκt. These loans are intra-period, assumed to be contracted at the risk free rater_t^∗. Then,

κt

1+r^∗_t ≥

∫︂ ∞

p^∗_jm^∗_jd j.

Under these assumptions, the objective function is π_t^f = ϵt

(︂M(m^d_t,m^∗_t))︂αM(︂

L_t^f)︂αL

k^α^k −r^∗_t

∫︂ θ 0

p^∗_jm^∗_jd j−

∫︂ 1

p^∗_jm^∗_jd j− p^m_t m^d_t −wtL_t^f.

As seen from the equation, the final goods producer faces a static optimization problem in the same way as the households’. This setting implies a pricing for the bundle of imported inputs of,

P^∗(r_t^∗)=[︄∫︂ θ 0

(︂p^∗_j(1+r^∗_j))︂_ν−1^ν

d j+∫︂ 1 θ

(︂p^∗_j)︂_ν−1^ν d j

]︄^ν−ν¹

in normal times, while in autarky, it is instead P^∗_aut = [︄∫︂ 1

(︂p^∗_j)︂_ν−1^ν d j

]︄^ν−1ν

3.4.3. Domestic intermediate good producer

The intermediate good producer hires labor at market wages and maximizes periodtprof- its given by

π^m_t = p^m_t A(L^m_t )^γ −wtL^m_t .

Here, m^d_t = A(L^m_t )^γ. The optimality condition for this problem produces a labor demand function given by,

γp^m_t A(L^m_t )^γ−1 =wt.

3.4.4. Private sector equilibrium

The optimatility conditions for these agents characterize the private sector equilibrium.

For convenience we present these conditions here. As seen, the private sector problem is fully static.

ϵtαM

(︂M(m^d_t,m^∗_t))︂αM−µ(︂

L_t^f)︂αL

k^α^k(1−λ)(m^∗_t)^µ−¹ =P^∗(r^∗_t) ϵtαM

(︂M(m^d_t,m^∗_t))︂αM−µ(︂

L_t^f)︂αL

k^α^kλ(m^d_t)^µ−1 = p^m_t ϵtαL

(︂M(m^d_t,m^∗_t))︂αM (︂

L_t^f)︂αL−1

k^α^k =wt

γp^m_t A(L^m_t )^γ−1 = wt

g^′(Lt)=wt

L_t^f +L^m_t = Lt

A(L^m_t )^γ =m^d_t 3.4.5. Government

The government is the only agent that takes intertemporal decisions. As standard in the literature we follow Eaton and Gersovitz [1981b] setting where the government issues one-period, non-state-contingent discount bonds (incomplete markets) and in the event of a sovereign default, the government is excluded from financial markets in the same period and re-enters with exogenous probabilityϕeach period.

This setting, as Mendoza and Yue [2012], implies an endogenous link between the default decisions and the business cycle. Particularly, during default both sovereign and the private sector are excluded from credit markets. That is, the private sector is forced to modify the combination of inputs for the production of the final good, which operates as an endogenous default cost.

The government chooses the debt policy, consumption and factors allocations to solve the recursive social planner’s problem with states given by (bt, ϵt) and the bond pricing functionq(bt+1,zt,Wt)

V(bt,zt,Wt)=max{︂

V^C(bt,zt,Wt),V^D(zt)}︂

, V^C(bt,zt,Wt)= max

c_t,m^d_t,m^∗_t,L_t^f,L^m_t,Lt,bt+1

u(ct−g(Lt))+βE[V(bt+1,zt+1,Wt+1)], subject to

ct+q(bt+1,zt,Wt)bt+1−bt ≤ ϵtf(M(m^∗_t,m^d_t),L_t^f,k)−m^∗_tP^∗(r^∗), L^m_t +L_t^f =Lt; A(L^m_t )^γ =m^d_t.

And

V^D(zt)= max

c_t,m^d_t,m^∗_t,L_t^f,L^m_t ,Lt

u(ct−g(Lt))+βE

[︂(1−ϕ)V^D(zt+1)+ϕV(0,zt+1,Wt+1)]︂

, subject to

ct ≤ ϵtf(M(m^∗_t,m^d_t),L_t^f,k)−m^∗_tP^∗_aut, L^m_t +L_t^f =Lt; A(L^m_t )^γ =m^d_t. 3.4.6. International investors

Our departure from Mendoza and Yue [2012] lies in the design of international investors.

This is key for our purpose as it allow us to introduce world liquidity in a simple way. The investors follow an overlapping generation structure, so that each period the small open economy faces a new generation of risk averse investors that stay for two periods. They arrive with a certain stochastic wealth, and choose how to invest this wealth between risk free bonds,a˜, and the bonds issued by the small open economy, b˜, where the tildes indi- cate that this is the amount purchased by the intermediary (who operates under no-price internalization).

The price of each type of debt,q^a(b^′,y,w) andq^b(b^′,y,w) respectively, depends on the amount of new debt issued by the small open economy, its endowment and the wealth of the international investors. The objective of the investors is to maximize the utility that they obtain from the total returns in the second period from their investments. This returns are constituted by the repayment of the principal of the risk free bonds, the repayment of the principal of the maturing risky bonds and the payment of the coupon and the selling value of the non maturing risky bonds. The problem of the the representative investor of a generation when the small open economy is not excluded from the market can be written as:

I^C(bt,zt,Wt)=max

µt

E[u(dt+1)]

s.t. dt+1 = (1−µt)Wt

q^a − µtWt

q^b (1−D(bt+1,zt+1,Wt+1))

We denote the fraction of wealth used to purchase the risk free asset by (1−µt), while µt represents the fraction used to purchase the one-period non-contingent bonds issued by the government. In equilibrium, given that the international investors are the only buyers of the sovereign debt, we will have^µ_q^t^Wb^t =bt. It is worth noticing that we allow forµt >1, which implies that investors are financing the purchase of risky debt by shorting the risk free asset. Similarly, we also allow forµ < 0, which in turn means that investors are financing the purchase of risk free assets by shorting the risky debt.

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