metadata: authors: 0: author: Matsuoka,Hideaki
count: World
docna: 0: docna: Debt Intolerance : Threshold Level and Composition
docty: Policy Research Working Paper
subtopic: Public Finance Decentralization and
            Poverty Reduction,Public Sector Economics,Financial Structures,Macroeconomic Management,Economic Conditions and Volatility,International Trade and Trade Rules
teratopic: Public Sector Development,Finance and Financial Sector Development,Macroeconomics and Economic Growth,International Economics and Trade
abstracts: cdata!: Fiscal vulnerabilities depend on both
            the level and composition of government debt. This study
            examines the role of debt thresholds and debt composition in
            driving the non-linear behavior of long-term interest rates
            through a novel approach, a panel smooth transition
            regression with a general logistic model. The main findings
            are threefold. First, the impact of the expected public debt
            level on interest rates rises exponentially when the share
            of foreign private holdings exceeds approximately 20 percent
            of government debt denominated in local currency. Second,
            when the share of foreign private investors is 30 percent,
            an increase in the share of foreign private holdings of
            government debt could raise long-term interest rates once
            the public debt-to-GDP ratio exceeds 60 percent of GDP,
            offsetting the downward pressure on long-term interest rates
            from higher market liquidity. Third, out-of-sample forecasts
            of this novel non-linear model are more accurate than those
            of previous methods.
repnme: repnme: Debt Intolerance : Threshold Level and Composition
display_title: Debt Intolerance : Threshold Level
            and Composition
listing_relative_url: /research/2020/06/32120594/debt-intolerance-threshold-level-composition
topicv3: Macroeconomic Vulnerability and Debt
            m1326057 1104,Trade m1326924 698,Treasury m1327009 1045,Central Banks m1327453 1235,Monetary Policy m1327609 444
publishtoextweb_dt: 2020-06-11T00:00:00Z
historic_topic: Public Sector Development,Finance and Financial Sector Development,Macroeconomics and Economic Growth,International Economics and Trade
origu: EFI - Prospects Group (EPGDR)
no_of_pages: 42
author_keys: 0: author_key: 1463324
model_extractions: Policy Research Working Paper 9276 Debt Intolerance Threshold Level and Composition _Hideaki Matsuoka_ Prospects Group June 2020
Policy Research Working Paper 9276

# **Abstract**

Fiscal vulnerabilities depend on both the level and composition of government debt. This study examines the role of debt thresholds and debt composition in driving the non-linear behavior of long-term interest rates through a novel approach, a panel smooth transition regression with a general logistic model. The main findings are threefold. First, the impact of the expected public debt level on interest rates rises exponentially when the share of foreign private holdings exceeds approximately 20 percent of government debt denominated in local currency. Second, when the share of foreign private investors is 30 percent, an increase in the share of foreign private holdings of government debt could raise long-term interest rates once the public debt-to-GDP ratio exceeds 60 percent of GDP, offsetting the downward pressure on long-term interest rates from higher market liquidity. Third, out-of-sample forecasts of this novel non-linear model are more accurate than those of previous methods.

This paper is a product of the Prospects Group. 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 hmatsuoka@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
# Debt Intolerance: Threshold Level and Composition<sup>*</sup>

## Hideaki Matsuoka<sup>†</sup>

**Key Words:** _Generalized panel smooth transition regression, Expected public debt-to-GDP ratio, Foreign private investors, Long-term interest rate_

### **JEL Codes:** E43,E62,H63

> *The views expressed herein are my own and do not represent those of World Bank. I thank my discussant Mototsugu Shintani at the 21st Macroeconomics Conference (Osaka, Japan). I am grateful for valuable comments from Serkan Arslanalp, Tamon Asonuma, Tran Lam Anh Duong, Hurlin Christophe, Ichiro Fukunaga, Nobuyuki Harada, Ryo Horii, Kazumasa Iwata, Munechika Katayama, Atsushi Kawamoto, Junko Koeda, Ayhan Kose, Yoichi Matsubayashi, Ryota Nakatani, Boaz Nandwa, Futoshi Narita, Shin-Ichi Nishiyama, Franziska Ohnsorge, Masakatsu Okubo, Arito Ono, Jun Saito, Masaya Sakuragawa, Etsuro Shioji, Shigenori Shiratsuka, Kengo Tahara, Yuki Teranishi, Takayuki Tsuruga, Kozo Ueda, Lei Sandy Ye and participants at Georgetown Center for Economic Research Biennial Conference, the 4th annual conference of the International Association for Applied Econometrics, Norges Bank Workshop on Nonlinear Models in Macroeconomics and Finance for an Unstable World, 28th annual meeting of the Midwest Econometrics Group, Dynamic Econometrics Conference (George Washington University) and seminars at Japan Center for Economic Research, Kobe University, Waseda University and University of Tsukuba. I also thank Mark Edgar Felsenthal for editorial assistance.

> †World Bank, E-mail address:hmatsuoka@worldbank.org Postal address: 1818 H Street NW, MC2-204, Washington DC, 20433 USA /TEL:+1-202-473-8009.
_"The experiences of foreign economies suggest that the relationship between debt and interest rates is complex and likely non-linear, with the influence of greater debt on interest rates rising as the debt-to-GDP ratio reaches a trajectory at which investors have concerns about its sustainability."_ _"The level of debt that is sustainable in an economy is not a constant. It can change over time and indeed has changed enormously over the last 150 years. The ratio of credit to GDP in the late Victorian British economy was under 20 percent. In the mid-twentieth century it was around 60 percent and by the early 1990s over 100 percent."_

# **1. Introduction**

As argued by Reinhart et al. (2003), fiscal vulnerabilities depend on both the level and composition (foreign vs. domestic) of government debt. They describe the “debt intolerance” phenomenon, in which interest rates in developing economies can spike above the “tolerance ceiling,” even if debt levels are considered manageable by advanced country standards. Long-term interest rates in advanced economies have been lower than those in emerging markets although much higher debt levels have been seen in advanced economies such as Japan, the United Kingdom and the United States (Figures 1 and 2). While research has estimated the marginal impact of public debt on long-term interest rates, the results vary widely, even when the studies control for fundamental variables such as inflation and growth expectations.<sup>1</sup> Meanwhile, the composition for government bond holdings varies widely across countries. The share of foreign private investors in emerging markets has been larger than in advanced economies since the global financial crisis (Figure 3).<sup>2</sup> Also, major central banks in advanced economies have been important participants in government bond markets, purchasing government bonds financed by central bank reserves through quantitative easing. This paper examines the implications of the level and composition (foreign or domestic, official or private) of government bond holdings for long-term yields.

> 1Please see Section 3.4 for details.

> 2According to Arslanalp and Tsuda (2014a), the average local currency share of external public debt in 14 emerging markets increased from 24 percent in 2009Q4 to 42 percent in 2018Q2. To understand these recent dynamics, Ottonello and Perez (2019) develop a model of optimal choice of debt denominated in foreign and local currency and conclude that prolonged economic expansion and stabilization of inflation during this period can account for most of the observed changes in the currency composition of sovereign debt. By contrast, the temptation to reduce debt repayments in local currency through inflation is high during recessions since the marginal benefit of saving resources for consumption is high. To mitigate higher incentives to dilute debt, the government optimally chooses to tilt its currency composition towards foreign currency.

2
Some studies maintain that foreign investors require higher risk premia than domestic ones when a government is likely to repay domestic investors first.<sup>3</sup> Azzimonti and Quadrini (2017), investigating the role of portfolio diversification on optimal default of sovereign debt, show that financial market integration increases the incentives of a given country to default. This is not only attributed to partial ownership of the defaulted debt by foreigners, but also because the macroeconomic cost of a default is smaller when the defaulting country is financially integrated. Gros (2013), Ichiue and Shimizu (2015) and Tenreyro (2019) also argue that if domestic financial institutions have a large share of government bonds, the losses they might incur would be large. To avoid this, governments would have a clear incentive to undertake fiscal consolidation rather than undergo default.

Dell’Erba et al. (2013) and Ichiue and Shimizu (2015) document that when an increase in debt is financed through foreign borrowing, the increase in interest rates is greater than under domestically-financed debt.<sup>4</sup> Similarly, Agca and Celasun (2012) show that the impact of domestic public debt on syndicated loan yield spreads is not statistically significant, whereas the analogous impact for external public debt is significant. Brzoza-Brzezina and Kotlowski (2018), using the panel smooth transition regression (PSTR) model developed by González et al. (2017), show that risk premia increase slowly with deteriorating net financial asset positions, and then suddenly jump once a threshold is reached.

Meanwhile, Reinhart and Trebesch (2015) argue that an increase in the share of foreign investors is associated with lower long-term interest rates because these holdings supplement domestic saving in capital-scarce countries, especially in times of ample global liquidity. Peiris (2013) documents that while domestic investors are typically buy-and-hold investors, foreign investors are more likely to trade. Some empirical studies support

> 3This argument is based on the assumption that a government can default selectively on foreign investors. Erce and Mallucci (2018) find that selective defaults have been frequent over the period 1980-2015. Since 1980, about two-thirds of defaults have selectively involved either foreign-law bonds or domestic-law bonds. By contrast, Sturzenegger and Zettelmeyer (2008) conclude that with a few exceptions, domestic investors do not appear to have been treated systematically better than foreign investors between 1998 and 2005. Broner et al. (2014) argue that selective default can happen when the government can impose capital controls that make discrimination easier. Meanwhile, Broner et al. (2010) show that secondary markets both reduce the probability of default on foreigners and make it difficult for the government to discriminate among creditors.

> 4Asonuma et al. (2015) also show that higher home bias mitigates the upward pressure of higher public debt on bond spreads, relying on three home bias indicators: (1) Banks’ holding of domestic sovereign claims relative to banks’ total assets, (2) Banks’ holding of domestic sovereign claims relative to banks’ holding of sovereign claims and (3) Banks’ holding of domestic sovereign claims relative to public debt. Their result is line with the fiscal crisis model of Sakuragawa and Sakuragawa (2016), which explains why domestic investors do not require a risk premium against large outstanding debt when there is a strong home bias in the asset portfolio of domestic bondholders. The reason is that these investors turn out to have no access to any assets that hedge fiscal risk. Ongena et al. (2019) find that during the acute phase of the European sovereign debt crisis when the government had to roll over substantial sovereign debt, domestic banks that were smaller, less well capitalized, had a lower ratio of liquid assets, and had received government support in the past were more likely to purchase domestically-issued sovereign debt than foreign banks.

3
this downward effect (Arslanalp and Poghosyan (2016), Carvalho and Fidora (2015), Ebeke and Lu (2015) and Warnock and Warnock (2009)). Azzimonti et al. (2014) illustrate that small countries facing a larger world market relative to their own economies perceive the interest rate as less sensitive to their own debt, as in a globally integrated economy both the demand and supply of the government debt come not only from domestic investors and the government but also from foreign sources.

Although a large research program documents both positive and negative impacts of an increase in the share of foreign debt on government bond yields, only a few studies have reconciled these mixed impact estimates by investigating thresholds. Our work is closely related to Ebeke and Lu (2015) and Brzoza-Brzezina and Kotlowski (2018). Ebeke and Lu (2015) show that in emerging markets an increase in the share of foreign debt holdings has a negative impact on yields but if either the lagged external debt-to-GDP ratio exceeds 90 percent or the lagged short-term debt-to-GDP ratio exceeds 21.5 percent, the corresponding impacts turn positive. Brzoza-Brzezina and Kotlowski (2018) find that the country’s risk premium gets significantly larger when the net financial assets position is below about 75 percent of GDP.

This paper contributes to two strands of the literature, extending and complementing Ebeke and Lu (2015) and Brzoza-Brzezina and Kotlowski (2018). First, it makes a methodological contribution towards the generalized panel smooth transition regression (GPSTR) model by combining two approaches: the panel smooth transition regression (PSTR) and the general logistic model (GLM). Ebeke and Lu (2015) and Brzoza-Brzezina and Kotlowski (2018) employ the interaction-term (IT) and PSTR models, respectively.<sup>5</sup> The biggest difference between the GPSTR model and previous methods is the GPSTR model can allow for potential point asymmetries whereas the IT and PSTR models exhibit point symmetry. If the impact of an increase in expected public debt on the interest rate is highly non-linear, the novel model used here can improve the estimation. Here, the performance of the GPSTR model is evaluated by comparing the out-of-sample forecast error with those of other methods employed in previous studies.

Second, this paper simultaneously estimates two types of threshold values to address the following questions:

> 5The motivation of Brzoza-Brzezina and Kotlowski (2018) in employing the PSTR model is that the dynamic stochastic general equilibrium (DSGE) literature such as Schmitt-Grohe and Uribe (2003), Adolfson et al. (2007) and García-Cicco et al. (2010) that assumes a nonlinear (e.g., exponential) relationship between risk premia and foreign debt. As these DSGE studies do not assume that the government has public debt, the country risk premium used in these studies does not necessarily represent the sovereign risk premium. However, since Brzoza-Brzezina and Kotlowski (2018) use the PSTR model and the difference between a country’s long-term and the US interest rate as a proxy for the country risk premium, their study is the most closely related to this paper.

4
- **(i)** What is the threshold of the share of foreign private investor financing that triggers an increase in the marginal impact of higher expected public debt on government bond yields?

- **(ii)** What is the threshold of public debt that triggers an increase in the marginal impact of a higher share of foreign private investor financing on government bond yields?

Ebeke and Lu (2015) and Brzoza-Brzezina and Kotlowski (2018) investigate only one type of threshold, whereas this paper investigates two types of threshold values simultaneously.<sup>6</sup> The remainder of this paper is organized as follows. Section 2 examines non-linear models: the IT, PSTR and GPSTR to explore threshold values, based on the data for 11 advanced economies and 14 emerging markets. Section 3 presents the baseline estimation results, the model evaluation, and comparison with other studies. Section 4 concludes.

# **2. Empirical strategy and data**

Local currency bonds can be held by both domestic and foreign investors, whereas foreign currency bonds are assumed to be held by only foreign investors. To estimate the threshold of the composition for government bond holdings (foreign vs. domestic), we employ local currency bond yields because they reflect the behavior of both domestic and foreign investors.<sup>7</sup> We examine three models, namely, the (i) Interaction term model (IT), (ii) Panel Smooth Transition Regression (PSTR), and (iii) Generalized Panel Smooth Transition Regression (GPSTR) models.

The (i) IT model is a simple specification with an interaction term between the share of foreign private investors and the expected public debt level. The (ii) PSTR model, developed by González et al. (2017) and Fok et al. (2005), includes a standard logistic function that exhibits point symmetry with one slope parameter and one location parameter. Brzoza-Brzezina and Kotlowski (2018) is relevant to our empirical strategy because they employ the PSTR model to examine a nonlinear relationship between a country’s risk premium and net

> 6These two previous studies use actual debt data, whereas this paper uses a wide range of forecast data to exclude any effects from current economic conditions on interest rates as well as to consider the forward-looking behavior of financial markets.

> 7Ebeke and Lu (2015) and Brzoza-Brzezina and Kotlowski (2018), who also use local currency bonds in emerging markets, control for exchange rate risk whereas Moore et al. (2013) controls for it indirectly by estimating the share of foreign investors that is affected by exchange rate risk. We include exchange rate risk in the baseline estimation but exclude it as a robustness check. Amstad et al. (2020), using the average credit ratings provided by Standard and Poor’s, Moody’s and Fitch find a slow and steady convergence of sovereign risk in local and foreign currency due to higher availability of foreign currency via FX reserves and smaller dependence on foreign currency borrowing (decline of original sin) over the past 20 years.

5
financial assets. To grasp the potential point asymmetry, this paper develops the (iii) GPSTR model by replacing the standard logistic function employed by González et al. (2017) with GLM, as suggested by Stukel (1988).

# **2.1 Interaction term (IT)**

We examine how the interaction term between the share of foreign private investors and the expected public debt level affects the interest rate as follows: where a country _푖_ = 1, _..._ , _푁_ at a time _푡_ = 1, _..._ , _푇_ ,E _푡 퐿푖,푡_ + _푛_ is the _푛_ −year-ahead forward long-term interest rate, E _푡 퐷푒푏푡푖,푡_ + _푛_ is the _푛_ -year-ahead projection for public debt (percent of GDP), _푓푝푖,푡_ −1 is lagged share of private foreign investors and **zit** describes control variables.<sup>8</sup> We analyze the effect of forward-looking projections of public debt on forward interest rates to exclude any effects of current economic conditions. As discussed by Engen and Hubbard (2005), Ichiue and Shimizu (2015) and Laubach (2009), when a deterioration of fiscal conditions and a decrease in interest rates due to expected accommodative monetary policy occur simultaneously during a recession, the upward effect of fiscal deterioration on long-term interest rates could be underestimated even if we control for other variables. In addition, the government bond yield is influenced by forward-looking variables. _훽_ 1 is expected to be larger than _훽_ 0 : domestic investors may not require a risk premium against large debt when there is strong home bias without any other assets hedging fiscal risk. _훿_ is expected to be negative: while domestic investors are typically buy-and-hold investors, foreign investors are more likely to trade. This could be supportive of increased market liquidity.

# **2.2 PSTR and GPSTR**

The PSTR model, developed by González et al. (2017) and Fok et al. (2005) can allow for a continuum of regimes, each one being characterized by a different value of the transition variable. Replacing E _푡 퐷푒푏푡푖,푡_ + _푛 푓푝푖,푡_ −1 in the IT model (1) with E _푡 퐷푒푏푡푖,푡_ + _푛푔_ ( _푓푝푖,푡_ −1; _훾_ 1 _,푐_ ) gives the PSTR model:

> 8We take a lagged value of foreign investors to avoid a simultaneity bias because the interest rate affects their behaviors. We discuss this endogeneity in Section 3.2.

6
E _푡 퐿푖,푡_ + _푛_ = _훼푖_ + _훽_ 0E _푡 퐷푒푏푡푖,푡_ + _푛_ + _훽_ 1E _푡 퐷푒푏푡푖,푡_ + _푛_ · _푔_ ( _푓푝푖,푡_ −1; _훾_ 1 _,푐_ ) + _훿푓푝푖,푡_ −1 + _휙_ **zi** _,_ **t** + _휀푖,푡_ (2) <u>1</u> where _푔_ ( _푓푝푖,푡_ −1; _훾_ 1 _,푐_ ) is the standard logistic function ( 1+exp(− _훾_ 1 ( _푓푝푖,푡_ −1− _푐_ ))<sup>_,훾_1</sup><sup>_>_0)thatdependsonthe</sup> threshold variable _푓푝푖,푡_ −1, the slope parameters _푟_ 1 and location parameters _푐_ .<sup>9</sup> This standard logistic function _푔_ ( _푓푝푖,푡_ −1; _훾_ 1 _,푐_ ) exhibits point symmetry with one slope parameter _푟_ 1. In other words, regardless of whether the threshold variable is larger or smaller than the location _푐_ , the impact of public debt across all regimes could be affected by one slope parameter _푟_ 1. Figure 4 shows examples for the standard logistic function as well as the interaction term that exhibit point symmetry. To investigate potential point asymmetry, we introduce two slope parameters ( _훾_ 1 and _훾_ 2), replacing the standard logistic function with the general logistic model suggested by Stukel (1988).

The generalized panel smooth transition regression (GPSTR) is as follows: Following Stukel (1988), the general logistic model (GLM), _푔_ ( _푓푝푖,푡_ −1; _훾_ 1 _,훾_ 2 _,푐_ ) is defined as follows: For _푓푝푖,푡_ −1 − _푐_ ⩽ 0, For _푓푝푖,푡_ −1 − _푐_ ⩾ 0, 9 When _푟_ 1 →∞, the PSTR model reduces to the two-regime panel threshold model by Hansen (1999).

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The transition functions _푔_ ( _푓푝푖,푡_ −1; _훾_ 1 _,훾_ 2 _,푐_ ) depend on the lagged share of private foreign investors _푓푝푖,푡_ −1, the slope parameters _푟_ 1 , _푟_ 2 and location parameters _푐_ . Figure 5 shows examples for the GLM _푔_ ( _푓푝푖,푡_ −1; _훾_ 1 _,훾_ 2 _,푐_ ) that exhibit point asymmetry. The estimation of the parameters of the GPSTR model eliminates individual effects _훼푖_ by removing individual-specific means and then applying non-linear least squares to the transformed model. The matrix of transformed explanatory variables is � � where E<sup>�</sup> _푡 퐿푖,푡_ + _푛_ = E _푡 퐿푖,푡_ + _푛_ − _퐿푖_ , E _푡 퐷푒푏푡푖,푡_ + _푛_ = E _푡 퐷푒푏푡푖,푡_ + _푛_ − _퐷푒푏푡푖_ , _푓푝_<sup>�</sup> _푖,푡_ −1 = _푓푝푖,푡_ −1 − _푓푝푖_ and **zi** _,_ **t** = **zi** _,_ **t** − **<u>zi</u>** . _퐺_ � _푖,푡_ + _푛_ ( _훾_ 1 _,훾_ 2 _,푐_ ) = E _푡_ � _퐷푒푏푡푖,푡_ + _푛_ · _푔_ ( _푓푝푖,푡_ −1; _훾_ 1 _,훾_ 2 _,푐_ ) − _푇_<sup><u>1</u></sup> � _푇푡_ =1<sup>E</sup><sup>_푡퐷푒푏푡푖,푡_+</sup><sup>_푛_·</sup><sup>_푔_(</sup><sup>_푓푝푖,푡_−1;</sup><sup>_훾_1</sup><sup>_,훾_2</sup><sup>_,푐_)is the transformed</sup> explanatory variables in the second regime that depends on the parameters and the transition function. Given a couple ( _훾_ 1 _,훾_ 2 _,푐_ ), the parameters can be estimated by ordinary least squares, which yields: where Ψ<sup>�</sup> ( _훾_ 1 _,훾_ 2 _,푐_ ) is conditional to the values ( _훾_ 1 _,훾_ 2 _,푐_ ). For the next step, by increasing the number of combinations for ( _훾_ 1 _,훾_ 2 _,푐_ ) _,_ the parameters of the transition function _훾_ 1 , _훾_ 2 and _푐_ are estimated by non-linear least squares : Consequently , ( _훽_<sup>ˆ</sup> 0 : _훽_<sup>ˆ</sup> 1 :<sup>�</sup> _훿_ : _휙_<sup>�</sup> ) ′ = �Ψ( ˆ _훾_ 1 _,_ ˆ _훾_ 2 _,_ � _푐_ ). The practical computation follows two steps.

- Step1. The initial values can be obtained by starting a grid search across the parameters _훾_ 1 , _훾_ 2 and _푐_ where grid points are _푛훾_ 1=21 _푛훾_ 2=21 and _푛푐_ =30. Hence, the number of regressions is 13,230.

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- Step2. We employ the Nelder–Mead simplex algorithm to find a local minimizer of the function nonlinear least squares, using the initial values.<sup>10</sup>

# **2.3 Threshold level and composition**

_휕_ E _푡 퐿푖,푡_ + _푛_ Using estimated parameters and solving _휕_ E _푡 퐷푒푏푡푖,푡_ + _푛_<sup>=0 and</sup><sup>_휕_</sup> _휕푓푝_<sup>E</sup><sup>_푡퐿_</sup> _푖,푡_<sup>_푖,푡_</sup> −<sup>+</sup> 1<sup>_푛_=0 can address the following two questions:</sup>

- **(i)** What is the threshold of foreign private investor financing share that triggers an increase in the marginal impact of higher expected public debt on government bond yields?

- **(ii)** What is the threshold of public debt level that triggers an increase in the marginal impact of higher share of foreign private investor financing on government bond yields?

Table 1 shows the threshold values that affect the marginal impact of expected public debt (E _푡 퐷푒푏푡푖,푡_ + _푛_ ) and the share of foreign private investors ( _푓푝푖,푡_ −1) on interest rates.

The first column shows the share of foreign private investors _푓푝푖,푡_ −1 that triggers a surge in government bond yields through an increase in the expected public debt. Such threshold values depend on the ratio of the first regime parameter of expected public debt ( _훽_ 0) to the second regime parameter of expected public debt ( _훽_ 1, _훽_ 1( _푓푝푖,푡_ −1; _훾_ 1 _,푐_ ) or _훽_ 1( _푓푝푖,푡_ −1; _훾_ 1 _,훾_ 2 _,푐_ )).

The second column shows the expected public debt level E _푡 퐷푒푏푡푖,푡_ + _푛_ that triggers a surge in government bond yields through an increase in the share of foreign investors.<sup>11</sup> The threshold of expected public debt becomes smaller if investors are more sensitive to the expected public debt. As a result, an increase in foreign private holdings of government debt would cause an increase in long-term interest rates, offsetting the downward effect on long-term interest rates from expanding market liquidity, even if foreign investors can support higher market liquidity.

> 10 This algorithm uses a simplex of n + 1 points for n-dimensional vectors and discards the current worst point to reduce the difference between the current best point and other points in simplex at each step in the iteration. See Lagarias et al. (1998) and Miranda and Fackler (2002) for details. Computational codes are based on Colletaz and Hurlin (2006) and Fouquau et al. (2008). 11 See Appendix A.2 for the derivatives of the transition function _푔_ ( _푓푝푖,푡_ −1; _훾_ 1 _,훾_ 2 _,푐_ ).

9
Table 1: Estimated threshold values of the impact of the increase in the share of foreign private investors ( _푓푝푖,푡_ −1) and the expected public debt (E _푡 퐷푒푏푡푖,푡_ + _푛_ <u>) on the interest rate</u>

||Threshold composition<br>|Threshold level|
|---|---|---|
|(1) IT|_푓푝푖,푡_−1= <sup>−</sup><sup>_훽_0</sup><br>_훽_1<br>|E_푡퐷푒푏푡푖,푡_+_푛_= <sup>−</sup><sup>_훿_</sup><br>_훽_1|
|(2) PSTR|_푓푝푖,푡_−1=<br>−_훽_0<br>_훽_1(_푓푝푖,푡_−1;_훾_1_,푐_)<br>|E_푡퐷푒푏푡푖,푡_+_푛_=<br>−_훿_<br>_훽_1<br>�_휕푔_(_푓푝푖,푡_−1;_훾_1_,,푐_)<br>_휕푓푝푖,푡_−1<br>�|
|(3) GPSTR|_푓_=<br>−_훽_0|E_퐷푒푏푡_=<br>−_훿_|
||_푝푖,푡_−1 <br>_훽_1(_푓푝푖,푡_−1;_훾_1_,훾_2_,푐_)|_푡푖,푡_+_푛_<br>_훽_1<br>�_휕푔_(_푓푝푖,푡_−1;_훾_1_,훾_2_,푐_)<br>_휕푓푝푖,푡_−1<br>�|

# **2.4 Data**

## **2.4.1 Data coverage**

Based on forecast data availability, we use bi-annual data of 25 countries: 11 advanced economies and 14 emerging markets during 2006H2-2018H2. Advanced economies include Australia, Canada, the Czech Republic, Denmark, Japan, the Republic of Korea, Norway, Sweden, Switzerland, the United Kingdom, and the United States. Emerging markets include Bulgaria, Colombia, China, Hungary, India, Indonesia, Malaysia, Mexico, Peru, the Philippines, Poland, Thailand, Turkey, and South Africa. The Euro area countries are omitted from advanced economies for the following reasons. As discussed by Ichiue and Shimizu (2015) and Wright (2011), this is because their term structures had been highly correlated with those of Germany since the introduction of the euro. Therefore, it would be difficult to identify how much long-term interest rates in the Euro area have reflected the fundamentals of these countries. In this regard, the share of foreign private investors in the euro area has been higher relative to others (Arslanalp and Tsuda (2014a)). In the euro area, the zero percent risk weight has been a major driver of banks’ holdings of foreign debt securities denominated in the local currency due to Basel capital regulation. Bonner (2016) shows that capital regulation encourages banks to substitute other bonds with government bonds. Because of this regulatory impact, the impact of foreign investors on interest rates for the euro area could be different from that of other countries. Hence, euro area countries are omitted.<sup>12</sup>

> 12Brzoza-Brzezina and Kotlowski (2018) employing the PSTR model also use data from both advanced economies and emerging markets. However, they use actual data, not forecast data

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# **2.4.2 Forward interest rates**

We use forward interest rates instead of current bond yields as the dependent variable. According to Shiller et al. (1983), the _푚_ -to- _푚_ + _푛_ -year forward nominal interest rate E _푡 퐿푖,푡_<sup>_푛_</sup> + _푚_<sup>is implied from the year-end</sup><sup>_푛_−and</sup> _푚_ + _푛_ −year zero-coupon interest rates as follows: We employ the 5-to-10-year forward real interest as the dependent variable.<sup>13</sup>

# **2.4.3 Expected public debt**

We employ projections of gross public debt to-GDP-ratio E _푡 퐷푒푏푡푖,푡_ + _푛_ by the IMF _World Economic Outlook_ , _Article IV Consultations_ , OECD _Economic Outlook_ , European Commission (EC) _European Economic Forecast_ , and Economist Intelligence Unit (EIU). Following Gruber and Kamin (2012) and Ichiue and Shimizu (2015), we use two-year-ahead projections of gross public debt-to-GDP-ratio as an independent variable.<sup>14</sup> Since the IMF _World Economic Outlook_ releases its public debt projections for most countries twice a year, we use biannual data. However, as OECD, EC and IMF _Article IV Consultations_ had made two-year-ahead projections once a year over the years, we interpolate the same projections to construct bi-annual data.

# **2.4.4 Foreign private holdings ratio**

We use the lagged share of private foreign investors _푓푝푖,푡_ −1 as the threshold variable and one independent variable. The composition of government bond holdings is drawn from Arslanalp and Tsuda (2014a) and Arslanalp and Tsuda (2014b). As we use forward interest rates for government debt securities denominated in the local currency, the foreign private holdings ratio _푓푝푖,푡_ −1 is measured as the foreign private holdings share of government debt securities denominated in the local currency.<sup>15</sup>

> 13The zero-coupon interest rate can be obtained from Bloomberg. To deflate the nominal interest rate into the real interest rate, we use two-year-ahead projections of inflation E _푡 휋푖,푡_ +2 due to data availability. The robustness check examines the nominal interest rate as well.

> 14Moreover, real-time vintages of data could affect long-term interest rates because fiscal data have been revised largely (De Castro et al. (2013)).

> 15While Arslanalp and Tsuda (2014b) provide foreign holdings share of central government debt securities denominated in local currency for emerging markets,Arslanalp and Tsuda (2014a) do not have the corresponding ratio in advanced economies but provide total general government debt securities, including debt denominated in both local and foreign currency. Hence, assuming that only foreign investors hold government debt securities denominated in foreign currency (data that can be obtained from the Bank

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# **2.4.5 Other control variables**

A vector of control variables **zi** _,_ **t** includes several variables. First, we use the lagged domestic official sector holdings ratio _푑표푖,푡_ −1 as a control variable. Major central banks in advanced economies have been important players in the government bond markets, purchasing government bonds financed by the creation of central bank reserves through quantitative easing — which central banks have implemented to put downward pressure on interest rates when policy rates were at or near zero. The portfolio balance channel operates when the central bank’s bond purchases, which change the relative supply of assets held by the private sector, induce equilibrating changes in the relative yields.<sup>16</sup> In the United States, Gagnon et al. (2011) show a cumulative decline in the 10-year Treasury yields by about 91 basis points after announcements of quantitative easing. According to Joyce et al. (2011), the corresponding impacts in the United Kingdom is estimated to be 100 basis points.

Second, we add the lagged foreign official holdings ratio _푓표푖,푡_ −1 using data from Arslanalp and Tsuda (2014a) and Arslanalp and Tsuda (2014b). The U.S. long-term interest rates remained low in the mid-2000s despite increases in the federal funds rate, a phenomenon Alan Greenspan labeled as a “conundrum” (Greenspan (2005)). Bernanke (2005) hypothesized that a global saving glut – driven by net savings in Asia and oilexporting countries – lowered long-term interest rates through an accumulation of foreign exchange reserves. Warnock and Warnock (2009) show that a 12-month total of foreign flows of 1 percentage point of GDP is associated with a 40 basis point reduction. Beltran et al. (2013) find that a 10 percentage point increase in foreign official flows into and out of Treasuries lowers the five-year term premium by 135 basis points.

Third, following Gruber and Kamin (2012), we add two-year-ahead projections of real GDP growth rate E _푡 푦푖,푡_ +2 which can be obtained from Consensus Economics _Consensus Forecast_ , the IMF _World Economic Outlook_ , _Article IV Consultations_ , OECD _Economic Outlook_ , European Commission (EC) _European Economic Forecast_ and the EIU.

Finally, we control for expected exchange depreciation over a two-year horizon : the rate of change between the two-year-ahead projections of the expected exchange rate and the current year estimation of each currency’s

> for International Settlements _Debt Securities Statistics_ ), we make an approximate estimate of the foreign holdings share of general government debt securities denominated in local currency by removing the amount of debt securities denominated in foreign currency from the total. Finally, we divide the foreign holdings ratio into a foreign private holdings ratio _푓푝푖,푡_ −1 and a foreign official holdings ratio _푓표푖,푡_ −1 using data from Arslanalp and Tsuda (2014a) and Arslanalp and Tsuda (2014b). 16Christensen and Rudebusch (2012), D’Amico et al. (2012) and Joyce et al. (2017) provide further discussion.

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exchange rate against the US dollar E _푡 퐸푥푐h푎푛푔푒푟푎푡푒푖,푡_ +2, using _Consensus Forecast_ . As foreign investors may be measuring returns in exchange rate adjusted terms, currency depreciation would cause them to demand this risk premium. Ebeke and Lu (2015) control for the two-year-forward exchange rate of each currency against the US dollar.

# **3. Estimation results**

## **3.1 Baseline results**

Table 2 shows the baseline results. The tests for nonlinearity are significant with p-values smaller than 0.01.<sup>17</sup> Thus, we employ the IT, PSTR and GPSTR models instead of the linear model. This result illustrates that debt composition plays an important role on the non-linear behavior of the long-term interest rate.

### **3.1.1 Marginal impact of the expected public debt**

The main parameters of interest here are _훽_ 0 and _훽_ 1. As expected, _훽_ 1 is larger than _훽_ 0 in the IT, PSTR and GPSTR models. These results illustrate that the more public debt is financed by foreign private investors, the greater the marginal impact of the expected public debt on interest rates. Figure 6 shows this marginal impact ( _휕_ E _휕푡_ E _퐷푒푏푡푡 퐿푖,푡푖,푡_ + _푛_ + _푛_<sup>).One striking feature of this chart is that this impact, estimated through the GPSTR model,</sup> increases exponentially and significantly as the foreign private holdings ratio exceeds the location parameter, whereas the corresponding impact estimated through the IT model increases constantly and through the PSTR model becomes flattened. The right panel of Figure 6 shows if the share of foreign investors are 20, 30 and 40 percent, the marginal impacts of public debt on the interest rate are 1.7, 3.3 and 5.5 percentage points, respectively.<sup>18</sup> The result of the GPSTR model is consistent with DSGE studies, such as Schmitt-Grohe and Uribe (2003), Adolfson et al. (2007), and García-Cicco et al. (2010) that assume an exponential relationship between risk premia and foreign debt.

By contrast, when the foreign private holding ratios are below about 20 percent, the result of the GPSTR

> 17In the linearity test, we follow Luukkonen et al. (1988) and Terasvirta (1994), replacing the transition function _푔_ (·) of the PSTR and GPSTR models with the first-order Taylor expansion (please see Appendix A.1 for details). The conversion gives the IT model. Hence, the tests of the IT, PSTR and GPSTR models for nonlinearity show the same results.

> 18Following Driscoll and Kraay (1998), standard errors are corrected for serial correlation, heteroskedasticity, and cross-sectional dependence.

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model illustrates that there is no significant impact of public debt on long-term government bond yields. This implies that domestic investors are insensitive to expected public debt. In other words, domestic investors may not require a risk premium against large debt when there is strong home bias without any other assets hedging fiscal risk, which is line with Japan’s debt literature (Sakuragawa and Sakuragawa (2016)).

Figure 8 shows the range of the time-varying impacts of expected public debt-to-GDP ratio on the interest rate during 2006H2-2018H2. Given that the share of foreign private investors in the small open economy is easily affected by the capital flows, sovereign risk can be volatile over the short-term. On the other hand, the corresponding impact would be small and stable in large economies or countries with capital control or higher home bias because the share of foreign private investors is low. According to the upper panel, a problem with the IT model is that some estimated impacts are negative in countries where the share of private foreign investors is low. This unreasonable result suggests that a highly non-linear model is appropriate. The middle and upper panels show there are no negative estimates from the PSTR and GPSTR.

# **3.1.2 Marginal impact of the share of foreign private investors**

Another parameter of interest here is the coefficient on the lagged share of foreign private investors; _훿_ . According to Table 2 and consistent with the literature (Arslanalp and Poghosyan (2016) and Ebeke and Lu (2015)), an increase in foreign private holdings of government debt is associated with a reduction in the interest rate as downward pressure on long-term interest rates results from expansion of market liquidity.

Figure 7 shows the marginal impact of the share of foreign investors on long-term interest rates (<sup>_휕_</sup> _휕푓푝_<sup>E</sup><sup>_푡퐿_</sup> _푖,푡_<sup>_푖,푡_</sup> −<sup>+</sup> 1<sup>_푛_) .</sup> The left panel of Figure 7 from the result of the IT model shows that this impact varies, depending on the public debt to GDP ratio. The expected public debt-to-GDP ratio E _푡 퐷푒푏푡푖,푡_ + _푛_ is estimated to be about 120 percent of GDP when the marginal impact of the share of foreign private investors on the interest rate is zero.<sup>19</sup> That is, although an increase in foreign private holding of government debt is associated with a reduction in interest rates, this downward effect would be reversed if the expected public debt-to-GDP ratio exceeds this threshold.

The right panel of Figure 7 from the GPSTR model shows that the marginal impact of the share of foreign investors on long-term interest rates also depends on the composition of debt, as well as the expected public debt. Expected public debt E _푡 퐷푒푏푡푖,푡_ + _푛_ triggers a surge in government bond yields through an increase in the 19The threshold can be calculated from E _푡 퐷푒푏푡푖,푡_ + _푛_ = − _훽_ 1 _<u>훿</u>_<sup>in Table 1.</sup> 14
share of foreign investors. Given that the marginal impact of the share of foreign private investors on the interest rate is zero, the threshold of expected public debt is high (low) when the share of foreign investors is low (high). For example, when the share of foreign investors is 15 percent, the threshold of expected public debt is 91 percent. In comparison, when the share of foreign investors is 30 percent, the threshold is 59 percent.<sup>20</sup> As the impact of public debt on interest rates based on the GPSTR model continues to increase exponentially depending on the foreign private holdings ratio, an increase in foreign private holdings of government debt would cause a rise in long-term interest rates even if the debt level is low. Hence, the result of the GPSTR model differs substantially from those of the IT and PSTR models.<sup>21</sup>

# **3.2 Robustness check**

We consider a wide range of exercises to check the robustness of our headline findings, including the following specifications to control for global and country-specific factors.

## **3.2.1 Global factor**

Robustness check 1 (controlling for U.S. monetary conditions): The baseline might already incorporate global factors because it includes the share of foreign investors. A growing literature also investigates how bond spreads especially in emerging markets, are related to global factors, especially U.S. monetary conditions. For example, Mauro et al. (2002) and González-Rozada and Levy Yeyati (2008), using sovereign bonds denominated in U.S. dollars conclude that spreads comove across emerging markets and tend to be most related to global events and global liquidity. Foley-Fisher and Guimaraes (2013) and Gilchrist et al. (2019) also examine spillovers from changes in U.S. interest rates on sovereign bond yields denominated in foreign currencies. Moreover, Longstaff et al. (2011) find similar evidence based on the sovereign CDS market where the reference obligation is a US dollar-denominated issue or a euro-dominated issue.

While foreign currency bonds have been widely used by previous works as discussed above, recent literature has examined local currency bonds as well. For instance, Moore et al. (2013) analyze the effect of US monetary

> 20The threshold can be calculated from E _푡 퐷푒푏푡푖,푡_ + _푛_ = _휕푔_ ( _푓푝푖,푡_ − _<u>훿</u>_ −1; _훾_ 1 _,훾_ 2 _,푐_ ) in Table 1. _훽_ 1 <u>�</u> _휕푓푝푖,푡_ −1 <u>�</u>

> 21As shown in the central panels of Figure 7 for the PSTR model, the marginal impacts of the share of foreign investor on the long-term interest rates over the location parameter are the same because of the assumption of the point symmetry. This result, which is difficult to interpret, is one reason why we develop the GPSTR model to investigate point asymmetry.

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policy on local currency sovereign yields.

Although the baseline might already incorporate global factors through the share of foreign investors, we control for the U.S. 10-year term premia based on Adrian and Crump (2013), excluding the observation of the United States from the sample.<sup>22</sup>

# **3.2.2 Country-specific factors**

Robustness check 2 (excluding exchange rate risk): The baseline includes both the share of foreign investors and expected exchange depreciation as independent variables. Although we take a lagged value of the share of foreign investors, it may decline due to expected exchange depreciation if they exhibit forward-looking behavior. Given possible multicollinearity between these two variables, we exclude expected exchange depreciation.

Robustness check 3 (controlling for net foreign assets position): Following Brzoza-Brzezina and Kotlowski (2018), we control for the lagged net foreign assets to GDP ratio _푁퐹퐴푖,푡_ −1. Reinhart and Trebesch (2015) argue that an increase in the share of foreign investors is associated with lower long-term interest rates, as these holdings supplement domestic savings in capital-scarce countries. By contrast, a chronic excess of saving over investments may cause low real interest rates.

Robustness check 4 (controlling for capital control): Capital control would lower sovereign risk because the regulation of capital flows may possibly prevent crises (Wright (2006)). Fernández et al. (2016) construct an index of capital control restrictions for bond inflow and outflow. Hence, we add this capital control dummy variable _퐶퐶푖,푡_ −1 as an additional robustness check.

Robustness check 5 (controlling for short-term interest rate): We employ forward interest rates to omit any effects of current economic conditions. However, if current monetary policy affects forward interest rates, omitted variable bias would occur due to misspecification. Hence, we control for the one-year zero coupon rate

# _푆푇푅푖,푡_ .

> 22We directly control for U.S. monetary conditions. However, as a manifestation of the investors’ risk-taking behavior amid low interest rates of advanced economies, the “search-for-yield” could cause the share of private foreign investors to increase in emerging markets. Moore et al. (2013) show that a 1 percentage point drop in the US 10-year Treasury bond yield leads on average to a 4.2 percentage point increase in foreign holdings of government bonds in emerging markets. Therefore, future research could control for U.S. monetary conditions indirectly by using the instrumental variables to deal with the endogeneity of the share of foreign investors without taking a lagged value. However, Yu (2013) finds inconsistency in the two-step-least-squares estimators in threshold models when the threshold variable is endogenous. Caner and Hansen (2004) use two-step least square estimators in the threshold model where they allow for endogenous regressors, but they assume the threshold variable to be exogenous. Furthermore, Yu (2013) points out that the estimator based on a misspecified reduced form is inconsistent even if the threshold variable is exogenous. Employing instrumental variables is an interesting future topic for research.

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Robustness check 6 (dependent variable: nominal interest rates): Ichiue and Shimizu (2015) use the 6-to10-year-ahead projection of the inflation rate to match the horizon reflected in the 5-to-10-year forward interest rates for 10 advanced economies. However, our baseline deflates the 5-to-10-year nominal forward rates by two-year-ahead projections of inflation due to data availability. Hence, an additional robustness check can use the nominal interest rate as the dependent variable and add the two-year-ahead projections of inflation as the independent variable.

According to Tables 3, 4, 5 and Figure 9, the results of the robustness checks are in line with the baseline results. According to the results for the GPSTR model, the impact of expected public debt on interest rates increases exponentially and significantly as the foreign private holdings ratio exceeds the location parameter. For robustness check 2, the estimated impact of a 1 percentage point increase in the U.S. 10-year term premium is about 0.5 percentage point. Instead, the marginal impact of the share of foreign investors becomes smaller than the baseline because US monetary conditions now also affect the behavior of foreign investors. Moreover, the corresponding impact of public debt is also smaller than the baseline when the share of the private investors is higher. The results of robustness checks 3 and 4 show that both higher net foreign assets position and capital controls lower the interest rates.<sup>23</sup>

# **3.3 Model evaluation**

The IT, PSTR, and GPSTR models are competing models, as non-linearity tests reject the null hypothesis of the linear model. As argued by Granger (2001), it is well known that nonlinear models are inclined to overfit the data and thus, out-of-sample forecasting evaluation is recommended. Hence, we employ cross-validation to calculate the mean squared error (MSE).

We start to estimate three models for the new in-sample by leaving out all observations of the _푖_ th crosssection. Using estimated parameters, we plug in all observations of the _푖_ th cross-section and then calculate the

> 23An additional robustness check considers the expectation for fiscal consolidation so as to avoid sovereign default. This idea is derived from “fiscal limit”, i.e., a point where the government no longer has the ability to finance higher debt levels by increasing the tax rate to the revenue-maximizing tax rate (Bi (2012)). The sovereign risk premium is related to the fiscal limit, assuming that sovereign default occurs when government debt exceeds the fiscal limit. Empirically, Nakamura and Yagi (2017) use the national burden ratio, measured as the sum of tax payments and social security fees as a ratio to nominal GDP, as a variable representing expectation for fiscal consolidation. They find that a low national burden ratio keeps long-term interest rates at low levels in 23 advanced economies. However, as our sample includes emerging markets, we do not find similar results. A possible reason is that although the national burden ratio in emerging markets is lower than in advanced economies, this does not necessarily mean that the government can increase tax revenue, as many types of structural obstacles may exist (e.g., a large informal sector and dependence on a few natural resources). Please see Besley and Persson (2014) for further details.

17
MSE, comparing the estimated fitted values and the actual values as below: <u>1 1</u> whereΨ<sup>�</sup> − _푖_ (·) is computed by leaving out all observations of the _푖_ th cross-section. _푁푇_<sup>_푒_ˆ2</sup> _퐼푇 푁푇_<sup>_푒_ˆ2</sup> _푃푆푇푅_<sup>,and</sup> <u>1</u> _푁푇_<sup>_푒_ˆ</sup> _퐺푃푆푇푅_<sup>2are MSEs of the IT, PSTR, and GPSTR models, respectively.</sup> Table 6 shows the comparison of MSEs across the three models and illustrates that the out-of-sample forecast errors of the GPSTR model are smaller than those of the IT and PSTR models for all cases. This means that the GPSTR model is robust to the sample selection.

# **3.4 Comparison with other studies**

Table 7 compares our estimates with those of other studies in three dimensions: (1) the impact of an increase in expected public debt on government bond yields, (2) the impact of an increase in the share of foreign investors on government bond yield, and (3) the threshold value for the impact of an increase in the share of foreign investors.

First, significant research has been devoted to estimating the positive impact of public debt on long-term interest rates, focusing on government debt securities denominated in local currency. The estimated impacts founds for advanced economies are smaller than for emerging markets (Arslanalp and Poghosyan (2016), Gruber and Kamin (2012), Ichiue and Shimizu (2015) and Jaramillo and Weber (2013)).<sup>24</sup> Our result shows the impact of an increase in expected public debt on forward interest rate rises with the share of foreign private financing in public debt. Overall, the range of our estimated impacts is consistent with that of the existing literature.

Second, our result shows that higher foreign private holdings of government debt is also associated with lower in long-term interest rates, consistent with the literature (Arslanalp and Poghosyan (2016) and Ebeke and Lu (2015)).

Third, Ebeke and Lu (2015) show that in emerging markets an increase in the share of foreign holdings has a negative impact on yield, but this impact turns positive if either the lagged external debt-to-GDP ratio

> 24As the studies employ different sample periods, they are not necessarily comparable.

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exceeds 90 percent or the lagged short-term debt-to-GDP ratio exceeds 21.5 percent. Our corresponding result from the GPSTR model indicates that the threshold of expected public debt is high (low) when the share of foreign investors is low (high). For example, when the share of foreign investors is 15 percent, the threshold of the expected public debt is 91 percent. In comparison, when the share of foreign investors is 30 percent, the threshold is 59 percent. As the marginal impact of expected public debt on interest rates under the GPSTR model increases exponentially, depending on the foreign private holdings ratio, an increase in foreign private holdings of government debt would cause a rise in long-term interest rates, even if the debt level is low. Hence, the result of the GPSTR model differs substantially from that of the IT model.

# **4. Conclusion**

This study examines threshold values to understand the non-linear behavior of long-term interest rates using a novel approach, a panel smooth transition regression with a general logistic model. This paper examines how the interaction between the funding source and the expected public debt level affects interest rates, based on the data of 11 advanced economies and 14 emerging markets.

The main findings presented here are threefold. First, the impact of expected public debt levels on interest rates increases exponentially as the share of foreign private holdings exceeds 20 percent denominated in the local currency, even if strong home bias could mitigate this upward pressure. Second, if the expected public debt-to-GDP ratio exceeds a certain level, an increase in the share of foreign private holdings of government debt would raise long-term interest rates, offsetting the downward pressure on long-term interest rates from expanding market liquidity. Third, the out-of-sample forecasts of the generalized panel smooth transition regression model are more accurate than those of previously used methods.

The composition of government debt has a significant impact on the highly non-linear behavior of the longterm interest rate. Policy makers need to consider how government bond yields react to the level of public debt. In particular, as the share of foreign private investors in a small open economy is easily affected by capital flows, sovereign risk could fluctuate in the short-term. From a long-term perspective, Hoshi and Ito (2014) point out that an increase in local-currency-denominated domestic assets would slow down due to the rapid aging of the population in Japan. As the government cannot indefinitely rely on private domestic investors, foreign investors would have to step in and absorb the government debt at some point. Consequently, sovereign 19
risk would become more sensitive to these developments.

Future research could focus on the endogeneity of the share of foreign investors by using instrumental variables. This study used a lagged value of the foreign investor share to avoid simultaneity bias and it maintained the assumption of exogeneity. However, this assumption could be relaxed by allowing for endogenous regressors although that would lead to additional econometric challenges.

# **References**

- Adolfson, M., S. Laseen, J. Linde, and M. Villani. 2007. “Bayesian estimation of an open economy DSGE model with incomplete pass-through.” _Journal of International Economics_ 72:481–511.

- Adrian, T., and E. Crump, Richard Moench. 2013. “Pricing the term structure with linear regressions.” _Journal of Financial Economics_ 110:110–138.

- Agca, S., and O. Celasun. 2012. “Sovereign debt and corporate borrowing costs in emerging markets.” _Journal of International Economics_ 88:198–208.

- Amstad, M., F. Packer, and J. Shek. 2020. “Does sovereign risk in local and foreign currency differ?” _Journal of International Money and Finance_ 101:1–16.

- Arslanalp, S., and T. Poghosyan. 2016. “Foreign Investor Flows and Sovereign Bond Yields in Advanced Economies.” _Journal of Banking and Financial Economics_ 2016:45–67.

- Arslanalp, S., and T. Tsuda. 2014a. “Tracking Global Demand for Advanced Economy Sovereign Debt.” _IMF Economic Review_ 62:430–464.

- —. 2014b. “Tracking Global Demand for Emerging Market Sovereign Debt.” IMF Working Paper No. 14/39, International Monetary Fund, Washington, DC.

- Asonuma, T., S. Bakhache, and H. Hesse. 2015. “Is Banks’ Home Bias Good or Bad for Debt Sustainability?” IMF Working Paper No. 15/44, International Monetary Fund, Washington, DC.

- Azzimonti, M., E. de Francisco, and V. Quadrini. 2014. “Financial Globalization, Inequality, and the Rising Public Debt.” _American Economic Review_ 104:2267–2302.

20
- Azzimonti, M., and V. Quadrini. 2017. “The Politics of Sovereign Default under Financial Integration.”, Unpublished manuscript.

- Beltran, D.O., M. Kretchmer, J. Marquez, and C.P. Thomas. 2013. “Foreign holdings of U.S. Treasuries and U.S. Treasury yields.” _Journal of International Money and Finance_ 32:1120–1143.

- Bernanke, B.S. 2005. “The global saving glut and the U.S. current account deficit.” Speech 77, Board of Governors of the Federal Reserve System (U.S.).

- Besley, T., and T. Persson. 2014. “Why Do Developing Countries Tax So Little?” _Journal of Economic Perspectives_ 28(4):99–120.

- Bi, H. 2012. “Sovereign default risk premia, fiscal limits, and fiscal policy.” _European Economic Review_ 56:389–410.

- Bonner, C. 2016. “Preferential Regulatory Treatment and Banks’ Demand for Government Bonds.” _Journal of Money, Credit and Banking_ 48:1195–1221.

- Brainard, L. 2017. “Monetary Policy in a Time of Uncertainty : a speech at the Brookings Institution, Washington, D.C., January 17, 2017.” Speech 933, Board of Governors of the Federal Reserve System (U.S.).

- Broner, F., A. Erce, A. Martin, and J. Ventura. 2014. “Sovereign debt markets in turbulent times: Creditor discrimination and crowding-out effects.” _Journal of Monetary Economics_ 61:114–142.

- Broner, F., A. Martin, and J. Ventura. 2010. “Sovereign Risk and Secondary Markets.” _American Economic Review_ 100:1523–1555.

- Brzoza-Brzezina, M., and J. Kotlowski. 2018. “The nonlinear nature of country risk and its implications for DSGE models.” _Macroeconomic Dynamics_ , pp. 1–28.

- Caner, M., and B.E. Hansen. 2004. “Instrumental Variable Estimation of a Threshold Model.” _Econometric Theory_ 20:813–843.

- Carvalho, D., and M. Fidora. 2015. “Capital inflows and euro area long-term interest rates.” _Journal of International Money and Finance_ 54:186–204.

21
- Christensen, J.H.E., and G.D. Rudebusch. 2012. “The Response of Interest Rates to US and UK Quantitative Easing.” _The Economic Journal_ 122:385–414.

- Colletaz, G., and C. Hurlin. 2006. “Threshold Effects of the Public Capital Productivity : An International Panel Smooth Transition Approach.” LEO Working Papers/DR LEO 1669, Orleans Economics Laboratory, University of Orleans, Orleans.

- Cunliffe, J. 2019. “Financial stability post Brexit: risks from global debt, a speech at CFO Agenda, London, May 7, 2019.” Speech, Bank of England.

- D’Amico, S., W. English, D. López-Salido, and E. Nelson. 2012. “The Federal Reserve’s Large-scale Asset Purchase Programmes: Rationale and Effects.” _The Economic Journal_ 122:415–446.

- De Castro, F., J.J. Pérez, and M. Rodríguez-Vives. 2013. “Fiscal Data Revisions in Europe.” _Journal of Money, Credit and Banking_ 45:1187–1209.

- Dell’Erba, S., R. Hausmann, and U. Panizza. 2013. “Debt levels, debt composition, and sovereign spreads in emerging and advanced economies.” _Oxford Review of Economic Policy_ 29:518–547.

- Driscoll, J.C., and A.C. Kraay. 1998. “Consistent Covariance Matrix Estimation with Spatially Dependent Panel Data.” _The Review of Economics and Statistics_ 80:549–560.

- Ebeke, C., and Y. Lu. 2015. “Emerging market local currency bond yields and foreign holdings -A fortune or misfortune?” _Journal of International Money and Finance_ 59:203–219.

- Engen, E.M., and R.G. Hubbard. 2005. “Federal Government Debt and Interest Rates.” _NBER Macroeconomics Annual 2004_ 19:83–138.

- Erce, A., and E. Mallucci. 2018. “Selective Sovereign Defaults.” International Finance Discussion Papers 1239, Board of Governors of the Federal Reserve System.

- Fernández, M., Andrésand Klein, A. Rebucci, M. Schindler, and M. Uribe. 2016. “Capital Control Measures: A New Dataset.” _IMF Economic Review_ 64:548–574.

- Fok, D., D. Van Dijk, and P.H. Franses. 2005. “A multi-level panel STAR model for US manufacturing sectors.” _Journal of Applied Econometrics_ 20:811–827.

22
Foley-Fisher, N., and B. Guimaraes. 2013. “U.S. Real Interest Rates and Default Risk in Emerging Economies.” _Journal of Money, Credit and Banking_ 45:967–975.

- Fouquau, J., C. Hurlin, and I. Rabaud. 2008. “The Feldstein-Horioka puzzle: A panel smooth transition regression approach.” _Economic Modelling_ 25:284–299.

- Gagnon, J., M. Raskin, J. Remache, and B. Sack. 2011. “The Financial Market Effects of the Federal Reserve’s Large-Scale Asset Purchases.” _International Journal of Central Banking_ 7:3–43.

- García-Cicco, J., R. Pancrazi, and M. Uribe. 2010. “Real Business Cycles in Emerging Countries?” _American Economic Review_ 100:2510–31.

- Gilchrist, S., V. Yue, and E. Zakrajsek. 2019. “US Monetary Policy and International Bond Markets.” _Journal of Money, Credit and Banking_ 51:127–161.

- González, A., and T. Teräsvirta. 2006. “Simulation-based Finite Sample Linearity Test against Smooth Transition Models.” _Oxford Bulletin of Economics and Statistics_ 68:797–812.

- González, A., T. Teräsvirta, D. van Dijk, and Y. Yang. 2017. “Panel Smooth Transition Regression Models.” SSE/EFI Working Paper Series in Economics and Finance No 604, Stockholm School of Economics, Stockholm.

- González-Rozada, M., and E. Levy Yeyati. 2008. “Global Factors and Emerging Market Spreads.” _The Economic Journal_ 118:917–1936.

- Granger, C.W.J. 2001. “Overview of nonlinear macroeconometric empirical models.” _Macroeconomic Dynamics_ 5:466–481.

- Greenspan, A. 2005. “Federal Reserve Board’s semiannual monetary policy report to the Congress: testimony before the Committee on Banking, Housing, and Urban Affairs, U.S. Senate, February 16, 2005.” Speech 59, Board of Governors of the Federal Reserve System (U.S.).

- Gros, D. 2013. “Foreign debt versus domestic debt in the euro area.” _Oxford Review of Economic Policy_ 29:502– 517.

23
- Gruber, J.W., and S.B. Kamin. 2012. “Fiscal Positions and Government Bond Yields in OECD Countries.” _Journal of Money, Credit and Banking_ 44:1563–1587.

- Hansen, B.E. 1996. “Inference When a Nuisance Parameter Is Not Identified Under the Null Hypothesis.” _Econometrica_ 64:413–430.

- —. 1999. “Threshold effects in non-dynamic panels: Estimation, testing and inference.” _Journal of Econometrics_ 93:345–368.

- Hoshi, T., and T. Ito. 2014. “Defying gravity: can Japanese sovereign debt continue to increase without a crisis?” _Economic Policy_ 29:5–44.

- Ichiue, H., and Y. Shimizu. 2015. “Determinants of long-term yields: A panel data analysis of major countries.” _Japan and the World Economy_ 34-35:44–55.

- Jaramillo, L., and A. Weber. 2013. “Bond yields in emerging economies: It matters what state you are in.” _Emerging Markets Review_ 17:169–185.

- Joyce, M.A., A. Lasaosa, I. Stevens, and M. Tong. 2011. “The Financial Market Impact of Quantitative Easing in the United Kingdom.” _International Journal of Central Banking_ 7:113–161.

- Joyce, M.A., Z. Liu, and I. Tonks. 2017. “Institutional Investors and the QE Portfolio Balance Channel.” _Journal of Money, Credit and Banking_ 49:1225–1246.

- Lagarias, J.C., J.A. Reeds, M.H. Wright, and P.E. Wright. 1998. “Convergence Properties of the Nelder–Mead Simplex Method in Low Dimensions.” _SIAM Journal on Optimization_ 9:112–147.

- Laubach, T. 2009. “New Evidence on the Interest Rate Effects of Budget Deficits and Debt.” _Journal of the European Economic Association_ 7:858–885.

- Longstaff, F., J. Pan, L. Pedersen, and K. Singleton. 2011. “How Sovereign Is Sovereign Credit Risk?” _American Economic Journal: Macroeconomics_ 3:75–103.

- Luukkonen, R., P. Saikkonen, and T. Terasvirta. 1988. “Testing Linearity Against Smooth Transition Autoregressive Models.” _Biometrika_ 75:491–499.

24
- Mauro, P., N. Sussman, and Y. Yafeh. 2002. “Emerging Market spreads:Then versus now.” _The Quarterly Journal of Economics_ 117:695–733.

- Miranda, M.J., and P.L. Fackler. 2002. _Applied computational economics and finance_ . MIT Press.

- Moore, J., S. Nam, M. Suh, and A. Tepper. 2013. “Estimating the Impacts of the U.S. LSAPs on Emerging Market Economies’ Local Currency Bond Markets.” Federal Reserve Bank of New York Staff Reports 595, Federal Reserve Bank of New York.

- Nakamura, K., and T. Yagi. 2017. “Fiscal Conditions and Long-term Interest Rates.” _Monetary and Economic Studies,Institute for Monetary and Economic Studies,Bank of Japan_ 35:59–88.

- Ongena, S., A. Popov, and N. Van Horen. 2019. “The Invisible Hand of the Government: Moral Suasion during the European Sovereign Debt Crisis.” _American Economic Journal: Macroeconomics_ 4:346–379.

- Ottonello, P., and D. Perez. 2019. “The Currency Composition of Sovereign Debt.” _American Economic Journal: Macroeconomics_ 11:174–208.

- Peiris, S.J. 2013. “Foreign Participation in Local Currency Bond Markets of Emerging Economies.” _Journal of International Commerce, Economics and Policy_ 04:1–15.

- Reinhart, C.M., K. Rogoff, and M. Savastano. 2003. “Debt Intolerance.” _Brookings Papers on Economic Activity_ 34:1–74.

- Reinhart, C.M., and C. Trebesch. 2015. “The pitfalls of external dependence: Greece, 1829-2015.” _Brookings Papers on Economic Activity_ 46:307–328.

- Sakuragawa, M., and Y. Sakuragawa. 2016. “Absence of safe assets and fiscal crisis.” _Journal of the Japanese and International Economies_ 40:59–76.

- Schmitt-Grohe, S., and M. Uribe. 2003. “Closing small open economy models.” _Journal of International Economies_ 61:163–185.

- Shiller, R.J., J.Y. Campbell, and K.L. Schoenholtz. 1983. “Forward Rates and Future Policy: Interpreting the Term Structure of Interest Rates.” _Brookings Papers on Economic Activity_ 14:173–224.

25
Stukel, T.A. 1988. “Generalized Logistic Models.” _Journal of the American Statistical Association_ 83:426–431.

- Sturzenegger, F., and J. Zettelmeyer. 2008. “Haircuts:Estimating investor losses in sovereign debt restructurings,1998-2005.” _Journal of International Money and Finance_ 27:780–805.

- Tenreyro, S. 2019. “Monetary policy and open questions in international macroeconomics, a speech at at the John Flemming Memorial Lecture, London, October 28, 2019.” Speech, Bank of England.

- Terasvirta, T. 1994. “Specification, Estimation, and Evaluation of Smooth Transition Autoregressive Models.” _Journal of the American Statistical Association_ 89:208–288.

- Traum, N., and S.C.S. Yang. 2015. “When Does Government Debt Crowd Out Investment?” _Journal of Applied Econometrics_ 30:24–45.

- Warnock, F.E., and V.C. Warnock. 2009. “International Capital Flows and U.S. Interest Rates.” _Journal of International Money and Finance_ 28:903–919.

- Wright, J.H. 2011. “Term Premia and Inflation Uncertainty: Empirical Evidence from an International Panel Dataset.” _American Economic Review_ 101:1514–1534.

- Wright, M. 2006. “Private capital flows, capital controls, and default risk.” _Journal of International Economics_ 69:120–149.

- Yu, P. 2013. “Inconsistency of 2SLS estimators in threshold regression with endogeneity.” _Economics Letters_ 120:532–536.

26
Figure 1: 5-to-10 year forward interest rates of government debt securities denominated in local currency <!-- Start of picture text --> Advanced economies excl. the euro area Emerging markets<br>10 10<br>9 9<br>8 8<br>7 7<br>6 6<br>5 5<br>4 4<br>3 3<br>2 2<br>1 1<br>0 0<br>06 07 08 09 10 11 12 13 14 15 16 17 18 06 07 08 09 10 11 12 13 14 15 16 17 18<br>(%) (%)<br><!-- End of picture text --> Figure 2: Two-year-ahead expected public debt to GDP ratio <!-- Start of picture text --> Advanced economies excl. the euro area Emerging markets<br>100 100<br>90 90<br>80 80<br>70 70<br>60 60<br>50 50<br>40 40<br>30 30<br>20 20<br>10 10<br>0 0<br>06 07 08 09 10 11 12 13 14 15 16 17 18 06 07 08 09 10 11 12 13 14 15 16 17 18<br>Figure 3: The share of government debt securities denominated in local currency<br>Advanced economies excl. the euro area Emerging markets<br>100 100<br>90 90<br>80 80<br>70 70<br>Foreign private<br>60 60 Foreign official<br>Foreign private<br>50 Foreign official 50 Domestic private<br>Domestic official<br>40 Domestic private 40<br>Domestic official<br>30 30<br>20 20<br>10 10<br>0 0<br>06 07 08 09 10 11 12 13 14 15 16 17 18 06 07 08 09 10 11 12 13 14 15 16 17 18<br>(%) (%)<br>(%) (%)<br><!-- End of picture text --> Notes: Advanced economies excluding the euro area(Australia, Canada, the Czech Republic, Denmark, Japan, Korea, Norway, Sweden, Switzerland , the United Kingdom and United States) and emerging markets(Bulgaria, Columbia, China, Hungary, India, Indonesia, Malaysia, Mexico, Peru, the Philippines, Poland, Thailand, Turkey and South Africa). Lines and shadow areas show the median and interquartile range within each country group, respectively. Calculations of share of governmet debt based on data from Arslanalp and Tsuda (2014a), Arslanalp and Tsuda (2014b) and BIS Debt Securities Statistics (See 2.4 Data for details).

27
Figure 4: Examples of interaction term and standard logistic model <!-- Start of picture text --> Interaction term Standard logistic model<br>1 1<br>1 =10<br>0.8 0.8 1 =5<br>1 =1<br>0.6 0.6<br>0.4 0.4<br>0.2 0.2<br>0 0<br>0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1<br>Threshold variable Threshold variable<br>Figure 5: Examples of general logistic model (GLM)<br> 0 and 0 and 0<br>1 2 1 2<br>1 1<br>1 =10 and 2 =10 1 =10 and 2 =-10<br>0.8 1 =5 and 2 =5 0.8 1 =5 and 2 =-5<br>1 =1 and 2 =1 1 =1 and 2 =-1<br>0.6 1 =0 and 2 =0 0.6 1 =0 and 2 =0<br>0.4 0.4<br>0.2 0.2<br>0 0<br>0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1<br>Threshold variable Threshold variable<br> 0 and 0 0 and 0<br>1 2 1 2<br>1 1<br>1 =-10 and 2 =10 1 =-10 and 2 =-10<br>1 =-5 and 2 =5 1 =-5 and 2 =-5<br>0.8 0.8<br>1 =-1 and 2 =1 1 =-1 and 2 =-1<br>1 =0 and 2 =0 1 =0 and 2 =0<br>0.6 0.6<br>0.4 0.4<br>0.2 0.2<br>0 0<br>0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1<br>Threshold variable Threshold variable<br><!-- End of picture text --> Notes: The location parameter _c=0.5._ 28
<u>Table 2: Baseline results</u>

|Model|IT|PSTR|GPSTR|
|---|---|---|---|
|_퐿푀퐹_nonlinearity tests<br>p-value|10.5<br>0.00***|10.5<br>0.00***|10.5<br>0.00***|
|Location parameter(_푐_)||0.288|0.092|
|Slope parameter1(_훾_1)||15.3|-64.0|
|Slopeparameter2(_훾_2)|||3.0|
|E_푡퐷푒푏푡푖,푡_+2|-0.008|0.000|-0.196***|
||(0.01)|(0.01)|(0.01)|
|E_푡퐷푒푏푡푖,푡_+2· _푓푝푡_−1|0.120***<br>(0.04)|||
|E_푡퐷푒푏푡푖,푡_+2·_푔_(·)||0.051*|0.402***|
|||(0.03)|(0.03)|
|E_푡푦푖,푡_+2|-0.008|0.000|0.042|
||(0.13)|(0.11)|(0.13)|
|_푑표푖,푡_−1|-0.099***|-0.085***|-0.089***|
||(0.01)|(0.01)|(0.01)|
|_푓표푖,푡_−1|-0.146***|-0.148***|-0.153***|
||(0.02)|(0.02)|(0.02)|
|_푓푝푖,푡_−1|-0.104***|-0.105***|-0.104***|
||(0.03)|(0.02)|(0.01)|
|E_푡퐸푥푐h푎푛푔푒푟푎푡푒푖,푡_+2|0.042***|0.043***|0.041***|
||(0.01)|(0.01)|(0.01)|
|AIC Criterion|-8.563|-8.562|-8.573|
|No. of observation|625|625|625|
|No. of countries|25|25|25|
|Sampleperiods|06:2-18:2|06:2-18:2|06:2-18:2|

Notes: IT=Interaction term model,PSTR=Panel Smooth Transition Regression and GPSTR=General Panel Smooth Transition Regression. E _푡 퐷푒푏푡푖,푡_ +2 is two-year-ahead expected public debt to GDP ratio, _푔_ (·) is transition function, E _푡 푦푖,푡_ +2 is two-year-ahead expected growth rate, _푑표푖,푡_ −1 is the lagged domestic official sector holdings ratio, _푓표푖,푡_ −1 the lagged foreign official sector holdings ratio, _푓푝푖,푡_ −1 is the lagged foreign private sector holdings ratio and E _푡 퐸푥푐h푎푛푔푒푟푎푡푒푖,푡_ +2 is the expected exchange rate depreciation in two-year horizon. The standard errors proposed by Driscoll and Kraay (1998) are reported in parentheses.<sup>∗∗∗</sup> p<0.01,<sup>∗</sup> p<0.05, ∗ p<0.1.

29
Figure 6: Marginal impact of the expected public debt-to-GDP ratio on the interest rate (Baseline) <!-- Start of picture text --> IT PSTR GPSTR<br>12 12 12<br>Advanced economies Advanced economies Advanced economies<br>Emerging markets Emerging markets Emerging markets<br>10 10 10<br>8 8 8<br>6 6 6<br>4 4 4<br>2 2 2<br>0 0 0<br>-2 -2 -2<br>-4 -4 -4<br>0 10 20 30 40 50 0 10 20 30 40 50 0 10 20 30 40 50<br>Share of the foreign private investors(%) Share of the foreign private investors(%) Share of the foreign private investors(%)<br>basis points basis points basis points<br><!-- End of picture text --> Notes: Shadow area refers to 90 percent confidence interval computed with Driscoll and Kraay (1998) standard errors. Circles and triangles correspond to observation for private foreign share. Broken lines represent location parameters.

Figure 7: Marginal impact of the share of foreign private investors on the interest rate (Baseline) <!-- Start of picture text --> IT PSTR GPSTR<br>200 10 10 200 200<br>7.5 7.5<br>150 5 5 150 150<br>2.5 2.5<br>0 0<br>100 100 100<br>-2.5 -2.5<br>-5 -5<br>50 50 50<br>-7.5 -7.5<br>-10 -10<br>0 0 0<br>0 10 20 30 40 50 0 10 20 30 40 50 0 10 20 30 40 50<br>Share of the foreign private investors(%) Share of the foreign private investors(%) Share of the foreign private investors(%)<br>-10 -10<br>-7.5<br>-7.5 -5<br>-2.5<br>-10<br>-7.5<br>-10<br>-5<br>0 2.5<br>5<br>-2.5<br>-5<br>7.5<br>10<br>2.5<br>5<br>10<br>7.5<br>7.5<br>-2.5<br>10<br>5<br>0<br>2.5 0<br>-7.5<br>-2.5<br>2.50<br>-5<br>-7.5<br>5<br>-7.5<br>7.5<br>-5<br>10<br>-2.5<br>10<br>7.55<br>0<br>2.5<br>-7.5<br>-2.5<br>0<br>-5-2.5<br>Expected public debt to GDP ratio(%) Expected public debt to GDP ratio(%) Expected public debt to GDP ratio(%) 02.55<br><!-- End of picture text --> Notes: Basis points.
Figure 8: Range of the time-varying impact of the expected public debt-to-GDP ratio on the interest rate during 2006H2-2018H2 (Baseline) <!-- Start of picture text --> IT<br>12<br>10<br>8<br>6<br>4<br>2<br>0<br>-2<br>AUSCAN CZE DEN JPN KORNORSWECHEGBRUSABGRCHNCOLHUNPOL TUR IND IDN MYSMEXPER PHL ZAF THL<br>PSTR<br>12<br>10<br>8<br>6<br>4<br>2<br>0<br>-2<br>AUSCAN CZE DEN JPN KORNORSWECHEGBRUSABGRCHNCOLHUNPOL TUR IND IDN MYSMEXPER PHL ZAF THL<br>GPSTR<br>12<br>10<br>8<br>6<br>4<br>2<br>0<br>-2<br>AUSCAN CZE DEN JPN KORNORSWECHEGBRUSABGRCHNCOLHUNPOL TUR IND IDN MYSMEXPER PHL ZAF THL<br>basis points<br>basis points<br>basis points<br><!-- End of picture text --> Notes: The range is the difference between the maximum and minimum point estimate during 2006H2-2018H2. AUS:Australia, CAN:Canada, CZE:the Czech Republic, DEN:Denmark, JPN:Japan, KOR:Korea, NOR:Norway, SWE:Sweden, CHE:Switzerland, GBR:the United Kingdom, USA:the United States, BGR:Bulgaria, CHN:China,COL:Columbia, HUN:Hungary, POL:Poland, TUR:Turkey, IND:India,IDN:Indonesia, MYS: Malaysia, MEX:Mexico, PER:Peru, PHL:the Philippines, ZAF:South Africa, THL:Thailand 31
<u>Table 3: Robustness Checks 1 and 2</u>

||———|(R1)|———|———|(R2)|———|
|---|---|---|---|---|---|---|
||IT|PSTR|GPSTR|IT|PSTR|GPSTR|
|_퐿푀퐹_nonlinearity test|9.4|9.4|9.4|11.6|11.6|11.6|
|p-value|0.00***|0.00***|0.00***|0.00***|0.00***|0.00***|
|Location parameter(_푐_)||0.295|0.069||0.293|0.092|
|Slope parameter1(_훾_1)||14.3|-56.6||14.2|-51.1|
|Slopeparameter2(_훾_2)|||0.03|||3.1|
|E_푡퐷푒푏푡푖,푡_+2|-0.008|-0.001|-0.282|-0.007|0.000|-0.220***|
||(0.01)|(0.01)|(0.01)|(0.01)|(0.01)|(0.01)|
|E_푡퐷푒푏푡푖,푡_+2· _푓푝푡_−1|0.110***<br>(0.03)|||0.127***<br>(0.04)|||
|E_푡퐷푒푏푡푖,푡_+2·_푔_(·)||0.049**|0.557***||0.056|0.450***|
|||(0.02)|(0.03)||(0.04)|(0.03)|
|E_푡푦푖,푡_+2|-0.117|-0.111|-0.083|0.011|0.020|0.063|
||(0.15)|(0.15)|(0.14)|(0.13)|(0.13)|(0.13)|
|_푑표푖,푡_−1|-0.067***|-0.054***|-0.057***|-0.111***|-0.097***|-0.098***|
||(0.02)|(0.01)|(0.02)|(0.01)|(0.01)|(0.01)|
|_푓표푖,푡_−1|-0.098***|-0.100***|-0.093***|-0.153***|-0.154***|-0.159***|
||(0.03)|(0.02)|(0.03)|(0.02)|(0.02)|(0.02)|
|_푓푝푖,푡_−1|-0.080***|-0.081***|-0.082***|-0.115***|-0.115***|-0.118***|
||(0.02)|(0.02)|(0.02)|(0.02)|(0.03)|(0.02)|
|E_푡퐸푅푖,푡_+2|0.039***<br>(0.01)|0.039***<br>(0.01)|0.036***<br>(0.01)||||
|_푈푆푡푝푡_−1|0.542***<br>(0.14)|0.543***<br>(0.11)|0.540***<br>(0.13)||||
|AIC Criterion|-8.636|-8.636|-8.640|-8.547|-8.545|-8.559|
|No. of observation|600|600|600|625|625|625|
|No. of countries|24|24|24|25|25|25|
|Sampleperiods|06:2-18:2|06:2-18:2|06:2-18:2|06:2-18:2|06:2-18:2|06:2-18:2|

Notes: IT=Interaction term model,PSTR=Panel Smooth Transition Regression and GPSTR=General Panel Smooth Transition Regression. The sample of (R1) excludes the U.S. E _푡 퐷푒푏푡푖,푡_ +2 is two-year-ahead expected public debt to GDP ratio, _푔_ (·) is transition function, E _푡 푦푖,푡_ +2 is two-year-ahead expected growth rate, _푑표푖,푡_ −1 is the lagged domestic official sector holdings ratio, _푓표푖,푡_ −1 the lagged foreign official sector holdings ratio, _푓푝푖,푡_ −1 is the lagged foreign private sector holdings ratio, E _푡 퐸푥푐h푎푛푔푒푟푎푡푒푖,푡_ +2 is the expected exchange rate depreciation in two- year horizon and _푈푆푡푝푡_ −1 is the lagged U.S. 10-year term premia. The standard errors proposed by Driscoll and Kraay (1998) are reported in parentheses.<sup>∗∗∗</sup> p<0.01,<sup>∗</sup> p<0.05,<sup>∗</sup> p<0.1 32
Table 4: <u>(Continued) Robustness Checks 3 and 4</u>

||———|(R3)|———|———|(R4)|———|
|---|---|---|---|---|---|---|
||IT|PSTR|GPSTR|IT|PSTR|GPSTR|
|_퐿푀퐹_nonlinearity test<br>p-value|7.0<br>0.01***|7.0<br>0.01***|7.0<br>0.01***|10.0<br>0.00***|10.0<br>0.00***|10.0<br>0.00***|
|Location parameter(_푐_)||0.335|0.092||0.264|0.103|
|Slope parameter1(_훾_1)||15.0|-35.8||16.2|-74.8|
|Slopeparameter2(_훾_2)|||4.0|||0.3|
|E_푡퐷푒푏푡푖,푡_+2|-0.006|0.002|-0.162***|-0.011|-0.004|-0.321***|
||(0.01)|(0.01)|(0.03)|(0.01)|(0.01)|(0.05)|
|E_푡퐷푒푏푡푖,푡_+2· _푓푝푡_−1|0.099***<br>(0.03)|||0.119***<br>(0.03)|||
|E_푡퐷푒푏푡푖,푡_+2·_푔_(·)||0.050*|0.331***||0.048*|0.646***|
|||(0.03)|(0.05)||(0.03)|(0.09)|
|E_푡푦푖,푡_+2|-0.015|-0.002|0.030|-0.041|-0.038|0.037|
||(0.14)|(0.11)|(0.14)|(0.12)|(0.10)|(0.12)|
|_푑표푖,푡_−1|-0.099***<br>(0.01)|-0.087***<br>(0.01)|-0.090***<br>(0.01)|-0.094***<br>(0.01)|-0.081***<br>(0.01)|-0.089***<br>(0.01)|
|_푓표푖,푡_−1<br>_푓푝푖,푡_−1|-0.142***<br>(0.02)<br>-0.096***<br>(0.02)|-0.144***<br>(0.01)<br>-0.096***<br>(0.02)|-0.149***<br>(0.02)<br>-0.104***<br>(0.01)|-0.170***<br>(0.02)<br>-0.094***<br>(0.02)|-0.170***<br>(0.02)<br>-0.097***<br>(0.02)|-0.179***<br>(0.02)<br>-0.090***<br>(0.01)|
|E_푡퐸푅푖,푡_+2|0.029***<br>(0.01)|0.028***<br>(0.01)|0.027***<br>(0.01)|0.038***<br>(0.01)|0.039***<br>(0.01)|0.039***<br>(0.01)|
|_푁퐹퐴푖,푡_−1|-0.014***<br>(0.00)|-0.015***<br>(0.00)|-0.014***<br>(0.00)||||
|_퐶퐶푖,푡_−1||||-3.900***<br>(1.10)|-3.892***<br>(1.00)|-4.141***<br>(1.09)|
|AIC Criterion|-8.547|-8.581|-8.640|-8.612|-8.611|-8.626|
|No. of observation|625|625|625|625|625|625|
|No. of countries|25|25|25|25|25|25|
|Sampleperiods|06:2-18:2|06:2-18:2|06:2-18:2|06:2-18:2|06:2-18:2|06:2-18:2|

Notes: IT=Interaction term model,PSTR=Panel Smooth Transition Regression and GPSTR=General Panel Smooth Transition Regression. E _푡 퐷푒푏푡푖,푡_ +2 is two-year-ahead expected public debt to GDP ratio, _푔_ (·) is transition function, E _푡 푦푖,푡_ +2 is two-year-ahead expected growth rate, _푑표푖,푡_ −1 is the lagged domestic official sector holdings ratio, _푓표푖,푡_ −1 the lagged foreign official sector holdings ratio, _푓푝푖,푡_ −1 is the lagged foreign private sector holdings ratio, E _푡 퐸푥푐h푎푛푔푒푟푎푡푒푖,푡_ +2 is the expected exchange rate depreciation in two-year horizon, _푁퐹퐴푖,푡_ −1 is the lagged net foreign assets to GDP ratio and _퐶퐶푖,푡_ −1 is the lagged capital control dummy. The standard errors proposed by Driscoll and Kraay (1998) are reported in parentheses.<sup>∗∗∗</sup> p<0.01,<sup>∗</sup> p<0.05,<sup>∗</sup> p<0.1 33
Table 5: <u>(Continued) Robustness Checks 5 and 6</u>

||———|(R5)|———|———|(R6)|———|
|---|---|---|---|---|---|---|
||IT|PSTR|GPSTR|IT|PSTR|GPSTR|
|_퐿푀퐹_nonlinearity test<br>p-value|9.5<br>0.00***|9.5<br>0.00***|9.5<br>0.00***|20.0<br>0.00***|20.0<br>0.00***|20.0<br>0.00***|
|Location parameter(_푐_)||0.306|0.092||0.292|0.093|
|Slope parameter1(_훾_1)||14.0|-47.5||12.3|0.0|
|Slopeparameter2(_훾_2)|||5.8|||5.0|
|E_푡퐷푒푏푡푖,푡_+2|-0.004|0.003|-0.096***|-0.019**|-0.011|-0.186***|
||(0.01)|(0.01)|(0.02)|(0.01)|(0.01)|(0.01)|
|E_푡퐷푒푏푡푖,푡_+2· _푓푝푡_−1|0.101***<br>(0.04)|||0.160***<br>(0.03)|||
|E_푡퐷푒푏푡푖,푡_+2·_푔_(·)||0.044|0.206***||0.076***|0.363***|
|||(0.03)|(0.03)||(0.03)|(0.03)|
|_푆푇푅푖,푡_|0.388***<br>(0.05)|0.385***<br>(0.04)|0.381***<br>(0.05)||||
|E_푡휋푖,푡_+2||||0.358***<br>(0.13)|0.351***<br>(0.12)|0.355***<br>(0.12)|
|E_푡푦푖,푡_+2|-0.060|-0.051|-0.022|0.087|0.097|0.127|
|_푑표푖,푡_−1|(0.12)<br>-0.081***|(0.11)<br>-0.070***|(0.10)<br>-0.072***|(0.12)<br>-0.069***|(0.12)<br>-0.053***|(0.12)<br>-0.053***|
||(0.01)|(0.01)|(0.01)|(0.12)|(0.01)|(0.01)|
|_푓표푖,푡_−1|-0.099***|-0.101***|-0.105***|-0.139***|-0.140***|-0.145***|
||(0.02)|(0.02)|(0.01)|(0.02)|(0.02)|(0.02)|
|_푓푝푖,푡_−1|-0.088***|-0.086***|-0.087***|-0.115***|-0.116***|-0.116***|
||(0.03)|(0.02)|(0.01)|(0.02)|(0.02)|(0.02)|
|E_푡퐸푅푖,푡_+2|0.002|0.003|0.001|0.045***|0.046***|0.043***|
||(0.01)|(0.01)|(0.01)|(0.01)|(0.01)|(0.01)|
|AIC Criterion|-8.800|-8.796|-8.805|-8.649|-8.651|-8.657|
|No. of observation|625|625|625|625|625|625|
|No. of countries|25|25|25|25|25|25|
|Sampleperiods|06:2-18:2|06:2-18:2|06:2-18:2|06:2-18:2|06:2-18:2|06:2-18:2|

Notes: IT=Interaction term model,PSTR=Panel Smooth Transition Regression and GPSTR=General Panel Smooth Transition Regression. E _푡 퐷푒푏푡푖,푡_ +2 is two-year-ahead expected public debt to GDP ratio, _푔_ (·) is transition function, E _푡 휋푖,푡_ +2 is two-year-ahead expected inflation, E _푡 푦푖,푡_ +2 is two-year-ahead expected growth rate, _푑표푖,푡_ −1 is the lagged domestic official sector holdings ratio, _푓표푖,푡_ −1 the lagged foreign official sector holdings ratio, _푓푝푖,푡_ −1 is the lagged foreign private sector holdings ratio, E _푡 퐸푥푐h푎푛푔푒푟푎푡푒푖,푡_ +2 is the expected exchange rate depreciation in two-year horizon, and _푆푇푅푖,푡_ is one-year zero coupon rate. The standard errors proposed by Driscoll and Kraay (1998) are reported in parentheses.<sup>∗∗∗</sup> p<0.01,<sup>∗</sup> p<0.05,<sup>∗</sup> p<0.1 34
Figure 9: Marginal impact of the expected public debt-to-GDP ratio on the interest rate (Baseline and robustness check) <!-- Start of picture text --> IT PSTR GPSTR<br>10 10 10<br>Baseline Baseline Baseline<br>Robustness1 Robustness1 Robustness1<br>8 Robustness2 8 Robustness2 8 Robustness2<br>Robustness3 Robustness3 Robustness3<br>6 Robustness4 6 Robustness4 6 Robustness4<br>Robustness5 Robustness5 Robustness5<br>Robustness6 Robustness6 Robustness6<br>4 4 4<br>2 2 2<br>0 0 0<br>-2 -2 -2<br>0 10 20 30 40 50 0 10 20 30 40 50 0 10 20 30 40 50<br>Share of the foreign private investors(%) Share of the foreign private investors(%) Share of the foreign private investors(%)<br>basis points basis points basis points<br><!-- End of picture text --> Notes: Basis points. The baseline and robustness1-5 employ real forward interest rates as a dependent variable. The baseline equation includes the two-year-ahead expected public debt to GDP ratio, the two-year-ahead expected growth rate, the lagged domestic official sector holdings ratio, the lagged foreign official sector holdings ratio, the lagged foreign private sector holdings ratio and the expected exchange rate depreciation in two-year horizon. Robustness1: Controlling for US monetary condition. Robustness2: Excluding the expected exchange rate depreciation. Robustness3: Controlling for the net foreign assets position. Robustness4: Controlling for the capital control. Robustness5: Controlling for the short-term interest rate. Robustness6: Dependent variable: nominal interest rates.
Table 6: Cross validations: comparison of out-of-sample forecast errors

||(1)IT vs. GPSTR|(2)PSTR vs. GPSTR|
|---|---|---|
||_푀푆퐸퐺푃푆푇푅_−_푀푆퐸퐼푇_<br>_푀푆퐸퐼푇_<br>×100|_푀푆퐸퐺푃푆푇푅_−_푀푆퐸푃푆푇푅_<br>_푀푆퐸푃푆푇푅_<br>×100|
|Baseline|-7.2%|-4.0%|
|Robustness check1<br>(Controlling_푈푆푡푒푟푚푝푟푒푚푖푢푚_)|-5.2%|-4.0%|
|Robustness check2|-6.0%|-3.0%|
|(excl. _푒푥푐h푎푛푔푒푟푎푡푒푑푒푝푟푒푐푖푎푡푖표푛_)|||
|Robustness check3<br>(Controlling_푛푒푡푓표푟푒푖푔푛푎푠푠푒푡푠_)|-4.4%|-2.6%|
|Robustness check4<br>(Controlling_푐푎푝푖푡푎푙푐표푛푡푟표푙_)|-0.8%|-3.7%|
|Robustness check5|-8.7%|-4.8%|
|(Controlling_푠h표푟푡_−_푡푒푟푚푖푛푡푒푟푒푠푡푟푎푡푒_)|||
|Robustness check6|-8.2%|-0.6%|
|(Dependent variable: _푛표푚푖푛푎푙푖푛푡푒푟푒푠푡푟푎푡푒_)|||

2 Note: _푀푆퐸_ indicates mean squared error. _푀푆퐸_ = _푁푇_ <u>1</u> � _푖푁_ =1 � _푇푡_ =1 <u>��</u> _푦푖,푡_ − Ψ<sup>�</sup> − _푖_ ( _푥푖,푡_<sup>∗)</sup> <u>�</u> where Ψ<sup>�</sup> − _푖_ (·) is computed by leaving out all observations of the _푖_ th cross-section.
Table 7: Comparison with other studies

|**(1) Marginal impact of**<br>**expected public debt on**|basis point<br>per 1 percent|Forecast data|Countries/Group||
|---|---|---|---|---|
|**government bondyields**|||||
|This study|0.9-2.0(the share of foreign investors is 20 percent)<br>2.8-3.8(the share of foreign investors is 30 percent)<br>4.2-6.2(the share of foreign investors is 40 percent)|IMF, OECD, EC, EIU|11 AEs and 14 EMs||
|Engen and Hubbard(2005)|2.8|CBO|U.S||
|Laubach(2009)|3 to 4.4|CBO|U.S||
|Traum and Yang(2015)|3|DEGE implied data|U.S||
|Arslanalp and Poghosyan(2016)|2.7 to 2.8|IMF|22 AEs||
|Gruber and Kamin(2012)|0.4 to 1.3|OECD|19 OECD countries||
|Ichiue and Shimizu(2015)|0.7 to 0.9|OECD|10 OECD countries||
|Jaramillo and Weber (2013)|4 to 6|EIU|26 EMs||
|**(2) Marginal impact of**|basis point|Forecast data|Countries|Investor type|
|**the share of foreign investors**|per 1 percent||||
|**ongovernment bondyields**|||||
|This study|-11.8 to -8.2|IMF, OECD, EC, EIU|11 AEs and 14 EMs|Foreign Private|
|This study|-17.9 to -14.5|IMF, OECD, EC, EIU|11 AEs and 14 EMs|Foreign Offcial|
|Arslanalp and Poghosyan(2016)|-11.5 to -6.9|IMF|22 AEs|Foreign Private|
|Arslanalp and Poghosyan(2016)|-6.9 to -5.5|IMF|22 AEs|Foreign Offcial|
|Ebeke and Lu (2015)|-10.6 to -6.5|Actual data|13 EMs|Foreign|
|**(3) Estimated tipping points**|Threshold value of debt|Forecast data|Countries|Investor type|
|**for the impact of the increase in**|to GDP ratio||||
|**foreign investors**|||||
|This study (Baseline)|59 percent (Expected gross public debt)<br>when the share of foreign investors is 30 percent<br>91 percent (Expected gross public debt)|IMF, OECD, EC, EIU<br>IMF, OECD, EC, EIU|11 AEs and 14 EMs<br>11 AEs and 14 EMs|Foreign Private<br>Foreign Private|
||when the share of foreign investors is 15 percent||||
|Ebeke and Lu(2015)|90 percent (Lagged external debt)|Actual data|13 EMs|Foreign|
|Ebeke and Lu (2015)|21.5percent(Lagged short-term debt)|Actual data|13 EMs|Foreign|
|Notes: AEs=advanced economies<br>and EMs=emerging markets.|||||