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Archives of Business Research – Vol. 10, No. 8

Publication Date: August 25, 2022

DOI:10.14738/abr.108.12889. Fujita, Y. (2022). Does Depreciation of Currency Always Invite Debt Trap? Archives of Business Research, 10(8). 109-113.

Services for Science and Education – United Kingdom

Does Depreciation of Currency Always Invite Debt Trap?

Yasunori Fujita

Ph.D, Professor of Economics, Keio University, Japan

ABSTRACT

In the present paper, motivated by the debate over the causes of the debt trap Sri

Lanka fell into and by extending Padoan et al (2012) that focused on a country with

domestic debt only, we construct a theoretical model that incorporates the foreign

debt to investigate the condition where the debt trap is avoided. The results we

obtain are as follows.

(1) Country falls into the debt trap no matter what the exchange rate is if the growth

rate of the GDP without foreign debt is low, the government expenditure is not

effective, increase in the foreign debt is smaller the foreign interest rate is high.

(2) Depreciation of the currency is necessary for the country to avoid the debt trap

if the growth rate of the GDP without foreign debt is high, the government

expenditure is effective, increase in the foreign debt is large or the foreign interest

rate is low.

(3) The more the foreign debt influences the GDP, the weaker its currency should

be in order to avoid the debt trap.

Key words: debt trap, exchange rate, depreciation of currency, foreign debt, foreign

interest rate

INTRODUCTION

Much attention has been paid to the cause of debt trap since Sri Lanka plunged into its worst

financial crisis owing to the debt trap this year. Some point out China’s strategic diplomacy as

a root of Sri Lanka’s financial crisis, while others regard long-term economic mismanagement

as its prime cause. In fact, according to Asia Financial (2022), Dr. Gareth Price, a senior research

fellow at Chatham House claims that while it is sensible to borrow money for infrastructural

projects that are going to be economically viable, Sri Lanka borrowed from China for

infrastructure projects that were white elephants.

In the present paper, by extending the seminal paper, Padoan et al (2012), which focused on a

country with domestic debt only, and by following the spirit of also the distinguished work,

Reinhart and Rogoff (2009), which took notice of foreign debt and carried out empirical

research, we construct a theoretical model that incorporates the foreign debt to investigate the

condition where the debt trap is avoided.

We also note the argument over whether the foreign debt has positive effect on its GDP or not

(Geiger (1990), Mohamed (2005), Hameed et al. (2008), Butts (2009), Shabbir (2013) and so

on) and obtain the following results about the relationships between exchange rate and the

debt trap.

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Archives of Business Research (ABR) Vol. 10, Issue 8, August-2022

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(1) Country falls into the debt trap no matter what the exchange rate is if the growth rate of the

GDP without foreign debt is low, the government expenditure is not effective, increase in the

foreign debt is small or the foreign interest rate is high.

(2) Depreciation of the currency is necessary for the country to avoid the debt trap if the growth

rate of the GDP without foreign debt is high, the government expenditure is effective, increase

in the foreign debt is large or the foreign interest rate is low.

(3) The more the foreign debt influences the GDP, the weaker its currency should be in order

to avoid the debt trap.

Structure of this paper is as follows. After constructing a basic model in section 2, section 3

reveals the no-debt-trap condition i.e., the condition where the country is able to avoid the debt

trap. Concluding remarks are made in section 4.

BASIC MODEL

Let us consider a country whose GDP is Y(t) and that incurs F(t) amounts of foreign debt in

period t. We assume that the foreign debt F(t) is foreign-currency-denominated and its

domestic-currency-dominated value is eF(t), where e is a domestic-currency-dominated

exchange rate, which is assumed to be constant over time for the simplicity of analysis. By

assuming away the domestic debt, also in order to simplify the analysis, we can express no- debt-trap condition, i.e. the condition where the country is able to avoid the debt trap, as

!̇

($)

!($) ≤

&̇

($)

&($) (, where �̇ ≡

'!($)

'$

and �̇ ≡

'&($)

'$ ), which reduces to

!̇

($)

!($) = &̇

($)

&($)

. (1)

by assuming that the country is eager to borrow as much as it can from foreign countries.

Throughout the paper, we define the equation (1) as the no-debt-trap condition.

We also assume that the ratio of increase in the foreign debt to foreign-currency-denominated

GDP, &($)

( , is constant at q in every period, as in Padoan et al (2012) that focused on a country

that incurs domestic debt only.

Thus, by letting R(t) denote the foreign interest rate in period t, we have the dynamics of F(t)

as �̇

(�) = �(�)�(�) + �

&($)

( , which can be rewritten as a dynamics of !̇

($)

!($) by dividing it by F(t) ;

!̇

($)

!($) = �(�) + )

!"($)

&($)

. (2)

With respect to the foreign interest rate, R(t), we formulate it, also as in Padoan et al (2012)

and letting φ and θ be positive constants, as a function of /

!̇

($)

!($) − &̇

($)

&($)

1, difference of the growth

rates of the foreign debt and the GDP of the country;

�(�) = � + � /

!̇

($)

!($) − &̇

($)

&($)

1. (3)

As for the dynamics of the GDP of the country, on the other hand, by paying attention to the

argument over whether the foreign debt has positive effect on its GDP or not (Geiger (1990),

Hameed et al. (2008), Mohamed (2005), Shabbir (2013) and so on) and by extending Padoan et

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Fujita, Y. (2022). Does Depreciation of Currency Always Invite Debt Trap? Archives of Business Research, 10(8). 109-113.

URL: http://dx.doi.org/10.14738/abr.108.12889

al (2012), we formulate it as �̇

(�) = ��(�) − ��(�) + ���(�), where a, β and g be positive

parameters, meaning that the GDP of the country increases more if the GDP is more abundant

(the first term aY) or the government spends larger amount of domestic-currency-denominated

money financed by the foreign debt(the third term geF), while the GDP of the country decreases

more if the burden of the foreign-currency-dominated foreign debt is higher (the second term

- � !

&). In the following, by dividing the equation �̇

(�) = ��(�) − ��(�) + ���(�) by Y(t), we

rewrite it as dynamics of &̇

($)

&($)

;

&̇

($)

&($) = � − � !($)

&($) + ��. (4)

NO-DEBT-TRAP CONDITION

Based on the above analysis, this section derives the no-debt-trap condition, that is, the

condition where the debt trap is avoided.

Firstly, by solving (2) and (3) with respect to !̇

($)

!($) and R(t), and making use of (4), we obtain

!̇

($)

!($) = *

*+, {� − �(� − � !($)

&($) + ��) + )

!"($)

&($)

}; (5)

�(�) = *

*+, {� − �(� − � !($)

&($) + ��) + � )

!"($)

&($)

}. (6)

Then, by substituting (4) and (5)into (1), the no-debt-trap condition is expressed as a quadratic

equation of !($)

&($) as

−�(

!($)

&($)

)- + (� + �� − �) !($)

&($) − )

( = 0. (7)

Since coefficient of (

!($)

&($)

)-is negative, we can see that the following two conditions are necessary

for !($)

&($) to have positive solutions;

(i) � + �� − � > 0, (8)

which means that axis of symmetry is positive when drawing the graph of the right hand side

of (7), � /

!($)

&($)

1 ≡ −�(

!($)

&($)

)- + (� + �� − �) !($)

&($) − )

( on

!($)

&($) − � space.

(ii) (� + �� − �)- − ./)

( > 0, (9)

which means that determinants of (7) is positive.

First of all, from the condition (i), we obtain the following proposition.

Proposition1:

If � + �� − � < 0 holds, the country falls into the debt trap because of the inability to reach the

steady state.

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This proposition 1 means that the country falls into the debt trap no matter what the exchange

rate is if the growth rate of the GDP without foreign debt is low (, which is expressed as small

a), the government expenditure is not effective (,which is expressed as small g), increase in the

foreign debt is small (,which is expressed as small q) or the foreign interest rate is high (,which

is expressed as large φ).

Next, let us move on to the case where � + �� − � > 0 holds.

In this case, from (9), we see that

� > ./)

(012)+3)' (10)

must hold in order for !($)

&($) to have positive solutions. Thus, we obtain the following proposition.

Proposition2:

In the case of � + �� − � > 0, if the currency of the country depreciates so much as to satisfy

e>

./)

(012)+3)', the country can avoid the debt trap.

This proposition 2 tells that the depreciation of the currency is necessary for the country to

avoid the debt trap if the growth rate of the GDP without foreign debt is high (, which is

expressed as large a), the government expenditure is effective (,which is expressed as large g),

increase in the foreign debt is large (,which is expressed as large q) or the foreign interest rate

is low (,which is expressed as small φ).

From (10), we also see that e increases if β or q increases, which leads to the following

proposition.

Proposition3:

In the case of � + �� − � > 0, the currency of the country should increase in accordance with

increase in β or q, in order for the country to avoid the debt trap.

Parameters β and q express the effects of the foreign debt to the GDP of the country, proposition

3 implies that the more the foreign debt influences the GDP, the weaker its currency should be

in order to avoid the debt trap.

CONCLUSIONS

In the present paper, motivated by the debate over the causes of the debt trap Sri Lanka fell into

and by extending Padoan et al (2012) that focused on a country with domestic debt only, we

constructed a theoretical model that incorporates the foreign debt to investigate the condition

where the debt trap is avoided.

The results we obtained were more astonishing than we had imagined:

(1) Country falls into the debt trap no matter what the exchange rate is if the growth rate of the

GDP without foreign debt is low, the government expenditure is not effective, increase in the

foreign debt is smaller the foreign interest rate is high.

(2) Depreciation of the currency is necessary for the country to avoid the debt trap if the growth

rate of the GDP without foreign debt is high, the government expenditure is effective, increase

in the foreign debt is large or the foreign interest rate is low.

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Fujita, Y. (2022). Does Depreciation of Currency Always Invite Debt Trap? Archives of Business Research, 10(8). 109-113.

URL: http://dx.doi.org/10.14738/abr.108.12889

(3) The more the foreign debt influences the GDP, the weaker its currency should be in order

to avoid the debt trap.

In the present paper, we made some assumptions to simplify the analysis. It is necessary to

construct a theoretical model that incorporates both domestic and foreign debts. It is of interest

to explore the case where the exchange rates fluctuates depending on domestic interest rate,

foreign interest rate and so on. We will take up such analysis next.

References

Asia Financial. 2022. “Is Sri Lanka a Victim of China’s Debt-Trap Diplomacy?”, July 18, 2022.

Butts, Hector C. 2009. “Short Term External Debt and Economic Growth—Granger Causality: Evidence from Latin

America and the Caribbean”, The Review of Black political economy 36, 93–111.

Geiger, Linwood.T. 1990. “Debt and Economic Development in Latin America‖”, The Journal of Developing Areas,

24, 181-194.

Hameed, Abid. Hammad Ashraf, Muhammed Ali Chaudhary. 2008. “External Debt and its Impact on Economic

and Business Growth in Pakistan”, International Research Journal of Finance and Economics, 20, 132-140.

Mohamed, Mutasim Ahmed Abdelmawla. 2005. “The Impact of External Debts on Economic Growth: An

Empirical Assessment of the Sudan: 1978-2001”, Eastern Africa Social Science Research Review, 21(2), 53-66

Padoan, Pier Carlo, Urban Sila and Paul van den Noord. 2012. “Avoiding debt traps: Fiscal consolidation, financial

backstops and structural reforms”, OECD Journal: Economic Studies, Vol. 2012/1.

http://dx.doi.org/10.1787/eco_studies-2012-5k8xbnjbn9hl

Reinhart, C.M. and K.S. Rogoff. 2010. “Growth in a Time of Debt”, American Economic Review, 100.

Safia Shabbir. 2013. “Does External Debt Affect Economic Growth: Evidence from Developing Countries”, SBP

Working Paper Series 63, State Bank of Pakistan, Research Department.