Lee and Thampapillai_2016_External Debt in Macroeconomics_A Review

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Lee Kuan Yew School of Public Policy
Working Paper Series
External Debt in Macroeconomics: A Review
Kelvin Lee
School of Politics and International Relations
Australian National University
Email: kelvin.lee@anu.edu.au
Dodo J Thampapillai
Lee Kuan Yew School of Public Policy
National University of Singapore
Email: spptj@nus.edu.sg
February 25, 2016
Working Paper No.: LKYSPP 16-05

2
Abstract: The paper provides a concise review of the treatment of external debt in
macroeconomic analyses. In this regard, the paper considers: the development of
indicators to quantify external debt alongside theoretical and empirical developments
in which the indicators are utilized. Following the inherent limitations, the theoretical
and empirical studies tend to employ more than one indicator. Both theoretical and
empirical frameworks are distinguished in terms of whether they are static or dynamic
in nature. The theoretical studies were also distinguished in terms of the utilization of
discrete and continuous frameworks. The empirical models were distinguished with
reference to linearity and nonlinearity of the underlying premises. The review enables
the reader to appreciate the relative advantages and disadvantages of the various
frameworks and their contextual relevance. A key theme that runs through the studies
reviewed is the impact of external debt on economic performance. The results, which
are context specific, are mixed.
Keywords: External Debt, Debt-to-GDP Ratio, Debt Service, Difference and
Differential Equations; Static and Dynamic Models
Biographical notes: Kelvin Lee is a PhD candidate at the School of Politics and
International Relations, Australian National University. He graduated with a Master in
Public Policy in 2012 from the Lee Kuan Yew School of Public Policy, National
University of Singapore. Prior to commencing his PhD research, he worked as
researcher at the Lee Kuan Yew School of Public Policy and the Policy Unit of the
Asia-Pacific Economic Cooperation (APEC) office at Singapore.
Dodo J Thampapillai is a professor at the Lee Kuan Yew School of Public Policy
where he teaches economics. His areas of research interest are macroeconomics and
environmental economics. He has a teaching experience in excess of 30 years

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1. INTRODUCTION
This paper reviews the ways external debt has been incorporated into national income
determination to demonstrate the impact of external indebtedness on growth. At
present, it is not apparent in academic practice that external debt has been a common
explicit feature in national income accounting. Recent literature tends to equate
external debt to current account deficit. For instance, Villanueva and Mariano (2007)
identify net external debt as “external current account deficit (CAD)”, or savings by
non-residents; CAD is derived from the deduction of gross disposable national
income from the sum of domestic aggregate consumption and gross domestic
investment1
. Others like Hallwood and MacDonald (2000) and Hess and Ross (1997)
compute external debt based on the identity equation that demonstrates that the sum
of net domestic savings and net government (tax) revenue equates to the subtraction
of net interest paid abroad from net exports2
. Nevertheless, several studies including
those by Musa (2004) have attempted to link current account deficits and growth in
nominal national income3
, with such histories going back to Park (1986)4
.
Contemporaneously, the euro zone debt crisis witnessed a proliferation of
investigations on external debt-GDP linkages among sovereign and private debt, such
as Stein (2012) who interpreted national external debt through the lens of current
account deficit-to-GDP ratio to explain the financial upheaval in Greece5
. In short,
external debt appears to feature as addendum to national income accounting through
myriad methods as sampled above.
1
Delano P. Villanueva and Roberto S. Mariano, “External Debt, Adjustment, and Growth”, in Fiscal
Policy and Management in East Asia, eds. Takatoshi Ito and Andrew K. Rose (United States of
America: The University of Chicago Press, 2007), pp. 203-204.
2
That is, (X – M) – (R – F) = (S – I) + (T – G), where (X – M) stands for net exports, (R – F) as net
interest paid abroad, (S – I) as net domestic savings and (T - G) as net government (tax) revenue. See
C. Paul Hallwood and Ronald MacDonald, International Money and Finance, 3rd
edition (United
Kingdom: Blackwell Publishing, 2000), p. 459; Peter Hess and Clark Ross, Economic Development:
Theories, Evidence, and Policies (United States of America: The Dryden Press, Harcourt Brace &
Company, 1997), p. 477.
3
Michael Musa, “Exchange Rate Adjustments Needed to Reduce Global Payments Imbalances”, in
Dollar Adjustment: How Far? Against What?, eds. C. Fred Bergsten and John Williamson,
(Washington, DC: Institute for International Economics, 2004), pp. 113-138, in Barry Eichengreen,
Global Imbalances and the Lessons of Bretton Woods (United States of America: The MIT Press,
2007), p. 140.
4
Yung Chul Park, “Foreign Debt, Balance of Payments, and Growth Prospects: The Case of the
Republic of Korea, 1965-88”, World Development, Vol. 14, No. 8 (1986), p. 1048.
5
J.L. Stein, Stochastic Optimal Control and the U.S. Financial Debt Crisis (New York: Springer
Science+Business Media New York, 2012), pp. 137-138, 140, 141, 145.

4
In this paper, we examine how external debt is dealt with in the economics literature.
Despite overlaps, there appears to be three distinct categories:
(i) Development of indicators to quantify the extent of indebtedness;
(ii) Theoretical analyses where external debt is an explicit variable; and
(iii) Empirical analyses where external debt is an explicit variable.
Notwithstanding the differences among the contexts above which will be elaborated
on later, this paper assumes a common understanding of external debt as a concept.
That is, external debt is defined as the “long-term and short-term debt that is owed by
a country to non-residents”, according to Daud and Podivinsky (2011)6
. However, that
studies can differ in their foci of particular aspects of external debt necessitates a
decomposition of external debt as detailed by Clark (2002) below7
:
1. Long term external debt: “debt that has an original or extended maturity of
more than one year and that is owed to non-residents and repayable in foreign
currency, goods, or services”; which can be further sub-divided into:
a. Public debt: “an external obligation of a public debtor, including the national
government, a political subdivision or agency of either, and autonomous
public bodies”;
b. Publicly guaranteed debt: “an external obligation of a private debtor that is
guaranteed for repayment by a public entity”, and;
c. Private non-guaranteed external debt: “an external obligation of a private
debtor that is not guaranteed by a public entity”.
2. Short term external debt: “debt that has a maturity of one year or less and
includes no distinctions between public and private non-guaranteed short-term
debt”, and;
3. Use of International Monetary Fund (IMF) credit: “repurchase obligations to
the IMF with respect to all uses of IMF resources, excluding those resulting
from drawings in the reserve or first credit tranche.”
The paper is structured as follows. Each of the next three sections considers each
category of debt treatment. This then leads to a concluding review of main lessons.
6
Siti Nurazira Mohd Daud and Jan M. Podivinsky, “Debt-Growth Nexus: A Spatial Econometrics
Approach for Developing Countries”, Transition Studies Review, Vol. 18, No. 1 (September 2011), pp.
1-2.
7
Ephraim Clark, International Finance, 2nd
edition (United Kingdom: Thomson, 2002), pp. 261-262.

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2. INDICATORS OF FOREIGN DEBT
A straightforward application of external debt on growth assumes the form of
expressing the principal external debt quantum and/or debt servicing (i.e. interest on
external debt) as a ratio to or proportion of gross domestic product (GDP) or gross
national product (GNP). This singular expression measures the severity of foreign
indebtedness on economic development. Nallari and Griffith (2011) explain that this
proportion serves to indicate the ability of a country to service its debt8
. This
perspective finds support in Tilak (1990), Tahir (1998), and Reinhart and Rogoff
(2010). Tilak (1990) compares the total public external debt situation of 1970 against
that of 1984 among Sub-Saharan African countries through two indicators: total debt
as a percentage of GNP and debt service as a percentage of GNP. He diagnosed the
external public debt situation as “critical” through the imposition of a severe drag on
the development of African countries between 1970 and 1984 resulting in more
sovereign borrowing9
. In an apparent refinement, Tahir (1998) in his clarification of
Pakistan’s external debt in the 1990s introduced the concept of present value of debt
service to GNP and that to foreign exchange earnings; he considers a country as
“severely indebted” if debt/GNP ratio exceeded 80%10
, following the World Bank’s
threshold of more than 60% for debt/GNP ratio to be considered moderately
indebted11
. Nallari and Griffith (2011) note that such discounted present values factor
in additionally the future value of money, and thus a sovereign’s servicing capacity12
.
Perhaps, however, such indicators commanded greatest attention recently through
Reinhart and Rogoff’s (2010) study of the impact of total gross external debt (public
8
Raj Nallari and Breda Griffith, Understanding Growth and Poverty: Theory, Policy and Empirics
(Washington, D.C.: The International Bank for Reconstruction and Development/The World Bank,
2011), p. 170.
9
Jandhyala B. G. Tilak, “External Debt and Public Investment in Education in Sub-Saharan Africa”,
Journal of Education Finance, Vol. 15, No. 4, The Oxford Round Table (Spring 1990), pp. 470-471.
10
Pervez Tahir and Eatzaz Ahmad, “The Debt of the Nation [with Comments]”, The Pakistan
Development Review, Vol. 37, No. 4, Papers and Proceedings PART II Fourteenth Annual General
Meeting and Conference of the Pakistan Society of Development Economists Islamabad, January 28-
31, 1999 (Winter 1998), p. 339.
11
The World Bank, World Debt Tables 1992-1993 (Washington D.C.: The International Bank for
Reconstruction and Development/The World Bank, 1993) in Pervez Tahir and Eatzaz Ahmad, “The
Debt of the Nation [with Comments]”, The Pakistan Development Review, Vol. 37, No. 4, Papers and
Proceedings PART II Fourteenth Annual General Meeting and Conference of the Pakistan Society of
Development Economists Islamabad, January 28-31, 1999 (Winter 1998), p. 339.
12
Raj Nallari and Breda Griffith, Understanding Growth and Poverty: Theory, Policy and Empirics
(Washington, D.C.: The International Bank for Reconstruction and Development/The World Bank,
2011), p. 170.

6
and private) on economic growth of developed and developing economies. Average
growth of emerging markets “deteriorates markedly” when external debt is 60% of
GDP, and “further still” at 90% based on 1946-2009 data 13
.
Opinions vary on the choice of appropriate indicator. Subtle differences among the
indicators themselves are evident in the snapshot above. Debate appears to centre on
the accurate depiction of the burden external debt imposes on an economy. In his
study of India’s external debt 1992 through 2002, Gupta (1994) argues that the debt
service ratio should be “of real concern” than the external debt-to-GNP ratio as the
former measures a country’s “repayment abilities”14
. On the other hand, Mahmood,
Rauf and Ahmad (2009) aver the ‘importance’ of expressing external debt—along
with debt servicing—with relation to foreign exchange earnings and also that to
exports of goods and services. While they acknowledge the external debt-to-GDP
ratio as a fixture in their assessment of Pakistan’s public and external debt
sustainability for the 1970s-2000s duration, they argued that the ratio of external
debt/debt servicing to foreign exchange earnings and that to exports of goods and
services “mirror” a country’s capacity to manage its external imbalances and its
reforms on external debt which impact on foreign exchange earnings and exports15
.
Avramovic (1964) justifies the longevity of the external debt-to-current account ratio
due to four reasons: simplicity of comprehension, ease of computation requiring only
data on external debt and current account earnings, absence of alternative indicators
that apply to short term or long term view, and its flexibility as a short and long term
measurement heuristic when computed against proportion of scarce foreign exchange
earnings like capital inflows16
; these may very well apply to the external debt-national
income ratio.
13
Carmen M. Reinhart and Kenneth S. Rogoff, “Growth in a Time of Debt”, The American Economic
Review, Vol. 100, No. 2, PAPERS AND PROCEEDINGS OF THE One Hundred Twenty Second
Annual Meeting OF THE AMERICAN ECONOMIC ASSOCIATION (May 2010), pp. 574, 576-577.
14
S. P. Gupta, “Debt Crisis and Economic Reforms”, Economic and Political Weekly, Vol. 29, No. 23
(Jun. 4, 1994), p. 1411.
15
Tahir Mahmood, Shahnaz A. Rauf and Hafiz Khalil Ahmad, “Public and External Debt
Sustainability in Pakistan”, Pakistan Economic and Social Review, Vol. 47, No. 2 (Winter 2009), pp.
246, 256.
16
Dragoslav Avramovic, “Debt Service Ratio”, in Dragoslav Avramovic et. al., Economic Growth and
External Debt (Baltimore, Maryland: The Johns Hopkins Press, 1964), pp. 38, 42.

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That the external debt-as-indicator approach finds much support as in the studies
above does not detract from its shortcomings. A central tussle concerns whether such
indicators illustrate national debt burden. In his critique on applying external debt as a
percentage of GDP, Pilbeam (1998) faulted it for “saying nothing on the annual
burden imposed on the country, the amount of repayments falling due, or which
section of the community the burden will fall upon”17
; this ventures beyond the
preceding debate over which indicators ought to be selected. Another similar point of
contention involves the alternate measures mentioned previously. Pilbeam (1998)
criticized the external debt as a percentage of goods and services indicator on grounds
of yearly varying exports, and this indicator’s underlying assumption that increasing
export revenue is the sole debt servicing avenue18
. A similar indicator, the total debt
service as a percentage of exports of goods and services, also suffers from problems
such as fluctuations in export earnings and the point estimation of debt burden of a
single point, i.e. year, in time19
; these as well as biased measurements for long run
analysis caused by exceptional circumstances like bumpers of maturities.20
Doubts
over “critical” ratio thresholds that signify unsustainable debt levels and stock-versus-
flow conceptual confusion over external debt are further problems with external debt-
current account measure,21
but their application extends to external debt-national
income indicator when external debt as a stock concept does not reconcile with
national income which is a flow concept. Point data illustrations are an added concern.
As Ahmad (1998) observes in commenting on Tahir (1998) aforementioned, the static
depictions of the phenomenon presented by indicator data are useful as snapshots, but
are unable on their own to present a more dynamic analysis that formal modelling
would have provided22
.
Nevertheless, the indicators continue to be featured hitherto, in spite of serious pitfalls
mentioned above. As can be observed below, several authors actually select more than
17
Keith Pilbeam, International Finance, 2nd
edition (Great Britain: Macmillan Press Ltd, 1998), p. 405.
18
19
20
External Debt (Baltimore, Maryland: The Johns Hopkins Press, 1964), p. 42.
21
External Debt (Baltimore: The Johns Hopkins Press, 1964), pp. 39-41, 42.
22
Pervez Tahir and Eatzaz Ahmad, “The Debt of the Nation [with Comments]”, The Pakistan
Development Review, Vol. 37, No. 4, Papers and Proceedings PART II Fourteenth Annual General
Meeting and Conference of the Pakistan Society of Development Economists Islamabad, January 28-
31, 1999 (Winter 1998), p. 353.

8
one indicator to compensate for the weaknesses of the external debt/debt service-to-
national income indicator. It appears that the variant of indicators pitting foreign
indebtedness against foreign exchange earnings/export revenue serve a more
particular purpose by testing an economy’s foreign cash flow resilience23
; and hence
such indicators ought to be viewed as more specialized. Thus, it should not be
construed that some indicators could be superior to the rest, as their functions differ
and their respective weaknesses previously discussed cannot be made commensurate
when indicators are compared together.
3. THEORETICAL MODELLING
A more contextual study of foreign indebtedness in national income accounting is
obtained through theoretical modelling. External debt is assumed to be an endogenous
variable embedded within a series of mathematical models systematically expounded
in relation to other endogenous and exogenous variables and coefficients (i.e.
parameters) theorized. Such models allow the user to predict results through solving
for variables of interest, or to measure movements among variables by varying one or
more of the variables or coefficients pre-specified; numerical values need not be
inputed to these variables, unlike empirical models which rely on data24
. As an
example, in his argument for the superiority of the domestic consumer price index
over export, import and world price indices as deflator of external debt, Dornbusch
(1982) integrated external debt into “conventional treatment of the income effects of
price change”. Through a series of formulae integrating pre-specified exogenous
variables, he then demonstrated their application to the case of Brazil’s external debt
from 1973 to 198025
.
Generally, two types of theoretical models can be observed incorporating external
debt and national income: comparative statics models and dynamic models. The key
23
External Debt (Baltimore, Maryland: The Johns Hopkins Press, 1964), pp. 34-36.
24
Gary Evans, “Chapter 1: Economic Models”, Homepage for Prof. Gary R. Evans [cited 15 August
2003], available from: www2. hmc.edu/~evans/, p. 3.
25
Rudiger Dornbusch, “Consumption Opportunities and the Real Value of the External Debt”, Journal
of Development Economics, Vol. 10, No. 1 (February 1982), pp. 93, 94 and 99; Dornbusch’s equation
is given by c = (Y - i*ED – ED(ė – ṗ)) / P, where P = home consumer price index, Y = domestic
nominal value of output, D = external debt in dollars, E = exchange rate, cruzeiros/$, i* = world
nominal rate of interest, ė and ṗ = rates of depreciation and domestic inflation respectively.

9
difference between comparative statics models and dynamic models centres on time
dependency: dynamic models employ time dependent variables while non-time
dependent variables are inputed into comparative statics models26
. An example of the
comparative statics models is taken from Walther (1997) in his study of sustainable
debt. Where the external debt-to-gross national income ratio was a standalone
indicator in the earlier approach, it is now made the subject in an equation to
demonstrate the relationship between the rate of growth of the debt-to-income ratio
and other exogenous variables such as output, absorption, real interest rate on external
debt and the growth rate of real income27
. Other applications of comparative statics
models include Dornbusch (1982) introduced earlier.
Dynamic models can be further classified into models employing difference equations
(i.e. mathematical systems of difference) and models relying on differential
equations28
. Kohsaka (1991) is a classic example of difference equation models
whereby he defines GNP of current year as a function of GDP of current year and
external debt of previous year, among other variables, in his study of growth
achievement among middle income countries via external debt as capital inflows29
. In
measuring the macroeconomic impact external debt exerts on the growth of Barbados,
Boamah (1988) is another example where differences in the quantum of GDP and
external debt for adjacent years go towards determining an investment function in
current year30
. Difference equations can also be applied to the indicator approach,
such as in the assessment of Bangladesh’s public debt sustainability by Islam and
Biswas (2005) who modelled the change in the debt-to-GDP ratio at current year as a
function of the stock of debt-to-GDP ratio in the previous year31
.
26
2003], available from: www2. hmc.edu/~evans/, pp. 6-7.
27
Ted Walther, The World Economy (United States of America: John Wiley & Sons, Inc., 1997), pp.
375-378; Walther ‘s formula is given as ḋ = - (1 – a) + d(r – ẏ), where ḋ = rate of growth of the
external debt/income ratio, a = absorption/output ratio, d = external debt/income ratio, r = real interest
rate on external debt and ẏ = rate of growth of real income.
28
29
Akira Kohsaka, “Macroeconomic Management with External Debt – East Asian Experiences in the
1980s”, Asian Economic Journal, Vol. V, No. 3 (November 1991), pp. 262-263.
30
Daniel Boamah, “Some Macroeconomic Implications of External Debt for Barbados”, Social and
Economic Studies, Vol. 37, No. 4, Regional Programme of Monetary Studies (December 1988), pp.
189-191.
31
Md. Ezazul Islam and Bishnu Pada Biswas, “Public Debt Management and Debt Sustainability in
Bangladesh”, The Bangladesh Development Studies, Vol. 31, No. 1/2 (March-June 2005), p. 93.

10
Dynamic differential equations models are identified based on the differential
equations employed, although in reality they are not immediately apparent. For
example, in his study of comparative external and internal public debt burdens,
Carlberg (1985) resorted to an apparent comparative statics equation with factor
income made a function of output and along with some parameters; however, a few of
these parameters are themselves derived from time dependent external debt32
. Another
instance involves a simple macroeconomic aggregate model by Otani and Villanueva
(1989) on their study of growth oriented policies involving external debt and human
capital linkages. Along with visual (graphical) models, the central model ostensibly
employs a comparative statics model where real GNP is a function of output,
exchange rate, stock of net external liabilities and average cost of net foreign credits
(which is weighted by the stock of net external liabilities), but variables like capital
can vary with time33
. It appears that dynamic models featuring both difference and
differential equations also exist. For example, Dellas and Galor’s (1992) “designing
of Pareto welfare improving policies for economic growth” via external public debt
and controls on private capital outflows saw capital of proceeding year made a
function of production, capital and consumption of current year even as capital stock
is subjected to differentiation34
. Another is found in Stein’s (2005) exploration of
optimal debt and endogenous growth in models of international finance where short
term external debt of the next year is a function of GDP in the previous year, but long
term external debt is subjected to differentiation based on time35
.
Some comments can be made on the utility of these diverse models. Firstly, that
dynamic models offer certain advantages over comparative statics models does not
obviate the other. Evans (1997) contented that dynamic models can “remarkably
32
Michael Carlberg, “External versus Internal Public Debt – A Theoretical Analysis of the Long-Run
Burden”, Zeitschrift für Nationalökonomie/Journal of Economics, Vol. 45, No. 2 (1985), p. 143.
33
To be more precise, the model is Y = Q - reDf*/P where “real national income or real GNP (Y) is
equal to output (Q) less real value of interest payments on external debt (reDf*/P)”, where “r is the
average cost of foreign borrowing (or foreign debt), e is exchange rate expressed in local currency per
unit of foreign currency; and Df* is the stock of net external liabilities (external debt minus claims on
foreigners, including official international reserves), expressed in foreign currency”. This is to show as
“excessive” external debt necessitates the development of human capital. See Ichiro Otani and Delano
Villanueva, “Theoretical Aspects of Growth in Developing Countries: External Debt Dynamics and the
Role of Human Capital”, Staff Papers – International Monetary Fund, Vol. 36, No. 2 (Jun. 1989), p.
319.
34
Harris Dellas and Oded Galor, “Growth via External Public Debt and Capital Controls”,
International Economic Review, Vol. 33, No. 2 (May 1992), pp. 269, 271 and 272.
35
Jerome L. Stein, “Optimal Debt and Endogenous Growth in Models of International Finance”,
Australian Economic Papers, Vol. 44, No. 4 (December 2005), pp. 392, 399.

11
capture subtle feedback effects” like time lags that are overlooked in the static-like
depictions of comparative statics models; such feedback effects until recently can be
better executed through increasingly powerful and affordable computers allowing
near limitless experimentation with combinations of values and assumptions.
However, comparative statics models are preferred because of their ease of
mathematical resolution, at least in business cycle theory36
. Secondly, some
theoretical models appear more capable to demonstrate external debt burden, which
has been a contention as seen in the prior indicator approach. Consider Milbourne
(1997) and Dore (1998). Both are dynamic models that employ difference equations.
However, these studies differ from above models by further exploring the impact of
external debt per capita: on the accumulation of net foreign assets per capita in
Milbourne’s (1997) investigation of the relationship between growth, population
growth, capital accumulation and foreign debt37
, and; on income growth per person in
Dore’s (1998) focus on the growth potential of Sub Saharan African countries
incorporating government consumption and external debt servicing38
. The factoring in
of populations arguably allows a more accurate portrayal of external debt burden on
each individual beyond just a simple proportion of national income.
Theoretical modelling offers several important advantages, but these do not diminish
their limitations. A first advantage of theoretical models is their ability to show the
important variables that determine the variable in question, which finds support in
Walther (1997)39
. Sensitivity analysis among variables can thus be carried out by
calibrating the numerical values plugged into the variables, resulting in meaningful
relationships among variables obtained. Secondly, theoretical models compel the
clarification of assumptions. The need to express assumptions “explicit at every stage
of reasoning”40
in mathematical terms lend to their “high integrity” due to “rigorous
36
37
Ross Milbourne, “Growth, Capital Accumulation and Foreign Debt”, Economica, New Series, Vol.
64, No. 253 (Feb. 1997), pp. 1, 3.
38
M. H. I. Dore, “Income growth, debt and deficits: lessons from subSaharan Africa”, International
Review of Applied Economics, Vol. 2, No. 1 (1988), pp. 23, 27-28.
39
Ted Walther, The World Economy (United States of America: John Wiley & Sons, Inc., 1997), p.
378.
40
Alpha C. Chiang, Fundamental Methods of Mathematical Economics, 3rd
edition (United States of
America: McGraw-Hill, Inc., c1984), p.4.

12
standards of logic inherent in mathematics”41
. This would facilitate falsification of
theories. However, the demanding requirements of such models also contribute to
their weaknesses. Evans (1997) in his broad survey of literature listed three. Firstly,
improper assumptions can undermine a model’s usefulness. Simply put, wrong
assumptions can lead to erroneous calculations even if the model is still “logically
consistent internally”. This pitfall is compounded by the irresolution of contradictory
assumptions even as they appear logical42
. For example, Dore (1997) in his study
cautioned the assumption of steady state for the 1970-1983 period which had seen
“not only major price upheavals but also very important institutional and technical
changes”43
. Secondly, theoretical modelling has been accused of oversimplification of
reality. The linearity and even non-linearity of models do not suffice in aping reality
due to unpredictability and imperfect information; which has led Dore (1997) to
declare his assumption that the variables employed are linear, such as “simple
averages” instead of “steady state values” for the parameters for budget deficits and
external debt44
. Evans (1997) argues that simplicity of models has to be made “not
only expedient but necessary” in order to “make sense of this recondite chaos”45
.
However, Chiang (1984) disputes this on grounds that the very nature of theory as
“abstract” renders this criticism as “truism”46
. Thirdly, mathematical intractability can
render theoretical models useless. Their value lies in their ability to generate results or
show relationships clearly. Evans (1997) explains the need for linear equations in
order for them to be tractable (solvable) in view of “a large number of equations and
variables” found in macroeconomics47
. This explains Dore’s (1997) need for applying
linear values, which relates this criticism to the one just mentioned about the
complexity of reality confounding calculation.
41
42
43
Review of Applied Economics, Vol. 2, No. 1 (1988), p. 36.
44
Review of Applied Economics, Vol. 2, No. 1 (1988), pp. 35-36.
45
46
Alpha C. Chiang, Fundamental Methods of Mathematical Economics, 3rd
edition (United States of
America: McGraw-Hill, Inc., c1984), pp.4-5.
47

13
Although a representative sample of the genre cannot be claimed, some
commonalities can be drawn amidst the apparent differences exhibited by the studies
reviewed above. Firstly, many theoretical models operate on qualified findings, which
corroborate the above assessment. That is, their utility is effective to the extent that
underlying assumptions are met. Walther (1997), Boamah (1988), Milbourne (1997),
and Dore (1998) fit this observation. Secondly, the dynamism of these models is stark,
compared to the indicator approach. All dynamic equations models considered
account for lagged variables that are applied to cases over long periods of time.
Thirdly, as illustrated above, application of models to actual cases is not always
present. Milbourne (1997), Carlberg (1985), Otani and Villanueva (1989) and Dellas
and Galor (1992) are notable examples. These authors demonstrate that economic
inferences can still be drawn even in the absence of case studies by recourse to a
reflection of the theoretical outcomes.
4. EMPIRICAL MODELLING
Empirical models focus on the determinable strength of relationships between
variables through their correlations. This approach presents an even more nuanced
examination of the external debt-national income relationship compared to the
indicator and theoretical modelling approaches. Data gathered from multiple units of
observation are processed via statistical techniques; thus, empirical models are
developed from theoretical models but go beyond48
. In an empirical model typically
laid out as a system of interconnecting equations, external debt and national income
are portrayed as independent variables (i.e. regressors); dependent variables (that is,
regressands), or; both. Metwally and Tamaschke (1994a) serves as an instructive case
through their use of ordinary least squares in econometric techniques to model the
interaction between the rate of growth of GNP as regressand and external debt
servicing as regressor among other explanatory variables vis-à-vis three heavily
indebted North African countries 1975-199249
. In their study of external debt on
economic growth for 31 developing countries spanning four geographical regions,
Daud and Podivinsky (2011) employ spatial econometrics designating output as the
48
2003], available from: www2. hmc.edu/~evans/, pp. 5-6.
49
M. M. Metwally and Rick Tamaschke, “The Interaction Among Foreign Debt, Capital Flows, and
Growth: Case Studies”, Journal of Policy Modeling, Vol. 16, No. 6 (1994a), pp. 597, 599.

14
regressand, and debt service ratio as among the regressors.50
. Where external debt is
made the regressand and national income the regressor, Gani (1999) typifies the
econometric model applied to exploring the external debt burden on small island
developing countries in the South Pacific using a variant of the generalized least
squares method51
. Looney (1987) is another example applying a simple regression
model with total external public debt made a function of GDP among other regressors
which include military expenditures to investigate the “main causes of Third World
external public debt”52
.
Aside from commonly observed techniques as above, another application involves the
necessary assignment of both external debt and national income as regressor and
regressand within an empirical model. Several studies focus on exploring the degree
of cointegration between these two variables in a time series sense. One common test
of cointegration is Granger’s causality test which “examines the causal relationship
between a set of variables by testing for their predictability based on past and present
values”53
. Exploring Granger’s causality between short term external debt and GDP is
seen in Butts (2009) for 27 Latin American and Caribbean countries over 1970-
200354
. Other studies, however, explored the tri-causality between national income
and another variable with reference to external debt as a third variable. Such a
relationship between national income and exports have been explored by Ahmed, Butt
and Alam (2000) with reference to four South Asian and four Southeast Asian
countries from 1990 to 199755
, and Amoateng and Amoako-Adu (1996) with respect
50
Siti Nurazira Mohd Daud and Jan M. Podivinsky, “Debt-Growth Nexus: A Spatial Econometrics
Approach for Developing Countries”, Transition Studies Review, Vol. 18, No. 1 (September 2011), pp.
5-9.
51
Azmat Gani, “The Burden of External Debt in the South Pacific Island Countries”, Savings and
Development, Vol. 23, No. 1 (1999), pp. 33, 36.
52
Robert E. Looney, “Impact of Military Expenditures on Third World Debt”, Canadian Journal of
Development Studies/Revue canadienne d’études du development, Vol. 8, No. 1 (1987), p. 11.
53
Qazi Masood Ahmed, Mohammad Sabihuddin Butt, Shaista Alam and Aqdas Ali Kazmi,
“Economic Growth, Export, and External Debt Causality: The Case of Asian Countries [with
Comments]”, The Pakistan Development Review, Vol. 39, No. 4, Papers and Proceedings PART II
Sixteenth Annual General Meeting and Conference of the Pakistan Society of Development
Economists Islamabad, January 22-24, 2001 (Winter 2000), p. 597.
54
Hector C. Butts, “Short Term External Debt and Economic Growth—Granger Causality: Evidence
from Latin America and the Caribbean”, The Review of Black Political Economy, Vol. 36, No. 2 (June
2009), pp. 93, 95-96, 110.
55
Qazi Masood Ahmed, Mohammad Sabihuddin Butt, Shaista Alam and Aqdas Ali Kazmi, “Economic
Growth, Export, and External Debt Causality: The Case of Asian Countries [with Comments]”, The
Pakistan Development Review, Vol. 39, No. 4, Papers and Proceedings PART II Sixteenth Annual

15
to 35 African countries for the period 1971-199056
. Investigations of different
combinations of multi-variate causality variables—though not necessarily involving
Granger’s causality test—include Karagol (2006) involving GNP, defence
expenditures, external debt and total investment for Turkey for 1960-200257
.
Differences have been observed among the depiction of changes in national income
with respect to external debt and vice-versa. Magnitudes of changes in variables are
depicted either in linear or logarithmic measurements. With external debt assigned as
among regressors, linear changes like growth rates in national income as regressand
are seen in multivariate linear regression models. Such models include Fosu (1999)
exploring the effect of external debt burden on the economic growth of 35 sub-
Saharan African countries from 1980 to 199058
, and Metwally and Tamaschke
(1994b) also measuring external debt burden’s impact on economic growth in Algeria,
Egypt and Morocco from 1975 to 198959
. Linear changes in national income per
capita have also been observed in several papers, a sample of which include
Checherita-Westphal and Rother (2012) investigating the linkage between public
external debt and growth rate of GDP per capita in 12 euro area countries for a 40
year duration since 197060
; Vamvakidis (2008) investigating the propensity to adopt
economic reform by factoring in private external debt for developing and emerging
economies sampled from 1970 to 2000,61
and; for Granger causality test related,
Ahmed (2012) in his sample of 25 sub-Saharan African countries from 1988 to 2007
exploring multi-variate causality between real domestic income and real external debt
General Meeting and Conference of the Pakistan Society of Development Economists Islamabad,
January 22-24, 2001 (Winter 2000), pp. 598-603.
56
Kofi Amoateng and Ben Amoako-Adu, “Economic growth, export and external debt causality: the
case of African countries”, Applied Economics, Vol. 28, No. 1 (1996), pp. 23, 24-26.
57
Erdal Karagol, “The Relationship Between External Debt, Defence Expenditures and GNP Revisited:
The Case of Turkey”, Defence and Peace Economics, Vol. 17, No. 1 (2006), pp. 49-50, 55.
58
Augustin Kwasi Fosu, “The External Debt Burden and Economic Growth in the 1980s: Evidence
from sub-Saharan Africa”, Canadian Journal of Development Studies/Revue canadienne d’études du
development, Vol. 20, No. 2 (1999), pp. 310-313.
59
M. M. Metwally and Rick Tamaschke, “The Foreign Debt Problem of North African Countries”,
African Review of Money Finance and Banking, No. 1/2 (1994b), pp. 109, 115-116.
60
Cristina Checherita-Westphal and Philipp Rother, “The impact of high government debt on economic
growth and its channels: An empirical investigation for the euro area”, European Economic Review,
Vol. 56, No. 7 (2012), pp. 1395, 1398, 1403.
61
Athanasios Vamvakidis, “External debt and economic reform: does a pain reliever delay the
necessary treatment?”, Journal of Economic Policy Reform, Vol. 11, No. 3 (2008), p. 197.

16
together with other explanatory variables62
. Where external debt is the regressand,
Craigwell, Rock and Sealy (1988) have reported changes in public external debt as
shortfall in real output varies for observations of Barbados from 1959 to 198663
. On
the other hand, several other studies have chosen to report changes in national income
in percentages derived from logarithmic expressions instead. An example is Pattillo,
Poirson and Ricci (2003) who explored the channels through which external debt
impacted growth via panel regression for 61 developing countries during the period
1969-199864
. Logarithmic changes in national income per capita have been observed
in papers by Daud and Podivinsky (2012) on external debt-economic growth linkages
using “dynamic panel data of Generalized Method of Moments (GMM) framework”
for 31 countries 1970-200565
, and Shahbaz, Shabbir and Butt (2013) applying a multi-
variate Granger causality test to not only to the log of real GDP per capita, but also to
the log of external debt per capita for Pakistan’s case for the 1973-2009 duration66
.
The uncommon study where change in external debt service as regressand has been
reported in logarithm derived percentages from logarithmic change in income is
demonstrated by Hunte (2002) in his study of saving behaviour and external debt
servicing from data of 36 sub-Saharan African countries obtained in the Human
Development Report for year 200067
.
Similar to theoretical models, empirical models can also be segregated into static and
dynamic models. Such models are differentiated on usage of time lagged explanatory
variables: absence of such variables would render the model static, and dynamic for
the obverse. Multivariate linear regression models can exhibit both static and dynamic
62
Abdullahi D. Ahmed, “Debt Burden, Military Spending And Growth In Sub-Saharan Africa: A
Dynamic Panel Data Analysis”, Defence and Peace Economics, Vol. 23, No. 5 (2012), pp. 485, 493,
494.
63
Roland Craigwell, Llewyn Rock and Ronald Sealy, “On the Determination of the External Public
Debt: The Case of Barbados”, Social and Economic Studies, Vol. 37, No. 4, Regional Programme of
Monetary Studies (December 1988), pp. 137, 142-143.
64
Catherine A. Pattillo, Helene Poirson and Luca Antonio Ricci, “Through What Channels Does
External Debt Affect Growth?”, Brookings Trade Forum 2003, eds. Susan M. Collins and Dani Rodrik
(March 2, 2004), pp. 238, 245, 250.
65
Siti Nurazira Mohd Daud and Jan M. Podivinsky, “Revisiting the role of external debt in economic
growth of developing countries”, Journal of Business Economics and Management, Vol. 13, No. 5
(2012), pp. 968, 972-973.
66
Muhammad Shahbaz, Muhammad Shahbaz Shabbir and Muhammad Sabihuddin Butt, “Does
Military Spending Explode External Debt in Pakistan?”, Defence and Peace Economics (2013),
http:/ / dx.doi.org/ 10.1080/ 10242694.2012.724878, pp. 1, 5, 8.
67
C. Kenrick Hunte, “Saving Behaviour and External Debt-Service: Evidence from Sub-Saharan
Africa”, African Review of Money Finance and Banking (2002), pp. 70-72.

17
models. Such models of the static variety include previously mentioned studies such
as Metwally and Tamaschke (1994a), Metwally and Tamaschke (1994b) and Fosu
(1999). The input of year specific data, as they appear for Metwally and Tamaschke
(1994a)68
and Metwally and Tamaschke (1994b)69
, do not automatically preclude
their models as static so long as lagged variables have not been inputed, while Fosu
(1999)70
relies on country specific data. Dynamic multivariate linear regression
models include studies such as Tchereni, Sekahmpu and Ndovi’s (2013) examination
of the growth rate of Malawi’s GDP tied to stock of external debt among other
variables which justified the adoption of lags to present “a robust explanation of
macroeconomic factors that affect economic growth in Malawi”71
; Aizenman, Jinjarak
and Park (2013) whose study of change of GDP per capita subject to lagged short
term debt and the interaction variable between state fragility and short-term debt
among other variables employed lagged dependent and independent variables72
, and;
Hallak (2013) where growth of GDP per capita and growth of constant GDP are
assigned as dependent variables commensurate with private sector share of external
debt with control variables featuring lagged GDP per capita growth, inter alia73
.
Logarithmic-linear multivariate regression models also exhibit these twin types. Static
ones include Lin and Sosin (2001) measuring the logarithmic growth of GDP per
capita subject to foreign debt-to-GDP ratio among other variables who note that
exploring “time-related issues” is “not the purpose of the cross-section model
presented here”74
. Examples of dynamic multivariate logarithmic-linear models
include Pattillo, Poirson and Ricci (2003), Daud and Podivinsky (2012) and
Craigwell, Rock and Sealy (1988) all afore-mentioned. The Pattillo, Poirson and Ricci
68
M. M. Metwally and Rick Tamaschke, “The Interaction Among Foreign Debt, Capital Flows, and
Growth: Case Studies”, Journal of Policy Modeling, Vol. 16, No. 6 (1994a), p. 599.
69
M. M. Metwally and Rick Tamaschke, “The Foreign Debt Problem of North African Countries”,
African Review of Money Finance and Banking, No. 1/2 (1994b), pp. 115-116.
70
Augustin Kwasi Fosu, “The External Debt Burden and Economic Growth in the 1980s: Evidence
from sub-Saharan Africa”, Canadian Journal of Development Studies/Revue canadienne d’études du
development, Vol. 20, No. 2 (1999), pp. 310-311.
71
B. H. M. Tchereni, T. J. Sekhampu and R. F. Ndovi, “The Impact of Foreign Debt on Economic
Growth in Malawi”, African Development Review, Vol. 25, No. 1 (March 2013), p. 88.
72
Joshua Aizenman, Yothin Jinjarak and Donghyun Park, “Capital Flows and Economic Growth in the
Era of Financial Integration and Crisis, 1990-2010”, Open Economies Review, Vol. 24, No. 3 (July
2013), p. 17.
73
Issam Hallak, “Private sector share of external debt and financial stability: Evidence from bank
loans”, Journal of International Money and Finance, Vol. 32 (2013), p. 34.
74
Shuanglin Lin and Kim Sosin, “Foreign debt and economic growth”, Economics of Transition, Vol.
9, No. 3 (2001), pp. 639, 641, 642.

18
(2003) study includes lagged GDP per capita among the control variables75
. Daud and
Podivinsky (2012) base their analysis on a “general dynamic model”76
. Where change
in public external debt is the regressand, “cost of foreign credit variable” is designated
as a lagged regressor which renders Craigwell, Rock and Sealy’s (1988) model
dynamic77
. Virtually all cointegration models mentioned up to this point are dynamic
models. Further examples include Butts, Mitchell and Berkoh (2012) and Chowdhury
(1994). Butts, Mitchell and Berkoh (2012) utilized the “autoregressive distributed lag
model approach” to examine the “short- and long-run relationships between external
debt and economic growth in Thailand” from 19702 to 2003 with exchange rate and
international reserves as “auxiliary variables”78
. Chowdhury (1994) applied “lagged
dependent variables” in his causality test on total external debt and GNP to a total of
seven countries spanning South, Southeast and East Asia for the period 1970-8879
.
The usefulness of the empirical model approach merits discussion. While the diversity
of models introduced above prevents any specific meaningful critique, some common
advantages and disadvantages can be discerned from across the spectrum. The
empirical model approach seems to boast three advantages. Firstly, the strength of the
relationship among target variables can be measured. Causal effects can be precisely
computed mathematically. These have been borne out in expressions in linear and
logarithmic terms as mentioned. Even the direction of the magnitude change, i.e. in
increments or decrements, can be shown. Secondly, like theoretical models,
hypotheses can be tested. Regression requires subjecting some hypothesis to
verification. Such verification is processed through an algorithm of equations that
enables conclusions to be drawn from the data inputs through the variables pre-
specified. Inclusion of time dynamism, cointegration tests and analysis on different
75
Catherine A. Pattillo, Helene Poirson and Luca Antonio Ricci, “Through What Channels Does
External Debt Affect Growth?”, Brookings Trade Forum 2003, eds. Susan M. Collins and Dani Rodrik
(March 2, 2004), p. 245.
76
Siti Nurazira Mohd Daud and Jan M. Podivinsky, “Revisiting the role of external debt in economic
growth of developing countries”, Journal of Business Economics and Management, Vol. 13, No. 5
(2012), p. 974.
77
Roland Craigwell, Llewyn Rock and Ronald Sealy, “On the Determination of the External Public
Debt: The Case of Barbados”, Social and Economic Studies, Vol. 37, No. 4, Regional Programme of
Monetary Studies (December 1988), pp. 142-143.
78
Hector C. Butts, Ivor Mitchell and Albert Berkoh, “Economic Growth Dynamics and Short-term
External Debt in Thailand”, The Journal of Developing Areas, Vol. 46, No. 1 (Spring 2012), pp. 101,
107.
79
Khorshed Chowdhury, “A structural analysis of external debt and economic growth: some evidence
from selected countries in Asia and the Pacific”, Applied Economics, Vol. 26, No. 12 (1994), p. 1123.

19
dependent variables—external debt and national income—can thus be made possible.
Thirdly, empirical models arguably address the ‘lack of realism’ claim that theoretical
models suffer from. Data collected from fieldwork observations can ground
hypotheses through inductive inquiry. However, qualifications belie these pluses.
Firstly, some evidence of potential simultaneous causality bias exists. This occurs
when some empirical models do not adjust for reverse causality between variables.
Butts (2009) reports “bi-directional causality relationships” between economic growth
and short-term external debt in his study on 27 Latin American and Caribbean
countries80
. Secondly, data gaps can compromise the integrity of empirical models.
For example, insufficient data on external debt compelled Checherita-Westphal and
Rother (2012) to resort to gross government debt instead of external (public) debt as
one of the independent variables in a regression function with growth rate of GDP per
capita as dependent variable in their examination of 12 European countries81
. Thirdly,
apparent contradictory conclusions can be reached when relying on empirical
modelling. Such conflict weakens the consensus between Aizenman, Jinjarak and
Park (2013) and Tchereni, Sekhampu and Ndovi (2013) on the negative effects
external debt imposes on GDP82
, to the extent of the former’s conclusion that
“...short-term debt had a sizable negative impact on growth in the crisis period but no
impact in the noncrisis period”83
. Fourthly, conceptual confusion undermines an
empirical construct’s integrity. An instructive case is Kazmi’s criticism of the earlier
study by Ahmed, Butt and Alam (2000) for apparently liberally interpreting
interchangeably debt as a stock variable and debt-servicing as a flow variable, creating
“a diffused and blurred theoretical framework” giving rise to “contradictory results”84
.
80
Hector C. Butts, “Short Term External Debt and Economic Growth—Granger Causality: Evidence
from Latin America and the Caribbean”, The Review of Black Political Economy, Vol. 36, No. 2 (June
2009), p. 93.
81
Cristina Checherita-Westphal and Philipp Rother, “The impact of high government debt on economic
growth and its channels: An empirical investigation for the euro area”, European Economic Review,
Vol. 56, No. 7 (2012), pp. 1395, 1398.
82
2013), p. 386; B. H. M. Tchereni, T. J. Sekhampu and R. F. Ndovi, “The Impact of Foreign Debt on
Economic Growth in Malawi”, African Development Review, Vol. 25, No. 1 (March 2013), pp. 85, 88.
83
2013), p. 386.
84
Qazi Masood Ahmed, Mohammad Sabihuddin Butt, Shaista Alam and Aqdas Ali Kazmi, “Economic
Growth, Export, and External Debt Causality: The Case of Asian Countries [with Comments]”, The
Pakistan Development Review, Vol. 39, No. 4, Papers and Proceedings PART II Sixteenth Annual
General Meeting and Conference of the Pakistan Society of Development Economists Islamabad,
January 22-24, 2001 (Winter 2000), pp. 607-608.

20
Although perhaps unrepresentative of overall literature, four observations can
nevertheless be discerned. Firstly and obviously, empirical models appear to be
popular with studies centring on external debt’s impact on national income
accounting. The following papers bear testimony to this: Fosu (1999), Metwally and
Tamaschke (1994b), Lin and Sosin (2001), Aizenman, Jinjarak and Park (2013), Daud
and Podivinsky (2011), Daud and Podivinsky (2012), Vamvakidis (2008), Tchereni,
Sekahmpu and Ndovi (2013), Checherita-Westphal and Rother (2012), and Pattillo,
Poirson and Ricci (2003). Research on the impact on external debt seem confined to a
select few, such as Gani (1999), and Craigwell, Rock and Sealy (1988). That majority
of these studies are of contemporary vintage can be accounted for by modern
advances in statistical techniques as previously noted. Worth considering is the
evident scarcity of certain research topics which can serve to illuminate possible
literature gaps that future empirical studies can more intensively explore. Secondly,
most empirical models are efficacious as they present logical results that support the
hypotheses proposed. Only a few produce counter-intuitive ones: Tchereni, Sekahmpu
and Ndovi (2013), Chowdhury (1994) and Ahmed, Butt and Alam (2000). Excepting
the latter as critiqued by Kazmi, that their hypotheses are debunked do not
automatically dismiss their research, barring evidence of technical misapplication. In
a sense, healthy debate would benefit from more contrarian viewpoints and their
publication ought to be encouraged. Thirdly, the use of qualifiers has been prevalent,
as with theoretical models. These are observed in Fosu (1999), Metwally and
Tamaschke (1994b), Lin and Sosin (2001), Vamvakidis (2008), Checherita-Westphal
and Rother (2012), Pattillo, Poirson and Ricci (2003), Daud and Podivinsky (2012),
Gani (1999), Craigwell, Rock and Sealy (1988), Butts, Mitchell and Berkoh (2012),
and Karagol (2006). The use of assumptions warns that empirical models are relevant
only to the extent that they are valid and reliable for the assumptions fulfilled; and
thus should serve to indicate the veracity of a study which only those empirically
trained can capably identify. Fourthly and relatedly, studies conducted with empirical
models seem capable of providing only tentative conclusions. The use of assumptions
supports this view, exacerbated by assumptions’ dubious reflection of reality.
Moreover, the coefficients derived from empirical models are merely postulations
based on past examples; which can serve as useful guide for prediction but doubtful as
to their predictive powers for future cases.

21
5. CONCLUSIONS
Some recapitulation is in order. The indicator approach has been presented as a
relatively simple ratio or proportion that external debt occupies in national income.
The theoretical modelling approach situates external debt and national income as
endogenous variables that do not necessarily require numerical values for resolution
and demonstration of mutual impact. Empirical models build on theoretical models to
present measurable impacts that external debt exerts on national income and vice-
versa. Indicators perhaps find use in initial calculations, with more demanding studies
employing theoretical models and find demonstration through empirical techniques.
Barring their respective limitations, a possible—and possibly ideal—combination
works to express indicators as variables embedded in a series of theoretical models to
find expression through empirical (statistical) techniques. However, as said, each
approach comes with it certain limitations that remain to be seen whether they can be
addressed when applied in tandem.
A second inference results from the sense obtained that a hierarchical ranking of
approaches can be discerned in terms of their relative superiority. Empirical models, it
seems, are choice methods as observed from the plethora of studies churned out. That
empirical models are not only tractable but calculable probably explain their
popularity. However, it is also observed that greater demands are imposed
commensurate with the sophistication of approach adopted. A certain proficiency with
complex mathematical manipulations is presumed as prerequisite when considering
theoretical models—and even more so with empirical models85
, as compared to the
indicator approach.
The choice of approach for each study should be determined from the conditions
imposed by the phenomenon of interest. Limiting factors of a paper should go beyond
temporal, terrestrial and financial considerations to include technical restrictions as
manifested by the working assumptions under which each approach operates
effectively. That the use of qualifications abounds throughout the discussion of
various papers above should justify sounding out this cautionary word. Empirical
85

22
modelling appears to be the favoured choice from above as gleaned from the
multitude of papers derived from it, but that should not be read as discrimination
against the indicator and theoretical modelling approaches. Insofar that the external
debt-national income relationship ought to be fleshed out in as great detail and depth,
employment of empirical models poses its own serious risks that it must make sense
at times to fall back on indicators or theoretical models. Such a sober recognition of
realities is necessary, which goes towards informing the summarized description of
each approach in Table 1.

23
Table 1: Characteristics of 3 approaches.
Approach Purpose Variants Pros Cons
Indicator To measure the
severity of foreign
indebtedness on
national income
Choice of
denominators:
national income or
exports of goods and
services
1) Easy to calculate
and understand
2) Not data
intensive
3) Absent
alternative choices
of indicators
4) Flexible long
term and short term
convenient
measurement
1) As measure of
national debt
burden debatable
2) Fluctuating
data
3) Static, not
dynamic,
displays
4) Questions of
critical debt
thresholds
5) Stock-versus-
flow conceptual
confusion
Choice of
numerators: external
debt principal or
external debt service
Theoretical
models
To solve for
unknown variables
or measure
movements among
variables; need not
require numerical
values
Choice of static or
dynamic models
1) Show variables
that affect target
variable
2) Compel
clarification of
assumptions
1) Use of
improper
assumptions
2) Reductionist
by over-
simplifying
reality
3) Risk of
mathematical
intractability
Use of difference
equations,
differential
equations, or both
Empirical
models
To determine
strength of
relationships
between variables
through correlation
Choice of dependent
variable: external
debt or national
income, or both (for
cointegration
testing)
1) Strength of
relationship
between target
variables
measurable
2) Allows testing
of different
hypotheses
3) Models more
grounded in reality
with empirical data
1) Potential
simultaneous
causality bias
2) Data gaps can
compromise
integrity of
model
3) Risk of
drawing
contradictory
conclusions
4) Conceptual
confusion can
undermine
model’s integrity
Linear or
logarithmic
expressions of
dependent variable
Choice of static or
dynamic models

24
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