Skip to main content
SpringerLink
Log in

Optimal control of external debt for a developing economy

  • Application Article
  • Published:
OPSEARCH Aims and scope Submit manuscript

Abstract

When optimal trajectories are followed, what is the appropriate income tax rate on external debt? This study offers explanation to this question from the perspective of optimal control of external debt for a developing economy. The study proposes to use the methods of continuous-time optimal control theory to determine the external debt path wherein the welfare of the household sector is maximised over a given horizon. The implications of the obtained results are stated. The utility of the optimal debt policy is illustrated for the Nigerian case and the income tax rate that is consistent with the optimal external debt path is identified using the Kolmogorov–Smirnov test statistic. The analysis finds that there is a tendency for the optimal debt stock to fall as the income tax rate is increased.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

Notes

  1. Wages are determined on the basis of minimum wage legislation and implemented by the Income, Salaries and Wages Commission.

  2. This is because there is no provision for interest cancellation in debt rescheduling.

  3. Final consumption expenditure (formerly total consumption) is the sum of household final consumption expenditure (private consumption) and general government final consumption expenditure (general government consumption).

  4. General government final consumption expenditure (formerly general government consumption) includes all government current expenditures for purchases of goods and services (including compensation of employees).

  5. GDP is the sum of gross value added by all resident producers in the economy plus any product taxes and minus any subsidies not included in the value of the products.

  6. Gross capital formation (formerly gross domestic investment) consists of outlays on additions to the fixed assets of the economy plus net changes in the level of inventories.

References

  1. Abdullahi, M.M., Bt Abu Bakar, N.A., Hassan, S.B.: Determining the macroeconomic factors of external debt accumulation in Nigeria: an ARDL bound test approach. Proc. Soc. Behav. Sci. 211, 745–752 (2015)

    Article  Google Scholar 

  2. Abutaleb, A.S., Hamad, M.G.: Optimal foreign debt for Egypt: a stochastic control approach. Econ. Model. 29, 544–556 (2012)

    Article  Google Scholar 

  3. Adam, K.: Government debt and optimal monetary and fiscal policy. Eur. Econ. Rev. 55, 57–74 (2011). https://doi.org/10.1016/j.euroecorev.2010.11.003

    Article  Google Scholar 

  4. Ajayi, S.I. (1991) Macroeconomic approach to external debt: the case of Nigeria. AERC Research Paper 8. Initiatives Publishers, Nairobi

  5. Anita, S., Arnautu, V., Capasso, V.: An Introduction to Optimal Control Problems in Life Sciences and Economics. Springer, New York (2011)

    Book  Google Scholar 

  6. Anyanwu, J.C.: Nigerian Public Finance. Joanes Educational Publishers Ltd, Onitsha (1997)

    Google Scholar 

  7. Brock, W.E.: Trade and debt: the vital linkage. Foreign Aff. 62(5), 1037–1057 (1984)

    Article  Google Scholar 

  8. Casalin, F., Dia, E., Hallett, A.H.: Public debt dynamics with tax revenue constraints. Econ. Model. (2020). https://doi.org/10.1016/j.econmod.2019.11.035

    Article  Google Scholar 

  9. Datta, M.: Measurement of capital stock: the PIM and the equivalent proportional depreciation approach. Indian Econ. Rev. 41(2), 173–194 (2006)

    Google Scholar 

  10. Edo, S., Osadolor, N.E., Dading, I.F.: Growing external debt and declining export: the concurrent impediments in economic growth of sub-Saharan African countries. Int. Econ. (2019). https://doi.org/10.1016/j.inteco.2019.11.013

    Article  Google Scholar 

  11. Fleming, W.H., Stein, J.L.: Stochastic optimal control, international finance and debt. J. Bank. Financ. 28, 979–996 (2004)

    Article  Google Scholar 

  12. Gemmell, N.: Debt and the developing countries: a simple model of optimal borrowing. J. Dev. Stud. 24(2), 197–213 (1988). https://doi.org/10.1080/00220388808422063

    Article  Google Scholar 

  13. Guobadia, S.: Monetary policy, capital accumulation and output in the Nigerian economy. In: Iyoha, M.A., Itsede, C.O. (eds.) Nigerian Economy: Structure, Growth and Development, pp. 203–221. Mindex Publishing, Benin City (2002)

    Google Scholar 

  14. Greiner, A.: Human capital formation, public debt and economic growth. J. Macroecon. 30, 415–427 (2008)

    Article  Google Scholar 

  15. Kamien, M.I., Schwartz, N.L.: Dynamic Optimization: The Calculus of Variation and Optimal Control in Economics and Management, 2nd edn. Elsevier, Amsterdam (1992)

    Google Scholar 

  16. Lee, C., Wills, D., Schluter, G.: Examining the Leontief paradox in U.S. agricultural trade. Agric. Econ. 2, 259–272 (1988)

    Article  Google Scholar 

  17. Muhanji, S., Ojah, K.: Management and sustainability of external debt: a focus on the emerging economies of Africa. Rev. Dev. Fin. 1, 184–206 (2011)

    Article  Google Scholar 

  18. Muhanji, S., Ojah, K.: External shocks and persistence of external debt in open vulnerable economies: the case of Africa. Econ. Model. 28, 1615–1628 (2011)

    Article  Google Scholar 

  19. Nakajima, T., Takahashi, S.: The optimum quantity of debt for Japan. J. Jpn. Int. Econ. (2017). https://doi.org/10.1016/j.jjie.2017.08.002

    Article  Google Scholar 

  20. Nemlioglu, I., Mallick, S.: Does multilateral lending aid capital accumulation? Role of intellectual capital and institutional quality. J. Int. Money Financ. (2020). https://doi.org/10.1016/j.jimonfin.2020.102155

    Article  Google Scholar 

  21. Nikaido, H.: Prices and income distribution in a Leontief economy. J. Econ. Behav. Organ. 1, 61–79 (1980)

    Article  Google Scholar 

  22. Obadan, M.I.: External debt and management policy. In: Iyoha, M.A., Itsede, C.O. (eds.) Nigerian Economy: Structure, Growth and Development, pp. 327–350. Mindex Publishing, Benin City (2002)

    Google Scholar 

  23. Obstfeld, M., Rogoff, K.: Foundation of International Macroeconomics. The MIT Press, Cambridge (1996)

    Google Scholar 

  24. Qureshi, I., Liaqat, Z.: The long-term consequences of external debt: revisiting the evidence and inspecting the mechanism using panel VARs. J. Macroecon. 63, 103184 (2020). https://doi.org/10.1016/j.jmacro.2019.103184

    Article  Google Scholar 

  25. Raheem, M.I.: Assessing and managing external debt problems in Nigeria. World Dev. 22(8), 1223–1242 (1994)

    Article  Google Scholar 

  26. Siddique, A., Selvanathan, E.A., Selvanathan, S.: The impact of external debt on growth: evidence from Highly Indebted Poor Countries. J. Policy Model. (2016). https://doi.org/10.1016/j.jpolmod.2016.03.011

    Article  Google Scholar 

  27. Sanusi, G. P.: The impact of oil export earnings on Nigeria’s external debt. Working Paper, International Association for Energy Economics, USA (2010)

  28. Thanh, S.D., Canh, N.P., Ha, N.T.T.: Debt structure and earnings management: a non-linear analysis from an emerging economy. Finance Research Letters (2020). https://doi.org/10.1016/j.frl.2019.08.031

    Article  Google Scholar 

  29. Weber, T.A.: Optimal Control Theory with Applications in Economics. The MIT Press, Cambridge (2011)

    Book  Google Scholar 

  30. Yakita, A.: Sustainability of public debt, public capital formation, and endogenous growth in an overlapping generations setting. J. Public Econ. 92, 897–914 (2008)

    Article  Google Scholar 

Download references

Funding

No funding applicable for this research.

Author information

Authors and Affiliations

  1. Department of Statistics, University of Benin, P.M.B. 1154, Benin City, Nigeria

    Virtue U. Ekhosuehi

Authors
  1. Virtue U. Ekhosuehi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Virtue U. Ekhosuehi.

Ethics declarations

Conflict of interest

The author declares that there is no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ekhosuehi, V.U. Optimal control of external debt for a developing economy. OPSEARCH 58, 889–905 (2021). https://doi.org/10.1007/s12597-021-00514-8

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12597-021-00514-8

Keywords

Search

Navigation