Modeling Extremal Events: A Case Study of the Kenyan Public Debt

Josephat Onchangwa Motonu; Anthony Gichuhi Waititu; Joseph Kyalo Mung’atu

doi:doi:10.11648/j.ajtas.20160506.11

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Modeling Extremal Events: A Case Study of the Kenyan Public Debt

Josephat Onchangwa Motonu, Anthony Gichuhi Waititu, Joseph Kyalo Mung’atu

Received: 14 September 2016 Accepted: 23 September 2016 Published: 14 October 2016

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Abstract

Kenya’s public debt is sharply increasing and there are fears that in the long run, the situation in the country may, perhaps, be gravitating towards the boundaries of debt distress. This has been occasioned by the ever rising fiscal deficit as a result of high expenditure appetite and poor performance of tax revenue. In addition to that is the recent surge in mega infrastructure development which is anticipated to continue triggering uptake, and piling of more public debt. To model this phenomenon, this study has applied the Extreme Value Theory in modeling the public debt where Generalized Pareto Distribution has been used and subsequently, Value-at-Risk determined. Generally, the differenced debt stock data has been modeled by fitting the Generalized Pareto Distribution and a debt sustainability threshold has been determined as 1.263. This is interpreted to imply that the prevailing year's borrowing should not occasion a rise in public debt beyond 26.3 per cent of the previous year's level. Specifically, both the unconditional and conditional Value-at-Risk has been ascertained as 1.263 and 0.957 respectively, at α = 0.05 level of significance, which is the maximum tolerable debt limit. Further, by applying the loss function, it has been established that among the two methods, conditional Value-at-Risk is the efficient model for measuring public debt risk, connoting that at α = 0.05, the current year's borrowing, say, should occasion a public debt reduction by 4.27 per cent from the previous one for the country to vacillate within the debt sustainability realms. Finally, it is recommended that a further study be conducted by computing and using Net Present Value of debt indicators since the ones used in this study are aggregated in nominal terms.

DOI	10.11648/j.ajtas.20160506.11
Published in	American Journal of Theoretical and Applied Statistics (Volume 5, Issue 6, November 2016)
Page(s)	334-341
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Debt Distress, Fiscal Deficit, Generalized Pareto Distribution, Value-at-Risk, Loss Function, Debt Sustainability, Net Present Value

References

[1]	Alemayehu, F. G. (2003). The historical origin of African debt crisis. Eastern Africa Science Research Review, 19.
[2]	Lekomola, M. (2010). The African debt dilemma: An overview of magnitude, causes, effects and policy options. Journal of American Sciences, 6.
[3]	Reinhart, C. and Rogoff, K. (2011). From financial crash to debt crisis. American Economic Review, 101.
[4]	Panizza, U. (2008). Domestic and external public debt in developing countries. Policy Paper 188, UNCTAD.
[5]	Sarwaat, J., Xavier, M., Peter, A. C., and Sean, N. (2014). Staff guidance note on the fund’s engagement with small developing states. Policy Paper, International Monetary Fund, P.O. Box 92780, Washington D.C. 20090.
[6]	Ntawihebasenga, J. D., Mwita, J. K., and Mung’atu, J. K. (2014). Estimation of extreme value at risk in Rwanda exchange rate. European Journal of Statistics and Probability, 2: 14-22.
[7]	Koima, J. K., Mwita, P. N., and Nassiuma, D. K. (2013). An application of extreme value theory in the estimation of value-at-risk in Kenya stock market. Int. J. Cur. Tr. Res, 2: 276-284.
[8]	Valayoudoum, M, Bechir, R., and Abdelwahed, T. (2009). Extreme value theory and value-at-risk: Application to oil market. Energy Economics, (31).
[9]	Manfred, G. and Elvis, K. (2006). An application of extreme value theory for measuring financial risk. Computational Economics, 27(1): 1-23.
[10]	Ramazan, G. and Faruk, S. (2004). Extreme value theory and value-at-risk: Relative performance in emerging markets. International Journal of forecasting, 20: 287-303.
[11]	Fisher, R. and Tippet, L. (1928). Limiting forms of the frequency distribution of the largest or the smallest member of a sample. Proc. Cambridge Phil. Soc., 24: 180-190.
[12]	Davison, A. C. and Smith, R. L. (1990). Models for exceedance over high thresholds. Journal of Royal Statistics Society, B52 (3): 393-442.
[13]	Embrechts, P. Kluppelberg, C., and Mikosch, T. (1997). Modeling Extremal Events for Finance and Insurance. Springer.
[14]	Pickands, J. (1975). Statistical inference using extreme order statistics. Annals of Probability, 3: 119-131.
[15]	Balkema, A. and de Haan, L. (1974). Residual life time at great age. Annals of Probability, 3: 792-804.
[16]	Samuel, K. and Norman, L. J., editors (1992). Breakthroughs in Statistics, volume 1. Springer, New York, New York.
[17]	Tsay, R. S. (2005). Analysis of Financial Time Series. Wiley, New York.
[18]	Lopez, J. A. (1999). Methods of evaluating value-at-risk estimates. Federal Reserve Bank of San Francisco Economic Review, 2.

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APA Style

Josephat Onchangwa Motonu, Anthony Gichuhi Waititu, Joseph Kyalo Mung’atu. (2016). Modeling Extremal Events: A Case Study of the Kenyan Public Debt. American Journal of Theoretical and Applied Statistics, 5(6), 334-341. https://doi.org/10.11648/j.ajtas.20160506.11

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ACS Style

Josephat Onchangwa Motonu; Anthony Gichuhi Waititu; Joseph Kyalo Mung’atu. Modeling Extremal Events: A Case Study of the Kenyan Public Debt. Am. J. Theor. Appl. Stat. 2016, 5(6), 334-341. doi: 10.11648/j.ajtas.20160506.11

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AMA Style

Josephat Onchangwa Motonu, Anthony Gichuhi Waititu, Joseph Kyalo Mung’atu. Modeling Extremal Events: A Case Study of the Kenyan Public Debt. Am J Theor Appl Stat. 2016;5(6):334-341. doi: 10.11648/j.ajtas.20160506.11

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@article{10.11648/j.ajtas.20160506.11,
  author = {Josephat Onchangwa Motonu and Anthony Gichuhi Waititu and Joseph Kyalo Mung’atu},
  title = {Modeling Extremal Events: A Case Study of the Kenyan Public Debt},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {5},
  number = {6},
  pages = {334-341},
  doi = {10.11648/j.ajtas.20160506.11},
  url = {https://doi.org/10.11648/j.ajtas.20160506.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20160506.11},
  abstract = {Kenya’s public debt is sharply increasing and there are fears that in the long run, the situation in the country may, perhaps, be gravitating towards the boundaries of debt distress. This has been occasioned by the ever rising fiscal deficit as a result of high expenditure appetite and poor performance of tax revenue. In addition to that is the recent surge in mega infrastructure development which is anticipated to continue triggering uptake, and piling of more public debt. To model this phenomenon, this study has applied the Extreme Value Theory in modeling the public debt where Generalized Pareto Distribution has been used and subsequently, Value-at-Risk determined. Generally, the differenced debt stock data has been modeled by fitting the Generalized Pareto Distribution and a debt sustainability threshold has been determined as 1.263. This is interpreted to imply that the prevailing year's borrowing should not occasion a rise in public debt beyond 26.3 per cent of the previous year's level. Specifically, both the unconditional and conditional Value-at-Risk has been ascertained as 1.263 and 0.957 respectively, at α = 0.05 level of significance, which is the maximum tolerable debt limit. Further, by applying the loss function, it has been established that among the two methods, conditional Value-at-Risk is the efficient model for measuring public debt risk, connoting that at α = 0.05, the current year's borrowing, say, should occasion a public debt reduction by 4.27 per cent from the previous one for the country to vacillate within the debt sustainability realms. Finally, it is recommended that a further study be conducted by computing and using Net Present Value of debt indicators since the ones used in this study are aggregated in nominal terms.},
 year = {2016}
}

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TY  - JOUR
T1  - Modeling Extremal Events: A Case Study of the Kenyan Public Debt
AU  - Josephat Onchangwa Motonu
AU  - Anthony Gichuhi Waititu
AU  - Joseph Kyalo Mung’atu
Y1  - 2016/10/14
PY  - 2016
N1  - https://doi.org/10.11648/j.ajtas.20160506.11
DO  - 10.11648/j.ajtas.20160506.11
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 334
EP  - 341
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20160506.11
AB  - Kenya’s public debt is sharply increasing and there are fears that in the long run, the situation in the country may, perhaps, be gravitating towards the boundaries of debt distress. This has been occasioned by the ever rising fiscal deficit as a result of high expenditure appetite and poor performance of tax revenue. In addition to that is the recent surge in mega infrastructure development which is anticipated to continue triggering uptake, and piling of more public debt. To model this phenomenon, this study has applied the Extreme Value Theory in modeling the public debt where Generalized Pareto Distribution has been used and subsequently, Value-at-Risk determined. Generally, the differenced debt stock data has been modeled by fitting the Generalized Pareto Distribution and a debt sustainability threshold has been determined as 1.263. This is interpreted to imply that the prevailing year's borrowing should not occasion a rise in public debt beyond 26.3 per cent of the previous year's level. Specifically, both the unconditional and conditional Value-at-Risk has been ascertained as 1.263 and 0.957 respectively, at α = 0.05 level of significance, which is the maximum tolerable debt limit. Further, by applying the loss function, it has been established that among the two methods, conditional Value-at-Risk is the efficient model for measuring public debt risk, connoting that at α = 0.05, the current year's borrowing, say, should occasion a public debt reduction by 4.27 per cent from the previous one for the country to vacillate within the debt sustainability realms. Finally, it is recommended that a further study be conducted by computing and using Net Present Value of debt indicators since the ones used in this study are aggregated in nominal terms.
VL  - 5
IS  - 6
ER  -

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Author Information

Josephat Onchangwa Motonu

Parliamentary Budget Office, Parliament of Kenya, Nairobi, Kenya
Anthony Gichuhi Waititu

Department of Statistics and Actuarial Science, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
Joseph Kyalo Mung’atu

Department of Statistics and Actuarial Science, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya

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APA Style

Josephat Onchangwa Motonu, Anthony Gichuhi Waititu, Joseph Kyalo Mung’atu. (2016). Modeling Extremal Events: A Case Study of the Kenyan Public Debt. American Journal of Theoretical and Applied Statistics, 5(6), 334-341. https://doi.org/10.11648/j.ajtas.20160506.11

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ACS Style

Josephat Onchangwa Motonu; Anthony Gichuhi Waititu; Joseph Kyalo Mung’atu. Modeling Extremal Events: A Case Study of the Kenyan Public Debt. Am. J. Theor. Appl. Stat. 2016, 5(6), 334-341. doi: 10.11648/j.ajtas.20160506.11

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AMA Style

Josephat Onchangwa Motonu, Anthony Gichuhi Waititu, Joseph Kyalo Mung’atu. Modeling Extremal Events: A Case Study of the Kenyan Public Debt. Am J Theor Appl Stat. 2016;5(6):334-341. doi: 10.11648/j.ajtas.20160506.11

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@article{10.11648/j.ajtas.20160506.11,
  author = {Josephat Onchangwa Motonu and Anthony Gichuhi Waititu and Joseph Kyalo Mung’atu},
  title = {Modeling Extremal Events: A Case Study of the Kenyan Public Debt},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {5},
  number = {6},
  pages = {334-341},
  doi = {10.11648/j.ajtas.20160506.11},
  url = {https://doi.org/10.11648/j.ajtas.20160506.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20160506.11},
  abstract = {Kenya’s public debt is sharply increasing and there are fears that in the long run, the situation in the country may, perhaps, be gravitating towards the boundaries of debt distress. This has been occasioned by the ever rising fiscal deficit as a result of high expenditure appetite and poor performance of tax revenue. In addition to that is the recent surge in mega infrastructure development which is anticipated to continue triggering uptake, and piling of more public debt. To model this phenomenon, this study has applied the Extreme Value Theory in modeling the public debt where Generalized Pareto Distribution has been used and subsequently, Value-at-Risk determined. Generally, the differenced debt stock data has been modeled by fitting the Generalized Pareto Distribution and a debt sustainability threshold has been determined as 1.263. This is interpreted to imply that the prevailing year's borrowing should not occasion a rise in public debt beyond 26.3 per cent of the previous year's level. Specifically, both the unconditional and conditional Value-at-Risk has been ascertained as 1.263 and 0.957 respectively, at α = 0.05 level of significance, which is the maximum tolerable debt limit. Further, by applying the loss function, it has been established that among the two methods, conditional Value-at-Risk is the efficient model for measuring public debt risk, connoting that at α = 0.05, the current year's borrowing, say, should occasion a public debt reduction by 4.27 per cent from the previous one for the country to vacillate within the debt sustainability realms. Finally, it is recommended that a further study be conducted by computing and using Net Present Value of debt indicators since the ones used in this study are aggregated in nominal terms.},
 year = {2016}
}

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TY  - JOUR
T1  - Modeling Extremal Events: A Case Study of the Kenyan Public Debt
AU  - Josephat Onchangwa Motonu
AU  - Anthony Gichuhi Waititu
AU  - Joseph Kyalo Mung’atu
Y1  - 2016/10/14
PY  - 2016
N1  - https://doi.org/10.11648/j.ajtas.20160506.11
DO  - 10.11648/j.ajtas.20160506.11
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 334
EP  - 341
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20160506.11
AB  - Kenya’s public debt is sharply increasing and there are fears that in the long run, the situation in the country may, perhaps, be gravitating towards the boundaries of debt distress. This has been occasioned by the ever rising fiscal deficit as a result of high expenditure appetite and poor performance of tax revenue. In addition to that is the recent surge in mega infrastructure development which is anticipated to continue triggering uptake, and piling of more public debt. To model this phenomenon, this study has applied the Extreme Value Theory in modeling the public debt where Generalized Pareto Distribution has been used and subsequently, Value-at-Risk determined. Generally, the differenced debt stock data has been modeled by fitting the Generalized Pareto Distribution and a debt sustainability threshold has been determined as 1.263. This is interpreted to imply that the prevailing year's borrowing should not occasion a rise in public debt beyond 26.3 per cent of the previous year's level. Specifically, both the unconditional and conditional Value-at-Risk has been ascertained as 1.263 and 0.957 respectively, at α = 0.05 level of significance, which is the maximum tolerable debt limit. Further, by applying the loss function, it has been established that among the two methods, conditional Value-at-Risk is the efficient model for measuring public debt risk, connoting that at α = 0.05, the current year's borrowing, say, should occasion a public debt reduction by 4.27 per cent from the previous one for the country to vacillate within the debt sustainability realms. Finally, it is recommended that a further study be conducted by computing and using Net Present Value of debt indicators since the ones used in this study are aggregated in nominal terms.
VL  - 5
IS  - 6
ER  -

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