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

Published in American Journal of Theoretical and Applied Statistics (Volume 5, Issue 6)

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.

Published in	American Journal of Theoretical and Applied Statistics (Volume 5, Issue 6)
DOI	10.11648/j.ajtas.20160506.11
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), 2016. Published by Science Publishing Group

Keywords

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

References

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[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.
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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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