Modeling Extremal Events: A Case Study of the Kenyan Public Debt
American Journal of Theoretical and Applied Statistics
Volume 5, Issue 6, November 2016, Pages: 334-341
Received: Sep. 14, 2016; Accepted: Sep. 23, 2016; Published: Oct. 14, 2016
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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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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.
Debt Distress, Fiscal Deficit, Generalized Pareto Distribution, Value-at-Risk, Loss Function, Debt Sustainability, Net Present Value
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Josephat Onchangwa Motonu, Anthony Gichuhi Waititu, Joseph Kyalo Mung’atu, Modeling Extremal Events: A Case Study of the Kenyan Public Debt, American Journal of Theoretical and Applied Statistics. Vol. 5, No. 6, 2016, pp. 334-341. doi: 10.11648/j.ajtas.20160506.11
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