Derivation of a Stochastic Labour Market Model from a Semi – Markov Model
The labour Market which is a major component of any economy refers to the supply and demand for labour. The two possible labour market states are unemployment and employment, and the transitions between these states are described by Markov processes. This paper is aimed at deriving a two – state stochastic model from the interval transition probability of a Semi – Markov Model that can be used to study the transition rate between the two labour market states. A stochastic model of four equations is derived using the probable movement between the two labour market states. The solution of the model exist and it is unique.The derived model equations are solved analytically and matlab programmes are written to help in the computation of the probable transition probabilities. The results of applying this model to the Nigeria’s labour market shows that the rate at which individuals are moving from unemployment state to employment state is very small compared to the rate at which individuals are remaining unemployed: about 559,948 persons (0.69%) are likely to enter the employment state from the unemployment state in 2035 while about 80,445,864 (99.13%) persons are likely to remain unemployed in that same year (2035). Also, the rate at which individuals are moving from employment state to unemployment state is very small compared to the rate at which individuals are remaining employed: about 4,604,040 (6.80%) persons are likely to enter the unemployment state from the employment state in 2035 while about 55,532,851 (82.02%) persons are likely to remain employed in that same year (2035) thereby increasing the number of unemployed. The result also indicates that this model can only measure effectively short term movements between the two labour market states.
Von, V. (2009). Lessons Learned from Germany’s 2001-2006 Labor Market Reforms – Inaugural – Dissertation. Diplom – Volkswirtin Irene Schumm, geb. Endres. W¨urzburg. https://opus.bibliothek.uni-wuerzburg.de/opus4-wuerzburg/frontdoor/deliver/index/do cId/3538/file/Schummdiss.pdf./Accessed 27 March 2017.
National Bureau of Statistics (2015a). Presentation of Labour Statistics Based on Revised Concepts and Methodology for Computing Labour Statistics in Nigeria/http://www.nigerianstat.gov.ng/pages/download/Accessed 27 July 2017.
National Bureau of Statistics (2016). Unemployment/Under – Employment Watch-Q3. http://www.nigeriastat.ng/report/481/ Accessed 01 September 2017.
International Labour Organization (2012). Global employment trends for youth 2012. http://www.ilo.org/wcmsp5/groups/public/...dgreports/--dcomm/documents/publicatio n/wcms-180976.pdf/Accessed 9 July 2017.
Subair, G. (2013). Nigeria’s Unemployment rate hits 22%- World Bank. Nigerian Tribune Online. http://tribune.com.gn/Nigeria/Accessed Accessed 01 September 2017.
Asaju, K., Arome, S., Anyio, S. F. (2014b). The rising rate of unemployment in Nigeria: the socio-economic and political implications. Global Business and Economics Research Journal, 3(2), 12-32.
Uddin, P. S. O., Uddin, O. O. (2013). Causes, Effects and Solutions to Youth Unemployment Problems in Nigeria. Journal of Emerging Trends in Economics and Management Sciences (JETEMS), 4(4), 397-402.
Asaju, K., Adagba, S. O., Kajang, T. J. (2014a). The Efficacy of Fiscal Policy in promoting Economic Growth and Poverty Reduction in Nigeria. Research in World Economy, 5(1), 33-40.
Meron D. (2016). Modeling and Forecasting Unemployment Rate in Sweden using various Econometric Measures. M.SC. Thesis, Örebro University School of Business, Department of Applied Statistics. Available on https://www.diva-portal.org/smash/get/diva2:949512/FULLTEXT01 .pdf .59 pp.
Adenomon, M. O.: Modelling and Forecasting Unemployment Rates in Nigeria Using ARIMA Model. FUW Trends in Science & Technology Journal, www.ftstjournal.com. 2 (1B):525 – 531 (2017)
Ayinde, T. O., Adekunle, O. A. and Muritala, A. T. (2018): Economic Growth and Sustainable Employment Generation: Empirical Validation of Okun’s Law in Nigeria. Journal of Management, Economics and Industrial Organization. 2(2): 33-59. (2018)
ILO, (2019): World Employment and Social Outlook – Trends 2019 – ILO. Retrieved from https://www.ilo.org/wcmsp5/groups/public/---dgreports/---dcomm/---publ/docum ents/publication/wcms_670542.pdf on 30/11/2019
Swart, J and Winter, A. (2013): Markov Processes: Theory and Examples. Retived from https://www.uni-due.de on 27/22/2019.
Kulkarni, V. G. (2011). Introduction to Modeling and Analysis of Stochastic Systems. 2nd Edition, New York, Springer Science+Business Media, USA.
Von, V. (2009). Lessons Learned from Germany’s 2001-2006 Labor Market Reforms – Inaugural – Dissertation. Retrieved from https://opus.bibliothek.uni-wuerzburg.de/files/3538/Schummdiss.pdf on 27/07/2017. 78-92.
Howard, R. A. (1971). Dynamic Probabilistic Systems, John Wiley, New York. (1&2).
Lancaster, T. (1990). The Econometric Analysis of Transition Data, 1st edition. Cambridge University Press, Cambridge.
Gheorghe, A. V. (1990). Decision Processes in Dynamic Probabilistic Systems. Kluwer Academic Publishers, DORDRECHT/BOSTON/LONDON.
Mehlman, A. (1979). Semi-Markovian Manpower Models in Continuous Time. Journal of Applied Probability. 16:416-422.
Foucher, Y., Mathieu, E., Saint-Pierre, P., Durand, j. and Daur`es, J. (2005). A semi-Markov model based on generalized Weibull distribution with an illustration for HIV disease. Biometrical Journal. 47:825–833.
Sheldon, R. M. (1996), Stochastic Processes, 2nd edition. John Wiley & Sons, Hoboken.
Kwaghkor, L. M., Onah, E. S. and Bassi, I. G. (2018): Stochastic Modelling of the Effect of Deforestation in Nigeria. Journal of the Nigerian Association of Mathematical Physics. 45(3). 379-386.
Ricardo, H. (2003). A Modern Introduction to Differential Equations. Houghton Mifflin Company, Boston New York.
Zill, D. G.: A First Course in Differential Equations with Applications. 2nd Edition. PWS Publishers Boston (1982).
Bryan, K. (1990). The Existence and Uniqueness Theorem for ODE’s (MA 466). https://www.rose-hulman.edu/~bryan/lottamath/ uniqde.pdf/Accessed 28 October 2018.
National Bureau of Statistics (2015b). Unemployment/Under – Employment Watch-Q4. http://www.nigeriastat.ng/report/307/Accessed 01 September 2017.