Mailu, Stephen and Lukibisi, Barasa and Waithaka, Michael (2011): Application of various count models: Sahiwal demand from Naivasha.
Download (1MB) | Preview
Sahiwal bulls have been bred at the National Sahiwal Stud (NSS) in Naivasha since the late 1960s. The breed is credited for its ability to withstand conditions which other introduced cattle breeds find it difficult, especially those in the ASALs. The sahiwal will produce milk with little supplementation and can let down milk without calf on foot. Farmers interested in acquiring this germplasm to upgrade their local cattle do so either through use of AI with semen from CAIS or alternatively purchase live breeding stock directly from the NSS or other breeding farms. Over the years, this demand for the latter has been recorded through written requests to the farm management for bulls. Recently however, the NSS management has raised concern over its inability to service all the requests for breeding stock. A total of 802 letters were isolated from archived records which represented requests for a total of 5,531 animals from the NSS yielding a rough estimate of 6-7 animals per request where majority of the requests (42%) were for 1-2 animals and an additional 20% are composed of requests for between 3-5 animals. Graphical examination of count of requests for breeding stock for 1971-2007 shows a possible decline in these requests, which is at variance with what management is experiencing. We hypothesize that since the mobile phone boom starting in the early 2000s, demand may have been expressed differently rather than in written form. It would also be expected that as milk prices improve, farmers would increase their demand for breeding stock and conversely, as prices for the animals rise, their demand would decline. Rainfall improves pasture availability and we also hypothesize that this way, farmers are encouraged to increase their stock.
To explore these issues more systematically, we fit these monthly count data to Poisson Exponentially Weighted Moving Average (PEWMA), Poisson Autoregressive PAR(p) and poisson models with phone use, milk prices and rainfall as explanatory variables. These models are implemented in R and we use data for the period November 1990 to December 2007. In these models, we use real prices and the price of milk is used in place of the price for breeding animals. We do this for two reasons (i) to avoid multicollinearity since there is a high (+0.98) correlation between sahiwal prices and the price of milk and (ii) we believe that since breeding animals are acquired by farmers to upgrade their local cattle to produce more milk, the price of milk provides more information about the decision to invest in a breeding animal. We begin by examining the ACF plot to identify the presence of dynamics in the data. In addition, zero inflation is negligible and the zero inflation versions of these models are not necessary. The chi-square statistic used to compare the PAR(1) and PAR(2) is not large enough to reject the PAR(1) over the latter. Further, results show that phone use and prices led to reduced number written of requests for sahiwal animals while the contribution of rainfall is positive. The PAR(p) short run multipliers for phone use are computed as -0.77 and -0.67 for the PAR(1) and PAR(2) respectively while the long run multipliers are -0.95 and -0.91. We conclude that phone use may have changed the way demand for breeding animals is expressed.
|Item Type:||MPRA Paper|
|Original Title:||Application of various count models: Sahiwal demand from Naivasha|
|Keywords:||Count data; Sahiwal; Breeding; Mobile phones|
|Subjects:||Q - Agricultural and Natural Resource Economics; Environmental and Ecological Economics > Q1 - Agriculture > Q16 - R&D; Agricultural Technology; Biofuels; Agricultural Extension Services
C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C52 - Model Evaluation, Validation, and Selection
C - Mathematical and Quantitative Methods > C0 - General > C01 - Econometrics
|Depositing User:||Stephen Mailu|
|Date Deposited:||07. Jul 2011 13:01|
|Last Modified:||12. Feb 2013 10:38|
Aklilu Y (2002). An Audit of the Livestock Marketing Status in Kenya, Ethiopia and Sudan (Vol. I), Nairobi, April 2002
Bebe B.O., Thorpe W., Udo H.M.J. and Mulinge W. (2000). Breed preferences and breeding practices in smallholder dairy systems of the central highlands of Kenya. Paper presented at the 7th KARI Biennial Scientific Conference, 13-17 November 2000, KARI Headquarters, Nairobi, Kenya
Boone, R., BurnSilver, S., and Thornton, P., (2006) Optimizing aspects of land use intensification in Southern Kajiado District, Kenya. Final Report to the International Livestock Research Institute, Nairobi, Kenya. Reto-o-Reto Project, DGIC, December 2006. Available at: www.reto-o-reto.org
Brandt P.T. and Williams J.T. (2001) A Linear Poisson Autoregressive Model: the PAR(p). Political Analysis 9(2): 164-184
Brandt P.T., Williams J.T., Fordham B.O. and Pollins B. (2000) Dynamic Modeling for Persistent Event-Count Time Series. American Journal of Political Science, 44(4): 823–843
Cameron, A.C., and Trivedi, P.K. (1998). Regression Analysis of Count Data. NewYork: Cambridge University Press.
Caro T. and Scholte P. (2007) When protection falters. African Journal of Ecology, 45(3):233-253
Cecchi G., Wint W., Shaw A., Marletta A., Mattioli R. and Robinson T. (2009) Geographic distribution and environmental characterization of livestock production systems in Eastern Africa Agriculture, Ecosystems and Environment 135: 98–110
Cecchi G., Wint W., Shaw A., Marletta A., Mattioli R., and Robinson T. (2009) Geographic distribution and environmental characterization of livestock production systems in Eastern Africa Agriculture, Ecosystems and Environment 135: 98–110
Coe M.J., Cumming D.H and Phillipson J (1976) Biomass and production of large African herbivores in relation to rainfall and primary production. Oecologia 22: 341-354
EAC (2002) Freeing Cross Border Trade of Agricultural Products: Present Trade and Recommendations for Liberalizing Cross Border Trade, EAC Arusha, EAC; GTZ 2002, pp71
East R. (1984) Rainfall, soil nutrient status and biomass of large African savanna mammals. African Journal of Ecology 22(4):245-270
Gamba P. (2006). Beef and Dairy cattle Improvement Services: A Policy perspective, Tegemeo Working Paper No 23, 2006
Gruère G., Guiliani A and Smale M (2006) Marketing Underutilized Sepecies for the Benefit of the Poor: A Conceptual Framework, IFPRI EPT Discusion Paper No. 154
Heineny A. (2003) Modelling Time Series Count Data: An Autoregressive Conditional Poisson Model, MPRA Paper No. 8113 Online at http://mpra.ub.uni-muenchen.de/8113/
Illatsia E.D. Muasya T.K., Muhuyi W.B. and Kahi A.K. (2007) Milk production and reproductive performance of Sahiwal cattle in semi-arid Kenya, Tropical Science, 47(3): 120-127
Jung R. Kukuk M. and Liesenfeld R. (2005) Time Series of Count Data: Modelling and Estimation, Economics Department Economics, Christian-Albrechts-Universität Kiel Working Paper No 2005-08
KARI (2007) National Sahiwal Stud Bulletin, February 2007, KARI, National Animal Husbandry Research Centre
Khan M.S., G. Bilal G., Bajwa I.R., Rehman Z. and Ahmad S. (2008) Estimation of Breeding Values of Sahiwal Cattle Using Test Day Milk Yields, Pakistan Vet. J., 2008, 28(3): 131-135.
Kristjanson P., Radeny M., Nkedianye D., Kruska R., Reid R., Gichohi H., Atieno F. and Sanford R. (2002) Valuing alternative land-use options in the Kitengela wildlife dispersal area of Kenya. ILRI Impact Assessment Series 10. A joint ILRI (International Livestock Research Institute)/ACC (African Conservation Centre) Report. ILRI, Nairobi, Kenya. 61 pp.
Meyn K. and Wilkins J.V. (1974) Breeding for milk in Kenya, with particular reference to the Sahiwal Stud, available online http://www.fao.org/
Mpofu N. and Rege J.E.O. (2002) Monitoring of Sahiwal and Friesian cattle genetic improvement programmes in Kenya
Muhuyi WB, Lokwaleput I and Sinkeet SN (1999) Conservation and utilization of the Sahiwal cattle in Kenya. FAO Animal Genetics Research Information 26,35-44.
Muthee A. (2006) Kenya Livestock Sector Study: An Analysis of Pastoralist Livestock Products Market Value Chains and Potential External Markets for Live Animals and Meat, AU-IBAR&NEPDP
Ngigi M. (2005) The Case of Smallholder dairying in Eastern Africa, IFPRI, EPTD Discussion Paper No. 131, Washington D.C.
Nyariki D.M. (2009) Impacts of policy reforms on the livestock industry in Kenya: The case of the dairy sector, Livestock Research for Rural Development 21 (10) 2009
Omiti J. (2002) Impacts of liberalisation in Kenya's dairy sector : In Rangnekar D. and Thorpe W. (eds). 2002. Smallholder dairy production and marketing— Opportunities and constraints. Proceedings of a South–South workshop held at NDDB, Anand, India, 13–16 March 2001. NDDB (National Dairy Development Board), Anand, India, and ILRI (International Livestock Research Institute), Nairobi, Kenya. 538 pp.
Rasmussen H.B., Wittenmyer G and Hamilton-Douglas I. (2006) Predicting time-specific changes in demographic processes using remote-sensing data. Journal of Applied Ecology 43:366-376
Scarpa R., Ruto E.S.K., Kristjanson P., Radeny M., Drucker A.G. and Rege J.E.O. (2003) “Valuing indigenous cattle breeds in Kenya: An empirical comparison of stated and revealed preference value estimates”, Ecol. Econ. 45 (3): 409-426
Sileshi G. (2008). The excess-zero problem in soil animal count data and choice of appropriate models for statistical inference Pedobiologia 52:1—17
Sileshi G., Hailu G. and Nyadzi G.I. (2009) Traditional occupancy–abundance models are inadequate for zero-inflated ecological count data, Ecological Modelling 220:1764–1775
Smith P.D., Tyler R.A. and Young E.M. (eds) (1996) Review of Kenyan Agricultural Research, (Vol. 1) Kenya Agricultural Research Institute, CAZS, University of Wales, Gwynned, United Kingdom
Tin A. (2008) Modeling Zero-Inflated Count Data with Underdispersion and Overdispersion, Paper 372-2008 SAS Global Forum Statistics and Data Analysis, Research Foundation for Mental Hygiene, New York, NY
Trial J.M.C., and K. E. Gregory (1981) Characterization of the Boran and Sahiwal Breeds of Cattle for Economic Characters Journal of Animal Science 52:1286-1293
Xu S., Jones R.H. and Grunwald G.K. (2007) Analysis of longitudinal count data with Serial Correlation Biometrical Journal 49(3): 416-428