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Maximum Likelihood Estimation of Singular Equation Systems with Autoregressive Disturbances


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  • Charles M. Beach
  • James G. MacKinnon


Maximum likelihood estimation of equation systems with first-order autocorrelation should, in principle, take into account the first observation and associated stationarity condition. In the general case, this leads to computational difficulties compared with conventional procedures, which perhaps explains the failure of the latter to incorporate the initial observation. However, in a special case where the autoregressive process has only one parameter, which is widely used for single equation systems such as demand systems, taking the first observation into account is no more difficult than ignoring it. The paper presents empirical results of estimating a demand system with Canadian data which suggest that maximizing the full likelihood function can yield very different and more reasonable estimates than maximizing the conventional one.

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Bibliographic Info

Paper provided by Queen's University, Department of Economics in its series Working Papers with number 276.

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Length: 20
Date of creation: 1977
Date of revision:
Publication status: Published in International Economic Review, 20, 1979
Handle: RePEc:qed:wpaper:276

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Cited by:
  1. Ge, Jiaoju & Kilmer, Richard L. & Washington, Andrew A., 2005. "The Derived Demand for Imported Cheese into Hong Kong," Policy Briefs 15694, University of Florida, International Agricultural Trade and Policy Center.
  2. Harri, Ardian & Muhammad, Andrew & Anderson, John D., 2008. "Estimating a Demand System with Seasonally Differenced Data," 2008 Annual Meeting, July 27-29, 2008, Orlando, Florida 6427, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
  3. Muhammad, Andrew & D’Souza, Anna & Amponsah, William, 2013. "Violence, Instability, and Trade: Evidence from Kenya’s Cut Flower Sector," World Development, Elsevier, vol. 51(C), pages 20-31.
  4. Frank T. Denton & Dean C. Mountain, 2007. "Exploring the Effects of Aggregation Error in the Estimation of Consumer Demand Elasticities," Social and Economic Dimensions of an Aging Population Research Papers 226, McMaster University.
  5. Turkington, Darrell A., 1998. "Efficient estimation in the linear simultaneous equations model with vector autoregressive disturbances," Journal of Econometrics, Elsevier, vol. 85(1), pages 51-74, July.
  6. Gary Wong, 2001. "Towards A More General Approach To Testing The Time Additivity Hypothesis," School of Economics and Finance Discussion Papers and Working Papers Series 098, School of Economics and Finance, Queensland University of Technology.
  7. Muhammad, Andrew, 2008. "Allowing for Group Effects When Estimating Import Demand for Source and Product Differentiated Goods," 2008 Annual Meeting, July 27-29, 2008, Orlando, Florida 6364, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
  8. Cooper, Russel J. & McLaren, Keith R. & Wong, Gary K. K., 2001. "On the empirical exploitation of consumers' profit functions in static analyses," Economics Letters, Elsevier, vol. 72(2), pages 181-187, August.
  9. K. K. Gary Wong, 2003. "Towards a more general approach to testing the time additivity hypothesis," Applied Economics, Taylor & Francis Journals, vol. 35(16), pages 1729-1738.
  10. Kilmer, Richard L. & Washington, Andrew A., 2000. "The Derived Demand For Imported Cheese In Hong Kong Differentiated By Source Country Of Production," 2000 Annual meeting, July 30-August 2, Tampa, FL 21724, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
  11. Kanniainen, Juho & Lin, Binghuan & Yang, Hanxue, 2014. "Estimating and using GARCH models with VIX data for option valuation," Journal of Banking & Finance, Elsevier, vol. 43(C), pages 200-211.
  12. Muhammad, Andrew & Ngeleza, Guyslain K., 2009. "European Union preferential trade agreements with developing countries and their impact on Colombian and Kenyan carnation exports to the United Kingdom:," IFPRI discussion papers 862, International Food Policy Research Institute (IFPRI).
  13. Gary K.K. Wong & Keith R. McLaren, 2002. "Regular and Estimable Inverse Demand Systems: A Distance Function Approach," Monash Econometrics and Business Statistics Working Papers 6/02, Monash University, Department of Econometrics and Business Statistics.
  14. Andrew Muhammad & Richard L. Kilmer, 2008. "The impact of EU export subsidy reductions on U.S. dairy exports," Agribusiness, John Wiley & Sons, Ltd., vol. 24(4), pages 557-574.
  15. Deschamps, Philippe J., 1998. "Full maximum likelihood estimation of dynamic demand models," Journal of Econometrics, Elsevier, vol. 82(2), pages 335-359, February.
  16. Capps, Oral, Jr., 1983. "Alternative Estimation Methods Of Nonlinear Demand Systems," Western Journal of Agricultural Economics, Western Agricultural Economics Association, vol. 8(01), July.
  17. Denton, Frank T. & Mountain, Dean C., 2011. "Exploring the effects of aggregation error in the estimation of consumer demand elasticities," Economic Modelling, Elsevier, vol. 28(4), pages 1747-1755, July.
  18. Washington, Andrew A. & Kilmer, Richard L., 2001. "The Derived Demand For Imported Cheese Into Japan By Country," International Trade in Livestock Products Symposium, January 18-19, 2001, Auckland, New Zealand 14551, International Agricultural Trade Research Consortium.
  19. Muhammad, Andrew & Ngeleza, Guyslain K., 2009. "The role of the Generalised System of Preferences (GSP) in determining carnation demand in the United Kingdom: implications for Colombian and Kenyan exports," Agrekon, Agricultural Economics Association of South Africa (AEASA), vol. 48(3), September.


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