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A semiflexible normalized quadratic inverse demand system: an application to the price formation of fish

Author

Listed:
  • Richard C. Bishop

    (Department of Agricultural and Applied Economics, University of Wisconsin, Madison, 423 Lorch Street, Taylor Hall, Madison, Wisconsin, 53706-1503, USA)

  • Matthew T. Holt

    (Departments of Agricultural and Resource Economics and Economics, North Carolina State University, Box 8110, Raleigh, NC 27695-8110, USA)

Abstract

We propose a new inverse demand system, the normalized quadratic distance function, which is similar to the normalized quadratic expenditure function of Diewert and Wales (1988a). Aside from being able to maintain concavity in quantities globally, the resulting specification is also `flexible.' In addition, to obtain more parsimonious specifications, we apply the rank reduction procedures of Diewert and Wales (1988b) to the model's Antonelli matrix. We illustrate the techniques by estimating a system of inverse demands for bi-monthly fish landings, 1971-1991, for U.S. Great Lakes ports. To illustrate the model's usefulness, exact welfare measures associated with catch restrictions are derived.

Suggested Citation

  • Richard C. Bishop & Matthew T. Holt, 2002. "A semiflexible normalized quadratic inverse demand system: an application to the price formation of fish," Empirical Economics, Springer, vol. 27(1), pages 23-47.
    • Handle: RePEc:spr:empeco:v:27:y:2002:i:1:p:23-47
    Note: received: May 1999/Final version received: November 2000
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    Citations

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    Cited by:

    1. Christiana E. Hilmer & Matthew T. Holt & Richard C. Bishop, 2010. "Bootstrapping Your Fish or Fishing for Bootstraps? Precision of Welfare Loss Estimates from a Globally Concave Inverse Demand Model of Commercial Fish Landings in the U.S. Great Lakes," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 93(1), pages 98-112.
    2. Allen M. Featherstone & Thomas A. Garrett & Thomas L. Marsh, 2003. "Input inefficiency in commercial banks: a normalized quadratic input distance approach," Working Papers 2003-036, Federal Reserve Bank of St. Louis.
    3. Lee, Young-Jae & Kennedy, P. Lynn, 2013. "Quantity And Exchange Rate Effects On U.S. Trout Prices," 2013 Annual Meeting, February 2-5, 2013, Orlando, Florida 142133, Southern Agricultural Economics Association.
    4. Robert H. Beach & Matthew T. Holt, 2001. "Incorporating Quadratic Scale Curves in Inverse Demand Systems," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 83(1), pages 230-245.
    5. Coralie KERSULEC & Luc DOYEN, 2022. "From fork to fish: The role of consumer preferences on the sustainability of fisheries," Bordeaux Economics Working Papers 2022-10, Bordeaux School of Economics (BSE).
    6. Marsh, Thomas L. & Featherstone, Allen M., 2003. "Inverse Demand Relationships For Wheat Food Use By Class," 2003 Annual meeting, July 27-30, Montreal, Canada 22001, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    7. Huang, Pei, 2014. "An Inverse Demand System for Blue Crab in the Chesapeake Bay: Endogeneity and Seasonality," 2014 Annual Meeting, July 27-29, 2014, Minneapolis, Minnesota 169827, Agricultural and Applied Economics Association.
    8. Speers, Ann E. & Besedin, Elena Y. & Palardy, James E. & Moore, Chris, 2016. "Impacts of climate change and ocean acidification on coral reef fisheries: An integrated ecological–economic model," Ecological Economics, Elsevier, vol. 128(C), pages 33-43.
    9. Ly, Nguyen & Henry, Kinnucan, 2016. "Some Effects of Income and Population Growth on Fish Price and Welfare," 2016 Annual Meeting, February 6-9, 2016, San Antonio, Texas 229892, Southern Agricultural Economics Association.
    10. K. K. Gary Wong & Hoanjae Park, 2018. "Consumption dynamics in inverse demand systems: an application to meat and fish demand in Korea," Agricultural Economics, International Association of Agricultural Economists, vol. 49(6), pages 777-786, November.
    11. Chris Moore & Charles Griffiths, 2018. "Welfare analysis in a two-stage inverse demand model: an application to harvest changes in the Chesapeake Bay," Empirical Economics, Springer, vol. 55(3), pages 1181-1206, November.
    12. Sooriyakumar Krishnapillai & Sarujan Sathiyamoorthy & Anushiya Sireeranhan, 2020. "Impact of Milk Powder Imports on Local Milk Industry and Consumers Welfare in Sri Lanka," International Journal of Economics and Financial Issues, Econjournals, vol. 10(5), pages 165-170.
    13. Thomas L. Marsh, 2005. "Economic substitution for US wheat food use by class," Australian Journal of Agricultural and Resource Economics, Australian Agricultural and Resource Economics Society, vol. 49(3), pages 283-301, September.
    14. Keith R. McLaren & K.K. Gary Wong, 2009. "Effective global regularity and empirical modelling of direct, inverse, and mixed demand systems," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 42(2), pages 749-770, May.
    15. Keith R. McLaren & K. K. Gary Wong, 2009. "The Benefit Function Approach to Modeling Price-Dependent Demand Systems: An Application of Duality Theory," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 91(4), pages 1110-1123.
    16. Michele Baggio & Jean-Paul Chavas, 2006. "On the Consumer Value of Environmental Diversity," Working Papers 35/2006, University of Verona, Department of Economics.
    17. Marsh, Thomas L. & Piggott, Nicholas E., 2013. "Measuring Pre-Commited Quantities Through Consumer Price Formation," 2013 Conference (57th), February 5-8, 2013, Sydney, Australia 152165, Australian Agricultural and Resource Economics Society.
    18. Toshinobu Matsuda, 2007. "Linearizing the inverse quadratic almost ideal demand system," Applied Economics, Taylor & Francis Journals, vol. 39(3), pages 381-396.
    19. Fengxia Dong & Thomas L. Marsh & Kyle W. Stiegert, 2006. "State Trading Enterprises in a Differentiated Product Environment: The Case of Global Malting Barley Markets," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 88(1), pages 90-103.
    20. Lee, Min-Yang A. & Thunberg, Eric M., 2012. "An Inverse Demand System for New England Groundfish: Welfare Analysis of the Transition to Catch Share Management," 2012 Annual Meeting, August 12-14, 2012, Seattle, Washington 123879, Agricultural and Applied Economics Association.
    21. 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.
    22. Pei Huang, 2015. "An Inverse Demand System for the Differentiated Blue Crab Market in Chesapeake Bay," Marine Resource Economics, University of Chicago Press, vol. 30(2), pages 139-156.
    23. Färe, Rolf & Grosskopf, Shawna & Hayes, Kathy J. & Margaritis, Dimitris, 2008. "Estimating demand with distance functions: Parameterization in the primal and dual," Journal of Econometrics, Elsevier, vol. 147(2), pages 266-274, December.
    24. Moore, Chris, 2015. "Welfare Estimates of Avoided Ocean Acidification in the U.S. Mollusk Market," Journal of Agricultural and Resource Economics, Western Agricultural Economics Association, vol. 40(1), pages 1-13.

    More about this item

    Keywords

    Global concavity; Distance function; Normalized quadratic; Inverse demands;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • D12 - Microeconomics - - Household Behavior - - - Consumer Economics: Empirical Analysis
    • Q21 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Renewable Resources and Conservation - - - Demand and Supply; Prices

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