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Projecting the Size Distribution of Agricultural Firms—An Application of a Markov Process with Non-Stationary Transition Probabilities

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  • M. C. Hallberg

Abstract

The first-order Markov chain model is frequently used to project the future size distribution of firms in a particular industry. This model, however, is based on the rather restrictive assumption that the transition probabilities remain constant over time. This assumption was found to be inappropriate in the case of plants manufacturing frozen milk products in Pennsylvania during the period 1944–1963 and, if adopted, could lead to erroneous results as some actual predictions indicated. This article suggests a method, based on multiple regression techniques, of replacing the constant transition probabilities with probabilities which are a function of various factors including structural characteristics in the industry. The results of this procedure compared quite favorably with those of the assumption of constant probabilities.

Suggested Citation

  • M. C. Hallberg, 1969. "Projecting the Size Distribution of Agricultural Firms—An Application of a Markov Process with Non-Stationary Transition Probabilities," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 51(2), pages 289-302.
    • Handle: RePEc:oup:ajagec:v:51:y:1969:i:2:p:289-302.
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    Cited by:

    1. Zimmermann, Andrea & Heckelei, Thomas, 2012. "Differences of farm structural change across European regions," Discussion Papers 162879, University of Bonn, Institute for Food and Resource Economics.
    2. Christina M. L. Kelton, 1984. "Nonstationary Markov Modeling: An Application to Wage-Influenced Industrial Relocation," International Regional Science Review, , vol. 9(1), pages 75-90, September.
    3. Davis, Kathy J. & Thornsbury, Suzanne & Ward, Ronald W., 2002. "Consolidation In The Fresh Florida Grapefruit Packing Industry," 2002 Annual meeting, July 28-31, Long Beach, CA 19815, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    4. Legrand D. F. Saint-Cyr & Laurent Piet, 2017. "Movers and stayers in the farming sector: accounting for unobserved heterogeneity in structural change," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 66(4), pages 777-795, August.
    5. Jeffrey M. Gillespie & Joan R. Fulton, 2001. "A Markov chain analysis of the size of hog production firms in the United States," Agribusiness, John Wiley & Sons, Ltd., vol. 17(4), pages 557-570.
    6. Saint-Cyr, Legrand D. F., 2016. "Farm segmentation and agricultural policy impacts on structural change: evidence from France," 149th Seminar, October 27-28, 2016, Rennes, France 244789, European Association of Agricultural Economists.
    7. Madior Fall & Laurent Piet & Muriel Roger, 2010. "Trends in the French commercial farm population," Review of Agricultural and Environmental Studies - Revue d'Etudes en Agriculture et Environnement, INRA Department of Economics, vol. 91(3), pages 279-295.
    8. Stokes, Jeffrey R., 2006. "Entry, Exit, and Structural Change in Pennsylvania's Dairy Sector," Agricultural and Resource Economics Review, Cambridge University Press, vol. 35(2), pages 357-373, October.
    9. Thornsbury, Suzanne & Davis, Kathy J. & Ward, Ronald W., 2005. "Fresh Grapefruit Supply-Chain Adjustments: Consolidation in Produce Packing?," Journal of Food Distribution Research, Food Distribution Research Society, vol. 36(3), pages 1-12, November.
    10. Rahelizatovo, Noro C. & Gillespie, Jeffrey M., 1999. "Dairy Farm Size, Entry, And Exit In A Declining Production Region," Journal of Agricultural and Applied Economics, Southern Agricultural Economics Association, vol. 31(2), pages 1-15, August.
    11. Burnham, Bruce O., 1973. "Markov Intertemporal Land Use Simulation Model," Southern Journal of Agricultural Economics, Southern Agricultural Economics Association, vol. 5(1), pages 1-6, July.
    12. Karantininis, Kostas, 2002. "Information-based estimators for the non-stationary transition probability matrix: an application to the Danish pork industry," Journal of Econometrics, Elsevier, vol. 107(1-2), pages 275-290, March.
    13. Ethridge, Don E. & Roy, Sujit K. & Myers, David W., 1983. "Changes in the Structure of the Texas High Plains Cotton Ginning Industry, 1967-1999," Archive 259788, Texas Tech University, Department of Agricultural and Applied Economics.
    14. Legrand D. F. Saint‐Cyr, 2022. "Heterogeneous farm‐size dynamics and impacts of subsidies from agricultural policy: Evidence from France," Journal of Agricultural Economics, Wiley Blackwell, vol. 73(3), pages 893-923, September.
    15. Alexander Gocht & Norbert Röder & Sebastian Neuenfeldt & Hugo Storm & Thomas Heckelei, 2012. "Modelling farm structural change: A feasibility study for ex-post modelling utilizing FADN and FSS data in Germany and developing an ex-ante forecast module for the CAPRI farm type layer baseline," JRC Research Reports JRC75524, Joint Research Centre.
    16. Legrand D. F, Saint-Cyr, 2017. "Farm heterogeneity and agricultural policy impacts on size dynamics: evidence from France," Working Papers SMART 17-04, INRAE UMR SMART.
    17. Dent, Warren Thomas & Ballintine, Richard, 1971. "A Review Of The Estimation Of Transition Probabilities In Markov Chains," Australian Journal of Agricultural Economics, Australian Agricultural and Resource Economics Society, vol. 15(2), pages 1-13, August.
    18. Piet, Laurent, 2008. "The evolution of farm size distribution: revisiting the Markov chain model," 2008 International Congress, August 26-29, 2008, Ghent, Belgium 44269, European Association of Agricultural Economists.
    19. Smith, Matthew G., 1988. "A Conditional Approach To Projecting Farm Structure," Staff Reports 278025, United States Department of Agriculture, Economic Research Service.
    20. Saint-Cyr, Legrand D. F., 2016. "Accounting for farm heterogeneity in the assessment of agricultural policy impacts on structural change," 2016 Annual Meeting, July 31-August 2, Boston, Massachusetts 235778, Agricultural and Applied Economics Association.

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