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On Estimating the Transition Probabilities of a Markov Process

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  • T. C. Lee
  • G. G. Judge
  • T. Takayama

Abstract

This article is concerned with estimating transition probabilities reflecting the behavior of micro units when only aggregated outcome data are available. A proposal by Miller and others relating to least squares estimates of the transition probabilities is reviewed, and alternative estimators are formulated. The estimators are applied to both actual and hypothetical data. As a result of the limited examples analyzed, it appears that the restricted least squares estimator, based on quadratic programming procedures, provides a systematic way to achieve transition probability estimates which satisfy the Goodman criterion and provides a basis for combining prior and sample information in estimating the parameters of regression and other linear statistical models.

Suggested Citation

  • T. C. Lee & G. G. Judge & T. Takayama, 1965. "On Estimating the Transition Probabilities of a Markov Process," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 47(3), pages 742-762.
    • Handle: RePEc:oup:ajagec:v:47:y:1965:i:3:p:742-762.
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    Cited by:

    1. Rao, Dayakar & Parwez, Shahid, 2005. "Dynamics of Cropping Pattern in Sorghum Growing States of India," Indian Journal of Agricultural Economics, Indian Society of Agricultural Economics, vol. 60(4), pages 1-16.
    2. Disney, W. Terry & Duffy, Patricia A. & Hardy, William E., Jr., 1988. "A Markov Chain Analysis Of Pork Farm Size Distributions In The South," Southern Journal of Agricultural Economics, Southern Agricultural Economics Association, vol. 20(2), pages 1-8, December.
    3. García, Jorge H. & Garmestani, Ahjond S. & Karunanithi, Arunprakash T., 2011. "Threshold transitions in a regional urban system," Journal of Economic Behavior & Organization, Elsevier, vol. 78(1), pages 152-159.
    4. Andrei Rogers, 1967. "Estimating Interregional Population And Migration Operators From Interregional Population Distributions," Demography, Springer;Population Association of America (PAA), vol. 4(2), pages 515-531, June.
    5. Miller, Douglas J., 1994. "Entropy Methods For Recovering Information From Economic Models," 1994 Quantifying Long Run Agricultural Risks and Evaluating Farmer Responses Risk, Technical Committee Meeting, March 24-26, 1994, Gulf Shores State Park, Alabama 271680, Regional Research Projects > S-232: Quantifying Long Run Agricultural Risks and Evaluating Farmer Responses to Risk.
    6. 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.
    7. 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.
    8. Pathak, Santosh & Wang, Hua & Adusumilli, Naveen C., 2021. "Quantifying the dynamics of agricultural conservation practices in the Delta region," 2021 Annual Meeting, August 1-3, Austin, Texas 313916, Agricultural and Applied Economics Association.
    9. Saint-Cyr, Legrand D. F., 2017. "Farm heterogeneity and agricultural policy impacts on size dynamics: evidence from France," Working Papers 258013, Institut National de la recherche Agronomique (INRA), Departement Sciences Sociales, Agriculture et Alimentation, Espace et Environnement (SAE2).
    10. 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.
    11. Stokes, Jeffrey R., 2006. "Entry, Exit, and Structural Change in Pennsylvania's Dairy Sector," Agricultural and Resource Economics Review, Northeastern Agricultural and Resource Economics Association, vol. 35(2), pages 1-17, October.
    12. W. Wilson & W. Koo & A. Carter, 1990. "Importer Loyalty In The International Wheat Market," Journal of Agricultural Economics, Wiley Blackwell, vol. 41(1), pages 94-102, January.
    13. Davor Kunovac, 2011. "Estimating Credit Migration Matrices with Aggregate Data – Bayesian Approach," Working Papers 30, The Croatian National Bank, Croatia.
    14. Davis, Ernest E., 1971. "Future Structure Of The Texas Cattle Feeding Industry As Projected By Transition Probabilities Utilizing A Convex Program," Southern Journal of Agricultural Economics, Southern Agricultural Economics Association, vol. 3(1), pages 1-7, December.
    15. Tran, Dat Q. & Kurkalova, Lyubov A., 2017. "Estimation of the changes in the dynamics of tillage choices in Iowa, 1992-2008," 2017 Annual Meeting, July 30-August 1, Chicago, Illinois 258443, Agricultural and Applied Economics Association.
    16. Saint-Cyr, Legrand D. F. & Piet, Laurent, 2014. "Movers and Stayers in the Farming Sector: Another Look at Heterogeneity in Structural Change," 2014 International Congress, August 26-29, 2014, Ljubljana, Slovenia 183068, European Association of Agricultural Economists.
    17. Schaible, Glenn D. & Kim, C.S., 1989. "Forecasting Irrigation Technology with Transition Probabilities in the Pacific Northwest," WAEA/ WFEA Conference Archive (1929-1995) 244966, Western Agricultural Economics Association.
    18. Tran, Dat Q. & Kurkalova, Lyubov A., 2017. "Testing for complementarity between the use of continuous no-till and cover crops: an application of Entropy approach," 2017 Annual Meeting, July 30-August 1, Chicago, Illinois 259149, Agricultural and Applied Economics Association.
    19. 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.
    20. Piet, Laurent, 2011. "Assessing structural change in agriculture with a parametric Markov chain model. Illustrative applications to EU-15 and the USA," 2011 International Congress, August 30-September 2, 2011, Zurich, Switzerland 114668, European Association of Agricultural Economists.
    21. Lin, William W. & Coffman, George & Penn, J. B., 1980. "U.S. Farm Numbers, Sizes, and Related Structural Dimensions: Projections to Year 2000," Technical Bulletins 157730, United States Department of Agriculture, Economic Research Service.
    22. Veeman, M.M. & Veeman, T.S. & Dong, X.Y., 1989. "Market Share Competition in World Wheat Markets," Project Report Series 232074, University of Alberta, Department of Resource Economics and Environmental Sociology.
    23. Smith, Matthew G., 1988. "A Conditional Approach To Projecting Farm Structure," Staff Reports 278025, United States Department of Agriculture, Economic Research Service.
    24. 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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