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Stochastic key sector analysis: an application to a regional input–output framework


Limits on the precision of technical relationships within input–output frameworks have led to the use of stochastic analytical methods. The notion of stochastic analysis is developed in this paper to discern how the inherent imprecision effect, when aggregated data are utilised, affects the concomitant key sector analysis. Through a Monte Carlo based simulation, the stochastic key sector graph is introduced, with numerical expressions defined which quantify the association of the individual sectors to quadrants of the graph. The technical developments are benchmarked on a small problem, before a stochastic key sector analysis on an aggregated regional input–output table is reported. Comparisons are made between results when the aggregation of sectors is not employed. The paper reveals that aggregation in key sector analysis is inevitably a poor idea. However, it is argued that aggregation is often a practical necessity, so quantifying the uncertainty that is attendant on this aggregation is important, with the “association” expressions introduced potentially central to elucidate this uncertainty. The conclusions of this paper suggest that where analysts and decision makers are obliged to aggregate tables for analytical purposes then problems might be mitigated where marginal sectors are treated with care.

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  1. 1.

    Ara K (1959). The aggregation problem in input–output analysis. Econometrica 27(2): 257–262

  2. 2.

    Bryan J, Jones C, Munday M and Roberts A (2004). Welsh input–output tables for 2000. Cardiff Business School, Cardiff, UK

  3. 3.

    Bryan J, Jones C and Munday M (2005). Investigating the potential of key sectors using multisectoral qualitative analysis: a Welsh case study. Environ Plann C 23(5): 633–656

  4. 4.

    Cmiel A and Gurgul H (1996). Input–output models with stochastic matrices and time lags. Econ Syst Res 8(2): 133–143

  5. 5.

    De Mesnard L and Dietzenbacher E (1995). On the interpretation of fixed coefficients under aggregation. J Reg Sci 35: 233–243

  6. 6.

    Didonato AR and Morris AH (1992). Significant digit computation of the incomplete beta function ratios. ACM Trans Math Softw 18(3): 360–373

  7. 7.

    Dietzenbacher E (1992). The measurement of inter-industry linkages: key sectors in the Netherlands. Econ Modell 9(4): 419–437

  8. 8.

    Dietzenbacher E (1997). In vindication of the Ghosh model: reinterpretation of a price model. J Reg Sci 26: 515–531

  9. 9.

    Dietzenbacher E (2002). Interregional multipliers: looking backward, looking forward. Reg Stud 36(2): 125–136

  10. 10.

    Dietzenbacher E (2006). Multiplier estimates: to bias or not to bias. J Reg Sci 46(4): 773–786

  11. 11.

    Hewings G (1982). The empirical identification of key sectors in an economy: a regional perspective. Develop Econ 20(2): 173–195

  12. 12.

    Jackson RW (1986). The full-distribution approach to aggregate representation in the input–output modelling framework. J Reg Sci 26(3): 515–531

  13. 13.

    Kop Jansen PSM (1994). Analysis of multipliers in stochastic input–output models. Reg Sci Urban Econ 24: 55–74

  14. 14.

    Lahr ML and Stevens BH (2002). A study of the role of regionalization in the generation of aggregation error in regional I–O models. J Reg Sci 42(3): 477–507

  15. 15.

    Magura M (1998). IO and spatial information as Bayesian priors in an employment forecasting model. Ann Reg Sci 32: 495–503

  16. 16.

    Midmore P, Munday M and Roberts A (2006). Assessing industry linkages using regional input–output tables. Reg Stud 40: 329–343

  17. 17.

    Miller G and Blair P (1981). Spatial aggregation in interregional input–output models. Pap Reg Sci Assoc 44: 150–164

  18. 18.

    Miller RE and Lahr ML (2001). A taxonomy of extractions. In: Lahr, ML and Miller, RE (eds) Regional science perspectives in economics: A festschrift in memory of Benjamin H Stevens, pp 407–441. Elsevier, Amsterdam

  19. 19.

    Parzen E (1962). On estimation of a probability density function and mode. Ann Math Stat 33: 1065–1076

  20. 20.

    Rasmussen P (1956). Studies in inter-sectoral relations. North-Holland, Amsterdam

  21. 21.

    Rey SJ, West GR and Janikas MV (2004). Uncertainty in integrated regional models. Econ Syst Res 16(3): 259–278

  22. 22.

    Rickman DS (2002). A Bayesian forecasting approach to constructing regional input–output based employment multipliers. Pap Reg Sci 81: 483–498

  23. 23.

    Roberts B and Stimson R (1998). Multi-sectoral qualitative analysis: a tool for assessing the competitiveness of regions and formulating strategies for economic development. Ann Reg Sci 32: 469–494

  24. 24.

    Sonis M, Hewings G and Guo J (2000). A new image of classical key sector analysis: minimum information decomposition of the Leontief inverse. Econ Syst Res 13(3): 401–423

  25. 25.

    ten Raa T and Steel MFJ (1994). Revised stochastic analysis of an input–output model. Reg Sci Urban Econ 24: 361–371

  26. 26.

    West GR (1982) Approximating the moments and distribution of input–output multipliers. Working papers in Economics 36, University of Queensland, New Zealand

  27. 27.

    West GR (1986). A stochastic analysis of an input–output model. Econometrica 54(2): 363–374

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Correspondence to Malcolm J. Beynon.

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Beynon, M.J., Munday, M. Stochastic key sector analysis: an application to a regional input–output framework. Ann Reg Sci 42, 863–877 (2008).

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JEL Classification

  • R15
  • C15
  • C67