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Cluster effects and simultaneity in multilevel models


  • Richard Blundell

    () (Institute for Fiscal Studies and IFS and UCL)

  • Frank Windmeijer

    () (Institute for Fiscal Studies and University of Bristol)


For small group sizes, the Generalised Least Squares (CLS) estimator in multilevel models is biased and inconsistent when the random cluster effects are correlated with the regressors. A fixed effects approach, conditioning on the cluster effects, provides consistent estimates for the slope parameters. The two estimators are equivalent when group sizes are large. The same results obtain for two stage estimation procedures that allow for some of the regressors to be simultaneously determined with the variable. The GLS and fixed effects estimators are applied to data on hospital utilization in the UK, allowing for health authority district effects. These data and models have been used by Smith et al. (1994) for developing a formula for the regional distribution of the UK National Health Service revenues.

Suggested Citation

  • Richard Blundell & Frank Windmeijer, 1997. "Cluster effects and simultaneity in multilevel models," IFS Working Papers W97/05, Institute for Fiscal Studies.
  • Handle: RePEc:ifs:ifsewp:97/05

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    References listed on IDEAS

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    Cited by:

    1. Luisa Corrado & Bernard Fingleton, 2012. "Where Is The Economics In Spatial Econometrics?," Journal of Regional Science, Wiley Blackwell, vol. 52(2), pages 210-239, May.
    2. Roy Carr-Hill & Paul Dixon & Russell Mannion & Nigel Rice & Kai Rudat & Ruth Sinclair & Peter Smith, 1997. "A model of the determinants of expenditure on children's personal social services," Working Papers 030cheop, Centre for Health Economics, University of York.
    3. Richard Blundell & Frank Windmeijer, 2000. "Identifying demand for health resources using waiting times information," Health Economics, John Wiley & Sons, Ltd., vol. 9(6), pages 465-474.
    4. Rabe-Hesketh, Sophia & Skrondal, Anders & Pickles, Andrew, 2005. "Maximum likelihood estimation of limited and discrete dependent variable models with nested random effects," Journal of Econometrics, Elsevier, vol. 128(2), pages 301-323, October.
    5. Thompson, Simon G. & Nixon, Richard M. & Grieve, Richard, 2006. "Addressing the issues that arise in analysing multicentre cost data, with application to a multinational study," Journal of Health Economics, Elsevier, vol. 25(6), pages 1015-1028, November.
    6. Nigel Rice & Paul Dixon & David Lloyd & David Roberts, 1999. "Derivation of a needs based capitation formula for allocation prescribing budgets," Working Papers 034cheop, Centre for Health Economics, University of York.
    7. Kathleen Carey, 2000. "A multilevel modelling approach to analysis of patient costs under managed care," Health Economics, John Wiley & Sons, Ltd., vol. 9(5), pages 435-446.
    8. Marc Saez & Carme Saurina & Germà Coenders & Sònia González-Raya, 2006. "Use of primary health care services according to the different degrees of obesity in the Girona Health Region, Spain," Health Economics, John Wiley & Sons, Ltd., vol. 15(2), pages 173-193.
    9. Bache, Stefan Holst Milton & Kristensen, Troels, 2013. "A simple but efficient approach to the analysis of multilevel data," COHERE Working Paper 2013:6, University of Southern Denmark, COHERE - Centre of Health Economics Research.
    10. Guillem López-Casasnovas & Marc Saez, 2007. "A multilevel analysis on the determinants of regional health care expenditure: a note," The European Journal of Health Economics, Springer;Deutsche Gesellschaft für Gesundheitsökonomie (DGGÖ), vol. 8(1), pages 59-65, March.
    11. Matthew Sutton & Peter Lock, 2000. "Regional differences in health care delivery: implications for a national resource allocation formula," Health Economics, John Wiley & Sons, Ltd., vol. 9(6), pages 547-559.

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