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The heterogeneous thresholds ordered response model: identification and inference

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  • Franco Peracchi
  • Claudio Rossetti

Abstract

Although surveys routinely ask respondents to evaluate various aspects of their life on an ordered scale, there is concern about interpersonal comparability of these self-assessments. Statistically, the problem is one of identification in ordered response models with heterogeneous thresholds. As a solution to the identification problem, King et al. (2004) proposed using anchoring vignettes, namely brief descriptions of hypothetical people or situations that survey respondents are asked to evaluate on the same scale they use to rate their own situation. While vignettes have been introduced in several social surveys and are increasingly employed in a variety of fields, reliability of this approach hinges crucially on the validity of the assumptions of response consistency and vignette equivalence. This paper proposes a joint test of these key assumptions based on the fact that the underlying statistical model is overidentified if the two assumptions hold. Monte Carlo results show that the proposed test has good size and power properties in finite samples. We apply our test to self-assessment of pain using data from the first wave of the Survey of Health, Ageing and Retirement in Europe (SHARE). We find that, when using only one of the three available vignettes, or when the test is carried out separately by subgroups of respondents, the overidentifying restrictions are less likely to be rejected.

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File URL: http://hdl.handle.net/10.1111/j.1467-985X.2012.01066.x
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Bibliographic Info

Article provided by Royal Statistical Society in its journal Journal of the Royal Statistical Society: Series A (Statistics in Society).

Volume (Year): 176 (2013)
Issue (Month): 3 (06)
Pages: 703-722

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Handle: RePEc:bla:jorssa:v:176:y:2013:i:3:p:703-722

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References

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  1. Yann Bramoullé & Habiba Djebbari & Bernard Fortin, 2007. "Identification of Peer Effects through Social Networks," Cahiers de recherche 0705, CIRPEE.
  2. Franklin Allen & Ana Babus & Elena Carletti, 2010. "Financial Connections and Systemic Risk," Economics Working Papers ECO2010/30, European University Institute.
  3. Cohen-Cole, Ethan, 2006. "Multiple groups identification in the linear-in-means model," Economics Letters, Elsevier, vol. 92(2), pages 157-162, August.
  4. Antoni Calvo-Armengol & Eleonora Patacchini & Yves Zenou, 2008. "Peer Effects and Social Networks in Education," CReAM Discussion Paper Series 0814, Centre for Research and Analysis of Migration (CReAM), Department of Economics, University College London.
  5. Ethan Cohen-Cole & Giulio Zanella, 2007. "Unpacking social interactions," Risk and Policy Analysis Unit Working Paper QAU07-4, Federal Reserve Bank of Boston.
  6. de Paula, Áureo, 2009. "Inference in a synchronization game with social interactions," Journal of Econometrics, Elsevier, vol. 148(1), pages 56-71, January.
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Cited by:
  1. Carmelo León & Jorge Araña & Javier León, 2013. "Correcting for Scale Perception Bias in Measuring Corruption: an Application to Chile and Spain," Social Indicators Research, Springer, vol. 114(3), pages 977-995, December.
  2. Andrew M. Jones; Nigel Rice, Silvana Robone; & Nigel Rice; & Silvana Robone:, 2012. "A comparison of parametric and non-parametric adjustments using vignettes for self-reported data," Health, Econometrics and Data Group (HEDG) Working Papers 12/10, HEDG, c/o Department of Economics, University of York.

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