The heterogeneous thresholds ordered response model: identification and inference. (28th December 2012) - Peracchi, Franco; Rossetti, Claudio
<x xml:space="preserve">Abstract</x> Summary. 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 and his colleagues proposed the use of anchoring vignettes, namely brief descriptions of hypothetical people or situations that survey respondents are asked to evaluate on the same scale as they use to rate their own situation. Although vignettes have been introduced in several social surveys and are increasingly employed in a variety of fields, the reliability of this approach hinges crucially on the validity of the assumptions of response consistency and vignette equivalence. The 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 test proposed has good size and power properties in finite samples. We apply our test to self‐ assessment of pain by using data from the first wave of the Survey of Health, Ageing and Retirement in Europe. 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.