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Uncertain identification

Working Paper

Uncertainty about the choice of identifying assumptions is common in causal studies, but is often ignored in empirical practice. This paper considers uncertainty over models that impose different identifying assumptions, which, in general, leads to a mix of point- and set-identified models. We propose performing inference in the presence of such uncertainty by generalizing Bayesian model averaging. The method considers multiple posteriors for the set-identified models and combines them with a single posterior for models that are either point-identified or that impose non-dogmatic assumptions. The output is a set of posteriors (post-averaging ambiguous belief) that are mixtures of the single posterior and any element of the class of multiple posteriors, with weights equal to the posterior model probabilities. We suggest reporting the range of posterior means and the associated credible region in practice, and provide a simple algorithm to compute them. We establish that the prior model probabilities are updated when the models are "distinguishable" and/or they specify different priors for reduced-form parameters, and characterize the asymptotic behavior of the posterior model probabilities. The method provides a formal framework for conducting sensitivity analysis of empirical findings to the choice of identifying assumptions. In a standard monetary model, for example, we show that, in order to support a negative response of output to a contractionary monetary policy shock, one would need to attach a prior probability greater than 0.32 to the validity of the assumption that prices do not react contemporaneously to such a shock. The method is general and allows for dogmatic and non-dogmatic identifying assumptions, multiple point-identified models, multiple set-identified models, and nested or non-nested models.

18 April 2017

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Social capital, deprivation and self-rated health: does reporting heterogeneity play a role? Results from the English Longitudinal Study of Ageing.

Journal article

Self-rated health (SRH) is commonly assessed in large surveys, though responses can be influenced by different individuals' perceptions of and beliefs about health. Therefore, instead of providing evidence of 'true' health disparities across groups, findings may actually reflect reporting heterogeneity. Using data from participants aged 50 years and older from the English Longitudinal Study of Ageing (ELSA) Wave 3 (2006/07; participation rate = 73%), associations between three dimensions of social capital (local area & trust, social support and social networks), deprivation and SRH were examined using the vignette methodology in 2341 individuals who completed both the self-report and at least one of the 18 vignettes. Analysis employed a hierarchical probit model (HOPIT). Individuals expressing low local area & trust social capital (beta = -0.276, p < 0.001) and those with poor social networks (beta = -0.280, p < 0.001) were more likely to report poor SRH in HOPIT models accounting for reporting heterogeneity, but unadjusted ordered probit analyses still correctly show a negative relationship between low local area & trust social capital (beta = -0.243, p < 0.001) and those with poor social networks (beta = -0.210, p < 0.01), though they somewhat tend to underestimate its strength. Neither social support nor deprivation appeared to have any effect on SRH regardless of reporting heterogeneity. Anchoring vignettes offer a relatively uncomplicated and cost-effective way of identifying and correcting for reporting heterogeneity to improve comparative validity of self-report measures of health. This analysis underlines the need for caution when using unadjusted self-reported measures to study the effects of social capital on health.

12 April 2017

Article graphic

Scotland’s income tax schedule to differ from rest of the UK for first time

Comment

From tomorrow, Scottish residents will for the first time be subject to a different income tax schedule from those resident elsewhere in the UK. This is because of the Scottish parliament’s decision to use recently devolved powers over income tax bands and rates for non-savings and non-dividend income to freeze the higher-rate threshold (the point at which the rate of income tax rises from 20% to 40%) for the new financial year. Doing so exacerbates some existing deficiencies that afflict the tax system throughout the UK, and highlights the continuing need for tax reform.

5 April 2017