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How Much Does the Cardinal Treatment of Ordinal Variables Matter? An Empirical Investigation

Published online by Cambridge University Press:  26 February 2021

Jeffrey R. Bloem Open the ORCID record for Jeffrey R. Bloem [Opens in a new window]
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Abstract

Many researchers use an ordinal scale to quantitatively measure and analyze concepts. Theoretically valid empirical estimates are robust in sign to any monotonic increasing transformation of the ordinal scale. This presents challenges for the point-identification of important parameters of interest. I develop a partial identification method for testing the robustness of empirical estimates to a range of plausible monotonic increasing transformations of the ordinal scale. This method allows for the calculation of plausible bounds around effect estimates. I illustrate this method by revisiting analysis by Nunn and Wantchekon (2011, American Economic Review, 101, 3221–3252) on the slave trade and trust in sub-Saharan Africa. Supplemental illustrations examine results from (i) Aghion et al. (2016, American Economic Review, 106, 3869–3897) on creative destruction and subjective well-being and (ii) Bond and Lang (2013, The Review of Economics and Statistics, 95, 1468–1479) on the fragility of the black–white test score gap.

Keywords

ordinal variablespartial identificationset estimationlinear regressionhappinesssubjective well-beingtrusttest scores
Type
Article
Information
Political Analysis , Volume 30 , Issue 2 , April 2022 , pp. 197 - 213
Copyright
© The Author(s) 2021. Published by Cambridge University Press on behalf of the Society for Political Methodology

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Footnotes

Edited by Jeff Gill

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