🔎 What this study addresses

Many researchers treat ordinal scales as numeric measures. Theory guarantees only that estimates keep the same sign under any monotonic increasing transformation of an ordinal scale, which leaves important parameters underidentified. This paper develops a practical way to test how much reported empirical estimates depend on the implicit "cardinal" treatment of ordinal variables.

🧪 How robustness is tested

• Introduces a partial identification approach that allows a researcher to specify a plausible range of monotonic increasing transformations of an ordinal variable.
• Derives bounds on effect estimates that are consistent with every transformation in that range, producing transparent "plausible bounds" around reported coefficients.
• Makes explicit the identification limits created by treating ordinal measures as interval-scale quantities and provides a formal test of robustness to scale choice.

📚 Demonstrations on influential studies

• Revisits Nunn and Wantchekon (2011, American Economic Review, 101, 3221–3252) on the slave trade and trust in sub-Saharan Africa, applying the bounding method to their trust measures.
• Provides supplemental illustrations using: Aghion et al. (2016, American Economic Review, 106, 3869–3897) on creative destruction and subjective well-being; and Bond and Lang (2013, The Review of Economics and Statistics, 95, 1468–1479) on the fragility of the black–white test score gap.

⭐ Why it matters

• Supplies a transparent sensitivity tool for any empirical work that uses ordinal outcomes.
• Helps distinguish findings that are robust to scale choices from those that rely heavily on implicit cardinalization.
• Improves credibility and interpretability of empirical claims where point-identification is threatened by ordinal measurement choices.