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

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.