How threatening are transformations of happiness scales to subjective wellbeing research?

Two recent papers argue that many results based on ordinal reports of happiness can be reversed with suitable monotonic increasing transformations of the associated happiness scale (Bond and Lang 2019; Schröder and Yitzhaki 2017). If true, empirical research utilizing such reports is in trouble. Against this background, we make four main contributions. First, we show that reversals are fundamentally made possible by explanatory variables having heterogenous effects across the distribution of happiness. We derive a simple test of whether reversals are possible by relabelling the scores of reported happiness and deduce bounds for ratios of coefficients under any labelling scheme. Second, we argue that in cases where reversals by relabelling happiness scores are impossible, reversals using an alternative method of Bond and Lang, which is based on ordered probit regressions, are highly speculative. Third, we make apparent that in order to achieve reversals, the analyst must assume that respondents use the response scale in a strongly non-linear fashion. However, drawing from the economic and psychological literature, we present arguments and evidence which suggest that respondents likely use response scales in an approximately linear manner. Fourth, using German SOEP data, we provide additional empirical evidence on whether reversals of effects of standard demographic variables are both possible and plausible. It turns out that reversals by either relabelling or by using Bond & Lang's approach are impossible or implausible for almost all variables of interest. Although our analysis uses happiness as a special case, our theoretical considerations are applicable to any type of subjective ordinal report.