Although survey data on happiness are increasingly used in economics, their reliability is a long-standing concern. Two recent studies argue that results based on such data can be reversed with monotonic increasing transformations of the associated happiness scale (Bond and Lang 2019; Schröder and Yitzhaki 2017). These studies raise a serious and widely applicable issue. In response, we make three main contributions. First, we derive a simple test of whether OLS coefficients can be reversed by relabelling the scores of reported happiness and deduce bounds for ratios of coefficients under any labelling scheme. Second, we show that when reversals of OLS coefficients are impossible, reversals using ordered probit regressions (as proposed by Bond and Lang) become speculative from an empirical point of view. Third, we make apparent that in order to achieve reversals, respondents must be assumed to use the response scale in a strongly non-linear fashion. However, drawing from the economic and psychological literature, we present arguments and evidence that respondents use response scales in an approximately linear manner. The paper’s main ideas are illustrated using American GSS data. Additionally, using German SOEP data, we empirically show that sign reversals are impossible or implausible for a wide range of demographic variables. Although our analysis uses happiness as a special case, our theoretical considerations are applicable to any type of subjective ordinal report.
Kaiser C. & Vendrik M.C.M. (2021). 'How threatening are transformations of happiness scales to subjective wellbeing research?'. Working Paper. https://osf.io/gzt7a/. Revise & resubmit at the Economic Journal.