# Chronotype, Risk and Time Preferences, and Financial Behaviour
## Appendix B Robustness Check  
We changed the dichotomously measured morningness in the benchmark analysis to a continuum scale because based on the idea proposed by [PERSON] et al. (2016) that using a continuum scale for morningness-eveningness could provide richer information regarding the hypothesized relationships. We also used a different single self-reported question, as proposed by [PERSON] et al. (2016), to measure risk preference, and generate an all-around factor to predict risky behaviour. In addition, we added both risk and time preference measures in all settings of regressions and path analyses, as risk and time are intertwined. It would be problematic to isolate risk attitude when examining the effect of time preference on certain behaviour ([PERSON] et al., 2016), as uncontrolled risk can create present-biased choices or behaviour. By changing the measurements of the interested variables and increasing bootstrap sample size from 5000 to 50,000, we intend to verify the robustness of the results.  
The continuum form of morningness-eveningness (_Circadian rhythm_) ranges from 15 to 51, where a higher score indicates greater morning orientation. General risk preference is a single indicator with a higher score presenting a higher level of risk taking, ranging from 1 to 11.  
We conducted a robustness check on hypotheses (H1, H2, H3, H4, H6), because these hypotheses were supported by the benchmark results. First, we tested the link between circadian rhythm and revolving credit card debt.  
The results recorded in Table 1 indicate that circadian rhythm is negatively associated with the possibility of delinquent credit card payments (b = \(-0.012\), SE = \(0.003\), z = \(-3.37\), \(p<0.01\)), which supports Hypothesis 1.  
Second, we tested whether time preference mediates the relationship between circadian rhythm and delinquent credit card debt. Table A2 conveys the results (bootstrapping coefficient of indirect effect = \(-\)0.107, bootstrapping SE = 0.006, 95% C = [\(-\)0.024, \(-\)0.001]), which supports Hypothesis 2.  
Third, we set out to verify whether income moderates the time preference-delinquent credit card debt relationship, and whether the indirect effect of circadian rhythm on delinquent credit debt payments through time perspective, is moderated by monthly income, such that an indirect effect exists for those whose income is at low to average level. Table A3 reports the corresponding results, which supports Hypothesis 3 (The coefficient of interaction item monthly income \(\times\) time preference = 0.065, SE = 0.028, \(p\) < 0.05) and Hypothesis 4 (Index of moderated mediation = 0.008, Boot SE = 0.004, 95%CI = [0.001, 0.018]).  
Finally, we examined whether financial risk preference mediates the relationship between circadian rhythm and the likelihood of investments in the stock market. Table 13 shows the results (bootstrapping coefficient of indirect effect = 0.010, bootstrapping SE = 0.006, 95% CI = [0.0002, 0.022]) that support Hypothesis 6.  
To summarize, after changing the measures of morningness-eveningness, and the measure of risk preference, the results are robust and support the findings in the benchmark analysis.