# Chronotype, Risk and Time Preferences, and Financial Behaviour
## 3 Methods
### Econometrics Model  
To test the direct effect of morningness on delinquent credit card payments (Hypothesis 1) and on investments in stock (Hypothesis 5), we use a logistic regression model, since delinquent credit card payments and investments in stock are dichotomously-measured dependent variables. Additionally, logistic regression also has a number of advantages. First, neither the dependent nor the independent variables have to be normally distributed. Similarly, logistic regression does not assume that the error terms have to be in normal distribution. More importantly, it does not assume that the relationships between the independent and dependent variables are linear. We specify the following logistic models to test the relationship between morning-type and delinquent credit card payments (Hypothesis 1):  
\[Delinquent\;credit\;card\;payment_{i}=\beta_{0}+\beta_{1}\mathit{Morningness}+ \beta_{2}\mathit{Time\;preference}+\sum_{k=5}^{K}\beta_{k}X_{ik}+\epsilon_{i} \tag{1}\]  
where \(X_{ik}\) is the set of control variables of individual \(i\), including age, male, marital status, education, and monthly income. \(\epsilon_{i}\) is the error term. The model specification to examine the link between morning-type and stock ownership is as follows (Hypothesis 5): \begin{table}
\begin{tabular}{l c c c c c} \hline \hline \multicolumn{1}{c}{**Variables**} & **Observations** & **Mean** & **SE** & **Min** & **Max** \\ \hline Morningness & 455 & 0.132 & 0.339 & 0 & 1 \\ Age & 455 & 1.378 & 0.485 & 1 & 2 \\ Male & 455 & 0.389 & 0.488 & 0 & 1 \\ Married & 455 & 0.752 & 0.432 & 0 & 1 \\ Education & 455 & 3.936 & 0.558 & 1 & 6 \\ Monthly income & 455 & 3.342 & 1.105 & 1 & 6 \\ Time preference & 455 & 25.164 & 2.959 & 13 & 32 \\ Financial risk preference & 455 & 7.569 & 1.926 & 1 & 11 \\ Stock market participation & 455 & 0.657 & 0.475 & 0 & 1 \\ Delinquent credit card payments & 455 & 0.341 & 0.474 & 0 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Descriptive statistics of the study’s variables. \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline \multicolumn{1}{c}{**Variables**} & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** \\ \hline
1. Morningness & & & & & & & & \\
2. Age & 0.058 & & & & & & & \\
3. Male & \(-0.058\) & \(-0.006\) & & & & & & \\
4. Married & 0.014 & \(0.291\) & \(-0.105\) & & & & & \\
5. Education & 0.033 & \(0.002\) & \(0.010\) & \(0.025\) & & & & \\
6. Monthly income & 0.067 & \(0.152\) & \(\pm 1.12\) & \(0.183\) & \(\pm 0.354\) & \(\pm 0.037\) & & \\
7. Time preference & 0.262 & \(\pm 1.04\) & \(\pm 1.067\) & \(\pm 0.020\) & \(0.188\) & \(\pm 0.037\) & & \\
8. Financial risk preference & 0.131 & \(\pm 1.002\) & \(0.020\) & \(0.088\) & \(0.042\) & \(0.240\) & \(0.080\) & \\
9. Stock participation & 0.104 & \(\pm 0.048\) & \(0.159\) & \(\pm 0.110\) & \(\pm 0.175\) & \(\pm 0.157\) & \(0.025\) & \(0.303\) \(\pm 1 \\
10. Delinquent credit card payments & \(-0.157\) & \(\pm 0.004\) & \(0.016\) & \(0.038\) & \(-0.043\) & \(0.050\) & \(-0.156\) \(\pm 0.053\) & \(0.031\) \\ \hline \hline \end{tabular} Note: ** and *** indicate significance at the 5% level (2-sided) and 1% level, respectively.  
\end{table} 
Table 2: Pearson’s correlation coefficients for key study variables. \[Owing\;stock_{i}=\beta_{0}+\beta_{1}Morningness+\beta_{2}Finanical\;risk\; preference+\sum\limits_{k=5}^{K}\beta_{k}X_{ik}+\epsilon_{i} \tag{2}\]  
where \(X_{ik}\) is a vector of control variables of individual \(i\), including age, male, marital status, education, and monthly income. \(\epsilon_{i}\) is the error term. To test the moderating role of income on the link between time preference and delinquent credit card debt (Hypothesis 3), we use a logistic regression model with an interaction item (_Time preference_\(\times\)_Monthly income_), as delinquent credit card debt is a dichotomous variable. The model specification is:  
\[