The universal health insurance system in Taiwan was formed with good intentions to help vulnerable groups. However, the possibility of bankrupting the system due to wasted medical resources. In this study, using the medical expenditures of the Taiwanese Government and gross domestic product (GDP) as variables, the wavelet analysis method was used to empirically study the correlations and leading-lagging relationships in quarterly data in the period from 1996 to 2016. In addition, the dependent population of the insured was used as the control variable. This population had no income and had high medical demands. Results: After the dependent population was included as a control variable, there was a period of low-frequency (one to four years short-term) linkage correlation, as well as a period of high-frequency (four to eight years long-term) linkage correlation. In addition, for more than eight years, there was also a high degree of linkage correlation, indicating that the linkage between medical expenditures and GDP occurred over the long term. Moreover, since medical expenditures positively affected GDP, one-way causality was observed. However, after 2008, regardless of whether a long or short term was examined, there was almost no linkage correlation. Before 2008, the medical expenditures of the government were positively correlated with economic growth; i.e., they enhanced economic growth. But, after 2008, this effect had already disappeared. The universal health insurance system has long been denounced as a waste of medical resources, and the waste must be immediately stopped. The government urgently needs to find a new solution.

We used the Bootstrap ARDL method to test the relationship between the export trades, FDI and CO₂ emissions of the BRICS countries. We found that China's foreign direct investment and the lag one period of CO₂ emissions have a cointegration on exports. South Africa's foreign direct investment and CO₂ emissions have a cointegration relationship with the lag one period of exports, and South Africa's the lag one period of exports and foreign direct investment have a cointegration relationship with the lag one period of CO₂ emissions. But whether it is China or South Africa, these three variables have no causal relationship in the long-term. Among the variables of other BRICS countries, Russia is the only country showed degenerate case #1 in McNown et al. mentioned in their paper. When we examined short-term causality, we found that CO₂ emissions and export trade showed a reverse causal relationship, while FDI and carbon emissions were not so obvious. Export trade has a positive causal relationship with FDI. Those variables are different from different situations and different countries.