# Estimation of Association between Healthcare System Efficiency and Policy Factors for Public Health
## 4 Discussion  
The main contents of our analysis are as follows: (1) the Social Health Insurance system showed the least efficiency score on average when compared to other types of systems but we could not find evidences of a statistically significant difference of healthcare efficiency between the four types of healthcare system; and (2) through the Tobit Regression, user information (quality on the prices of various health care services), user choice (for basic insurance coverage), and decentralization (to sub-national governments) showed that these three policy factors had a negative impact on the efficiency of healthcare systems. [PERSON] et al. [31] used six classification types (based on cluster analysis) and could not also find evidence of a healthcare system that systematically performed better than another. However, countries with Social Health Insurance, except Luxembourg, showed a remarkably low efficiency score (Austria 34 th, Germany 35 th, Switzerland 28 th). In [PERSON]'s work [36] with 2010 data, Austria (29 th out of 31 countries), Germany (28 th), and Switzerland (25 th) were considered inefficient. In [PERSON] et al. 's work [14] with 2000 data, Austria, Germany, and Switzerland were also among the inefficient group (eight countries). In Austria, Germany, and Switzerland, societal actors rather than the state are in charge of both regulating and financing the healthcare system, which means being less centralized and having less robust regulation than other systems. [PERSON] [37] pointed out that due to insufficient regulation, the costs of collecting revenues are high and therefore the cost efficiency to deliver healthcare service may be poor. He further added that non-enrollment and evasion exacerbated healthcare financing \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Policy Variable** & \
\begin{tabular}{c} **Above Median Eff.** \\ **(n = 13)** \\ \end{tabular} &
\begin{tabular}{c} **Equal/Below Median Eff.** \\ **(n = 16)** \\ \end{tabular} & \(p\)**Value** \\ \hline User choice of insurers & 0.500 (877) & 1.938 (2.081) & 0.053 * \\ Private Provision & 2.223 (1.501) & 3.069 (1.165) & 0.219 \\ Regulation of provider prices & 4.150 (1.126) & 4.081 (.983) & 0.313 \\ User information & 0.479 (836) & 1.538 (1.418) & 0.039 ** \\ Regulation of workforce \& equipment & 2.850 (1.674) & 2.800 (.991) & 0.617 \\ Choice among providers & 4.407 (2.114) & 4.169 (2.033) & 0.271 \\ Gatekeeping & 2.071 (2.386) & 3.750 (2.266) & 0.114 \\ Budget Constraint & 3.071 (2.057) & 2.563 (2.065) & 0.322 \\ Decentralization & 1.193 (1.743) & 2.438 (1.567) & 0.003 ** \\ Consistency & 4.386 (1.501) & 4.531 (1.564) & 0.757 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Mann-Whitney U test results on policy indicator variables between two groups of countries. (* \(<\) 0.10; ** \(<\) 0.05; *** \(<\) 0.01). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Variable** & **Coefficient** & **Std. Error** & **z-Statistic** & \(p\)**-Value** \\ \hline Constant & 0.934 & 0.041 & 22.812 & 2 \(\times\) 10\({}^{-16}\) \\ UCI & \(-\)0.074 & 0.028 & \(-\)2.65 & 0.00812 *** \\ UI & \(-\)0.110 & 0.035 & \(-\)3.15 & 0.00165 *** \\ DC & \(-\)0.064 & 0.030 & \(-\)2.16 & 0.03049 ** \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Tobit regression results. (** \(<\) 0.05; *** \(<\) 0.01). under healthcare systems such as those in Austria, Germany, and Switzerland. This is because in those systems, tax financing is limited and health expenditure is mostly financed via individual funds [38]. However, Luxembourg, the only country other than those countries that have societal actors taking charge of regulation and financing, showed the highest efficiency when compared to any other country. Luxembourg only has 2.86 of practicing physicians _per capita_ (23 rd), but showed a 356.14 infant survival rate (9 th), and a 85.2 year life expectancy (6 th). We found that Luxembourg is a single-payer system while Austria, Germany, and Switzerland are multi-payer systems [39].