Payment schemes and cost efficiency: evidence from Swiss public hospitals

Abstract

This paper aims at analysing the impact of prospective payment schemes on cost efficiency of acute care hospitals in Switzerland. We study a panel of 121 public hospitals subject to one of four payment schemes. While several hospitals are still reimbursed on a per diem basis for the treatment of patients, most face flat per-case rates—or mixed schemes, which combine both elements of reimbursement. Thus, unlike previous studies, we are able to simultaneously analyse and isolate the cost-efficiency effects of different payment schemes. By means of stochastic frontier analysis, we first estimate a hospital cost frontier. Using the two-stage approach proposed by Battese and Coelli (Empir Econ 20:325–332, 1995), we then analyse the impact of these payment schemes on the cost efficiency of hospitals. Controlling for hospital characteristics, local market conditions in the 26 Swiss states (cantons), and a time trend, we show that, compared to per diem, hospitals which are reimbursed by flat payment schemes perform better in terms of cost efficiency. Our results suggest that mixed schemes create incentives for cost containment as well, although to a lesser extent. In addition, our findings indicate that cost-efficient hospitals are primarily located in cantons with competitive markets, as measured by the Herfindahl–Hirschman index in inpatient care. Furthermore, our econometric model shows that we obtain biased estimates from frontier analysis if we do not account for heteroscedasticity in the inefficiency term.

Appendices

Appendix A

Table 6 Regression of the average LOS on payment scheme variables

Table 7 Parameter estimates for the non-switching hospitals

Appendix B

In order to show that the efficiency function $e(p)$ is concave, it is sufficient to prove that

$$\begin{aligned} \frac{\partial ^{2}e}{\partial p^{2}}<0\quad \forall \, p\in \left\{ 0,c\right\} . \end{aligned}$$

Differentiating (3) with respect to $p$ and defining $A=(c-p)t_{ee}+\gamma _{ee}$, one obtains

$$\begin{aligned} \frac{\partial ^{2}e}{\partial p^{2}}=\frac{\frac{\partial e}{\partial p}[A\cdot t_{ee}-t_{e}t_{eee}(c-p)-t_{e}\gamma _{eee}]+t_{e}t_{ee}}{A^{2}}. \end{aligned}$$

Using (3) and rearranging yields

$$\begin{aligned} \frac{\partial ^{2}e}{\partial p^{2}}=\frac{2}{A^{2}}t_{e}t_{ee}-\frac{t_{e}^{2}}{A^{3}}[(c-p)t_{eee}+\gamma _{eee}], \end{aligned}$$

Table 8 Mean inefficiency estimates by payment scheme and year

Table 9 Parameter estimates for the variable cost function

which is strictly negative for all $p\le c$, given that $\gamma _{eee}\ge 0$ and provided that $t_{eee}$ does not fall below a certain negative value, $t_{eee}\ge \frac{2At_{ee}-\gamma _{eee}t_{e}}{(c-p)t_{e}}$ . Hence, under reasonable assumption with regard to the curvature of $t(e)$ and $\gamma (e)$, the model indicates that the loss of cost efficiency effort is concave in $p$.$\square$