Spatial dependence in hospital efficiency: a spatial econometric approach for Ecuadorian public hospitals

ABSTRACT

This study analyses whether the efficiency of Ecuadorian public hospitals experiences spatial dependence. We investigate whether demand variations have affected public hospitals’ efficiency performance through direct and spillover effects since the adoption of the current constitution in 2008. Our analysis exploits an innovative two-stage approach to estimate hospital efficiency in the first stage and then applies a spatial econometric framework to disentangle direct and spillover effects in the second. The results confirm positive spatial interactions among public hospitals’ efficiency, as well as positive direct and spillover effects coming from demand increases, which have been reinforced since 2008.

KEYWORDS:

• healthcare efficiency
• spatial dependence
• healthcare reforms
• strategic interactions

JEL:

• C21
• D61
• I11
• I18

ACKNOWLEDGEMENTS

I acknowledge the support of the Pre-doctoral Trainee Research Scholarship (PIF) at the Autonomous University of Barcelona (UAB). I also thank my supervisors, Rosella Nicolini and Diego Prior, the participants at the Applied Lunch at the UAB and the University of Barcelona, and the scientific committee of the PhD in Applied Economics, Nicola Pontarollo, Judit Vall, and the anonymous referees for their valuable comments. Any remaining errors are my own responsibility.

DISCLOSURE STATEMENT

No potential conflict of interest was reported by the author.

Notes

1. The term ‘strategic interactions’ is used in the literature to refer to the interdependence among features or actions of selected units stemming from competition between those units. Strategic interactions arise due to the existence of spillover effects (Brueckner, 2003) that cause the levels of the variables of one unit to be affected by the levels of the same variables of neighbouring units.

2. See Appendix A in the supplemental data online for a description of the institutional healthcare setting in Ecuador.

3. Here we consider technology as the set of constraints defining how one can combine or convert inputs (e.g., number of physicians, beds, etc.) into outputs (e.g., number of discharges or procedures carried out) in the production process. In this particular context, this can relate to the availability of human capital, infrastructure, etc.

4. In Ecuador, cantons are second-level administrative divisions. The Republic of Ecuador is divided into 24 provinces, which in turn are divided into 221 cantons. The cantons in turn are subdivided into parishes.

5. According to the Public Ministry of Health (MSP), between 2006 and 2010 the number of surgeries increased by 47% and hospital discharges by 43% (Ministerio de Salud Pública, 2012).

6. As will be described in following sections, Ecuador has a reduced number of well-endowed public hospitals that are capable of treating complex diseases where patients can receive free medical treatment due to the reforms carried out since 2008. So, given the reduced barriers of access, it is very likely that patients perceive these hospitals as providing the best quality they can obtain. In fact, Piedra-Peña (2021) demonstrates that those best-performing and well-endowed hospitals, located in developed regions, have a significant pulling effect to attract patients. These movements might also be induced by hospital reputation, built over years, referrals or public news.

7. In fact, according to Villacrés and Mena (2017), the current funding scheme of the country can generate inefficiencies given that hospitals have an incentive to attract patients and inflate costs.

8. Although the scope of our study is in line with non-parametric methods, see Colombi et al. (2017) for a thorough discussion of the recent literature using parametric stochastic frontier models.

9. We can apply DMU to any unit of analysis such as individuals, departments, firms, municipalities, or, in the case of this study, hospitals.

10. For an in-depth description of Piedra-Peña and Prior’s (2020) approach, see Appendix C in the supplemental data online.

11. For a discussion on how occupancy rate is used to proxy hospital demand, see section 5.2.

12. See Appendix F in the supplemental data online for an explanation of LeSage and Pace’s (2009) spatial effects and the respective partitioning analysis.

13. We make use of hospital occupancy rate to measure demand. This is further explained in section 5.2.

14. The constitution came into force in October 2008.

15. Regarding our two-stage application, some remarks are in order. As pointed out by Simar and Wilson (2007), conventional regression models (such as ordinary least squares – OLS) applied in the second stage yield biased results because the efficiency scores estimated in the first stage are serially correlated. In addition, possible correlation of the contextual variables with the error term is another possible source of bias. The authors propose new methods based on bootstrapping to overcome these problems. We therefore employ maximum likelihood (ML) estimates that are consistent with involving DEA efficiency scores. Plus, the logarithmic transformation of the efficiency scores ensures an unbounded dependent variable and thus enables a consistent ML estimation (Simar & Wilson, 2007). Finally, we ensure valid inference of the estimated marginal effects by simulating the distribution of the direct and spillover effects using the variance–covariance matrix implied by the ML estimates, as proposed by LeSage and Pace (2009).

16. We excluded psychiatric, dermatologic and geriatric hospitals because they focus on specific illnesses and patients that require different treatments that could bias the efficiencies.

17. All the variables expressed as percentages were on a 0–100 scale before obtaining the logarithms in order to facilitate the estimations and interpretation of the results.

18. We acknowledge that occupancy rates may also increase either by reducing the number of beds or by augmenting the patient’s length of stay, and not just due to the increase in hospital admissions. However, in our dataset, neither the average number of beds nor the number of bed days per patient has drastically changed over the years. The former went from 75 beds in 2006 to 86 in 2014, on average. The latter went from 8.8 days of care per patient in 2006 to 11.67 in 2014. Hence, it is valid to attribute the sudden change in occupancy rate in our data (as will be seen in the following sections) to the increase in demand for medical care.

19. We use hospital feature averages in this analysis given that Moran’s I-statistic is a cross-sectional approach. We also carried out the same analysis for each year. The results are comparable and available from the author upon request.

20. We reproduced the same test for three other hospital features: number of beds, medical equipment and hospital personnel (not including physicians). The results are comparable and available from the author upon request.

21. Complete results tables are available from the author upon request.

22. We also estimate progressive estimations to check the robustness of our results to the inclusion of control variables. The results are robust and the size is comparable. The estimations are shown in Appendix H in the supplemental data online.

23. Henceforth, this will be used for interpretation because it is a more realistic matrix of hospital interactions than that of Euclidean distances (${\mathit{W}}_d$).

24. We tested the direction of the causality between hospital efficiency and demand as well as for hospital efficiency and market shares. We used Granger’s (1969) causality test for panel data models as adapted by Dumitrescu and Hurlin (2012). The test rejects the null hypothesis of non-causality in both cases.

25. Estimation results with the other weight matrix are comparable and available from the author upon request.

26. The impact of the marginal change in demand for hospital i on its own efficiency is the result of local effects plus feedback effects that pass mainly through its direct neighbour j.

27. Robustness analysis is carried out in Appendix H in the supplemental data online.